ELEMENTARY TREATISE ON PHYSICS EXPERIMENTAL AND APPLIED FOR THE USE OF COLLEGES AND SCHOOLS (■ TRANSLATED AND EDITED FROM GANOT'S ELEMENTS DE PHYSIQUE {wi'ik M£ Author^ s sanction) /. A E. ATiUNSON, Ph.D.,- F.C.S. v'* <"i«[-EssoR Qf >exm;rimental science, staff college, sandhukst xntb ^bilion, ^bis^b anb (Sitlargib ILLUSTRATED BY \ COLOURED PLATES AND 758 WOODCUTS NEW YORK WILLIAM WOOD AND CO., PUBLISHERS 27 GREAT JONES STREET 1875 '^^ t In QCI'h I T""^ ADVERTISEMENT THE SEVENTH EDITION. The present edition contains seventeen entirely new illustrations. A very large number of the old illustrations have been recut. The additions to the text amount to twenty-seven pages. In making these additions, while I have consulted the wants of the general reader, my principal aim has been, as in former editions, to render the book more usefulYor the student of Physical Science. ^ I have also added an Appendix containing a series of numerical A)roblems and examples in Physics. This Appendix is based upon a similar one contained in the French edition of the work. But I have been able to use only a sanall proportion of the problems con- tained in that Appendix, as the interest of the solution was in most cases geometrical or algebraical. Hence I have substituted or added others, which have been so selected as to involve in the solution a knowledge of some definite physical principle. Such an Appendix has from time to time been urged upon me b^ teachers and others who use the work. It will, I conceive, be more useful to those students who have not the advantage of regular instruction ; affording to them a means of personally testing their knowledge. Such a student should not aim solely at getting a result which numerically agrees with the answer. He should habituate himself to write out at length the several steps by which the result is obtained, so that he may bring clearly before himself the physical principles involved in each stage. Some of^^the solution^ of the problems are therefore worked out at lengtii. Those of the questions which are not original, have been taken from various sources. My thanks^re especially due to my friend Mr. Eve, of Wellington College, wht) has placed at my disposal a collection of problems in Electricity of which I have extensively availed myself. E. A. Staff College : yune iS-JS. ^ I Q'r *)• • TRANSLATOR'S PREFACE TO THE FIRST EDITION. The Elements de Physique of Professor Ganot, of which the present work is a translation, has acquired a high reputation as an Intro- duction to Physical Science. In France it has passed through Nine large editions In little more than as many years, and it has been, translated into German and Spanish. This -reputation it doubtless owes to the clearness and conciseness with which the principal physical laws and phenomena are explained, to its methodical arrangement, and to the excellence of its illustra- tions. In undertaking a translation, I was influenced by the favour- able opinion which a previous use of it in teaching had enabled me to form. I found that its principal defect consisted in its too close adapta- tion to the French systems of instruction, and accordingly, my chief labour, beyond that, of mere translation, has been expended in making such alterations and additions as might render it more useful to the English student. I have retained throughout the use of the cdhtigrade thermometer, and in some cases have expressed the smaller linear measures on the metrical system. These systems are now everywhere gaining ground, and an apology is scarcely needed for an innovation which may help to familiarise the English student with their use in the perusal of the larger and more complete works on Physical Science to which this work may serve as an introductJoR. E. ATKINSON. Royal Military College, Sandhurst : 1863. CONTENTS. BOOK I. ON MATTER, FORCE, AND MOTION. CHAPTER I'AGES I. General Notions ...... i II. General Properties of Bodies .... 3 III. On Force, Equilibrium, and Motion .... 9 BOOK II. GRAVITATION AND MOLECULAR ATTRACTION. # I. Gravity, Centre of Gravity, the Balance . . - 43 II. Laws of Falling Bodies. Intensity of Terrestrial Gravity. The Pendulum . . . . .52 III, Molecular Forces . . . . . .61 IV. Properties peculiar to Solids . . . -63 BOOK in. ON LIQUIDS. I. Hydrostatics . . . . . . .70 II. Capillarity, Endosmose, Effusion, Absorption, and Im- bibition . . . ". . . '97 BOOK IV. ON GASES. I. Properties of Gases. Atmosphere, Barometers . . 109 11. Measurement of the Elastic Force of Qases . . 127 III. Pressure on Bodies in Air, Balloons . . -137 IV. Apparatus founded on the Properties of Air . . 141 Vlll • Contents. CHAl'TER I. II. III. IV. V. ^ VI. BOOK V. ACOUSTICS. PAGE Production, Propagation, and Reflection of Sound . i66 Measurement of the Number of Vibrations . . i8i The Physical Theory of Music . . . .186 Vibrations of Stretched Strings, and of Columns of Air 201 Vibrations of Rods, Plates, and Membranes . .214 Graphical Method of Studying Vibratory Motions . 217 BOOK VI. ON HEAT. I. Preliminary Ideas. Thermometers II. Expansion of Solids .... III. Expansion of Liquids .... IV. Expansion and Density of Gases ► V. Changes of Condition. Vapours VI. Hygrometry . . . VII. Conductivity of Solids, Liquids, and Gases VIII. Radiation of Heat .... IX. Calorimetry ..... X. Steam Engines ..... XI. Sources of Heat and Cold . XII. Mechanical Equivalent of Heat . 227 240 247 253 262 306 315 321 358 375 388 401 BOOK VII. ON LIGHT. I. Transmission, Velocity, and Intensity of Light II. Reflection of Light. Mirrors III. Single Refraction. Lenses . IV. Dispersion and Achromatism. V. Optical Instruments . . VI. The Eye considered as an Optical Instrument VII. Sources of Light. Phosphorescence VIII. Double Refraction. Interference. Polarisation 409 420 439 459 480 508 dn 525 528 Contents. IX BOOK VIII. ON MAGNETISM. CHAPTER I. Properties of Magnets II. Terrestrial Magnetism. Compasses III. Laws of Magnetic Attractions and Repulsions IV. Processes of Magnetisation . 566 572 585 589 BOOK IX. FRICTIONAL ELECTRICITY. I, Fundamental Principles ..... 597 II. Quantitative Laws of Electrical Action . . 604 III. Action of Electrified Bodies on Bodies in the Natural State. Induced Electricity. Electrical Machines . 612 IV. Condensation of Electricity .... 636 BOOK X. DYNAMICAL ELECTRICITY. I. Voltaic Pile. Its Modifications . II. Detection and Measurement of Voltaic Currents III. Effects of the Current .... IV. Electrodynamics. Attraction and Repulsion of Currents BY Currents ..... V. Magnetisation by Currents. Electromagnets. Electric Telegraphs ...... VI. Voltaic Induction ..... VII. Optical Effects of Powerful Magnets. Diamagnetism VIIL Thermo-electric Current .... IX. Determination of Electrical Conductivhy X. Animal Electricity. Application of Electricity to Therapeutics ..... Elementary Outlines of Meteorology and Cllmatology INDEX . . . . . 667 688 700 726 745 767 805 809 819 830 836 889 LIST OF TABLES. Absorbing powers . Absorption of gases . — heat by gases liquids vapours 346, 349, 351 Breaking weight of substances Boiling point Combustion, heat of Conducting powers of solids for heat . liquids for heat Conductors of electricity Densities of gases . — of vapours Density of water Diathermanous power Diffusion of solutions . Diamagnetism . Endosmotic equivalents Elasticity , Electrical series . — conductivity . Electromotive force of different elements Expansion, coefficients of solids, liquids gases Eye, dimensions of . — refractive indices of media of Freezing mixtures . Fusing points of bodies 243 PAGE 333 107 345 344 352 68 280 395 317 319 599 261 305 253 345 104 808 103 65 602 825 685 ,244 250 257 511 511 267 263 Glaisher's factors . . .312 Gravity, force of, at different levels 5 8 Hardness, scale of . Latent heat, of evaporation liquefaction Magnetic declination — inclination .... — intensity .... Radiating powers , . 333, Radiation of powders Refraction, angle of double Refractive indices of media of eye Reflecting powers . . 332, Specific gravity of solids . — elasticity liquids — heat of solids and liquids gases — inductive capacities Temperatures, various remark able ... — of different latitudes — thermal springs Tension of aqueous vapour — different liquids . Thermo-electric series Undulations, length of . Velocity of sound in rocks gases . liquids metals and woods PAGE 69 286 371 574 581 583 334 356 534 449 511 333 92 65 94 365 369 617 239 866 867 276 277 810 529 1 172 174 176 176 LIST OF PLATES. Table of Spectra . . . . . . . . Frontispiece Coloured Rings produced by Polarised Light in Double Refracting Crystals 552 IsoGONic Lines for the Year i860 575 IsocLiNic Lines for the Year i860 580 1 1 1 1 M 1 1 |ii.-h |2 1^5 4 llllllllll' Millimetres |2 13 |4 15 |6 17 |« Centimetres The area of the figure within the heavy Hnes is that of a square decimetre. A cube, one of whose sides is this area, is a cubic decimetre or litre. A litre of water at the temperature of 4° C. weighs a kilogramme. A litre of air at 0° C. and 760™™ pressure weighs i -293 grammes. A litre is rj6 pints ; a pint is 0-568 of a litre. The smaller figures in dotted lines represent the areas of a square centimetre and of a square inch. A cubic centimetre of water at 4° C. weighs a gramme. |9 10 9 Square Inch Square ! Centimetre; ! Metres. Feet. 0-03937 00328 I 0-39371 0032819 3 '93708 0*328090 39*37079 3*280899 7070000 3280-899167 f Millimetre Centimetre Decimetre Metre Kilometre A Hectare or loooo square metres is equal to 2 -471 14 acres, each of which is 43560 square feet. A kilometre is 0-6214 of a statute mile, A statute mile is i -609 kilometres. A knot (in telegraphy) is 2029 yards or i'i528 statute miles. Measures of Capacity. Cubic centimetre or millitre Litre or cubic decimetre Kilolitre or cubic metre Cubic Inches. 0-06103 61 "02705 . 61027 -05152 Measures of Weight. Milligramme Gramme , Kilogramme . English grains. 001543 15 "43235 15432-34880 Cubic Feet. C728 c. in. =1 c. ft. 0-000035 0-035317 35-316581 Avoirdupois pounds of 7000 grains . 0-0000022 0-0022046 2-2046213 I grain =0-064799 gramme ; i pound avoirdupois is 0-453593 kilogramme. Errata Page 17, line 28 from top, for -129-9 reac i + 129-9 „ 67, ,, 27 ,, „ ,, inversely >h directly „ 235, ,, 29 ,, ,, ,, + ,j X ,, J, ,, 33 ,, ,, ,, (F.=32) „ (F.-32) ,, ,, ,, 4 ,, bottom, 1 5, 33 ,, 32 ,, 255, ,, 17 ,, top. ,, V + 760 ,, VX760 „ 302, ,, 18 ,, ,, ,, yellow ,, violet „ 330, bottom line, ,, fig. 304 ,, fig. 303 ., 363, line 8 from top, ,, M (T- ) ,, M (T-fl) „ 405, top line, ,, p{h-h) ,, p{h-h) „ 447, line 5 from top, ,, LDL ,j LDC „ 487, ,, 16 ,, ,j ,j fig- 435 J, fig. 434 ,, ,, ,, 21 >, », ,, „ 424 ,, „ 436 In fig. 437 the positions of the letters r Rv' and v Vv' should be interchanged Page 595, line 17 from bottom, y^/- n read n, „ 700, „ 10 ,, top,/?r4'3 rmi/4-6 Gnnot's Physics «? i ELEMENTARY TREATISE ON PHYSICS. BOOK I. ON MATTER, FORCE, AND MOTION. CHAPTER I. GENERAL NOTIONS. 1. Object of Pbyslcs. — The object oi Physics is the study of the phe- nomena presented to us by bodies. It should, however, be added, that changes in the nature of the body itself, such as the decomposition of one body into others, are phenomena whose study forms the more immediate object of chemistry. 2. laatter.— That which possesses the properties whose existence is revealed to us by our senses, we call matter or substance. All substances at present known to us may be considered as chemical combinations of sixty-five elementary or simple substances. This number, however, may hereafter be diminished or increased by a more powerful chemical analysis. 3. Atoms, Molecules. — From various properties of bodies we con- clude that the matter of which they are formed is not perfectly continuous, but consists of an aggregate of an immense number of exceedingly small portions or atoms of matter. These atoms cannot be divided physically, they are retained side by side, without touching each other, being separated by distances which are great in comparison with their supposed dimensions. A group of two or more atoms forms a molecule^ so that a body may be considered as an aggregate of very small molecules, and these again as aggregates of still smaller atoms. The smallest masses of matter we ever obtain artificially are particles and not molecules or atoms. Molecules retain their position in virtue of the action of certain forces called mole- cular foixes. B 2 On Matter, Force, and Motion. [4- From considerations based upon various physical phenomena Sir W. Thomson has calculated that in ordinary solids and liquids the average distance between contiguous molecules is less than the hundred millionth and greater than the two thousand millionth of a centimetre. To give an idea of the degree of the size of the molecules Sir W. Thomson gives this illustration : * Imagine a drop of rain, or a glass sphere the size of a pea, magnified to the size of the earth, the molecules in it being increased in the same proportion. The structure of the mass would then be coarser than that of a heap of fine shot, but probably not so coarse as that of a heap of cricket-balls.' 4. Molecular state of bodies. — With respect to the molecules of bodies three different states of aggregation present themselves. First, the solid state, as observed in woods, stones, metals, etc., at the ordinary temperature. The distinctive character of this state is, that the relative positions of the molecules of the bodies cannot be changed with- out the expenditure of more or less force. As a consequence, solid bodies tend to retain whatever form may have been given to them by nature or by art. Secondly, the liquid state, as observed in water, alcohol, oil, etc. Here the relative position of the molecules is no longer permanent, the mole- cules glide past each other with the greatest ease, and the body assumes with readiness the form of any vessel in which it may be placed. Thirdly, the gaseous state, as in air. In gases the mobility of the molecules is still greater than in liquids ; but the distinctive character of a gas is its incessant struggle to occupy a greater volume, or the tendency of its molecules to recede from each other. The general ttrm Jluid is applied to both liquids and gases. We shall see in the sequel that the state of a body depends upon the relations which exist between its molecular attractions and repulsions, and that for one and the same body these relations vary with the temperature. On this account most simple bodies, and many compound ones, may be made to pass successively through all the three states. Water presents the most familiar example of this. 5. Physical phenomena, laxirs, and theories. — Every change which can happen to a body, mere alteration of its chemical constitution being excepted, may be regarded as a. physical phe?to?nenon. The fall of a stone, the vibration of a string, and the sound which accompanies it, the rippling of the surface of a lake, and the freezing of water, are examples of such phenomena. A physical law is the constant relation which exists between any phe- nomenon and its cause. As an example, we have the phenomenon of the diminution of the volume of a gas by the application of pressure ; the corresponding law has been determined, and is expressed by saying that the volume of a gas is inversely proportional to the pressure. In order to explain whole classes of phenomena suppositions, or hypo- theses are made use of ; the utility and probability of an hypothesis or theory is the greater the simpler it is, and the more varied and numerous are the phenomena which are explained by it ; that is to say, are brought -7] General Properties of Bodies. 3 into regular causal connection among themselves and with other natural phenomena. Thus the adoption of the undulatory theory of light is justified by the simple and unconstrained explanation it gives of all lumi- nous phenomena, and by the connection it reveals with the phenomena of heat. 6. Physical agrents. — In our attempts to ascend from a phenomenon to its cause, we assume the existence oi physical agents^ or natural forces^ acting upon matter ; as examples of such we have gravitation^ heat, lights magnetism, and electricity. Since these physical agents are disclosed to us only by their effects, their intimate nature is completely unknown. In the present state of science, we cannot say whether they are properties inherent in matter, or whether they result from movements impressed on the mass of subtile and imponderable forms of matter diffused through the universe. The latter hypothesis is however generally admitted. This being so it may be further asked are there several distinct forms of imponderable matter, or are they in reality but one and the same ? As the physical sciences extend their limits, the opinion tends to prevail that there is a subtile, imponderable, and eminently elastic fluid called the ether distributed through the entire universe; pervading the mass of all bodies, the densest and most opaque, as well as the lightest or the most transparent. It is also considered that the intimate particles of which matter is made up are capable of definite motions varying in character and velocity, and which can be communicated to the ether. A motion of a particular kind communicated to the ether can give rise to the phenomenon of heat ; a motion of the same kind, but of greater velocity, produces light ; and it may be that a motion different in form or in character is the cause of electricity. Not merely do the atoms of bodies commu- nicate motion to the atoms of the ether, but this latter can impart it to the former. Thus the atoms of bodies are at once the sources and the recipients of the motion. All physical phenomena, referred thus to a single cause, are but transformations of motion. CHAPTER II; GENERAL PROPERTIES OF BODIES. 7. Different kinds of properties. — By the term properties as ap- plied to bodies, we understand the different ways in which bodies present themselves to our senses. We distinguish general from specific properties. The former are shared by all bodies, and amongst them the most impor- tant are ijnpenetrability , extension, divisibility, porosity, compressibility , elasticity, mobility, and inertia. Specific properties are such as are observed in certain bodies only, or in certain states of these bodies ; such are solidity , fiuidity , tenacity, duc- tility, malleability, hardness, transparency, colour, etc. With respect to the above general properties, it may be remarked At On Matter^ Force^ and Motion. [8- that impenetrability and extension might be more aptly termed essential attributes of matter, since they suffice to define it ; and that divisibility, porosity, compressibility, and elasticity, do not apply to atoms, but only to bodies or aggregates of atoms (3). 8. Impenetrability. — Impenetrability is the property in virtue of which two portions of matter cannot, at the same time, occupy the same portion of space. Strictly speaking, this property applies only to the atoms of a body. In many phenomena bodies appear to penetrate each other ; thus, the volume of a compound body is always less than the sum of the volumes of its constituents ; for instance, the volume of a mixture of water and sul- phuric acid, or of water and alcohol, is less than the sum of the volumes before mixture. In all these cases, however, the penetration is merely apparent, and arises from the fact that in every body there are interstices or spaces unoccupied by matter. 9. Extension. — Extension or magnitude is the property in virtue of which every body occupies a limited portion of space. Many instruments have been invented for measuring linear extension or lengths with great precision. Two of these, the vernier and micro- meter screw, on account of their great utility, deserve to be here mentioned. 10. Vernier. — The vernier forms a necessary part of all instruments where lengths or angles have to be estimated with precision ; it derives its name from its inventor, a French mathematician, who died in 1637, and consists essentially of a short graduated scale, ab, which is made to A B ! i\ 1C\ ^'\ ) 1 1 1 1 1 . 1 1 1 1 1 1 1 i 1 1 1 I 1 1 1 1 1 1 1 I ' 1 A. a b S\ 10, /il ^^^^^^^^^^^;n 1 1 1 1 III 1 1 1 1 1 1 m ii 1C\ Fig. I. slide along a fixed scale, AB, so that the graduations of both may be compared with each other. The fixed scale, AB, being divided into equal parts, the whole length of the vernier, ab, may be taken equal to nine of those parts, and itself divided into ten equal parts. Each of the parts of the vernier, ab^ will then be less than a part of the scale by one tenth of the latter. This granted, in order to measure the length of any object, mn, let us suppose that the latter, when placed as in the figure, has a length greater than four but less than five parts of the fixed scale. In order to determine by what fraction of a part mn exceeds four, one of the ends, a, of the ver- nier, ab^ is placed in contact with one extremity of the object, mn^ and the division on the vernier is sought which coincides with a division on the scale, AB. In the figure this coincidence occurs at the eighth divi- sion of the vernier, counting from the extremity, ;/, and indicates that the -12] Micrometer Srew. 5 fraction to be measured is equal to /oths of a part of the scale, AB. In fact, each of the parts of the vernier being less than a part of the scale by j^^th of the latter, it is clear that on proceeding towards the left from the point of coincidence, the divisions of the vernier are respectively one, two, three, etc., tenths behind the divisions of the scale ; so that the extremity, ;/, of the object (that is to say, the eighth division of the vernier) is jo^hs behind the division marked 4 on the scale ; in other words, the length of inn is equal to 4/0^^^ ^^ ^^ parts into which the scale AB is divided. Consequently, if the scale AB were divided into inches, the length of mn would be 4yo = 4| inches. The divisions on the scale remaining the same, it would be necessary to increase the length of the vernier in order to measure the length mil more accurately. For instance, if the length of the vernier were equal to nineteen of the parts on the scale, and this length were divided into twenty equal parts, the length mn could be deter- mined to the twentieth of a part on a scale, and so on. In instruments like the theodolite, intended for measuring angles, the scale and vernier have a circular form, and the latter usually carries a magnifier, in order to determine with greater precision the coincident divisions of vernier and scale. 11. micrometer screw. — Another useful little instrument for mea- suring small lengths with precision is the micrometer screw. It is used under various forms, but the principle is the same in all, and may be illustrated by a simple example. Suppose the distance between the threads of an accurately cut screw to be equal to j^th of an inch, and the head of the screw to be a tolerably large circle divided into one hundred equal parts. If the screw is fixed in such a manner that it can only turn on its axis, but neither advance nor recede, and if it work in a nut held between guides which prevent it from turning, then every turn of the screw will cause the nut to advance through the tenth part of an inch. If a fixed pointer be placed before the divided circle at the head of the screw, and the latter turned through so small an angle that only one division of the circle passes under the pointer, the hundredth part of a turn will have been given to the screw, and the nut thereby caused to advance o4» recede through the hundredth part of the distance between two threads* — that is to say, through the jo^oo^^ P^^^ °^ ^^ inch. Applications of this principle to the measurement of small lengths are met with in the sphe- rometer, and in the dividing machitie^ and will be readily understood when seen. 12. Bivisibility — is the property in virtue of which a body may be separated into distinct parts. Numerous examples may be cited of the extreme divisibility of matter. The tenth part of a grain of musk will continue for years to fill a room with its odoriferous particles, and at the end of that time will scarcely be diminished in weight. Blood is composed of red, flattened globules, floating in a colourless liquid called serum. In man the diameter of one of these globules is less than the 3,500th part of an inch, and the drop of blood which might be suspended from the point of a needle would contain about a million of globules. On Matter, Force, and Motion. [12- Again, the microscope has disclosed to us the existence of insects smaller even than these particles of blood; the struggle for existence reaches even to these little creatures, for they devour still smaller ones. If blood runs in the veins of these devoured ones, how infinitesimal must be the magnitude of its component globules ! Has then the divisibility of matter no limit ? Although experiment fails to determine such limit, many facts in chemistry, such as the in- variability in the relative weights of the elements which combine with each other, would lead us to believe that a limit does exist. It is on this account that bodies are conceived to be composed of extremely minute and indivisible parts called atoms (3). 13. Porosity. — Porosity is the quality in virtue of which interstices or ^ores exist between the molecules of a body. Two kinds of pores may be distin- guished : physical pores, where the inter- stices are so small that the surrounding molecules remain within the sphere of each other's attracting or repelling forces; and sensible pores, or actual cavities across which these molecular forces cannot act. The contractions and dilatations resulting from variations of temperature are due to the existence of physical pores, whilst in the organic world the sensible pores are the seat of the phenomena of exhalation and absorption. In wood, sponge, and a great number of stones, for instance, pumice stone, the sensible pores are apparent ; physical pores never are. Yet, since the volume of every body may be diminished, we conclude that all possess physical pores. The existence of sensible pores may be shown by the following experiment: — A long glass tube, A (fig. 2), is provided with a brass cup, in, at the top, and a brass foot made to screw on to the plate of an air-pump. The bottom of the cup con- sists of a thick piece of leather. After pouring mercury into the cup so as en- tirely to cover the leather, the air-pump is put in action, and a partial vacuum produced within the tube. By so doing a shower of mercury is at once produced within the tube, for the atmos- pheric pressure on the mercury forces that liquid through the pores of the leather. In the same manner water or mercury may be forced through the pores of wood, by replacing the leather in the above experi- ment by a disc of wood cut perpendicular to the fibres. Fig. 2. r ^ -16] Compressibility. * 7 When a piece of chalk is thrown into water, air-bubbles at once rise to the surface, in consequence of the air in the pores of the chalk being expelled by the water. The chalk will be found to be heavier after im- mersion than it was before, and from the increase of its weight the volume of its pores may be easily determined. The porosity of gold was demonstrated by the celebrated Florentine experiment made in 1661. Some academicians at Florence, wishing to try whether water was compressible, filled a thin globe of gold with that liquid, and, after closing the orifice hermetically, they exposed the globe to pressure with a view of altering its form, well knowing that any altera- tion in form must be accompanied by a diminution in volume. The consequence was, that the water forced its way through the pores of the gold, and stood on the outside of the globe like dew. More than twenty years previously the same fact was demonstrated by Francis Bacon by means of a leaden sphere, the experiment has since been repeated with globes of other metals, and similar results obtained. 14. Apparent and real volumes. — In consequence of the porosity of bodies, it becomes necessary to distinguish between their real and appa- rent volumes. The real volume of a body is the portion of space actually occupied by the matter of which the body is composed ; its apparent vohcine is the sum of its real volume and the total volume of its pores. The real volume of a body is invariable, but its apparent volume can be altered in various ways. 15. Applications. — The property of porosity is utilised in filters of paper, felt, stone, charcoal, etc. The pores of these substances are suffi- ciently large to allow liquids to pass, but small enough to arrest the passage of any substances which these liquids may hold in suspension Again, large blocks of stone are often detached in quarries by introducing wedges of dry wood into grooves cut in the rock. These wedges being moistened, water penetrates their pores, and causes them to swell with considerable force. Dry cords, when moistened, increase in diameter and diminish in length, a property of which advantage is sometimes taken in order to raise great weights. 16. Compressibility. — Compressibility is the property in virtue of which the volume of a body m.ay be diminished by pressure. This pro- perty is at once a consequence and a proof of porosity. Bodies differ greatly with respect to compressibility. The most com- pressible bodies are gases ; by sufficient pressure they may be made to occupy ten, twenty, or even a hundred times less space than they do under ordinary circumstances. In most cases, however, there is a limit beyond which, when the pressure is increased, they become liquids. The compressibility of solids is much less than that of gases, and is found in all degrees. Cloths, paper, cork, woods, are amongst the most compressible. Metals are so also to a great extent, as is proved by the process of coining, in which the metal receives the impression from the die. There is, in most cases, a limit beyond which, when the pressure is increased, bodies are fractured or reduced to powder. The compressibility of liquids is so small as to have remained for a 8 On Matter, Force, and Motion. [17- long time undetected : it may, however, be proved by experiment, as will be seen in the chapter on Hydrostatics. 17. Elasticity. — Elasticity is the property in virtue of which bodies resume their original form or volume, when the force which altered that form or volume ceases to act. Elasticity may be developed in bodies by pressure, by traction or pullinf^, flexion or bending, and by torsion or twisting. In treating of the general properties of bodies, the elasticity developed by pressure alone requires consideration ; the other kinds of elasticity being peculiar to solid bodies, will be considered amongst their specific properties (arts. 81, 82, 83). Gases and liquids are perfectly elastic ; in other w^ords, after under- going a change in volume they regain exactly their original volume when the pressure becomes what it originally was. Solid bodies present different degrees of elasticity, though none present the property in the same perfection as liquids and gases, and in all it varies according to the time during which the body has been exposed to pressure. Caoutchouc, ivory, glass, and marble possess considerable elasticity ; lead, clay, and fats, scarcely any. There is a limit to the elasticity of solids, beyond which they either break or are incapable of regaining their original form and volume. This is called the limit of elasticity . In sprains, for instance, the elasticity of the tendons has been exceeded. In gases and liquids, on the contrary, no such limit can be reached ; they always regain their original volume. If a ball of ivory, glass, or marble, be allowed to fall upon a slab of polished marble, which has been previously slightly smeared with oil, it will rebound and rise to a height nearly equal to that from which ii fell. On afterwards examining the ball a circular blot of oil will be found upon it, more or less extensive according to the height of the fall. From this we conclude that at the moment of the shock the ball was flattened, and that its rebound was caused by the effort to regain its original form. 18. Mobility, motion, rest. — Mobility is the property in virtue of which the position of a body in space may be changed. Motion and rest may be either relative or absolute. By the 7-elative motion or rest of a body w^e mean its change or permanence of position with respect to surrounding bodies ; by its absolute motion or rest we mean the change or permanence of its position with respect to ideal fixed points in space. Thus a passenger in a railway carriage may be in a state of relative rest with respect to the train in which he travels, but he is in a state of relative motion with respect to the objects, such as trees, houses, etc., past which the train rushes. These houses again enjoy merely a state of relative rest, for the earth itself which bears them is in a state of inces- sant relative motion with respect to the celestial bodies of our solar system, inasmuch as it moves at the rate of more than eighteen miles in a second. In short, absolute motion and rest are unknown to us ; in nature, relative motion and rest are alone presented to our observation. 19. Inertia. — Inertia is a purely negative property of matter ; it is the incapability of matter to change its own state of motion or rest. ^ -21] Measure of Time, 9 A body when unsupported in mid-air does not fall to the earth in virtue of any inherent property, but because it is acted upon by the force of gravity. A billiard ball gently pushed does not move more and more slowly, and finally stop, because it has any preference for a state of rest, but because its motion is impeded by the friction on the cloth on which it rolls, and by the resistance of the air. If all impeding causes were with- drawn, a body once in motion would continue to move for ever. 20. Applic£ition. — Numerous phenomena may be explained by the inertia of matter. For instance, before leaping a ditch we run towards it, in order that the motion of our bodies at the time of leaping may add itself to the muscular effort then made. On descending carelessly from a carriage in motion, the upper part of the body retains its motion, whilst the feet are prevented from doing so by friction against the ground ; the consequence is we fall towards the moving carriage. A rider falls over the head of a horse if it suddenly stops. In fixing the head of a hammer by striking the handle against the ground w€ have an application of inertia. The terrible accidents on qur railways are chiefly due to inertia. When the motion of the engine is suddenly arrested the carriage^ strive to continue the motion they had acquired, and in doing so are shattered against each other. Hammers, pestles, stampers are applications qf inertia. So are also the enormous iron fly-wheels, by which the motion of steam engines is regulated. CHAPTER III, ON force;, e;quilibrium, and, motion, 21. XMCeti'Sure of Time. — To obtain a proper measure of force it is necessary, as a preliminary, to define certain conceptions which are pre- supposed in that measure ; and, in the first place, it is necessary to define the unit of time. Whenever a second is spoken of without qualification it is understood to be a second of mean solar time. The exact length of this unit is fixed by the following consideration. The instant when the sun's centre is on an observer's meridian — in other words, the instant of the transit of the sun's centre — can be determined with exactitude, and thus the interval which elapses between two successive transits also admits of exact determination, and is called an apparent day. The length of this interval differs slightly from day to day, and therefore does not serve as a convenient measure of time. Its average length is free from this inconvenience, and therefore serves as the required measure, and is called a mean solar day. The short hand of a common clock w^ould go exactly twice round the face in a mean solar day if it went perfectly. The mean solar day consists of 24 equal parts called hours, these of 60 equal parts called minutes^ and these of 6q equal parts called seconds. Consequently, the second is the 86,400th part of a mean solar day, and is the generally received unit of time, 10 On Matter, Force, and Motion. [22- 22. Measure of Space. — Space may be either length or distance, which is space of one dimension ; area, which is space of two dimensions ; or volume, which is space of three dimensions. In England the standard of length is the British Imperial Yard, which is the distance between two points on a certain metal rod, kept in the Tower of London, when the temperature of the whole rod is 6o° F. = i5°-5 C. It is, however, usual to employ as a unit, difoot, which is the third part of a yard. In France the standard of length is the metre ; this is approximately equal to the ten- millionth part of a quadrant of the earth's meridian, that is of the arc from the Equator to the North Pole ; it is practically fixed by the distance between two rnarks on a certain standard rod. The relation between these standards is as follows : I yard =0*914383 metre. I metre = i "093633 yard. The unit of length having been fixed, the units of area and volume are connected with it thus : the unit of area is the area of a square, one side of which is the unit of length. The unit of volunie is the volume of a cube, one edge of which is the unit of length. These units in the case of English measures are the square yard (or foot) and the cubic yard (or foot) respectively ; in the case of French measures, the square metre and cubic metre respectively. 23. Measure of XMEass. — Two bodies are said to have equal masses when, if placed in a perfect balance in vacuo, they counterpoise each other. Suppose we take lumps of any substance, lead, butter, wood, stone, etc., and suppose that any of them when placed on one pan of a balance will exactly counterpoise any other of them when placed on the opposite pan — the balance being perfect and the weighing performed in vacuo ; this being the case, these lumps are said to have equal masses. That these lumps differ in many respects from each other is plain enough ; in what respects they have the same properties in virtue of the equality of their masses is to be ascertained by subsequent enquiry. The British unit of mass is the standard pound (avoirdupois), which is a certain piece of platinum kept in the Exchequer Office in London. This unit having been fixed, the mass of a given substance is expressed as a multiple or submultiple of the unit. It need scarcely be mentioned that many distances are ascertained and expressed in yards which it would be physically impossible to measure directly by a yard measure. In like manner the masses of bodies are frequently ascertained and expressed numerically which could not be placed in a balance and subjected to direct weighing. 24. Density and Relative Density. — If we consider any body or portion of matter, and if we conceive it to be divided into any number of parts having equal volumes, then, if the masses of these parts are equal, in whatever way the division be conceived as taking place, that body is one of uniform density. The density of such a body is the mass of the unit of volume. Consequently if M denote the mass, V the volume, and D the density of the body, we have M=VD. -25] Velocity. 1 1 If now we have an equal volume V of any second substance whose mass is M' and density D', we shall have M' = VD'. Consequently D : D' :: M : M^ ; that is the densities of substances are in the same ratio as the masses of equal volumes of those substances. If now we take the density of distilled water at 4° C. to be unity, the relative density of any other substance is the ratio which the mass of any given volume of that substance at that temperature bears to the mass of an equal volume of water. Thus it is found that the mass of any volume of platinum is 22-069 times that of an equal volume of water, consequently the relative density of platinum is 22*069. The relative density of a substance is generally called its specific gravity. Methods of determining it are given in Book III. In French measures the cubic deciinetre or litre of distilled water at 4° C. contains the unit of mass, the kilogramme ; and therefore the mass in kilogrammes of V cubic decimetres of a substance whose specific gravity is D, will be given by the equation M = VD. The same equation will give the mass in grammes of the body, if V is given in cubic centimetres. It has been ascertained that 277274 cubic inches of distilled water at the temperature 1 5°-5 C. or 60° F. contain a pound of matter. Conse- quently, if V is the vohime of a body in cubic inches, D its specific gravity, its mass M in lbs. avoirdupois will be given by the equation M = ^• 277274 In this equation D is, properly speaking, the relative density of the sub- stance at 60° F. when the density of water at 60° F. is taken as the unit. 25. Velocity and Its measure. — When a material point moves, it describes a continuous line which may be either straight or curved, and is called its path and sometimes its trajectory. Motion which takes place along a straight line is called rectilinear motion ; that which takes place along a curved line is called curvilinear motion. The rate of the motion of a point is called its velocity. Velocity may be either uniform or variable ; it is u7iiform when the point describes equal spaces of portions of its path in all equal times ; it is variable when the point describes un- equal portions of its path in any equal times. Uniform velocity is measured by the number of units of space de- scribed in a given unit of time. The units commonly employed are feet and seconds. If, for example, a velocity 5 is spoken of without qualifica- tion, this means a velocity of 5 feet per second. Consequently, if a body moves for / seconds with a uniform velocity 7/, it will describe vt feet. The following are a few examples of different degrees of velocity ex- pressed in this manner. A snail 0*005 feet in a second; the Rhine between Worms and Mainz 3-3 ; military quick step 4-6 ; moderate wind 10 ; fast sailing vessel i8-o ; channel steamer 22*0 ; railway train 36 to 75 feet; racehorse and storm 50 feet ; eagle 100 feet ; carrier pigeon 12a 1 2 On Matter y Force ^ and Motion. [26- feet ; a hurricane i6o feet ; sound at 0^1090 ; a point on the Equator in its rotation about the earth's axis 1520 ; a Martini-Henry rifle bullet 1330 ; a shot from an Armstrong gun 1 180 ; the centre of the earth loiooo ; light and also electricity in a medium destitute of resistance 192000 miles. Variable velocity is measured at any instant by the number of units of space a body would describe if it continued to move uniformly from that instant for a unit of time. Thus, suppose a body to run down an inclined plane, it is a matter of ordinary observation that it moves more and more quickly during its descent ; suppose that at any point it has a velocity 15, this means that at that point it is moving at the rate of 15 ft. per second, or in other words, if from that point all increase of velocity ceased, it would describe 15 ft. in the next second. 26. Force. — When a material point is at rest, it has no innate power of changing its state of rest ; when it is in motion it has no innate power of changing its state of uniform motion in a straight line. This property of matter is termed its inertia (19). Any cause which sets a point in motion, or which changes the magnitude or direction of its velocity if in motion, is a force. Gravity , friction, elasticity of springs or gases, elec- trical or magnetic attraction or repulsion, etc. are forces. All changes observed in the motion of bodies can be referred to the action of one or more forces. 27. Accelerative effect of force. — If we suppose a force to con- tinue unchanged in magnitude, and to act along the line of motion of a point, it will communicate in each successive second a constant increase of velocity. This constant increase is the accelerative effect of the force. Thus, if at any given instant the body has a velocity 10, and if at the end of the first, second, third, etc., second from that instant its velocity is 13, 16, 19, etc., the accelerative effect of the force is 3 ; a fact which is expressed by saying that the body has been acted on by an accelerating force 3. If the force vary from instant to instant, its accelerative effect will also vary ; when this is the case the accelerative effect at any instant is mea- sured by the velocity it would communicate in a second if the force continued constant from that instant. By means of an experiment to be described below (76) it can be shown that at any given place the accelerative effect of gravity^ is constant ; but it is found to have different values at different places ; adopting the units of feet and seconds it is found that with sufficient approximation ^=/ (l 0-00256 cos 20) at a place whose latitude is 0, where/" denotes the number 32 "1724, that is the effect of gravity in latitude 45°. If we adopt th^units of metres and seconds, then/ = 9-8059. 28. AKomentum or quantity of motion is a magnitude varying as the mass of a body and its velocity jointly, and therefore is expressed nume- rically by the product of the number of units of mass which it contains and the number of units of velocity in its motion. Thus a body con- taining 5 lbs. of matter, and moving at the rate of 12 ft. per second, has a momentum of 60. -30] Representation of Forces, 13 29. Measure of force. — Force, when constant, is measured by the momentiun it communicates to a body in a unit of time. If the force varies, it is then measured at any instant by the momentum it would communicate if it continued constant for a unit of time from the instant under consideration. The unit of force is that force which acting on a pound of matter would produce in one second a velocity of one foot per second. Consequently if a body contains m lbs. of matter, and is acted pn by a force whose accelerative effect is^^ that force contains a number of units of force (F), given by the equation F = mf. The weight of a body, when that term denotes a force, is the force exerted on it by gravity ; consequently, if m is the mass of the body, and g the accelerating force of gravity, the number of units of force W exeited on it by gravity is given by the equation W =^ mg or (27) ^ = mf{i — 0-00256 cos 20). From this it is plain that the weight of the same body will be different at different parts of the earth's surface ; this could be verified by attaching a piece of platinum (or other metal) to a delicate spring, and noting the variations in the length of the spring during a voyage from a station in the Northern Hemisphere to another in the Southern Hemisphere, for instance, from London to the Cape of Good Hope. When, therefore, 3.potmd\s used as a unit of force it must be under- stood to mean the force W exerted by gravity on a pound of matter in London. Now, in London, the latitude of which is 51-30, the numerical value of ^is 32-1912, so that W= I X 32-1912 ; in other words, when a pound is taken as the unit of force it contains 32-1912 units of force according to the measure given above. It will be observed that a pound of matter is a completely determinate quantity of matter irrespective of locality, but gravity exerts on a pound of matter a pound (or 32*1912 units) of force at London and other places in about the same latitude as London only ; this ambiguity in the term pound should be carefully noticed by the student ; the context in any treatise will always show in which sense the term is used. 30. Representation of forces. — Draw any straight line AB, and fix on any point O in it. We may suppose a force to act on the point O, along the line AB, either towards A or B : then O is called the point of application of the force, AB b m o ]« — a its line of action ; if it acts towards A, its direction p. is OA, if towards B, its direction is OB. It is rarely necessary to make the distinction between the line of action and direction of a force ; it being very convenient to make the convention that the statement — a force acts on a point O along the line OA — means that it acts from O to A. Let us suppose the force which acts on O along OA to contain P units of force ; from O towards A measure ON coni 14 Oil Matter, Force, and Motion. [30- taining P units of length, the hne ON is said to represent the force. It will be remarked that the analogy between the line and the force is very- complete ; the line ON is drawn from O in a given direction OA, and contains a given number of units P, just as the force acts on O in the direction OA, and contains a given number of units P. It is scarcely necessary to add, that if an equal force were to act on O in the opposite direction, it would be said to act in the direction OB, and would be re- presented by OM, equal in magnitude to ON. When we are considering several forces acting along the same line we may indicate their directions by the positive and negative signs. Thus the forces mentioned above would be denoted by the symbols + P and — P respectively. ; 31. Forces acting- along: the same line. — If forces act on the point i O in the direction OA equal to P and Q units respectively, they are \ equivalent to a single force R containing as many units as P and Q together, that is, R = P + Q. If the sign + in the above equation denote algebraical addition, the equation will continue true whether one or both of the forces act along OA or OB. It is plain that the same rule can be extended to any number of forces, and if several forces have the same line of action they are equivalent to one force containing the same number of units as their algebraical sum. Thus if forces of 3 and 4 units act on O in the direction OA, and a force of 8 in the direction OB, they are equivalent to a single force containing R units given by the equation R=3+4-8=-i; that is, R is a force containing one unit acting along OB. This force R is called their resultant. If the forces are in equilibrium R is equal to zero. In this case the forces have equal tendencies to move the point O in opposite directions. 32. Resultant and components. — In the last article we saw that a single force R could be found equivalent to several others ; this is by no J, I means peculiar to the case in which all the forces have the same line of action ; in fact, when a material point, A (fig. 4), remains in equilibrium under the action of several forces, S, P, Q, it does so because any one of the forces, as S, is capable of neutralising the combined effects of all the others. If the force S, therefore, had its direction reversed, so as to act along \ AR, the prolongation of AS, it would produce the \ same effect as the system of forces P, Q. \ Now, a force whose effect is equivalent to the com- \ bined effects of several other forces is called their re- P sultanty and with respect to this resultant, the other ^^ ^ forces are termed components. When the forces, P, Q, act on a point they can only have otie resultant ; -33] Parallelogram of Forces. 15 but any single force can be resolved into components in an indefinite number of ways. If a point move from rest under the action of any number of forces it will begin to move in the direction of their resultant. 33. Parallelograxu of forces. — When two forces act on a point their resultant is found by the following theorem, known as the principle of the parallelogram of forces: — If two forces act on a point , arid if lines be drawn from that point representing the forces in magnitude and direction, and oji these lines as sides a parallelogram be cotistructed, their resultant will be represented in 7nagnitude and direction by that diagonal which passes through the point. Thus let P and Q (fig. 5) be two forces acting on the point A along AP and AQ respectively, and let AB and AC be taken containing the same number of units of length that P and Q con- tain units of force ; let the parallelogram AB DC be completed, and the diagonal AD drawn ; then the theorem states that the resultant, R, of P and Q is represented by AD ; that is to say, P and Q together are equal to a single force R acting along the line AD, and containing as many units of force as AD contains units of length. Fie. 6. Proofs of this theorem are given in treatises on Mechanics ; we will here give an account of a direct experimental verification of its truth; but before doing so we must premise an account of a very simple experiment. Let A (fig. 6) be a small pulley, and let it turn on a smooth, hard, and thin axle with little or no friction : let W be a weight tied to the end of a fine thread which passes over the pulley ; let a spring CD be attached by one end to the end C of the thread and by the end D to another piece of thread, the other end of which is fastened to a fixed point B; a scale CE can be fastened by one end to the point C and pass inside the spring so that the elongation of the spring can be measured. Now it will be found on trial that with a given weight W the elongation of the spring will be the same whatever the angle contained between the parts of the string WA and BA. Also it would be found that if the whole were suspended from a fixed point, instead of passing over the pulley, the weight would in this case stretch the spring to the same extent as before. This experi- ment shows that when care is taken to diminish to the utmost the friction of the axle of the pulley, and the imperfect flexibility of. the thread, the i6 On Matter, Force, and Motio7i. [33- weight of W is transmitted without sensible diminution to B, and exerts on that point a pull or force along the line BA virtually equal to W. This being premised, an experimental proof, or illustration of the parallelogram of forces, may be made as follows : — Suppose H and K (fig. 7) to be two pulleys with axles made as smooth and fine as possible ; let P and Q be two weights suspended from fine and flexible threads which, after passing over H and K, are fastened at A to a third thread AL from which hangs a weight R ; let the three weights come to rest in the positions shown in the figure. Now the point A is acted on by three forces in equilibrium, viz., P from A to H, Q from A to K, and R from A to L, consequently any one of them must be equal and opposite to the resultant of the other two. Now if we suppose the apparatus to be arranged immediately in front of a large slate, we can draw lines upon it coinciding with AH, AK, and AL, If now we mea^ sure off along AH the part AB- containing as many inches as P contains pounds, and along AK the part AC containing as many inches as Q con- tains pounds, and complete the parallelogram ABCD, it will be found that the diagonal AD is in the same Hne as AL, and contains as many inches as R weighs pounds. Consequently, the resultant of P and Q is represented by AD. Of course, any other units of length and force might have been employed. Now it will be found that when P, Q, and R are changed in any way whatever, consistent with equilibrium, the same construction can be made, — the point A will have different positions in the different cases ; but when equilibrium is established, and the paral- lelogram ABCD is constructed, it will be found that AD is vertical, and contains as many units of length as R contains units of force, and conse- quently it represents a force equal and opposite to R, that is, it represents the resultant of P and Q. 34. Resultant of any number of forces acting: in one plane on a point. — Let the forces P, Q, R, S (fig. 8) act on the point A, and let them be represented by the lines AB, AC, AD, Y\ AE, as shown in the figure. First, complete the parallelogram ABFC and join AF ; this line represents the resultant of P and Q. Secondly, complete the parallelogram AFGD and join AG; this line represents the resultant of P, Q, R. Thii'dly, complete the parallelogram AG HE and join AH ; this line represents the resultant of P, Q, R, S. It is manifest that the construc- tion can be extended to any number of forces. A little consideration will show that the line AH might be determined by the following through B draw BF parallel to, equal to, and towards the same part as AC; through F draw FG parallel to, equal to, and towards ^36] Conditions of Equilibrium of Forces. 17 Fig. 9. the same part as AD; through G draw GH parallel to, equal to, and towards the same part as AE; join AH, then AH represents the required resultant. In place of the above construction, the resultant can be determined by calculation in the following manner : — Through A draw any tvvo rectangular axes Ax and Ay (fig. 9), and let a, a:?, y be the angles made with the axis Ax by the lines representing the pressures, then P, Q, R can be resolved into P cos a, O cos |8, R cos y, acting along Ax, and P sin a, Q sin (5, R sin 7, acting along Ay. Now the former set of forces can be reduced to a single force X by addition, attention being paid to the sign of each component ; and in like manner the latter forces can be reduced to a single force Y, that is, X = P cos a + Q cos /3 + R cos y + . . . Y = P sin a + Q sin ^3 + R sin y + . . . Since the addition denotes the algebraical sum of the quantities on the right hand side of the equations, both sign and magnitude of X and Y are known. Suppose U to denote the required resultant, and ^ the angle made by the line representing it with the axis Ax ; then U cos ^ = X, and U sin •/> = Y. These equations give U2 = X2 + Y2, which determines the magnitude of the resultant, and then, since both sin ^ and cos ^ are known, is determined without ambiguity. Thus let P, Q, and R be forces of 100, 150, and 120 units, respectively, and suppose xAP, xAO, and xAR to be angles of 45°, 120*', and 210° re- spectively. Then their components along Ax are 707, — 75, — 103'9, ^^id their components along Ay are 707, — 129*9, — 60. The sums of these two sets being respectively — 108*2 and 140*6, we have U cos 0= —108*2 and U sin ^= 140*6. therefore U^ = (108*2)2 ^. (140*6)= or U =177-4 therefore I77'4 cos ^ = - 108*2, and 177*4 sin ^ = 140-6. If we made use of the former of these equations only, we should obtain ^ equal to 232° 25', or 127° 35', and the result would be ambiguous : in like manner, if we determined ^ from the second equation only, we should have equal to 52° 25', or 127° 35'; but as we have both equations, we know that ^ equals 127° 35', and consequently the force U is completely determined as indicated by the dotted line AU. 35. Conditions of equilibrium of any force actingr in one plane on a point. — If the resultant of the forces is zero, they have no joint tendency to move the point, and consequently are in equilibrium. This obvious principle enables us to deduce the following constructions and equations, which serve to ascertain whether given forces will keep a point at rest. Suppose that in the case represented in fig. 8, T is the force which will balance P, Q, R, S. It is plain that T must act on A along HA produced, i8 On Matter, Force, and Motio7t. [35- and in magnitude must be proportional to HA ; for then the resultant of the five forces will equal zero, since the broken line ABFGHA returns to the point A. This construction is plainly equivalent to the following : Let P, Q, R (fig. lo) be forces acting on the point O, as indicated, their magnitudes and directions being given. It is known that they are balanced by a fourth force, S, and it is required to determine the magnitude and direction of S. Take any point D, and draw any line parallel to and towards the same part as OP, draw AB parallel to and towards the same parts as OQ, and take AB such that P : Q : : DA : AB. Through B draw BC parallel to and towards the same part as OR, taking BC such that O : R::AB : BC; join CD; through O draw OS parallel to and towards the same part as CD, then the required force S acts along OS, and is in magnitude proportional to CD. Fig. lo. Fig. It is to be observed that this construction can be extended to any number of forces, and will apply to the case in which these directions are not in one plane, only in this case the broken line ABCD would not lie wholly in one plane. The above construction is frequently called the Polygon of Forces. The case of three forces acting on a point is, of course, included in the above ; but its importance is such that we may give a separate statement of it. Let P, Q, R (fig. 1 1) be three forces in equilibrium on the point O. From any point B draw BC parallel to and towards the same part OP, from C draw CA parallel to and towards the same part as 00, and take CA such that P : Q::BC : CA; then, on joining AB, the third force R must act along OR parallel to and towards the same part as AB, and must be proportional in magnitude to AB. This construction is frequently called the Triangle of Forces. It is evident that while the sides of the triangle are severally proportional to P, O, R, the angles A, B, C are supplementary to QOR, ROP, POQ respectively, consequently every trigonometrical relation existing between the sides and angles of ABC will equally exist between the forces P, Q, R, and the supplements of the angles between their directions. Thus in the triangle ABC it is known that the sides are proportional to the sines of the opposite angles ; now since the sines of the angles are equal to the sines of their supplements, we at once conclude that when three forces are in eqtiilibrium, each is propor- tional to the sine of the angle between the directio7is of the other two. -36] Parallel Forces. 1 9 We can easily obtain from the equations which determine the resultant of any number of forces (34), equations which express the conditions of equilibrium of any number of forces acting in one plane on a point ; in fact, if U = O we must have X = o and Y = O ; that is to say, the required conditions of equilibrium are these : — O = P. cos a + Q cos |3 + R cos y + .. . and O => P sin a + Q sin /3 + R sin y + . . . The first of these equations shows that no part of the motion of the point can take place along Ax, the second that no part can take place along Ay. In other words, the point cannot move at all. V 36. Composition and resolution of parallel forces. — The case of the equilibrium of three parallel forces is merely a particular case of the equilibrium of three forces acting on a point. In fact let P and O be two forces whose directions pass through the points A and B, and inter- sect in O ; let them be balanced by a third force R whose direction produced intersects the line AB in C. Now suppose the point O to move along AO, gradually receding from A, the magnitude and direction of R will con- tinually change, and also the point C will continually change its position, but will always lie between A and B. In the limit P and Q become parallel forces, acting towards the same part balanced by a parallel force R acting towards the contrary part through a point X between A and B. The question is : — First^ on this limiting case what is the value of R ; secondly., what is the position of X ? Now with regard to the a, first point it is plain, that if a triangle a b c were drawn iv as in art. 35, the angles a and b in the limit will Fig. 12. vanish, and ^ will become 180°, consequently rt; b ultimately equals ac -v cb; or R = P + Q. With regard to the second point it is plain that OC sin POR = OC sin AOC = AC sin CAO, and OC sin ROQ = OC sin BOC = CB sin CBO; therefore AC sin CAO : CB sin CBO :: sin POR : sin ROQ ::Q:P(35). \ Now in the limit, when OA and OB become parallel, OAB and OB A become supplementary ; that is, their sines become equal ; also AC and CB become respectively AX and XB ; consequently AX:XB::Q:P, a proportion which determines the position of X. This theorem at once leads to the rules for the composition of any two parallel forces, viz. I. When two parallel forces P and O act towards the same part, at rigidly connected points A and B, their resultant is a parallel force acting towards the same part, equal to their sum, and its direction divides the / 20 On Mattel', Force, and Motion. [36- line AR into two parts AC and CB inversely proportional to the forces P and Q. J II. When two parallel forces P and O J act towards contrary parts at rigidly con- / nected points A and B, of which P is the greater, their resultant is a parallel force acting towards the same part as P, equal to the excess of P over Q, and its direc- 'P^ tion divides BA produced in a point C such that CA and CB are inversely pro- ^'^- '3- ^^ portional to P and O. In each of the above cases if we were to apply R at the point C, in opposite direction to those shown in the figure, it would plainly (by the above theorem) balance P and O, and therefore when it acts as shown in figs. 13 and 14 it is the resultant of P and Q in those cases re- spectively. It will of course follow that / the force R acting at C can be resolved ^' into P and Q acting at A and B respect- '^' ^^' ively. If the second of the above theorems be examined, it will be found that no force R exists equivalent to P and Q when those forces are equal. Two such forces constitute a couple, which may be defined to be two equal parallel forces acting towards contrary parts ; they possess the remarkable property that they are incapable of being balanced by any single force whatsoever. In the case of more than two parallel forces the resultant of any two can be found, then of that and a third, and so on to any number ; it can be shown that however great the number of forces they will either be in ^ equilibrium or reduce to a single resultant or to a couple. 3c 37. Centre of parallel forces.— On referring to figs. 13 and 14, it will be remarked that if we conceive the points A and B to be fixed in the directions AP and BQ of the forces P and Q, and if we suppose those directions to be turned round A and B, so as to continue parallel and to make any given angles with their original directions, then the direction of their resultant will continue to pass through C ; that point is therefore called the centre of the parallel forces P and O. It appears from investigation, that whenever a system of parallel forces reduces to a single resultant, those forces will have a centre ; that is to say, if we conceive each of the forces to act at a fixed point, there will be a point through which the direction of their resultant will pass when the directions of the forces are turned through any equal angles round their points of application in such a manner as to retain the parallelism of their directions. The most familiar example of a centre of parallel forces is the case in which the forces are the weights of the parts of a body ; in this case the -39] Equality of Action and Reaction. 21 forces all acting towards the same part will have a resultant, viz. their Varum ; and their centre is called the ce7itre of gravity of the body. "^ 38. Moments of forces.— Let P denote any force acting from B to P, take A any point, let fall AN a perpendicular from A on BP. The product of the number of units of force in P, and the number of units of length in AN, is called the moment of P with respect to A. Since the force P can be represented by a straight line, the moment of P can be represented by an area. In fact, if BC is the line representing P, the moment is properly represented by twice the area of the triangle ABC. The perpendicular AN is sometimes called the arm of the pressure. Now if a watch were placed with its face upward on the paper, the force P would *» N" c p cause the arm AN to turn round A in the contrary Fig- ^5- direction to the hands of the watch. Under these circumstances, it is usual to consider the moment of P with respect to the point A to be positive. If P acted from C to B, it would turn NA in the satne direction as the hands of the watch, and now its moment is reckoned negative. The following remarkable relation exists between any forces acting in one plane on a body and their "resultant. Take the moments of the forces and of their resultant with respect to any one point in the plane. Then the moment of the resultant equals the sum of the moments of the several forces, regard being had to the signs of the moments. If the point about which the moments are measured be taken in the direction of the resultant, its moment with respect to that point will be zero ; and consequently the sum of the moments with respect to such point will be zero. \ 39. Equality of Action an d Reaction. — We will proceed to exemplify *^^ome of the principles now laid down by investigating the conditions of equilibrium of bodies in a few simple cases ; but before doing so we must notice a law which holds good whenever a mutual action is called into play between two bodies. Reaction is always equal and contrary to, action : that is to say, the mutual actiotis of two bodies on each other ai'e always forces equal in amount and opposite in direction. This law is per- fectly general, and is equally true when the bodies are in motion as well as when they are at rest. A very instructive example of this law has already been given (33), in which the action on the spring CD (fig. 6) is the weight W transmitted by the spring to C, and balanced by the re- action of the ground transmitted from B to D. Under these circum- stances, the spring is said to be stretched by a force W. If the spring were removed, and the thread were continuous from A to B, it is clear that any part of it is stretched by two equal forces, viz. an action and reaction, each equal to W, and the thread is said to sustain a tension W. When a body is urged along a smooth surface, the mutual action can only take place along the common perpendicular at the point of contact. If, how- ever, the bodies are rough, this restriction is partially removed, and now the mutual action can take place in any direction not making an angle greater than some determinate angle with the common perpendicular. 22 On Matter^ Force, and Motion. [40 This determinate angle has different values for different substances, and is sometimes called the limititig angle of resistance, sometimes the angle of repose. 40. Tlie lever is a name given to any bar straight or curved, AB, rest- ing on a fixed point or edge c called the fulcrum. The forces acting on the lever are the weight or resistance Q, Xho. power P, and the reaction of the fulcrum. Since these are in equilibrium, the re- sultant of P and Q must act through C, for otherwise they could not be balanced . "■"""'""""' by the reaction. Draw cb at right angles "^ to QB and ca to PA produced ; then ob- serving that P X ca, and (^xcb are the moments of P and Q with respect to c, and that they have contrary signs, we have by (38), V X ca = Oy. cb ; ^an equation commonly expressed by the Fig- 16. rule, that in the lever the power is to the weight in the i^iverse ratio of their arms. Levers are divided into three kinds, according to the position of the fulcrum with respect to the points of application of the power and the weight. \Ti2.lever of the frst kind the {ulcrum is between the power and resistance, as in fig. 16, and as in a poker and in the common steel- yard ; a pair of scissors and a carpenter's pincers are double levers of this kind. In a lever of the second kind Xhe resistance is between the power and the fulcrum, as in a wheelbarrow, or a pair of nutcrackers, or a door; in a lever of the third kind the power is between the fulcrum and the resistance, as in a pair of tongs or the treadle of a lathe. _V^ 41. The single pulley. — In the case of the single fixed pulley, shown m fig. 17, it follows at once from (33) that when the forces P and Q are in equilibrium they will be equal, the axle of the pulley being supposed perfectly smooth and the thread perfectly } \ ^. flexible. The same conclusion follows directly from the principle of m.oments ; for the resultant of P and Q must pass through C, or otherwise they would cause the pulley to turn ; now their moments are respectively P x CM and Q x CN, and since these have opposite signs we I have (38) Go PxCM = QxCN. Fig. 18. But CM and CN being equal, this equation shows that P and Q are equal. In the case of the single moveable pulley, shown in fig. 18, we have one end of the rope fastened to a point A in a beam. The pulley p ^ Fig. 17. -43] The Wedge, 23 V Fig. 19. is consequently supported by two forces, viz. P and the reaction of the fixed point which is equal to P ; these two forces support Q and the weight of the pulley w. In the case represented in the figure the parts of the rope are parallel, consequently (36) 2P = Q + 7t'. When several pulleys are united into one machine, they constitute a system of pulleys ; such are — the Block and Tackle, the Barton, White's Pulley, etc. 42. The Inclined plane. — A very instructive and useful application of "^ the resolution of forces is to be found in the case of a body supported on an inclined plane. Let AB (fig. 19) be the plane, AC its base, and BC its height ; let a body M considered as a point, whose mass is M and weight M^ or Q, be sup- ported on it by a force P acting along MB. The plane is supposed to be smooth, and therefore reacts on M with a force R at right angles to AB. Draw CD at right angles to AB, then the point M is held at rest by forces P, Q, R, whose direc- tions are severally parallel to the sides of the triangle DBC which is similar to CBA. ..Hence P : R : Q : : BD : DC : CB : : BC : CA : AB ; or since BC = AB sin A and CA = AB cos A, we have P = Q sin A and R = Q cos A. Or the same fact may be stated in this form : — When a mass M is placed on an inclined plane, its pressure on the plane is M^ cos A and its force down the plane is M^ sin A. In the above case these forces are balanced by P and R respectively. Thus suppose BC and CA to be 9 ft. and 12 ft, respectively, then AB will equal 1 5 ft. Consequently, if the weight of Q is 360 lbs. it produces on the plane a perpendicular pressure of 288 lbs,, and requires for its support a force of 216 lbs. acting up the plane. 43. Tne wedgre. — This instrument is nothing but a moveable inclined plane. It is used inseveral forms, of which the annexed is, perhaps, the best for showing the action of the forces called into play. AB is a fixed table. ACDE is a piece which is pre- vented from moving in a lateral direction by a fixed guide F. ABC is a wedge whose angle is such that one of its faces is in contact with a face of ACDE as shown in the figure. ABC being forced forward by P, overcomes the re- sistance Q acting on ACDE. The various forces called into play are represented in the diagram, namely, P, O, the reaction of the table S, the mutual action between the pieces R, R^ and the reaction T of the guide F. We will suppose the angles B, D, E, and EAB to be right angles, and that P and Q act at right angles to DE and ^: X. ^ 11 24 On Matter, Force, and Motion. [43- BC respectively. Moreover, since the surfaces in contact are smooth, S acts in a direction at right angles to AB, R and R^ to AC, and T to AE. Through C draw CG at right angles to AC ; then the body ABC being kept in equilibrium by three forces, P, R, S, whose directions are re- spectively parallel to the sides of the triangle DGC, we have P : R : : DO : GC. The body ACDE being kept in equilibrium by three forces, T, Rj, Q, whose directions are respectively parallel to the side of the triangle DGC, we have Ri : Q : : GC : CD. Now R and Rj are equal, being the mutual actions of the two bodies^ ABC, ACDE ; therefore compounding the ratios, we have P : Q ::DG : DC; or, by similar triangles, P : Q : : CB : BA, a proportion equivalent to the equation ', P = O tan A. 44. The screw. — It will be remarked that when the wedge is used as in the last article, Q cannot be many times greater than P, and also that the space through which P can lift Q is limited. The screw is merely a modification of the wedge by which the limits of its application in both these respects are extended. To explain this, it may be observed that if the thread of a screw were reduced to a line, it would become a curve called the helix, running in whorls round the cylinder; the distance between any two consecutive turns measured parallel to the axis of the cylinder being constant, and called the pitch of the screw. Now if ABC (fig. 20) were wrapped round a cylinder, whose dimensions were such that the base AB coincided with the circumference of the base of the cylinder, and the height BC with the pitch, the hypothenuse CA could be brought into coincidence with one whorl of the helix. Under these circumstances, the angle BAC (A) is called the inclination of the thread, and if r denote the radius of the base of the cylinder, h the pitch of the screw, we shall have, since AB tan A equals BC (fig. 20), 2 Trr tan A = /z. Moreover, if ACDE were wrapped round the inside of a hollow cylinder or nut (fig. 21) of equal radius it would take the form of a helix, or com- panion screw cut on the inside of the nut ; and if the screw were placed within the nut the two helices would be in exact contact. If now we sup- pose the power to act at the end of an arm, we shall have transformed the wedge of fig. 20 into a screw, one end of which works on a fixed table with a moveable nut. The annexed figure shows the arrangement, half the nut being removed in order to show how the thread of the screw works within the groove of the companion. When the arm is turned in the direction indicated by P the point B will pass to B', but as the nut is kept by the guides G, H from turning with the screw, it must now occupy -45] The Screw. Friction. 25 / \ the point C of the companion, and consequently the nut must be lifted so that C comes to B'. If the nut were fixed the screw would be depressed by the same amount, when P acts as indicated. If the screw were turned by a force P' acting tangentially to the base of the cylinder, it is plain that when all frictions are neglected the relation between P' and Q must be the same as that between P and Q in the last article, that is, P' = Q tan A 27rrP'=Q>^; but P acting perpendicularly at the end of an arm a will have (by equality of moments) the same tendency as P' to turn the screw, provided PV=P^, and therefore the relation between P and Q is given by the equation i-Ka P = O/i ; or the power has to the resistance the same ratio which the pitch of the screw has to the circumference of the circle described by the end of the arm ; for example, if h equal i inch, and a equals lix.,?^ power of 100 lbs. would overcome a resistance not exceeding 1 5,000 lbs. 45. Friction. — In the cases of the actions of machines which have een described, the resistances which are offered to motion have not been at all considered. The surfaces of bodies in contact are never perfectly smooth ; even the smoothest present inequalities which can neither be detected by the touch nor by ordinary sight ; hence when one body moves over the surface of another the elevations of one sink into the depressions of the other, like the teeth of wheels, and thus offer a certain resistance to motion ; this is what is called frictioti. It must be regarded as a force which continually acts in opposition to actual or possible motion. Friction is of two kinds : sliding, as when one body glides over another ; this is least when the two surfaces in contact remain the same, as in the motion of an axle in its bearing ; and rollifig friction, which occurs when one body rolls over ^nother, as in the case of an ordinary wheel. The latter is less than the former, for by the rolling the inequalities of one body are raised over those of the other. The force which is required to overcome friction and which is briefly spoken of as friction is proportional to the pressure of the two bodies against each other. That fraction of the pressure which is required to overcome friction is called the coefficient of friction. Friction is independent ot the extent of surfaces in contact, it is dimi- c 26 On Matter, Force, and Motion. I^S- nished by polishing and by smearing, but is increased by heat. It is greater as a body passes from the state of rest to that of motion than % during motion, but seems independent of the velocity. The coefficient of friction depends on the nature of the substances in contact ; thus, for oak upon oak it is 0*418 when the fibres are parallel, and 0-293 when they • cross ; for beech upon beech it is o* 36. Greasy substances which are not absorbed by the body diminish friction ; but increase it if they are ab- sorbed. Thus moisture and oil increase, while tallow, soap, and graphite diminish, the friction of wooden surfaces. In the sliding friction of cast iron upon bronze the coefficient was found to be 0-25 without grease ; with oil it was 0-17, fat o'li, soap 0-03, and with a mixture of fat and graphite 0*02. The coefficient of rolling friction for cast iron wheels on iron rails is o"oo4 ; for ordinary wheels on an ordinary road it is 0*04. As rolling friction is considerably less than sliding friction, it is a great ^ saving of power to convert the latter into the former, as is done in the case of the castors of chairs and other furniture. On the other hand, it is sometimes useful to change rolling into sliding friction, as when drags are placed on carriage wheels. Without friction on the ground, neither men nor animals, neither or- dinary carriages nor railway carriages could move. Friction is necessary for the transmission of power from one wheel to another by means of < bands or ropes ; and without friction we could hold nothing in the hands. X/ 46. TTniformly accelerated rectilinear motion. — Let us suppose a t^body containing m units of mass to move from rest under the action of a force, of F units, the body will move in the line of action of the force, and will acquire in each second an additional velocity/ given by the equation Y = mf consequently, if v is its velocity at the end of / seconds, we have v=ft, (I) To determine the space it will describe in / seconds, we may reason as follows : — The velocity at the time t being//, that at a time t + r will be fit + r). If the body moved uniformly during the time r with the former velocity it would describe a space s equal to fir, if with the latter velocity ■^ space s^ equal to f{t + t)t. Consequently, jj : j::/ + r : /, is indefinitely small, the limiting values of s and s^ are equal. Now since the body's velocity is continually increasing during the time r, the space actually described is greater than J, and less than s^ But since the limiting values of s and Sy are equal, the limiting value of the space described is the same as that of s or s^ In other words, if we suppose the whole time of the body's motion to be divided into any number of equal parts, if we determine the velocity of the body at the beginning of each of these parts, and if we ascertain 1 therefore, when T is inde B S 5^ t ^ e f ^ D K K « H C Fig 22. -46] Uniformly accelerated Motion. 27 the spaces described on the supposition that the body moves uniformly during each portion of time, the hmiting value of the sum of these spaces will be the space actually described by the body. Draw a line AC, and at A construct an angle CAB, whose tangent equals /; divide AC into any number of equal parts in D, E, F,...and draw PD, QE, RF,...BC at right angles to AC, then since PD=ADx/ QE = AE x/, RF = AF x/ EC = AC -/Wbration, its motion will be changed into that of a conical pendulum. ^ 54. Impulsive forces. — When a force acts on a body for an inappreci- ably short time, and yet sensibly changes its velocity, it is termed an mstaiitaneous or impulsive force. Such a force is called into play when one body strikes against another. A force of this character is nothing but a finite though very large force, acting for a time so short that its duration , is nearly, or quite, insensible. In fact, if M is the mass of the body, and the force contains M/ units, it will, in a time /, communicate a velocity //; now, however small /may be, M/ and therefore / may be so large that ft may be of sensible or even considerable magnitude. Thus if M contain a pound of matter, and if the force contain ten thousand units, though / were so short as to be only the jo^oo^^ °^ ^ second, the velocity communicated by the force would be one of 10 ft, per second. It is also to be remarked that the body will not sensibly move while this velocity is being communicated ; thus, in the case supposed, the body would only move through ^ //~ or the o^o^h of a foot while the force acts upon it. When one body impinges on another it follows from the law of the equality of action and reaction (39) that whatever force the first body exerts upon the second, the second will exert an equal force upon the first in the opposite direction ; now forces are proportional to the momenta generated in the same time ; consequently, these forces generate, during the whole or any part of the time of impact, in the bodies respectively, C3 34 On Matter, Force, and Motion. [54- Fig. 28. equal momenta with contrary signs ; and therefore the sum of the mo- menta of the two bodies will remain constant during and at the end of the impact. It is of course understood that if the two bodies move in contrary directions their momenta have opposite signs and the sum is an algebraical sum. In order to test the physical validity of this conclusion, Newton made a series of experiments, which may be briefly described thus :— two balls A and B are hung from points C, D, in the same hori- zontal line by threads in such a manner that their centres A and B are in the same horizontal line. With centre C and radius CA describe a semicircle EAF, and with centre D and radius DB describe a semicircle GBH on the wall in front of which the balls hang. Let A be moved back to R, and be allowed to descend to A ; it there im- pinges on B, both A and B will now move, along the arcs AF and BH respectively ; let A and B come to their highest points at r and k respectively. Now if V denote the velocity with which A reaches the lowest point, v and u the velocities with which A and B leave the lowest points after impact, and r the radius AC, it appears from (50) that _ V = chd AR /C, V = chd Ar /f , and u = chd Bk/-^, therefore if A and B are the masses of the two balls, the momentum at the instant before impact was A x chd AR and the momentum after impact was A x chd Ar+Bxchd Bk Now when the positions of the points R, r, and k had been properly corrected for the resistance of the air, it was found that these two expressions were equal to within quanti- ties so small that they could be properly referred to errors of observation. The experiment succeeded equally under every modification, whether A impinged on B at rest or in motion, and whatever the materials of A and B might be. 55. Direct collision of two bodies. — Let A and B be two bodies moving with velocities V and U respectively, along the same line, and let their mutual action take place in that line ; if the one overtake the other, I what will be their respective velocities at the instant after impact ? We will answer this question in two extreme cases. i. Let us suppose the bodies to be giii'te inelastic. In this case, when A touches B, it will continue to press against B until their velocities are equalised, when the mutual action ceases. For whatever deformation the bodies may have undergone, they have no tendency to recover their shapes. If, therefore, x is their common velocity after impact, we shall have hx + Bx their joint momentum at the end of impact, but their momentum before impact was AV + BU. Whence (A+B);ir = AV + BU, an equation which determines x. 56] Work: Meaning- of the Term. 35 ii. Let us suppose the bodies perfectly elastic. In this case they recover their shapes, with a force exactly equal to that with which they were compressed. Consequently, the whole momentum lost by the one, and gained by the other, must be exactly double of that lost while com- pression took place, that is up to the instant at which their velocities were equalised. But these are respectively AV-A;ir and Bjit-BU ; therefore, if V and u are the required final velocities, A?y = AV - 2(AV - A;f) or z/ = - V + 2:f B?/ = BU + 2(B;t--BU) or ?/ = 2.r-U, hence (A + B)-6/ = 2BU + (A-B)V and (A + B)u = 2AV - (A - B)U. The following conclusion from these equations may be noticed : suppose a ball A, moving with a velocity V, to strike directly an equal ball B at rest. In this case A = B, and U =0, consequently ?7 = o and u = V, that is, the former ball A is brought to rest, and the latter B moves on with a velocity V. If now B strike on a third equal ball C at rest, B will in turn be brought to rest, and C will acquire the velocity V. And the same is true if there is a fourth, or fifth, or indeed any number of balls. This result may be shown with ivory balls, and if carefully performed is a very jy remarkable experiment. 56. "Work : meaning: of tbe term. — It has been pointed out (19, 26) that a moving body has no power, of itself to change either the direction or the speed of its motion, and that, if any such change takes place, it is a proof that the body is acted upon by some external force. But although change of motion thus always implies the action of force, forces are often exerted without causing any change in the motion of the bodies on which they act. For instance, when a ship is sailing at a uniform speed the force exerted on it by the wind causes no change in its motion, but simply prevents such a change being produced by the resistance of the water ; or, when a railway-train is running with uniform velocity, the force of the engine does not change, but only maintains its motion in opposition to the forces, such as friction and the resistance of the air, which tend to destroy it. These two classes of cases, namely, first, those in which forces cause a change of motion ; and secondly, those in which they prevent, wholly or in part, such a change being produced by other forces, include all the effects to which the action of forces can give rise. When acting in either of these ways, a force is said to do work : an expression which is used scientifically in a sense somewhat more precise, but closely accord- ant with that in which it is used in common language. A little reflection will make it evident that, in all cases in which we are accustomed to speak of work being done,— whether by men, horse-power or steam- power, and however various the products may be in different cases, — the physical part of the process consists solely in producing or changing !>' 36 On Matter, Force, and Motion. [66- motion, or in keeping up motion in opposition to resistance, or in a combination of these actions. The reader will easily convince himself of this by calling to mind what the definite actions are which constitute the work done by (say) a navvy, a joiner, a mechanic, a weaver ; that done by a horse, whether employed in drawing a vehicle or in turning a gin ; or that of a steam-engine, whether it be used to drag a railway-train or to drive machinery. In all cases the work done is reducible, from a mechanical point of view, to the elements that have been mentioned, although it may be performed on different materials, with different tools, and with different degrees of skill. It is, moreover, easy to see (comp. 48, 49) that any possible change of n\otion may be represented as a gain by the moving body of an addi- tional (positive or negative) velocity either in the direction of its previous motion, or at right angles to it ; but a body which gains velocity is (27) said to be accelerated. Hence, what has been said above may be summed up as follows : — When a force produces acceleration, or when it maintai7is motion unchanged in opposition to resistance, it is said to do WORK. 57. nceasure of "Work. — In considering how work is to be measured, or how the relation between different quantities of work is to be ex- pressed numerically, we have, in accordance with the above, to consider first, work of acceleration ; and secondly, work against resistance. But in order to make the evaluation of the two kinds of work consistent, we must bear in mind that one and the same exertion of force will result in work of either kind, according to the conditions under which it takes place : thus, the force of gravity acting on a weight let fall from the hand causes it to move with a continually accelerated velocity until it strikes the ground ; but if the same weight, instead of being allowed to fall freely through the air, be hung to a cord passing round a cylinder by means of which various degrees of friction can be applied to hinder its descent, it can be made to fall with a very small and practically uniform velocity. Hence, speaking broadly, it may be said that, in the former case, the work done by gravity upon the weight is work of acceleration only, while in the latter case it is work against resistance (friction) only. But it is very important to note that an essential condition, without which a force, however great, cannot do work either of one kind or the other, is that the thing acted on by it shall move while the force continues to act. This is obvious, for if no motion takes place it clearly cannot be either accelerated or maintained against resistance. The motion of the body on which a force acts being thus necessarily involved in our notion of work being done by the force, it naturally follows that, in estimating how much work is done, we should consider how much — that is to say, how far — the body moves while the force acts upon it. This agrees with the mode of estimating quantities of work in common life, as will be evident if we consider a very simple case, for instance, that of a labourer employed to carry bricks up to a scaffold : in such a case a double number of bricks carried would represent a double quantity of work done, but so also would a doubled height of the scaffold, for whatever amount of work -57] Measure of Work. 37 is done in raising a certain number to a height of twenty feet, the same amount must be done again to raise them another twenty feet, or the amount of work done in raising the bricks forty feet is twice as great as that done when they are raised only twenty feet. It is also to be noted that no direct reference to time enters into the conception of a quantity of work : if we want to know how much work a labourer has done, we do not ask how long he has been at work, but what he has done, —for instance, how many bricks he has carried, and to what height; — and our estimate of the total amount of work is the same whether the man has spent hours or days in doing it. The foregoing relations between force and work may be put into definite mathematical language as follows : — If the point of appHcation of a force moves in a straight line, and if the part of the force resolved along this line acts in the direction of the motion, the product of that component and the length of the line is the work done by the force. If the com- ponent acts in the opposite direction to the motion, the component may be considered as a resistance and the product is work done against the resistance. Thus, in (42) if we suppose M to move up the plane from A to B, the work done by P is P x AB ; the work done against the resist- ance O is Q sin A X AB. It will be observed that if the forces are in equilibrium during the motion, so that the velocity of M is uniform, P equals O sin A, and consequently the work done by the power equals that done against the resistance. Also since AB sin A equals BC, the work done against the resistance equals Q x BC. In other words, to raise Q from A to B requires the same amount of work as to raise it from C to B. If, however, the forces are not in equilibrium, the motion of M will not be uniform, but accelerated ; the work done upon it will neverthe- less still be represented by the product of the force into the distance through which it acts. In order to ascertain the relation between the amount of work done a.nd the change produced by it in the velocity of the moving mass, we must recall one or two elementary mechanical principles. Let F be the resultant force resolved along the direction of motion, and S the distance through which its point of application moves: then, according to what has been said, the work done by the force = FS. Further, it has been pointed out (29), that a constant force is measured by the momentum produced by it in a unit of time : hence, if T be the time during which the force acts, Vq the velocity of the mass M at the beginning of this period, and V^ the velocity at the end of it, the momentum produced during the time T is MVi — MV., and consequently the momentum produced in a unit of time, or, in other words, the measure of the force is — M(V,-V.) F= ^ . The distance S through which the mass M moves while its velocity changes from the value V. to the value V^, is the same as if it had moved during the whole period T with a velocity equal to the average value of the varying velocity which it actually possesses. But a constant force 38 On Matter, Force, and Motion. [57- acting upon a constant mass causes its velocity to change at a uniform rate ; hence, in the present case, the average velocity is simply the arithmetical mean of the initial and final velocities, or S = HVi + V.)T. Combining this with the last equation, we get as the expression for the work done by the force F— - FS = ^M(Vi2-V„2); or, in words, when a constajit force acts on a mass so as to change its velocity, the work done by the force is equal to half the product of the mass into the change of the square of the velocity. The foregoing conclusion has been arrived at by supposing the force F to be constant, but it is easy to show that it holds good equally if F is the average magnitude of a force which varies from one part to another of the total distance through which it acts. To prove this, let the distance S be subdivided into a very great number ?i of very small parts each equal to s, so that n s = S. Then, by supposing s to be sufficiently small, we may without any appreciable error' consider the force as constant within each of these intervals and as changing suddenly as its point of application passes from one interval to the next. Let F^, Fg, F3 . . . . F„, be the forces acting throughout the ist, 2nd, 3rd .... ;/th interval respectively, and let the velocity at the end of the same intervals be centre of gravity, the body can only be in equilibrium when this point lies vertically under the point of suspension, that is in the prolongation of the suspended string. But the centre of gravity being in AB as well as in CD must coincide with the point of intersection of these two lines. 66. Equilibrium of heavy bodies. — Since the action of gravity upon a body reduces itself to a single vertical force applied at the centre of gravity and directed towards the earth's centre, equilibrium will be estab- lished only when this resultant is balanced by the resultant of other forces and resistances acting on the body at the fixed point through which it passes. When only one point of the body is fixed, it will be in equilibrium if the vertical line through its centre of gravity passes through the fixed point. If more than one point is supported, the body will be in equili- brium if a vertical line through the centre of gravity passes through a point within the polygon formed by joining the points of support. The Leaning Tower of Pisa continues to stand because the vertical ine drawn through its centre of gravity passes within its base. It is easier to stand on our feet than on stilts, because in the latter case the smallest motion is sufficient to cause the vertical line through the centre of gravity of our bodies to pass outside the supporting base, which is here reduced to a mere hne joining the feet of the stilts. Again, it is impossible to stand on one leg if we keep one side of the foot and head close to a vertical wall, because the latter prevents us from throwing the body's centre of, gravity vertically above the supporting base. 67. Bifferent states of equilibrium. — Although a body supported by a fixed point is in equilibrium whenever its centre of gravity is in the vertical line through that point, the fact that the centre of gravity tends -68] TJie 'Balance. 47 incessantly to occupy the lowest possible position leads us to distinguish between three states of equilibrium — stable^ unstable, 7ieutraL A body is said to be in stable equilibrium if it tends to return to its first position after the equilibrium has been slightly disturbed. Every body is in this state when its position is such that the slightest alteration of the same elevates its centre of gravity ; for the centre of gravity will descend again when permitted, and after a few oscillations the body will return to its original position. The pendulum of a clock continually oscillates about its position of stable equilibrium, and an t."C, increase in the same proportion as the times (i, 2, 3, . . . seconds) employed in their acquirement. By the definition (46), there- fore, the motion is uniformly accelerated. The same experiments will also serve to verify and illustrate the four laws of uniformly accelerated motion as enunciated in (46). For example, the spaces OB, OB^, OB'', described from a state of rest in i, 2, 3, ... . seconds, will be found to be proportional to the numbers i, 4, 9, . . . that is to say, to the squares of those numbers of seconds, as stated in the third law. Lastly, if the overweight m be changed, the acceleration or velocity BC acquired per second will also be changed, and we may easily verify the assertion in (29), that force is proportional to the product df the mass moved into the acceleration produced in a given time. For instance, assuming the pulley to be so light that its inertia can be neglected, if 7n weighed half an ounce, and M and M' each 1 5I ounces, the acceleration BC would be found to be six inches ; whilst if m weighed i ounce, and M and M' each 63^ ounces, the acceleration BC would be found to be three inches. Now in these cases the forces producing motion, that is the over- weights, are in the ratio of i : 2 ; while the products of the masses and the accelerations are in the ratio of (| + I5f + I5f) x 6 to (i + 63^ + 63^) x 3, that is, they are also in the i"atio of i : 2. Now the same result is obtained in whatever way the magnitudes of ;;z, ]\T, and M' are varied, and con- sequently in all cases the ratio of the forces producing motion equals the /atio of the momenta generated. 'JS. Morln's apparatus. — The principle of this apparatus, the original '"^Sdea of which is due to General Poncelet, is to make the body in falling trace its own path. Figure 43 gives a view of the whole apparatus, and figure 44 gives the details. The apparatus consists of a wooden frame- work, about 7 feet high, which holds in a vertical position a very light wooden cylinder, M, which can turn freely about its axis. This cylinder is coated with paper divided into squares by equidistant horizontal and vertical lines. The latter measure the path traversed by the body falling along the cylinder, while the horizontal lines are intended to divide the duration of the fall into equal parts. The falling body is a mass of iron, P, provided with a pencil which is pressed against the paper by a small spring. The iron is guided in its fall by two light iron wires which pass through guide-holes on the two sides. The top of this mass is provided with a tipper which catches against the end of a bent lever, AC. This being pulled by the string K attached at A, the weight falls. If the cylinder M were fixed, the pencil would trace a straight line on it ; but if the cylinder moves uni- formly, the pencil traces the line inn, which serves to deduce the law of the fall. The cylinder is rotated by means of a weight, Q, suspended to a cord which passes round the axle G. At the end of this is a toothed wheel, c, which turns two endless screws, a and b, one of which turns the cylinder, and the other, two vanes, x and x\ At the other end is a ratchet wheel, 56 Gravitation and Molecular A ttraction. [75- in which fits the end of a lever, B ; by pulling at a cord fixed to the other end of B, the wheel is liberated, the weight Q descends, and the whole system begins to turn. The motion is at first accelerated, but as the air offers a resistance to the vanes, which increases as the rotation becomes more rapid, the resistance finally equals the acceleration which gravity tends to impart. From this time the motion becomes uniform. This is Fig. 43. Fig. 44. the case when the weight O has traversed about three-quarters its course ; at this moment the weight P is detached by pulling the cord K, and the pencil then traces the curve vi7i. If, by means of this curve, we examine the double motion of the pencil on the small squares which divide the paper, we see that, for dis- placements of I, 2, 3, .... in a horizontal direction, the displacements -76] Length of the Compound Pendulum. 57 are i, 4, 9 .... in a vertical direction. This shows that the paths tra- versed in the direction of the fall are directly as the squares of the lines in the direction of the rotation, which verifies the second law of falling bodies. From the relation which exists between the two dimensions of the curve mn^ it is concluded that this curve is a parabola. ^ 76. ]Lengrtli of tlie compound pendulum. — The formula for the time of vibration of a simple pendulum, and the conclusions deduced from it (51) are also applicable to the compound pendulum, though in this case it will be necessary to define accurately what is meant by the length of such a pendulum. A compound pendulum being formed of a heavy rod terminated by a greater or less mass, it follows that the several material points of the whole system will strive to perform their oscilla- tions in different times, their distances from the axis of suspension being different, and the more distant points requiring a longer time to complete an oscillation. From this, and from the fact that being points of the same body they must oscillate together, it follows that the motion of the points near the axis of suspension will be retarded, whilst that of the more distant points will be accelerated, and between the two extremities there will necessarily be a series of points whose motion will be neither accelerated nor retarded, but which will oscillate precisely as if they were perfectly free and unconnected with the other points of the system. These points, being equidistant from the axis of suspension, constitute a parallel axis known as the axis of oscillation ; and it is to the distance between these two axes that the term le?igth of the compound pendulum is applied : we may say, therefore, that the length of a coinpoimd pendu- lum is that of the simple pendulum which would describe its oscillations in the same time. Huyghens, the celebrated Dutch physicist, discovered that the axes ot suspension and oscillation in a mutually convertible — that is to say, the time of oscillation will remain unaltered when the pendulum is suspended from its axis of oscillation. This remarkable fact enables us to determine experimentally the length of a compound pendulum. To do so the pen- dulum is inverted and suspended from a second and moveable axis, which, after some trials, is placed so that the inversion does not affect the number of oscillations made in a given time ; the length required is then the distance between the two axes, and on giving to / the value thus determined, the formula of (51) for the simple pendulum becomes appli- cable to the compound pendulum, whose oscillations, in vacuo, obey the same laws. The length of the seconds pendulum — that is to say, of the pendulum which makes one oscillation in a second — varies, of course, with the in- tensity of gravity. The following table gives its value at the sea level at various places. The accelerative effect of gravity at these places, according to formula (51), is obtained in feet and metres by multiplying the length of the seconds pendulum, reduced to feet and metres, by the square of 3-14159. D3 58 Gravitation and Molecular Attraction. [76- Length of Acceleration of Gravity Pendulum in in inches. feet. metres. Hammerfest . 7o°-4o'N. 39-1948 32-2364 9-8258 Konigsberg . . 54-42 39-1507 32-2002 9-8142 Greenwich . . 51-29 39-1398 32-1912 9-8115 Paris . . 48-50 39-1285 32-1819 9-8039 New York . . 40-43 39-1012 32-1594 9-8019 St. Thomas . 0-25 39-0207 32-0957 9-7826 Cape of Good Hope 33-55 S. 39-0780 32-1404 9-7962 t -S m-S SL Consequently, \g or the space described in the first second of its motion by a body falHng in vacuo from a state of rest (46) is 16-0478 feet or 4-891 metres at St. Thomas, 16-0956 „ „ 4-905 „ at London, and 16-1182 „ ,,4-913 „ at Hammerfest. In all calculations which are used for the sake of illustration, we may take 32 feet and 9-8 metres as the accelerative effect due to gravity. From observations of this kind, after applying the necessary correc- tions, and taking into account the effect of rotation (79), the form of the earth can be deduced. T]. Verification of the laws of the pendulum. — In order to verify the laws of the simple pendulum (51) we are com- pelled to employ a compound one, whose construction differs as little as possible from that of the former. For this purpose a small sphere of a very dense substance, such as lead or platinum, is suspended from a fixed point by means of a very fine thread. A pendulum thus formed oscil- lates almost likea simple pendulum, whose length is equal to the distance of the centre of the sphere from the point of suspension. In order to verify the isochronism of small oscillations, it is merely necessary to count the number of oscillations made in equal times, as the amplitudes of these oscillations diminish from 3 degrees to a fraction of a degree; this number is found to be constant. That the time of vibration is propor- tional to the square root of the length is verified by causing pendulums, whose lengths are as the numbers i, 4, 9, . . . . to oscillate simultaneously. The corre- sponding numbers of oscillations in a given time are then found to be proportional to the fractions i f, |, etc which shows that the times of oscillation increase as the numbers 1, 2, 3, . . . . etc. Fig- 45- -78] Application of the Pendulum to Clocks. 59 By taking several pendulums of exactly equal length, B^ C, D (fig. 45)^ but with spheres of different substances, lead, copper, ivory, it is found that, neglecting the resistance of the air, these pendulums oscillate in equal times, thereby showing that the accelerative effect of gravity on all bodies is the same at the same place. By rheans of an arrangement resembling the above, Newton verified the fact that the masses of bodies are determined by the balance ; which, it will be remarked, lies at the foundation of the measure of force (29). For it will be seen on comparing (50) and (51) with (47) that the law of the time of a small oscillation is obtained on the supposition that the force of gravity on all bodies is represented by M^, in which M is determined by the balance. In order to verify this, he had made two round equal wooden boxes ; he filled one with wood, and as nearly as possible in the centre of oscillation of the other he placed an equal weight of gold. He then suspended the boxes by threads eleven feet long, so that they formed pendulums exactly equal so far as weight, figure, and resistance of the air were concerned. Their oscillations were performed in exactly the same time. The same results were obtained when other substances were used, such as silver, lead, glass, sand, salt, wood, water, corn. Now all these bodies had equal weights, and if the inference that therefore they had equal masses had been erroneous by so much as the one thousandth part of the whole, the experiment would have detected it. 78. Application of tlie pendulum to clocks. — The regulation of the motion of clocks is effected by means of pendulums, that of watches by balance-springs. Pendulums were first applied to this purpose by Huyghens in 1658, and in the same year Hooke applied a spiral spring to the balance of a watch. The manner of employing the pendulum is shown in fig. 46. The pendulum rod passing between the prongs of a fork a communicates its motion to a rod b, which oscillates on a horizontal axis 0. To this axis is fixed a piece mn called an escapemetit or crutch^ terminated by two projections ox pallets, which work alternately with the teeth of the escapement wheel R. This wheel being acted on by the weight tends to move continuously, let us say, in the direction indicated by the arrow-head. Now if the pendulum is at rest, the wheel is held at rest by the pallet /«, and with it the whole of the clockwork and the weight. If, however, the pendulum moves and takes the position shown by the dotted line, 7n is raised, the wheel escapes from the confinement in which it was held by the pallet, the weight de- scends, and causes the wheel to turn until its motion is arrested by the other pallet n ; which in consequence of the motion of the pendulum will be brought into contact with another tooth of the escapement wheel. In this manner the descent of the weight is alter- Fig. 46. 6o Gravitation and Molecular A ttraction. [78 - nately permitted and arrested — or, in a word, regulated— \y^ the pen- dulum. By means of a proper train of wheelwork the motion of the escapement is communicated to the hands of the clock ; and consequently their motion, also, is regulated by the pendulum. The pendulum is also used for measuring great velocities. A large block of wood weighing from 3 to 5 tons is coated with iron ; against this arrangement, which is known as a ballistic penduhim, a shot is fired, and the deflection thereby produced is observed. From the laws of the impact of inelastic bodies, and from those of the pendulum, the velocity of the ball may be calculated from the amount of this deflection. 79. Causes which modify the intensity of terrestrial gravita- tion. — The intensity of the force of gravity at the earth's surface is modified by two causes, viz. by the form and by the rotation of the earth. i. If the earth were a sphere of uniform density the resultant of the attractions which its parts exert on an external point would be the same as if the whole of its mass were collected at its centre, and therefore the attraction at all points of its surface would be the same. In consequence of the flattening of the earth at its poles, this is no longer exactly, but only very nearly true ; and the attraction on an external point is only nearly inversely as the square of its distance from the earth's centre. As a further consequence of the flattening at the poles, the distance from the centre of a point on the surface decreases as we proceed from the equator to either pole ; but as the distance decreases the attraction will increase, and consequently the force of gravity increases as the latitude increases, being least at the equator, and greatest at the poles. This is what would be true if, other things remaining the same, the earth were at rest. ii. In consequence of the earth's rotation, the force of gravity is further modified. If we imagine a body relatively at rest on the equator, it really shares the earth's rotation, and describes, in the course of one day, a circle whose centre and radius are the centre and radius of the earth. Now since a body in motion tends by reason of its inertia to move in a straight line, it follows that to make it move in a circle, a force must be employed at each instant to deflect it from the tangent (49). Consequently, a certain portion of the earth's attraction must be employed in keeping the above body on the surface of the earth, and only the remainder is sensible as weight or accelerating force. It appears from calculation that on the equator the ^s^th part of the earth's attraction on any body is thus employed, so that the magnitude of g at the equator is less by the 219th part of what it would be were the earth at rest. If the body, instead of being on the equator, is in any given latitude, it will describe in one day a circle coinciding with the parallel of latitude on which it is situated. Now when bodies describe in the same time circles of different radii, it can be deduced from (49) that the forces required to keep them in those circles are proportional to their radii. Hence the force required in the case of a body in any given latitude is less than that required if the body were on the equator, and less -81] Molecular Forces. ' 6l as the latitude is greater, consequently were gravity diminished by the whole amount of this force the diminution would be less the nearer the body is to either pole. But since the force is produced only by an in- direct action of gravity, it appears that the diminution is thereby rendered still less as the latitude is greater. On the whole, therefore, the force of gravity increases as we pass from the equator to either pole, in conse- quence of the rotation of the earth. It will be observed that both causes, viz. the flattening of the earth ;it the poles, and its rotation, concur in producing an increase in the nsible force of gravity as the observer leaves the equator and approaches ither pole. CHAPTER III. MOLECULAR FORCES. 80. Xature of molecular forces. — The various phenomena which Ijodies present show that their molecules are under the influence of two contrary forces, one of which tends to bring them together, and the other to separate them from each other. The first force, which is called molecular attraction, varies in one and the same body with the distance only. The second force, which is due to the action of heat, varies with the intensity of this agent, and with the distance. It is the mutual re- lation between these forces, the preponderance of the one or the other, which determines the molecular state of a body (4), — whether it be solid, liquid, or gaseous. Molecular attraction is only exerted at infinitely small distances. Its effect is inappreciable when the distance between the molecules is appre- ciable. The laws which regulate this force are not known. According to the manner in Avhich it is regarded, molecular attraction is designated by the terms cohesion, affinity^ or adhesion. 81. Cohesion. — Cohesio7i is the force which unites two molecules of the same nature ; for example, two molecules of water, or two molecules of iron. Cohesion is strongly exerted in solids, less strongly in liquids, and scarcely at all in gases. Its intensity decreases as the temperature increases, because then the repulsive force due to heat increases. Hence it is that when solid bodies are heated they first liquefy, and are ultimately converted into the gaseous state, provided that heat produces in them no chemical change. Cohesion varies not only with the nature of bodies, but also with the arrangement of their molecules ; for example, the difference between tempered and untempered steel is due to a difference in the molecular arrangement produced by tempering. It is to the modifications which this force undergoes that many of the properties of bodies are due, such as tenacity, hardness, and ductility. In large masses of liquids, the force of gravity overcomes that of cohe- sion. Hence liquids acted upon by the former force have no special shape ; they take that of the vessel in which they are contained. But in 62 Gravitation and Molecular A ttraction. [81- smaller masses cohesion gets the upper hand, and hquids present then the spheroidal form. This is seen in the drops of dew on the leaves of plants ; it is also seen when a liquid is placed on a solid which it does not moisten ; as, for example, mercury upon wood. The experiment may also be made with water, by sprinkling upon the surface of the wood some light powder, such as lycopodium or lampblack, and then dropping some water on it. The following pretty experiment is an illustration of the force of cohesion causing a liquid to assume the spheroidal form. A saturated solution of sulphate of zinc is placed in a narrow-necked bottle, and a few drops of bisulphide of carbon, coloured with iodine, made to float on the surface. If pure water be now carefully added, so as to rest on the surface of the sulphate of zinc solution, the bisulphide collects in the form of a flattened spheroid, which presents the appearance of blown coloured glass, and is larger than the neck of the bottle, provided a sufficient quantity has been taken. 82. Affinity. — Chemical affinity is the force which is exerted between molecules not of the same kind. Thus, in water, which is composed of oxygen and hydrogen, it is affinity which unites these elements, but it is cohesion which binds together two molecules of water. In compound bodies cohesion and affinity operate simultaneously, while in simple bodies or elements cohesion has alone to be considered. To affinity are due all the phenomena of combustion, and of chemical combination and decomposition. The causes which tend to weaken cohesion are most favourable to affinity ; for instance, the action of affinity between substances is facili- tated by their division, and still more by reducing them to a liquid or gaseous state. It is most powerfully exerted by a body in its nascent state, that is, the state in which the body exists at the moment it is disengaged from a compound ; the body is then free, and ready to obey the feeblest affinity. An increase of temperature modifies affinity differ- ently under diffierent circumstances. In some cases, by diminishing cohesion, and increasing the distance between the molecules, heat pro- motes combination. Sulphur and oxygen, which at the ordinary tempe- rature are without action on each other, combine to form sulphurous acid when the temperature is raised : in other cases heat tends to decom- pose compounds by imparting to their elements an unequal expansi- iDility. Thus it is that many metallic oxides, as for example those of silver and mercury, are decomposed, by the action of heat, into gas and metal. 83. Adbesion. — The molecular attraction exerted between bodies in contact is called adhesioti. i. Adhesion takes place between solids. If two leaden bullets are cut with a penknife so as to form two equal and brightly polished surfaces, and the two faces are pressed and turned against each other until they are in the closest contact, they adhere so strongly as to require a force of more than 100 grammes to separate them. .The same experiment may be made with two equal pieces of glass, which are polished and made perfectly plane. When they are pressed one against the other, the -85] Properties peculiar to Solids. 63 adhesion is so powerful that they cannot be separated without breaking. As the experiment succeeds in vacuo, it cannot be due to atmospheric pressure, but must be attributed to a reciprocal action between the two surfaces. The attraction also increases as the contact is prolonged, and is greater in proportion as the contact is closer. In the operation of gluing, the pores and crevices of the fresh surfaces being filled with liquid glue, so that there is no empty space on drying, wood and glue form one compact whole. In some cases the adhesion of the cement is so powerful that the mass breaks more readily at other places than at the cemented parts. ii. Adhesion also takes place between solids and liquids. If we dip a glass rod into water, on withdrawing it a drop will be found to collect at its lower extremity, and remain suspended there. As the weight of the drop tends to detach it, there must necessarily be some force superior to this weight which maintains it there : this force is the force of adhesion. iii. The force of adhesion operates, lastly, between solids and gases. If a glass or metal plate be immersed in water, bubbles will be found to appear on the surface. As air cannot penetrate into the pores of the plate, the bubbles could not arise from the air which had been expelled. It is solely due to the layer of air which covered the plate, and moistened it like a liquid. In many cases when gases are separated in the nascent state on the surface of metals — as in electrolysis — the layer of gas which covers the plate has such a density that it is susceptible of very energetic chemi- cal actions. ^^ ^ CHAPTER W. PROPERTIES PECULIAR TO SOLIDS. 84. Various special properties. — After having described the princi- pal properties common to solids, liquids, and gases, we shall discuss the properties peculiar to solids. They are, elasticity of traction, elasticity oftorsioti, elasticity of flexure, teftacity, ductility, and hardness. 85. Elasticity of traction. — Elasticity, as a general property of matter, has been already mentioned (17), but simply in reference to the elasticity developed by pressure ; in solids it may also be called into play by traction, by torsion, and by flexure. The definitions there given re- quire some extension. In ordinary life we consider those bodies as highly elastic which, like caoutchouc, undergo considerable change on the appli- cation of only a small force. Yet the force of elasticity is greatest in many bodies, such as iron, which do not seem to be very elastic. For hy force of elasticity is understood the force with which the displaced particles tend to revert to their original position, and which force is equivalent to that which has brought about the change. Considered from this point of view, gases have the least force of elasticity ; that of liquids is con- siderably greater, and is, indeed, greater than that of many solids. Thus, the force of elasticity of mercury is greater than that of caoutchouc, glass, 64 Gravitation and Molecular A ttr action. [85- wood, and stone. It is, however, less than that of the other metals with the exception of lead. This seems discordant with ordinary ideas about elasticity ; but it must be remembered that those bodies which by the exertion of a small force, undergo a considerable change, generally have also the property of undergoing this change without losing the property of reverting completely to their original state. They have a wide limit of elasticity. Those bodies which require great force to effect a change are also for the most part, those on which the exertion of a force produces a permanent altera- tion ; when the force is no longer exerted, they do not completely revert to their original state. In order to study the laws of the elasticity of traction, Savart used the apparatus represented in fig. 47. It consists of a wooden support from which are suspended the rods or wires taken for experi- ment. At the lower extremity there is a scale pan, and on the wire two points, A and B, are marked, the distance between which is measured by means of the cathetojneter, before the weights are added. The cathetorneter consists of a strong brass support, K, divided into millimetres, and which can be adjusted in a vertical position by means of levelling screws and the plumb line. A small telescope, exactly at right angles to the scale, can be moved up and down, and is provided with a vernier which measures fiftieths of a millimetre. By fixing the telescope succes- sively on the two points A and B, as represented in the figure, the distance between these points is obtained on the gradu- Fig. 47- ated scale. Placing then weights in the pan, and measuring again the distance from A to B, the elongation is obtained. By experiments of this kind it has been ascertained that for elasticity effraction or pressure-- The alteration in length, within the limits of elasticity, is in propor- tion to the length and to the load actifig on the body, a?id is inversely as the section. It depends, moreover, on the specific elasticity, that is, on the material of the bodv. If this coefficient be denoted by E, and if the length, section. -86] Elasticity of Torsion. 65 and load are respectively designated by /, j, and P, then for the alteration in length e^ we have s The following are the best values for some of the principal sub- stances : — Steel . . 21000 Silver . 7400 W)?might Iron , Copps^r . 19000 Lead . . 1800 . 1 2400 Wood . 1 100 Brass .' . . 9000 Whalebone . . 700 Zinc . \ . . 8700 Glass 90 Thus, to d^ouble the length of a wrought iron wire a square millimetre in section, woii^d (if this were possible) require a weight of 19,000 kilo- grammes ; but i^>,weight of 1 5 kilogrammes produces a permanent altera- tion in length of x|Wth, and this is the limit of elasticity. Whalebone, on the contrary, has otiN a modulus of 700, and experiences a permanent change by a weight of \kilogrammes ; its limit is, therefore, much greater than that of iron. Steershas a high modulus, along with a wide limit. If in the above expresshm the sectional area be a square miUimetre, and P be one kilogramme, thi e = E/, fr^ which E = ^, which expresses by what fraction the length of a bar a square millimetre in section is altered by a load of a ki^gramme. This is called the coefficient of elasticity ; it is a very smalP^raction, and it is therefore desirable to use its reciprocal, that is the fractrism _ as the modulus of elasticity ; or the weight in kilogrammes which a]^lied to a bar would elongate it by its own length, assuming it to be peJsfectly elastic. This cannot be observed, for no body is perfectly elastic, but^it may be calcu- lated from any accurate observations by means of the above formula. Both calculation and experiment show that when bodies are lengthened by traction their volume increases. ' From numerous experiments on the elasticity of iron, copper, and brass, made by Kohlrausch, it follows that the modulus of elasticity diminishes as the temperature rises. 86. Elasticity of torsion. — The laws of the torsion of wires^were determined by Coulomb, by means of an apparatus called the tof^ioti balance (fig. 48). It consists of a metal wire, clasped at its upper extremity in a support. A, and holding at the other extremity a metallic sphere, B, to which is affixed an index, C. Immediately below this there is a graduated circle, CD. If the needle is turned from its position of equi- librium through a certain angle which is the aiigle of torsion, the force necessary to produce this effect is called the force of torsion. When, after this deflection, the sphere is left to itself, the reaction of torsion 66 Gravitation and Molecular Attraction. [86- produces its effect, the wire untwists itself, and the sphere rotates about its vertical axis with increasing rapidity until it reaches its position ot equilibrium. It does not, however, rest there ; in virtue of its inertia it passes this position, and the wire undergoes a torsion in the opposite direction. The equilibrium being again destroyed, the wire again tends to untwist itself, the same alterations are again produced, and the needle does not rest at zero of the scale until after a certain number of oscillations about this point have been completed, ,___^^ By means of this apparatus Coulomb found Tltat when the amplitude of the oscillations is within certain limits, the oscillations are subject to the following laws : — I. The oscillatio7is are very nearly iso- chronous. II. For the same wire, the angle of torsiori is proportional to the inoment of the force of torsion. III. With the same force of torsion, and with wires of the same diameter, the angles of torsion are proportional to the lengths of the wires. \ IV. The same force of torsion beingHpplied to wires of the same length, the angles of tor- sion are inversely proportional to the fourth powers of the diaineters. \ Wertheim has examined the elasticity of torsion in the case of stoiit rods by means of a different apparatus, and finds that it is also subject to\ these laws. He has further found that, all dimensions being the same, \ different substances undergo different degrees of torsion, and each sub- stance has its own coefficient of torsion, which is denoted by — . Fig. 48. The laws of torsion may be enunciated in the formula w = - II Tr* which w is the angle of torsion, F the moment of the force of torsion, / the length of the wire, r its diameter, and - the specific torsion- coefficient. 87. Elasticity of flexure. — A solid, when cut into a thin plate, and fixed at one of its extremities, after having been more or less bent, strives to return to its original position when left to itself. This property is the elasticity of flexure and is very distinct in steel, caoutchouc, wood, and paper. If a rectangular bar be clamped at one end and loaded at the other, the flexure e is represented by the formula P/ ^ t?hhn' -88] Tenacity. 67 where P is the load, / the length of the bar, b its breadth, h its vertical height, and in the modulus of elasticity. The elasticity of flexure is applied in a vast variety of instances, for example, in bows, watch springs, carriage springs ; in spring balances it is used to determine weights, in dynamometers to determine the force of agents in prime movers ; and, as existing in wool, hair, and feathers, it is applied to domestic uses in cushions and mattresses. Whatever be the kind of elasticity, there is, as has been already said, a limit to it — that is, there is a molecular displacement, beyond which bodies are broken, or at any rate do not regain their primitive form. This limit is affected by various causes. The elasticity of many metals is increased by hardening, whether by cold, by means of the draw-plate, by rolling, or iDy hammering. Some substances, such as steel, cast iron, and glass, become both harder and more elastic by tempering (91). Elasticity, on the other hand, is diminished by annealing, which con- sists in raising the body to a temperature lower than that necessary for tempering, and allowing it to copl slowly. It is by this means that the elasticity of springs may be regulated at pleasure. Glass, when it is heated, undergoes a true tempering^ in being rapidly cooled, and hence, in order to lessen the fragility of glass oibjects, they are reheated in a furnace, and are carefully allowed to cool slow^, so that the particles have time to assume their most stable position, 88. Tenacity. — Tenacity is the resi^nce which bodies oppose to traction. It is determined in different bodies by forming them into cylindrical or prismatic wires, and ascertainn^ the weight necessary to break them. Tenacity is directly proportional to the b7'eaking^eight, and inversely proportional to the area of a transverse secihm of the wire. Tenacity diminishes with the duration of the tracHon. A small force continuously applied for a long time will often break a\^ire, which would not at once be broken by a larger weight. Not only does tenacity vary with different substance\ but it also varies with the form of the body. Thus, with the same sectional area, a cylinder has greater tenacity than a prism. The quantity of matter being the same, a hollow cylinder has greater tenacity than asoHd one} and the tenacity of this hollow cylinder is greatest when the external radius is to the internal one in the ratio of 1 1 to 5. The shape has also the same influence on the resistance to crushing, as it has on the resistance to traction. A hollow cylinder with the samei mass, and the same weight, offers a greater resistance than a solid cyHn- der. Thus it is that the bones of animals, the feathers of birds, the stems of com and other plants, offer greater resistance than if they were solid, the mass remaining the same. Tenacity, like elasticity, is different in different directions in bodies. In wood, for example, both the tenacity and the elasticity are greater in the direction of the fibres than in a transverse direction. And this differ- ence obtains in general in all bodies, the texture of which is not the same in all directions. 68 Gravitation and Molecular A ttr action. [88- The following table having a sectional area Antimony, cast Bismuth, „ Lead, „ drawn Tin, „ „ cast . Zinc, annealed . „ drawn Gold, annealed . „ drawn Silver, annealed „ drawn Platinum, annealed „ drawn gives the breaking weight in pounds for wires of a square millimetre : — Copper, annealed . . 69*52 1-47 2*13 4-86 5-19 6-6o 9-15 31-68 34-58 24-20 6 1 -60 36-08 63-80 58-85 77-00 „ drawn . Iron, annealed . „ drawn Cast steel, drawn 90*20 [IO-55 [40*71 [84-36 Wood in the direction of the fibres. Mahogany . ii*o Oak ... . 15*4 Beech . 17*6 Fir ... . 19*8 Ash ... . 26*4 Box . . . . 30-8 In this table the bodies are supposed to be at the ordinary temperature. At a higher temperature the tenacity rapidly decreases. M. Seguin, sen., who has recently made some experiments on this point with iron and copper, has obtained the following values for the tenacity, in pounds, of millimetre wire at different temperatures : — Iron . . at 10°, 132*0; at 370°, 118-8 ; at 500°, 77-0 ; Copper . 46-2 [6-9 o. 89. Ductility. — Ductility is the property in virtue of which a great number of bodies change their forms by the action of traction or pres- sure. With certain bodies, such as clay, wax, etc., the application of a very little force is sufficient to produce a change ; with others, such as the resins and glass, the aid of heat is needed, while with the metals, more powerful agents must be used, such as percussion, the draw-plate, or the rolling-mill. Malleability is that modification of ductility which is exhibited by hammering. The most malleable metal is gold, which has been beaten into leaves about the gooW^^ ^^ ^"^ m^ thick. The most ductile metal is platinum. Wollaston obtained a wire of it 0-00003 of an inch in diameter. This he effected by covering with silver a platinum wire 0-0 1 of an inch in diameter, so as to obtain a cylinder 0-2 inch in diameter only, the axis of which was of platinum. This was then drawn out in the form of wire as fine as possible ; the two metals were equally extended. When this wire was afterwards treated with dilute nitric acid the silver was dissolved, and the platinum wire left intact. The wire was so fine that 1,060 yards only weighed 0-75 of a grain. 90. Hardness. — Hardness is the resistance which bodies offer to being scratched or worn by others. It is only a relative property, for a body which is hard in reference to one body may be soft in reference to others. -91] Hardness. 69 The relative hardness of two bodies is ascertained by trying which of them will scratch the other. Diamond is the hardest of all bodies, for it scratches all, and is not scratched by any. The hardness of a body is expressed by referring it to a scale of hardness : that usually adopted is — 1. Talc 5. Apatite 8. Topaz 2. Rock salt 6. Felspar 9. Corundum 3. Calcspar 7. Quartz 10. Diamond 4. Fluorspar Thus the hardness of a body which would scratch felspar, but would be scratched by quartz, would be expressed by the number 6'5. The pure metals are softer than their alloys. Hence it is that for jewellery and coinage gold and silver are alloyed with copper to increase their hardness. The hardness of a body has no relation to its resistance to compression. Glass and diamond are much harder than wood, but the latter offers far greater resistance to the blow of a hammer. Hard bodies are often used for polishing powders ; for example, emery, pumice, and tripoli. Diamond, being the hardest of all bodies, can only be ground by means of its own powder. 91. Temper. — By sudden cooling after they have been raised to a high temperature, many bodies acquire great hardness. This operation is called tempering. All cutting instruments are made of tempered steel. There are, however, some few bodies upon which tempering produces quite a contrary effect. An alloy of one part of tin and four parts of copper, called taintajn metal^ is ductile and malleable when rapidly cooled, buf hard and brittle as glass when cooled slowly. \ \ 70 On Liquids. [92- BOOK III. ON LIQUIDS. CHAPTER I. HYDROSTATICS. 92. Object of Hydrostatics. — The science of hydrostatics treats of the conditions of the equiHbrium of liquids, and of the pressures they exert, whether within their own mass or on the sides of the vessels in which they are contained. The science which treats of the motion of liquids is hydrodynamics, and the application of the principles of this science to conducting and raising water in pipes is known by the name of hydraulics. 93. General characters of liquids. — It has been already seen (4) that liquids are bodies whose molecules are displaced by the slightest force. Their fluidity, however, is not perfect, there is always a sufficient adherence between their molecules to produce a greater or less viscosity. Gases also possess fluidity, but in a higher degree than liquids. The distinction between the two forms of matter \$, that liquids are almost in- compressible and are comparatively inexpansible, while gases are eminently compressible and expand spontaneously. The fluidity of liquids is seen in the readiness with which they take all sorts of shapes. Their compressibility is established by the following experiment. 94. Compressibility of liquids. — From the experiment of the Floren- tine Academicians (13), liquids were for a long time regarded as being completely incompressible. Since then, researches have been made on this subject by various physicists, which have shown that liquids are really compressible. The apparatus used for rneasuring the compressibility of liquids has been named the piezometer {-KitX^hi, I compress, fihpov, measure). That shown in fig. 49 is the form invented by Oersted as improved by MM. Despretz and Saigey ; it consists of a strong glass cylinder, with very thick sides and an internal diameter of about 3^- inches. The base of the cylinder is firmly cemented into a wooden foot, and on its upper part is fitted a metallic cylinder closed by a cap which can be unscrewed. In this cap there is a funnel, R, for introducing water into the cylinder, and a small barrel hermetically closed by a piston which is moved by a screw, P. 94] Compressibility of Liquids. n In the inside of the apparatus there is a glass vessel, A, containing the liquid to be compressed. The upper part of this vessel terminates in a capillary tube, which dips under mercury, O. This tube has been previously divided into parts of equal capacity, and it has been determined how many of these parts the vessel A contains. The latter is ascertained by finding the weight, P, of the mercury which the reservoir. A, contains, and the weight, p, of the mercury contained in a certain number of divisions, ??, of the capil- lary tube. If N be the number of divisions of the small tube contained in the whole re- N P servoir, we have — = — , from which the value n p of N is obtained. There is further a ma- nometer. This is a glass tube, B, containing air, closed at one end, and the lower ex- tremity of which dips under mercury. When there is no pressure on the water in the cylinder, the tube B is completely full of air ; but when the water within the cylinder is compressed by means of the screw P, the pressure is transmitted to the mercury, which rises in the tube, compressing the air which it contains. A graduated scale fixed on the side of the tube shows the reduction of volume, and this reduction of volume in- Fis- 49- dicates the pressure exerted on the liquid in the cylinder, as will be seen in speaking of the manometer. In making the experiment, the vessel A is filled with the liquid to be compressed, and the end dipped under the mercury. By means of the funnel R the cylinder is entirely filled with water. The screw P being then turned the piston moves downwards, and the pressure exerted upon the water is transmitted to the mercury and the air ; in consequence of which the mercury rises in the tube B, and also in the capillary tube. The ascent of mercury in the capillary tube shows that the liquid in the vessel A has diminished in volume, and gives the amount of its compres- sion, for the capacity of the whole vessel A in terms of the graduated divisions on the capillary tube has been previously determined. In his first experiments. Oersted assumed that the capacity of the vessel A remained the same, its sides being compressed both internally and externally by the liquid. But mathematical analysis proves that this capacity diminishes in consequence of the external and internal pressures. Colladon and Sturm have made some experiments allowing for this change of capacity, and have found that for a pressure equal to that of the atmo- sphere, mercury experiences a compression of 0*000005 parts of its original volume ; water a compression of o'oooo5, and ether a compression of 72 On Liquids. [94- o-i^! '^"^ MM drical parts of unequal diameters, and filled with /l^^j^,,,,,,,,,!,,!^^!^ water to a. From what has been said before, the pj ^ bottom of the vessel CD supports the same pressure as if its diameter were everywhere the same as that of its lower part ; and it would at first sight seem that the scale MN of the balance, in which the vessel CD is placed, ought to show the same weight as if there had been placed in it a cylindrical vessel having the same height of water, and having the diameter of the part D. But the pressure exerted 'jS On Liquids. , [100- on the bottom of the vessel is not all transmitted to the scale M N ; for the iipzva7-d pressure upon the surface no of the vessel is precisely equal to the weight of the extra quantity of water which a cylindrical vessel would contain, and balances an equal portion of the downward pressure on m. Consequently, the pressure on the plate M N is simply equal to the weight of the vessel CD and of the water which it contains. CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS. loi. Equilibrium of a liquid in a sing^le vessel. — In order that a liquid may remain at rest in a vessel of any given form, it must satisfy the two following conditions : — I. Its surface mnst be, everywhere, perpendicular to the 7'esultant of the forces which. act on the molecules of the liquid. II. Every molecule of the mass of the liquid must be subject in every di7'ectioji to equal and contrary pressures. The second condition is self-evident ; for if, in two opposite directions, the pressures exerted on any given molecule were not equal and contrary, the molecule would be moved in the direction of the greater pressure, and there would be no equilibrium. Thus the second condition follows from the principle of the equality of pressures, and from the reaction which all pressure causes on the mass of hquids. To prove the first condition, let us suppose that mp is the resultant of all the forces acting upon any molecule m on the surface (fig. 57), and that this surface is inclined in reference to the force mp. The latter can consequently be decomposed into two forces, mq and mf; the one perpendicular to the sur- face of the liquid and the other to the direction ;;//. Now the first force, mq, would be de- stroyed by the resistance of the liquid, while the second would move the molecule in the direction Fig. 57. nif which shows that equilibrium is impossible. It gravity be the force acting on the liquid, the direction mp is verti- cal ; hence, if the liquid is contained in a basin or vessel of small extent, the surface ought to be plane and horizontal (64), because then the direc- tion of gravity is the same in every point. But the case is different with liquid surfaces of greater extent, like the ocean. The surface will be per- pendicular to the direction of gravity : but as this changes from one point to another, and always tends towards a point near the centre of the earth, . it follows that the direction of the surface of the ocean will change also, and assume a nearly spherical form. 102. Equilibrium of tbe same liquid in several communicatingT vessels. — When several vessels of any given form communicate with each other, there will be equilibrium when the liquid in'each vessel satis- fies the two preceding conditions (loi), and further, when the surfaces of the liquids in all the vessels are in the same horizontal plane. In the vessels ABCD (fig. 58), which communicate with each other, -104] Conditions of the Equilibrium of Liquids. 79 Fig. 58. let us consider any transverse section of the tube 7nn ; the liquid can only remain in equilibrium as long as the pressures which this section sup- ports from ;« in the direction of n, and from 71 in the direction of ;«. are equal and opposite. Now it has been already proved that these pressures are respectively equal to the weight of a column of water, whose base is the supposed section, and whose height is the distance from the centre of gravity of this section to the surface of the liquid. If we conceive, then, a horizontal plane, Jnn, drawn through the centre of gravity of ttiis section, it will be seen that there will only be equi ^ librium as long as the height of the liquid above this plane is the same in each vessel, which demonstrates the principle enunciated. 103. Eciuilibrium of superposed liquids In order that there should be equilibrium when several heterogeneous liquids are superposed in the same vessel, each of them must satisfy the conditions necessary for a single liquid (loi) ; and further, there will be stable eqiiilibriuin onlywhev the liquids ai^e arranged in the order of their decreasing densities from the bottom upwards. The last condition is experimentally demonstrated by means of the phial of four elements. It consists of a long narrow bottle containing mercury, water saturated with carbonate of potass, alcohol coloured red, and petroleum. When the phial is shaken the liquids mix, but when it is allowed to rest they separate ; the mercury sinks to the bottom, then comes the water, then the alcohol, and then the petroleum. This is the order of the decreasing densities of the bodies. The water is saturated with carbonate of potass to prevent its mixing with the alcohol. This separation of the liquids is due to the same cause as that which enables solid bodies to float on the surface of a liquid of greater density than their own. It is also' from this principle that fresh Avater, at the mouths of rivers, floats for a long time on the denser salt water of the sea ; and it is for the same reason that cream, which is lighter than milk, rises to the surface. 104. Equilibrium of two different liquids in communicatingr vessels. — When two liquids of different densities, which do not mix, are contained in two communicating vessels, they will be in equilibrium when, in addition to the preceding principles, they are subject to the following : that the heights above tJie Jiorizontal surface of contact of two columns of liquid in equilibrium are in tJie inverse ratio of their densities. To show this experimentally, mercury is poured into a bent glass tube, mn, fixed against an upright wooden support (fig. 59), and then water is poured into one of the legs, AB. The column of water, AB, pressing on 8o On Liquids. [104- rtie mercury at B, lowers its level in the leg AB, and raises it in the other by a quantity, CD ; so that if, when equilibrium is established, we imagine a horizontal plane, BC, to pass through B, the column of water in AB will balance the column of mercury CD. If the heights of these two columns are then measured, by means of the_ scales, it will be found that the height of the column of water is about 13^ times that of the height of the column of mercury. We shall presently see that the density of mercury is about 13I times that of water, from which it follows that the heights are inversely as the densities. It may be added, that the equilibrium cannot exist unless there is a sufficient quantity of the heavier liquid for part of it to remain in both legs of the tube. The preceding principle may be de- duced by a very simple calculation. Let d and df be the densities of water and mercury, and h and h' their respec- tive heights, and let g be the force of gravity. The pressure on B will be proportional to the density of the liquid, to its height, and to the force of gravity ; on the whole, therefore, to the product dhg. Similarly, the pressure at C will be proportional to d'h'g. But in order to produce equilibrium, dhg must be equal to d'h'g, or dh = d'h\ This is nothing more than an algebraical expression of the above principle ; for since the two products must always be equal, d' must be as many times greater than d, as h' is less than h. In this manner the density of a liquid may be determined. Suppose one of the branches contained water and the other oil, and their heights were, respectively 15 inches for the oil, and 14 inches for .the water. The density of water being taken as unity, and that of oil being called x, we shall have 14 I5x;i-=i4xi; whence x = — = 0-933. 15 Fig. 59- APPLICATIONS OF THE PRECEDING HYDROSTATIC PRINCIPLES. 105. — Hydraulic press. — The law of the equality of pressure has received a most important application in the hydraulic press, a machine by which enormous pressures may be produced. Its principle is due to Pascal, but it was first constructed by Bramah in 1 796. It consists of a cylinder, B, with very strong thick sides (fig. 60), in which there is a cast iron ram, P, working water tight in the collar of the cylinder. On the ram P there is a cast iron plate on which the substance to be pressed is placed. Four strong columns serve to support and fix a second plate, Q. -105] Hydratdic Press. 8i By means of a leaden pipe, K, the cylinder, B, which is filled with water, communicates with a small force pump. A, which works by means of a lever, M. When the piston of this pump p ascends, a vacuum is Fig. 60. produced and the water rises in the tube a, at the end of which there is a rose, to prevent the entrance of foreign matters. When the piston p descends, it drives the water into the cylinder by the tube K. Fig. 61. Fig. 61 represents a section, on a larger scale, of the system of valves necessary in working the apparatus. The valve o, below the piston p E3 82 On Liquids. [105- opens when the piston rises, and closes when it descends. The valve took for zero the point to which the apparatus sank in a solution of 10 parts of salt in 90 of water, and for 10° he took the level in distilled water. This distance he divided into 10°, and continued the division to the top of the scale. F5g. 78. 96 On Liq?nds. [124- The graduation of these hydrometers is entirely conventional, and they give neither the densities of the liquids, nor the quantities dissolved. But they are very useful in making mixtures or solutions in given propor- tions, the results they give being sufficiently near in the majority of cases. For instance, it is found that a well-made syrup marks 35° on Beaume's hydrometer, from which a manufacturer can readily judge whether a syrup which is being evaporated has reached the proper degree of concentration. 125. Gay-]bussac's alcobolometer. — This instrument is used to determine the strength of spirituous liquors ; that is, the proportion of pure alcohol which they contain. It differs from Beaume's hydrometer in the graduation. Mixtures of absolute alcohol and distilled water are made, containing 5, 10, 20, 30, etc., per cent, of the former. The alcoholometer is so con- structed that, when placed in pure distilled water, the bottom of its stem is level with the water, and this point is zero. It is next placed in absolute alcohol, which marks 100°, and then successively in mixtures of different strengths, containing 10, 20, 30, etc., per cent. The divisions thus obtained are not exactly equal, but their difference is not great, and they are subdivided into ten divisions, each of which marks one per cent, of absolute alcohol in a liquid. Thus a brandy in which the alcoholo- meter stood at 48°, would contain 48 per cent, of absolute alcohol, and the rest would be water. All these determinations are made at 15° C, and for that temperature only are the indications correct. For, other things being the same, if the temperature rises the liquid expands, and the alcoholometer will sink, and the contrary, if the temperature falls. To obviate this error, Gay- Lussac constructed a table which for each percentage of alcohol gives the reading of the instrument for each degree of temperature from 0° up to 30°. When the exact analysis of an alcoholic mixture is to be made, the temperature of the Hquid is first determined, and then the point to which the alcoholometer sinks in it. The number in the table corresponding to these data indicates the percentage of alcohol. From its giving the per- centage of alcohol, this is often called the ce7itesimal alcoholometer. 1 26. Salimeters. — Salimeters, or instruments for indicating the per- centage of salt contained in a solution, are made on the principle of the centesimal alcoholometer. They are graduated by immersing them in pure water, which gives the zero, and then solutions containing different percentages, 5, 10, 20, etc., of the salt, and marking on the scale the corresponding points. These instruments are so far objection- able, that every salt requires a special instrument. Thus one gradu- ated for common salt would give totally false indications in a solution of nitre. Lactometers and vino7neters are similar instruments, and are used for measuring the quantity of water which is introduced into milk or wine for the purpose of adulteration. But their use is limited, because the density of these liquids is very variable, even when they are perfectly natural, and an apparent fraud may be really due to a bad natural quantity of wine -128] Densimeter. 97 or milk. Urinometers^ which are of extensive use in medicine, are based on the same principle. 127. Densimeter. — The densimeter is an ap- paratus for indicating the specific gravity of a liquid. Gay-Lussac's densimeter has the same construction as Baume's hydrometer, but is gra- duated in a different manner. Rosseau's densi- meter (fig. 79) is of great use in many scientific investigations, in determining the specific gravity of a small quantity of a liquid. It has the same form as Beaume's hydrometer, but on the upper part of the stem there is a small tube AC, in which is placed the substance to be determined. A mark A on the side of the tube indicates a measure of a cubic centimetre. The instrument is so constructed that when AC is empty it sinks in^iistilled water to a point, B, just at the bottom of the stenj. It is then filled with distilled water to the height measured on the tube AC, which indicates a cubic centimetre, and the point to which it now sinks is 20°. The interval between o and 20 is divided into 20 equal parts, and this graduation is continued to the top of the scale. As this is of uniform bore each division corresponds to ^ gramme or 0*05. To obtain the density of any Hquid, bile for example, the tube is filled with it up to the mark A ; if the densimeter sinks to 20^ divisions, its weight is 0*05 + 20*5 = 1-025 5 that is to say, that with equal volumes the weight of water being i, that of bile is 1*025. The specific gravity of bile is therefore i'025. Fig. 79. ^¥^ ^i^ :af CAPILLARITY, ENDOSMOSE, EFFUSION, ABSORPTION, AND IMBIBITION. 128. Capillary ptaenomena. — When solid bodies are placed in con- tact with liquids, a class of phenomeha is produced called capillary phenomena, because they are best seen In tubes whose diameters are comparable with the diameter of a hair. Thfse phenomena are treated of in physics under the head of capillarity orxapillary attractio?i : the latter expression is also applied to the force which produces the pheno- mena. \ The phenomena of capillarit>' are very various, but may all be referred to the mutual attraction of the liquid molecules for each other, and to the attraction between these molecules and solid bodies. The following are some of these phenomena : — When a body is placed in a liquid which wets it, for example, a glass rod in water, the liquid, as if not subject to the laws of gravitation, is raised upwards against the sides of the solid, and its surface^j instead of 98 On Liquids, [128- being horizontal, becomes slightly concave (fig. 80). If, on the contrary, the solid is one which is not moistened by the liquid, as glass by mercury, the liquid is depressed against the sides of the solid, and assumes a convex shape, as represented in fig. 81. The surface of the liquid exhibits the same concavity or convexity against the sides of a vessel in which it is contained, according as the sides are or are not moistened by the liquid. Fig 80. Fig. 81 Fig. 82. Fig. 83. These phenomena are much more apparent when a tube of small dia- meter is placed in a liquid. And according as the tubes are or are not moistened by the liquid, an ascent or a depression of the liquid is produced, which is greater in proportion as the diameter is less (figs. 82 and 83). When the tubes are moistened by the hquid, its surface assumes the form of a concave hemispherical segment, called the concave meniscus (fig. 82) ; when the tubes are not moistened, there is convex meniscus (fig. 83). 129. ]Laws of tbe ascent and depression in capillary tubes. — Gay-Lussac has shown experimentally that the elevation and depression of liquids in capillary tubes are governed by the three following laws : — I. When a capillary tube is placed in a liquid, the liquid is raised or depressed according as it does or does not moisteii the tube. II. For the same liquid the elevation varies inversely as the diameter of the tube, when the diameter does not exceed two millimetres. III. The elevation varies with the nature of the liquid, and with the temperature, but is indepetidetit of the natui'e and thickness of the tube. These laws hold good in vacuo as well as in air. When liquids are in tubes which they do not moisten, the depression is in the inverse ratio of the diameter of the tubes ; but for tubes of the same diameter the depression depends on the substance of the tubes. For instance, in an iron tube i millimetre in diameter, the depression of mercury is 1-226 millimetre ; but in a platinum tube of the same diameter the depression is 0*655 niillimetre. Moreover, the depression depends on the height of the convex meniscus of the mercury, and this height varies for the same tube, according as the meniscus is formed during an ascend- ing or descending motion of the mercurial column in the tube. These results undergo modification if the mercury is impure. 1 30. iiscent and depression betixreen parallel or inclined surfaces. — When two bodies of any given shape are dipped in water, analogous capillary phenomena are produced, provided the bodies are sufficiently near. If, for example, two parallel glass plates are immersed in water - \ o- -132] Capillarity. 99 at a very small distance from each other, water will rise between the two plates in the inverse ratio of the distance which separates them. The height of the ascent for any given distance is half what it would be in a tube whose diameter is equal to the distance between the plates. If the parallel plates are immersed in mercury, a corresponding de- pression is produced, subject to the same laws. If two glass plates AB and AC with their planes vertical and inclined to, one another at a small angle, as represented in fig. 84, have their ends dipped into a liquid which wets them, the liquid will rise between them. The elevation will be greatest at the line of contact of plates and from thence gradually less, the surface taking the form of an equilateral hyper- bola, wh'bse asymptotes are respectively the line of intersection of the plates, ana^he line in which the plates cut the horizontal surface of the water. \ V V f V Fig. 84. Fig. 85. Fig. 86. If a drop of water be placed within a conical glass tube whose angle is small and axis horizontal, it will have a concave meniscus at each end (fig. 85), and will tend to move towards the vertex. But if the drop be of mercury it will have a convex meniscus at each end (fig. 86) and will tend to move from the vertex. 131. Attraction and repulsion produced by capillarity. — The attractions and repulsions observed between bodies floating on the surface of liquids are due to capillarity, and are subject to the following laws : — i. When two floating balls both moistened by the liquid, for example, cork upon water, are so near that the liquid surface between them is not level, an attraction takes place. ii. The same effect is produced when neither of the balls is moistened, as is the case with balls of wax on water. iii. Lastly, if one of the balls is moistened and the other not, as a ball of cork and a ball of wax in water, they repel each other if the curved surfaces of the liquid in their respective neighbourhoods intersect. As all these capillary phenomena depend on the concave or convex curvature which the liquid assumes in contact with the solid, a short ex- planation of the cause which determines the form of this curvature is necessary. 1 32. Cause of tbe curvature of liquid surfaces in contact with solids.— The form of the surface of a liquid in contact with a solid lOO On Liquids. [132 depends on the relation between the attraction of the solid for the liquid, and of the mutual attraction between the molecules of the liquid. Let 7)1 be a liquid molecule (fig. 87) in contact with a solid. This molecule is acted upon by three forces ; by gravity, which attracts it in the direction of the vertical ni9 ; by the attraction of the liquid F, which acts in the direction inY \ and by the attraction of the plate ;z, which is exerted in the direction mn. According to the relative intensities of these forces, their resultant can take three positions : — Fig. 87 i. The resultant is in the direction of the vertical ;;zR (fig. 87). In this case the surface in is plane and horizontal : for, from the condition of the equihbrium of liquids, the surface must be perpendicular to the force which acts upon the molecules. ii. If the force n increases or F diminishes, the resultant R is within the angle mnV (fig. 88) ; in this case the surface takes a direction perpen- dicular to ;;2R, and becomes concave. iii. If the force F increases, or n diminishes, the resultant R takes the direction ?/zR (fig. 89) within the angle PwF, and the surface becoming perpendicular to this direction is convex. 133. Influence of tbe curvature on capillary phenomena. — The elevation or depression of a liquid in a capillary tube depends on the concavity or convexity of the meniscus. In a concave meniscus, abed (fig. 90), the liquid molecules are sustained in equilibrium by the forces acting on them, and they exercise no downward pressure on the inferior Fig. 90. Fig. 91. layers. On the contrary, in virtue of the molecular attraction, they act on the nearest inferior layers, from which it follows that the pressure on any layer, mn^ in the interior of the tube, is less than if there were no meniscus. The consequence is, that the liquid ought to rise in the tube until the internal pressure on the layer w«, is equal to the pressure, op^ which acts externally on a point, p^ of the same layer. -134] VariouTVttptUary Phenomena. loi Where the meniscus is convex (fig. 90) equilibrium exists in virtue of the molecular forces acting on the liquid ; but as the molecules which would occupy the same space ghik, if there were no molecular action, do not exist, they exercise no attraction on the lower layers. Consequently, the pressure on any layer ;;z;/, in the interior of the tube, is greater than if the space ghik were filled, for the molecular forces are more powerful than gravity. The liquid ought, therefore, to sink in the tube until the internal pressure on a layer, inn, is equal to the external pressure on any point, p, of this layer. 134. Various capillary phenomena. — The following facts are among the many which are caused by capillarity : — When a capillary tube is immersed in a liquid which moistens it, and is then carefully removed, the column of liquid in the tube is seen to be longer than while the tube was immersed in the liquid. This arises from the fact that a drop adheres to the lower extremity of the tube and forms a concave meniscus, which concurs with that of the upper meniscus to form a longer column (128). For the same reason a liquid does not overflow in a capillary tube, although the latter may be shorter than the hquid column which would otherwise be formed in it. For when the liquid reaches the top of the tube, its upper surface, though previously concave, becomes convex, and as the downward pressure becomes greater than if the surface were plane, the ascending motion ceases. A drop of mercury on a table has a spherical shape, which, like that of the heavenly bodies, is due to attraction. The globule of mercury behaves as if its molecules had no weight, since it remains spherical. That is, the molecular attraction is far greater than the weight, which only alters the shape of the globule if the quantity of mercury is much greater ; it theil flattens, but always retains at its edge the convex form which attraction imparts to it. Insects can often move on the surface of water without sinking. This is a capillary phenomenon caused by the fact, that as their feet are not wetted by the water, a depression is produced which keeps them up in spite of their weight. Similarly a sewing needle gently placed on water, does not sink, because its surface being covered with an oily layer, does not become wetted. But if washed in alcohol, or in potash, it at once sinks to the bottom. It is from capillarity that oil ascends in the wicks of lamps, that water rises in wood, sponge, bibulous paper, sugar, sand, and in all bodies which possess pores of a perceptible size. Capillarity is, moreover, the cause of the following phenomenon : — When a porous substance, such as gypsum, or chalk, or even earth, is placed in a porous vessel of unbaked porcelain, and the whole is dipped in water, the water penetrates into the pores, and the air is driven inwards, so that it is under four or five times its usual pressure and density. Jamin has proved this by cementing a manometer into blocks of chalk, gyp-um, etc., and he has made it probable that a pressure of this kind, exerted upon the roots, promotes the ascent of sap in plants. 102 On Liquids. [136- ENDOSMOSE, EFFUSION, ABSORPTION, AND IMBIBITION. 135. Endosmose and exosmose. — When two different liquids are separated by a thin porous partition, either inorganic or organic, a current sets in from each hquid to the other ; to these currents the names etidos- niose and exosmose are respectively given. These terms which signify impulse from within and impulse frojfi without, were originally intro- duced by M. Dutrochet, who first drew attention to these phenomena. They may be well illustrated by means of the endosmoitieter. This consists of a long tube, at the end of which a mem- A branous bag is firmly bound (fig. 92). The S bag is then filled with a strong syrup, or ^ fespiaiiaaji ^ some other solution denser than water, I ' such as milk or albumen, and is immersed in water. The liquid is found gradually to rise in the tube, to a height which may attain several inches : at the same time, the level of the liquid in which the endos- mometer is immersed becomes lower. It follows, therefore, that some of the exter- nal liquid has passed through the mem- brane and has mixed with the internal liquid. The external liquid moreover is found to contain some of the internal liquid. Hence two currents have been produced in opposite directions. The flow of the liquid towards that which in- i creases in volume is endosmose, and the '^^ current in the opposite direction is exos- mose. If water is placed in the bag, and Fig. 92. immersed in the syrup, endosmose is pro- duced from the water towards the syrup, and the liquid in the interior diminishes in volume while the level of the exterior is raised. The height of the ascent in the endosmometer varies with different liquids. Of all vegetable substances, sugar is that which, for the same density, has the greatest power of endosmose, while albumen has the highest power of all animal substances. In general, it may be said that endosmose takes place towards the denser liquid. Alcohol and ether form an exception to this ; they behave like liquids which are denser than water. With acids, according as they are more or less dilute, the endosmose is from the water towards the acid, or from the acid towards water. According to Dutrochet, it is necessary for the production of endos- mose : i. that the liquids be different but capable of mixing, as alcohol and water ; there is no endosmose, for instance, with water and oil : -136] Diffusion of Liquids. 103 ii, that the liquids be of different densities ; and iii. that the membrane must be permeable to at least one of the substances. The current through thin inorganic plates is feeble, but continuous, while organic membranes are rapidly decomposed, and endosmose then ceases. The well-known fact that dilute alcohol kept in a porous vessel be- comes concentrated, depends on endosmose. If a mixture of alcohol and water be kept for some time in a bladder, the volume diminishes, but it becomes much more concentrated. The reason, doubtless, is that the bladder permits the endosmose of water rather than that of alcohol. Dutrochet's method is not adapted for quantitative measurements, for it does not take into account the hydrostatic pressure produced by the column. Jolly has examined the endosmose of various liquids by weighing the bodies diffused. He calls the endosmotic equivalent of a substance the number which expresses how many parts by weight of water pass through the bladder in exchange for one part by weight of the substance. The following are some of the endosmotic equivalents which he determined : — Chloride of sodium . 4-3 Caustic potass . . 215-0 Sulphate of magnesium . T17 Sulphuric acid . 0-4 copper . 9'5 Alcohol 4-2 Sugar .... . 7-1 He also found that the endosmotic equivalent increases with the tempera- ture ; and that the quantities of substances which pass in equal times through the bladder are proportional to the strength of the solution. 136. Diffusion of liquids. — If oil be poured on water no tendency to intermix is observed, and even if the two hquids be violently agitated together, on allowing them to stand, two separate layers are formed. With alcohol and water the case is different ; if alcohol, which is specifi- cally lighter, be poured upon water, the liquids gradually intermix, they diffuse into one another. The laws of this diffusion, in which no porous diaphragm intervenes, have been completely investigated by Graham. The method, by which his latest experiments were made, was the following : — In a glass vessel, containing about 700 cubic centimetres of distilled water, about 100 cubic centimetres of the solution to be examined were carefully added by means of a capillary tube so as to form a layer on the bottom. After a certain interval of time, successive layers were carefully drawn off by a syphon, and their contents examined. The general results of these investigations may be thus stated : — i. When solutions of the same substance, but of different strengths, are taken, the quantities diffused in equal times are proportional to the strengths of the solutions. ii. In the case of solutions containing equal weights of different sub- stances, the quantities diffused vary with the nature of the substances. Saline substances may be divided into a number of equidiffusive groups^ 104 On Liquids. [136- the rates of diffusion of each group being connected with the others by a simple numerical relation. iii. The quantity diffused varies with the temperature. Thus, taking the rate of diffusion of hydrochloric acid at 1 5° C. as unity ; at 49° C. it is 2-i8. iv. If two substances which do not combine be mixed in solution, they may be partially separated by diffusion, the more diffusive one passing out most rapidly. In some cases chemical decomposition even may be effected by diffusion. Thus bisulphate of potassium is decomposed into free sulphuric acid and neutral sulphate of potassium. V. If liquids be dilute a substance will diffuse into water, containing another substance dissolved as into pure water ; but the rate is materially reduced if a portion of the diffusing substance be already present. The following table gives the approximate times of equal diffusion : — Hydrochloric acid . . . I'o Sulphate of magnesium . 7*0 Chloride of sodium . . 2*3 Albumen . . . . 49-0 Sugar 7-0 Caramel .... 98-0 It will be seen from the above table that the difference between the rates of diffusion is very great. Thus, sulphate of magnesium, one of the least diffusible saline substances, diffuses 7 times as rapidly as albumen and 14 times as rapidly as caramel. These last substances, like hydrated silicic acid, starch, dextrine, gum, etc., constitute a class of substances which are characterised by their incapacity for taking the crystalline form and by the mucilaginous character of their hydrates. Considering gela- tine as the type of this class, Graham has proposed to call them colloids (k-o\Xt/, glue), in contradistinction to the far more easily diffusible aystal- loid substances. Graham has proposed a method of separating bodies based on their unequal diffusibility, which he calls dialysis. His dialyser consists of a ring of gutta percha over which is stretched while wet a sheet of parch- ment paper, forming thus a vessel about two inches high and ten inches in diameter, the bottom of which is of parchment paper. After pouring in the mixed solution to be dialysed, the whole is floated on a vessel containing a very large quantity of water. In the course of one or two days a more or less complete separation will have been effected. Thus a solution of arsenious acid mixed with various kinds of food readily diffuses out. The process has received important applications to laboratory and pharmaceutical purposes. For further information on this subject the student is referred to a very complete article on the diffusion of Hquids in the third volume of Watts's * Dictionary of Chemistry.' 137. Endosmose of grases. — The phenomena of endosmose are seen in a high degree in the case of gases. When two different gases are se- parated by a porous diaphragm, an exchange takes place between them, and ultimately the composition of the gas on both sides of the diaphragm is the same ; but the rapidity with which different gases diffuse into each other under these circumstances varies considerably. The laws regu- -138] Effusion and Transpiration of Gases. 105 lating this phenomenon have been investigated by Graham. Numerous experiments illustrate it, two of the most interesting of which are the fol- lowing : — A glass cylinder closed at one end is filled with carbonic acid gas, its open end tied over with a bladder, and the whole placed under a jar of hydrogen. Diffusion takes place between them through the porous dia- phragm, and after the lapse of a certain time hydrogen has passed throiigh the bladder into the cylindrical vessel in much greater quantity than the carbonic acid which has passed out, so that the bladder becomes very Fig. 93- Fig. 94. much distended outwards (fig. 93). If the cylinder be filled with hydro- gen and the bell-jar with carbonic acid, the reverse phenomenon will be produced — the bladder will be distended inwards (fig. 94). A tube about 12 inches long, closed at one end by a plug of dry plaster of Paris, is filled with dry hydrogen, and its open end then immersed in a mercury bath. Endosmose of the hydrogen towards the air takes place so rapidly that a partial vacuum is produced, and mercury rises in the tube to a height of several inches (fig. 95). If several such tubes are filled with different gases, and allowed to diffuse into the air in a similar manner, in the same time, different quantities of the various gases will diffuse, and Graham found that the law regulating these diffusions is, that the force of difftcsion is in- versely as the square roots of the densities of gases. Thus, if two vessels of equal capacity, containing oxygen and hydrogen, be separated by a porous plug, diffusion takes place ; and after the lapse of some time, for every one part of oxygen which has passed into the hydrogen, four parts of hydrogen have passed into the oxygen. Now the density of hydrogen being i, that of oxygen is 16, hence the force of diffusion is inversely as the square roots of these numbers. It is four times as great in the one which has j^th the density of the other. 138. Effusion and transpiration of grases. — Effusion is the term applied to the phenomenon of ^^s- 95- the passage of gases into vacuum, through a minute aperture not much F3 io6 On Liquids. [138- more or less than 0-013 millimetre in diameter, in a thin plate of metal or of glass. A gas can only flow from one space to another when the pressure in the one is greater than in the other. The term effusio7i is applied to the phenomenon of the passage of gases through minute apertures not much more or less than o-oi 3 millimetres in diameter. The velocity of the efflux is measured by the formula 7/ = ,^?^/z,in which h represents the pressure under M^hich the gas flows, expressed in terms of the height of a column of the gas, which would exert the same pressure as that of the effluent gas. Thus for air under the ordinary pressure flowing into a vacuum, the pressure is equivalent to a column of mercury 76 centimetres high ; and as mercury is approximately 10,500 times as dense as air, the equivalent column of air will be 76 centimetres x 10,500 = 7,980 metres. Hence the velocity of efflux of air into vacuum is = a/2 x 9-8 x 7,980 = 395-5 metres. This velocity into vacuum only holds, however, for the first moment, for the space con- tains a continually-increasing quantity of air, so that the velocity becomes continually smaller, and is null when the pressure on each side is the same. If the height of the column of air h^, corresponding to the external pressure, is known, the velocity may be calculated by the formula V = ,j2g{h-h^. For gases lighter than air a greater height must be inserted in the formula, and for heavier gases a lower height ; and this change must be inversely as the change of density. Hence the velocities of efflux of various gases must be inversely as the square roots of their densities. A simple inversion of this statement is that the dejtsities of two gases are inversely as the squares of their velocities of effusion. On this Bunsen has based an interesting method of determining the densities of gases and vapours. If gases issue through long, fine capillary tubes into a vacuum, the rate of efflux, or the velocity of transpiration ^ is independent of the rate of diffusion. i. For the same gas, the rate of transpiration increases^ other things being equal, directly as the pressure ; that is, equal volumes of air of different densities require times inversely proportional to their densities. ii. With tubes of equal diameters, the volume transpired in equal times is inversely as the length of the tube. iii. As the temperature rises the transpiration becomes slower. iv. The rate of transpiration is independent of the material of the tube. 139. Absorption and imbibition. — The words absorption and imbi- bition are used almost promiscuously in physics ; they indicate the penetration of a liquid or gas into a porous body. Absorption is used both for liquids and gases, while imbibition is restricted to liquids. In physiology an important distinction is made between the two words ; absorption means the penetration of a foreign substance into the tissues of a living body, while imbibition refers to penetration into bodies deprived of life, whether organic or not. 140. Absorption of grases. — The surfaces of all solid bodies exert an attraction on the molecules of gases with which they are in contact, of -140] Absorption of Gases. 107 such a nature, that they become covered with a more or less thick layer of co7idensed gas. When a porous body, which consequently presents an immensely increased surface in proportion to its size, is placed in a gas over mercury, the great diminution of volume which ensues indicates that considerable quantities of gas are absorbed. Now, although there is no absorption such as arises from chemical combinations between the solid and gas (as with phosphorus and oxy- gen), still the quantity of gas absorbed is not entirely dependent on the physical conditions of the solid body ; it is influenced in spme measure by the chemical nature both of the solid and the gas. Of all bodies box- wood charcoal has the greatest absorptive power. One volume of this substance at the ordinary temperature and pressure absorbs the following quantities of gas : — Ammonia . 90 vol. Carbonic oxide • . . 9-4 vol. Hydrochloric acid . . 85 . Oxygen . • 9-2 „ Sulphurous ,, . 65 „ Nitrogen. . 7-5 ,. Sulphuretted hydrogen . 55 ,, Hydrogen • 175 » Carbonic acid . • 35 ,, The absorption of gases is in general greatest in the case of those which are most easily liquefied. The absorptive power of pine charcoal is half as much as that of box- wood. The charcoal made from corkwood, which is very porous, is not absorbent ; neither is graphite. Platinum, in the finely divided form known as platinum sponge, is said to absorb 250 times its volume of oxygen gas. Many other porous substances, such as meerschaum, gypsum, silk, etc., are also highly absorbent. Graham found that at a high temperature platinum and iron allow hydrogen to traverse them even more readily than does caoutchouc in the cold. Thus while a square metre of caoutchouc 0-014 millimetres in thickness allowed 129 cubic centimetres of hydrogen at 20° to traverse it in a minute, a platinum tube n millimetres in thickness of the same surface allowed 489 cubic centi- metres to traverse it at a bright red heat. This is probably connected with the property which some metals, though destitute of physical pores, possess of absorbing gases either on their surface or in their mass ; and to which Graham has applied the term occlusion. It is best observed by allowing the heated metal to cool in contact with the gas. The gas cannot then be extracted by the air pump, but is disengaged on heating. In this way Graham found that platinum occluded four times its volume of hydrogen ; iron wire 0-44 times its volume of hydrogen, and 4*15 volumes of carbonic oxide; silver reduced from the oxide, absorbed about seven volumes of oxygen, and nearly one volume of hydrogen when heated to dull redness in these gases. This property is most remarkable in palladium, which absorbs hydrogen, not only in cooling after being heated, but also in the cold. When, for instance, a palladium electrode is used in the decomposition of water, one volume of the metal can absorb 980 times its volume of the gas. This gas is again drawn out on being heated, in which respect there is a io8 On Liquids. [140- resemblance to the solution of gases in liquids. By the occlusion of hydrogen the volume of palladium is increased by 0-09827 of its original amount, from which it follows that the hydrogen which under ordinary circumstances has a density of 0-000089546 of water has here a density nearly 9,868 times as great, or about 0-88 that of water. Hence the hydrogen must be in the liquid or even solid state ; it probably forms thus an alloy with palladium, like a true metal, a view of this gas, which is strongly supported by independent chemical considerations. The physical properties, in so far as they have been examined, support this view of its being an alloy. -141] Properties of Gases. 109 BOOK IV. ON GASES. CHAPTER I. PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS. 141. Pbysical properties of g-ases. — Gases are bodies whose mole- cules are in a constant state of repulsion, in virtue of which they possess the most perfect mobility, and are continually tending to occupy a greater space. This property of gases is known by the names expansibility^ tension^ or elastic force, from which they are often called elastic fluids. Gases and liquids have several properties in common, and some in which they seem to differ are in reality only different degrees of the same property. Thus, in both, the particles are capable of moving : in gases quite freely ; in liquids not quite freely, owing to a certain degree of vis- cosity. Both are compressible, though in very different degrees ; if a liquid and a gas both exist under the pressure of one atmosphere, and then the pressure be doubled, the water is compressed by about the 200*000 ^^ part, while the gas is compressed by one-half. In density there is a great difference ; water, which is the type of liquids, is 770 times as heavy as air, the type of gaseous bodies, while under a pressure of one atmosphere. The property by which gases are distinguished from liquids is their ten- dency to indefinite expansion. Matter assumes the solid, liquid, or gaseous form according to the relative strength of the cohesive and repulsive forces exerted between their particles. In liquids these forces balance ; in gases repulsion pre- ponderates. By the aid of pressure and of very low temperatures, the force of co- hesion may be so far increased in many gases that they are converted into liquids, and there is every reason for believing that with sufficient pressure and cold they might all be liquefied. On the other hand, heat, which increases the force of repulsion, converts liquids, such as water, alcohol, and ether, into the aeriform state in which they obey all the laws of gases. This aeriform state of liquids is known by the name of vapour^ while gases are bodies which, under ordinary temperature and pressure, remain in the aeriform state. In describing the properties of gases we shall, for obvious reasons, have exclusive reference to atmospheric air as their type. On Gases. [142- 142. Expansibility of gases.— This property of gases, their tendency to assume continually a greater volume, is exhibited by means of the following experiment. A bladder closed by a stopcock and about half full of air is placed under the receiver of the air pump (fig. 96), and a vacuum is produced, on which the bladder immediately distends. This arises from, the fact that the molecules of air repel each other and press against the sides of the bladder. Under ordinary conditions this internal pressure is counterbalanced by the air in the receiver, which exerts an equal and contrary pressure. But when this pressure is removed by exhausting the receiver, the internal pressure becomes evident. When air is admitted into the receiver, the bladder resumes its original form. 143. Compressibility of grases. — The compressibility of gases is readily shown by the pneimiatic syringe (fig. 97). This consists of a stout glass tube closed at one end, and provided with a tight-fitting solid piston. ^i^hen the rod of the down in the tube, and the air becomes Fie. 96. piston is pressed, it moves compressed into a smaller volume ; but as soon as the force is removed Fig. 97. the air regains its original volume, and the piston rises to its former position. 144. VTeigrlit of g-ases. — From their extreme fluidity and expansibility gases seem to be uninfluenced by the force of gravity ; they nevertheless possess weight, like solids and liquids. To show this, a glass globe of 3 or 4 quarts capacity is taken (fig. 98), the neck of which is provided with a stopcock, which hermetically closes it, and by which it can be screwed to the plate of the air pump. The globe is then exhausted, and its weight determined by means of a delicate balance. Air is now allowed to enter, and the globe again weighed. The weight in the second case will be found to be greater than before, and if the capacity of the vessel is known, the increase will obviously be the weight of that volume of air. 145] Pressure Exerted by Gases. II Fig. 98. By a modification of this method, and with the adoption of certain pre- cautions, the weight of air and of other gases has been de- termined. Perhaps the most accurate are those of Reg- nault, who found that a htre of dry air at 0° C, and under a pressure of 760 milhmetres weighs 1-293187 grammes. Since a Htre (or 1000 cubic centimetres) at 0° weighs 0*999877 grammes, the density of air is 0-00129334 that of water under the same circumstances ; that is, water is 773 times as heavy as air. Expressed in Enghsh measures, 100 cubic inches of dry air under the ordinary atmospheric pres- sure of 30 in. and at the temperature of 16° C, weigh 31 grains ; the same volume of carbonic acid gas under the same circumstances weighs 47*25 grains ; 100 cubic inches of hydrogen the Hghtest of all gases, weigh 2*14 grains : and 100 cubic inches of hydriodic acid gas weigh 146 grains. 145. Pressure exerted by grases — Gases exert on their own molecules and on the sides of vessels which contain them, pressures which may be regarded from two points of view : First, we may neglect the weight of the gas ; secondly, we may take account of its weight. If we neglect the weight of any gaseous mass at rest, and only consider its expansive force, it will be seen that the pressures due to this force act with the same intensity on all points, both of the mass itself and of the vessel in which it is con- tained. For it is a necessary consequence of the elasticity and fluidity of gases, that the repulsive force between the molecules is the same at all points, and acts equally in all directions. ' This principle of the equality of the pressure of gases in all directions may be shown experimentally by means of an apparatus resembling that by which the same principle is demonstrated for Hquids (fig. 51). If we consider the weight of any gas we shall see that it gives rise to pressures which obey the same laws as those produced by the weight of liquids. Let us imagine a cylinder, with its axis vertical, several miles high, closed at both ends and full of air. Let us consider any small portion of the air enclosed between two horizontal planes. This portion must sustain the weight of all the air above it, and transmit that weight to the air beneath it, and likewise to the curved surface of the cylinder which contains it ; and at each point in a direction at right angles to the surface. Thus the pressure increases from the top of the column to the base ; at any given layer, it acts equally on equal surfaces, and at right angles to them, whether they are horizontal, vertical, or inclined. The pressure acts on the sides of the vessel, and on any small surface it is equal to the weight of a column of gas, whose base is this surface, and whose height its distance from the summit of the column. The pressure is also independent of the shape and dimensions of the supposed cylinder, provided the height remains the same. For a small quantity of gas the pressures due to its weight are quite insignificant, and may be neglected; but for large quantities, like the atmosphere, the pressures are considerable, and must he allowed for. 112 On Gases, [146- 146. Tlte atmospbere. Its composition. — The atmosphere is the layer of air which surrounds our globe in every part. It partakes of the rotatory motion of the globe, and would remain fixed relatively to terrestrial objects, but for local circumstances, which produce winds, and are con- stantly disturbing its equihbrium. Air was regarded by the ancients as one of the four elements. Modern chemistry, however, has shown that it is a mixture of oxygen and nitro- gen gases in the proportion of 20-8 volumes of the former to 79*2 volumes of the latter. By weight it consists of 23 parts of oxygen to JJ parts of nitrogen. The atmosphere also contains a quantity of aqueous vapour, which varies with the temperature, the season, the locality, and the direction of the winds. It further contains a minute quantity of ammoniacal gas, and from 3 to 6 parts in 10,000 of its volume of carbonic acid. The carbonic acid arises from the respiration of animals, from the processes of combustion, and from the decomposition of organic substances. M. Boussingault has estimated that in Paris, the following quantities of carbonic acid are produced every 24 hours : — By the population and by animals . . 11,895,000 cubic feet By processes of combustion . . . 92,101,000 „ 103,996,000 Notwithstanding this enormous continual production of carbonic acid on the surface of the globe, the composition of the atmosphere does not vary ; for plants in the process of vegetation decompose the carbonic acid, assimilating the carbon, and restoring to the atmosphere the oxygen which is being continually consumed in the processes of respiration and combustion. 147. Atmospberic pressure. — If we neglect the perturbations to which the atmosphere is subject, as being inconsiderable, we may con- sider it as a fluid sea of a certain depth, surrounding the earth on all sides, and exercising the same pressure as if it were a liquid of very small density. Consequently, the pressure on the unit of area is constant at a given level, being equal to the weight of the column of atmosphere above that level whose horizontal section is the unit of area. It will act at right angles to the surface, whatever be its position. It will diminish as we ascend, and increase as we descend from that level. Consequently, at the same height, the atmospheric pressures on unequal plane surfaces will be proportional to the areas of those surfaces, provided they be small in proportion to the height of the atmosphere. In virtue of the expansive force of the air, it might be supposed that the molecules would expand indefinitely into the planetary spaces. But, in proportion as the air expands, its expansive force decreases, and is further weakened by the low temperature of the upper regions of the atmosphere, so that, at a certain height, an equilibrium is established between the expansive force which separates the molecules, and the action of gravity which draws them towards the centre of the earth. It is there- fore concluded that the atmosphere is limited. From the weight of the atmosphere, and its decrease in density, and -148] Crushing Force of the A tmosphere. 113 from the observation of certain phenomena of twilight, its height has been estimated at from 30 to 40 miles. Above that height the air is extremely rarefied, and at a height of 60 miles it is assumed that there is a perfect __^___ vacuum. On the other hand meteorites have - been seen at a height of 200 miles, and as their luminosity is due to the action of air, there must be air at such a height. Again, from certain observations made in the tropi- cal zone, and particularly at Rio Janeiro, on the twilight arc, M. Liais estimates the height of the atmosphere at between 198 and 212 miles, considerable higher, therefore, than what has hitherto been believed. As it has been previously stated that 100 cubic inches of air weigh 31 grains, it will readily be conceived that the whole atmo- sphere exercises a considerable pressure on the surface of the earth. The existence of this pressure is shown by the following ex- periments. 148. Crushing: force of tbe atmospbere. -On one end of a stout glass cylinder, about 5 inches high, and open at Fig. 100. Fig. loi. both ends, a piece of bladder is tied quite air-tight. The other end, the edge of which its ground and well-greased, is pressed on the plate of the air pump (fig. 99). As soon as a vacuum is produced in the vessel, by working the air pump, the bladder is depressed by the weight of the atmo- sphere above it, and finally bursts with a loud report caused by the sudden entrance of the air. 114 On Gases. [149- 149. nxagrdeburgr hemispheres. — The preceding experiment only serves to illustnate the downward pressure of the atmosphere. By means of the Magdeburg heinispheres (figs. 100 and loi), the invention of which is due to Otto von Guericke, burgomaster of Magdeburg, it can be shown that the pressure acts in all directions. This apparatus consists of two hollow brass hemispheres of 4 to 4^ inches diameter, the edges of which are made to fit tightly, and are well greased. One of the hemispheres is provided with a stopcock, by which it can be screwed on the air pump, and on the other there is a handle. As long as the hemispheres contain air they can be separated without any difficulty, for the external pressure of the atmosphere is counterbalanced by the elastic force of the air in the interior. But when the air in the interior is pumped out by means of the air pump, the hemispheres cannot be separated without a power- ful effort ; and as this is the case in whatever position they are held, it follows that the atmospheric pressure is transmitted in all directions. DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS. 150. Torricelli's experiment. — The above experiments demonstrate the existence of the atmospheric pressure, but they give no precise indica- tions as to its amount. The following experiment, which was first made, in 1643, by Torricelli, a pupil of Galileo, gives an exact measure of the weight of the atmosphere. A glass tube is taken, about a yard long and a quarter of an inch mternal diameter (fig. 102). It is sealed at one end, and is quite filled with mercury. The aperture C being closed by the thumb, the tube is inverted, the open end placed in a small mercury trough, and the thumb removed. The tube being in a vertical position, the column of mercury sinks, and, after oscillating some time, it finally comes to rest at a height A, which at the level of the sea is about 30 inches above the mer- cury in the trough. The mercury is raised in the tube by the pressure cf the atmosphere on the mercury in the trough. There is no contrary pressure on the mercury in the tube, because it is closed. But if the end of the tube be opened, the atmosphere will press equally inside and outside the tube, and the mercury will sink to the level of that in the trough. It has been shown in hydrostatics (104) that the heights of two columns of -152] A mount of the A tmospheric Pr^iire. 1 1 5 liquid in communication with each other are inversely as their densities, and hence it follows, that the pressure of the atmosphere is equal to that of a column of mercury, the height of which is 30 inches. If, however, the weight of the atmosphere diminishes, the height of the column which it can sustain must also diminish. 151. Pascal's experiments. — Pascal, who wished to prove that the force which sustained the mercury in the tube was really the pressure of the atmosphere, made the following experiments, i. If it were the case, the column of mercury ought to descend in proportion as we ascend in the atmosphere. He accordingly requested one of his relations to repeat Torricelli's experiment on the summit of the Puy de Dome in Auvergne. This was done, and it was found that the mercurial column was about 3 inches lower, thus proving that it is really the weight of the atmosphere which supports the mercury, since, when this weight diminishes, the height of the column also diminishes, ii. Pascal re- peated Torricelli's experiment at Rouen, in 1646, with other liquids. He took a tube closed at one end, nearly 50 feet long, and having filled it with water, placed it vertically in a vessel of water, and found that the water stood in the tube at a height of 34 feet; that is, 13-6 times as high as mercury. But since mercury is 13-6 times as heavy as water, the weight of the column of water was exactly equal to that of the column of mercury in Torricelli's experiment, and it was consequently the same force, the pressure of the atmosphere, which successively sup- ported the two liquids. Pascal's other experiments with oil and with wine gave similar results. 152. Amount of the atmospheric pressure. — Let us assume that the tube in the above experiment is a cylinder, the section of which is equal to a square inch, then since the height of the mercurial column in round numbers is 30 inches, the column will contain 30 cubic inches, and as a cubic inch of mercury weighs 3433*5 grains = 0-49 of a pound, the pressure of such a column on a square inch of surface is equal to 147 pounds. In round numbers the pressure of the atmosphere is taken at 1 5 pounds on the square inch. A surface of a foot square contains 144 square inches, and therefore the pressure upon it is equal to 2,160 pounds, or nearly a ton. Expressed in the metrical system, the standard atmospheric pressure at 0° and the sea level is 760 millimetres, which is equal to 29-9217 inches ; and a similar calculation to the above shows that the pressure on a square centimetre is = i -03296 kilogrammes. A gas or Hquid which acts in such a manner that a square inch of surface is exposed to a pressure of 15 pounds, is called a pressure of one atmosphe^-e. If, for instance, the elastic force of the steam of a boiler is so great that each square inch of the internal surface is exposed to a pressure of 90 pounds ( = 6x 15), we say it is under a pressure of six atmospheres. The surface of the body of a man of middle size is about 16 square feet ; the pressure, therefore, which a man supports on the surface of his body is 35,560 pounds, or nearly 16 tons. Such an enormous pressure might seem impossible to be borne ; but it must be remembered that in Ii6 jj^ On Gases. [152 all directions there are equal and contrary pressures which counter- balance one another. It might also be supposed that the effect of this force, acting in all directions, would be to press the body together and crush it. But the solid parts of the skeleton could resist a far greater pressure ; and as to the air and liquids contained in the organs and vessels, the air has the same density as the external air, and cannot be further compressed by the atmospheric pressure ; and from what has been said about liquids (94) it is clear that they are virtually incom- pressible. When the external pressure is removed from any part of the body, either by means of a cupping vessel or by the air pump, the pres- sure from within is seen by the distension of the surface. 153. Different kinds of barometers. — The instruments used for measuring the atmospheric pressure are called baj-ometers. In ordinary barometers, the pressure is measured by the height of a column of "mercury, as in Torricelli's experiment : the barometers which we are about to describe are of this kind. But there are barometers without any liquid, one of which, the aneroid (173), is remarkable for its simplicity and portability. 1 54. Cistern barometer. — The cistern barometer consists of a straight glass tube closed at one end, about 33 inches long, filled with mercury, and dipping into a cistern containing the same metal. In order to render the barometer more portable, and the variations of the level in the cistern less perceptible when the mercury rises or falls in the tube, several dif- ferent forms have been constructed. Fig. 103 represents one form of the cistern barometer. The apparatus is fixed to a mahogany stand, on the upper part of which there is a scale graduated in millimetres or inches from the level of the mercury in the cistern ; a moveable index, i, shows on the scale the level of the mercury. A thermometer on one side of the tube indicates the temperature. There is one fault to which this barometer is liable, in common with all others of the same kind. The zero of the scale does not always cor- respond to the level of the mercury in the cistern. For as the atmo- spheric pressure is not always the same, the height of the mercurial column varies : sometimes mercury is forced from the cistern into the tube, and sometimes from the tube into the cistern, so that, in the majority of cases, the graduation of the barometer does not indicate the true height. If the diameter of the cistern is large, relatively to that of the tube, the error from this source is lessened. The height of the barometer is the distance between the levels of the mercury in the tube and in the cistern. Hence the barometer should always be perfectly vertical ; for, if not, the tube being inclined, the column of mercury is elongated (fig. 104), and the number read off on the scale is too great. As the pressure which the mercury exerts by its weight at the base of the tube is independent of the form of the tube and of its diameter (104), provided it is not capillary, the height of the barometer is independent of the diameter of the tube and of its shape, but is inversely as the density of the liquid. With mercury the mean height at the level of the sea is 29*92, or in round numbers 30, inches ; in a water barometer it would be about 34 feet, or 10-33 metres. -155] Barometers. 117 155. Fortin's barometer. — Fortiii^s barometer differs from that just described, in the shape of the cistern. The base of the cistern is made of leather, and can be raised or lowered by means of a screw ; this has the advantage, that a constant level can be obtained, and also that the in- strument is made more portable. For, in travelling, it is only necessary to raise the leather until the mercury, which rises with it, quite fills the cistern; the barometer may then he inclined, and even inverted without. aii,y fear that a bubble of air may enter, or that the shock of the mercury may crack the tube. '^M^o.>^-'^^ ^ A.' IB Fig. 103. Fig. 104. Fig. 105. Fio-. 105 represents the arrangement of the barometer, the tube of which is placed in a brass case. At the top of this case, there are two longitudi- nal apertures, on opposite sides, so that the level of the mercury, B, is seen. The scale on the case is graduated in millimetres. An index A, moved by the hand, gives, by means of a vernier, the height of the mer- ii8 On Gases. [155 cury to j'^th of a millimetre. At the bottom of the case there is a cistern by containing mercury, O. Fig. io6 shows the details of the cistern on a larger scale. It consists of a glass cylinder b, through which the mercury can be seen ; this is closed at the top by a box-wood disc fitted on the under-surface of the brass cover M. Through this passes the barometer tube E, which is ^drawn out at the end, and dips in the mercury; the cistern and the tube are connected by a piece of buckskin ce, which is firmly tied at ^ to a contraction in the tube, and at ^ and ^. (i) Since the force of gravity is different for places in different lati- tudes, ^ will depend upon the latitude (79). It is found that if ^ is the accelerating force of gravity in latitude (p, and / that force in latitude 45°.- then ^~ I +0-00256 cos 29;' where / has a definite numerical value. (2) From what has been stated above it will be seen, that if p is the 126 On Gases. [165- density of air at a temperature of t° C, under Q the pressure exerted by 29-92 inches of mercury, we shall have But it will be afterwards shown that if p^ is the density of air under the same pressure O at 0° C, we shall have where a has a definite numerical value. Therefore -^ I +^/ Now if \ H X (in feet) - 60346 (i + 0-00256 cos 2 4.) (^1 + —^^~') log ^ ' which is La Place's barometric formula. In using it, it must be remem- bered that T and Tj ar>e temperatures on the Centigrade thermometer, and that H and H, are the heights of the barometer reduced to 0° C. Thus if // is the measured height of the barometer at the lower station we have \ 6=;oo/ 6500. If the height to be measured is not great, one observer is enough. For greater heights the ascent takes some time, and in the interval the pres- sure may vary. Consequently in this case there must be two observers, one at each station, who make simultaneous observations. Let us take the following example of the above formula:— Suppose that in latitude 65° N. at the lower of the two stations the height of the barometer were 30-025 inches, and the temperature of air and mercury 17^-32 C, while at the upper the height of the barometer was 28-230 inches, and the temperature of air and mercury was io°-55 C. Determine the height of the upper station above the lower. -166] \^oyles Law/) 127 (i) P'ind H and H^•. viz. H =30-025(1-^^) = 20-945; hence log — = i -4763243 - i -4500026 = 0-02632 1 7. (2) Find I + ^- lo^Q-- VIZ. 1-05574. (3) Find 1+0-002560052^. Since 0-00256 cos 130"^= -0*00256 cos 50^ = —0-001645, therefore i + 0-00256 cos 2p= -0-998355 ; hence the required height in feet equals 60346x0-998355 X 1-05574 X 0-263217 = 1674. It may be easily proved that if H and H^ do not greatly differ, the TT TT TJl Napierian logarithm of —7- equals 2 -^ — ^ if for instance H equals 30 inches, and Hj equals 29 inches, the resulting error would not exceed the 5,j^^^y part of the whole. Accordingly for heights not exceeding 2000 ft. we may without much error use the formula, X (m feet) = 52500 (i -f -^^^^) x -^-^^• CHAPTER 11. MEASUREMENT OF THE ELASTIC FORCE OF GASES. 166. Boyle's law. — The law of the compressibihty of gases was dis- covered by Boyle and Mariotte independently. In consequence it is in England commonly called ' Boyle's law,' and, on the Continent, 'Mariotte's law.' It is as follows : The temperature remaining the sa?ne, the volume of a given qiiajitity of gas is inversely as the pressure which it bears ? This law maybe verified by means of an apparatus called Ma?-iotte's tube (fig. 115). It consists of a long glass tube fixed to a vertical support ; it is open at the upper part, and the other end, which is bent into a short vertical leg, is closed. On the shorter leg there is a scale, which indi- cates equal capacities ; the scale against the long leg gives the heights. The zero of both scales is in the same horizontal line. 128 On Gases. [166 A small quantity of mercury is poured into the tube, so that its level in both branches is at zero, which is effected without much difficulty after a few trials (fig. 115). The air in the short leg is thus under the ordinary atmospheric pressure which is exerted through the open tube. Mercury is then poured into the longer tube until the volume of the air in the smaller tube is reduced to one-half ; that is, until it is reduced from 10 to 5, as shown in fig. 116. If the height of the riiercurial column, CA, be measured, it will be found exactly equal to the height of the barometer at g A ^80' . r^o -! 1 -1 ~—i^ + v^^+ . It obviously follows that if the pressures are all the same, the volume of the mixture equals the sum of the separate volumes. The first law was shown experimentally by Berthollet, by means of an apparatus represented in fig. 124. It consists of two glass globes pro- vided with stopcocks, which can be screwed one on the other. The upper globe was filled with hydrogen, and the lower one with carbonic acid, which has 22 times the density of hydrogen. The globes having been fixed together were placed in the cellars of the Paris Observatory and the stopcocks then opened, the globe containing hydrogen being uppermost. Berthollet found after some time that the pressure had not changed, and that, in spite of the difference in density, the two gases had become uniformly mixed in the two globes. Experiments made in 136 On Gases. [174- the same manner with other gases gave the same results, and it was found that the diffusion was more rapid in proportion as the difference between the densities was greater. The second law may be demonstrated by passing into a graduated tube, over mercury, known volumes of gas at known pressures. The pressure and volume of the whole mixture are then measured, and found to be in ac- cordance with the law. Gaseous mixtures follow Boyle's law, like simple gases, as has been proved for air (i66), which is a mixture of nitrogen and oxygen. 175. Mixture of g^ases and liquids. Absorption. — Water and many liquids possess the property of absorbing gases. Under the same conditions of pressure and temperature a liquid does not absorb equal quantities of different gases. At the ordi- nary temperature and pressure water dis- solves jflo its volume of nitrogen, ^^f- its volume of oxygen, its own volume of carbonic acid, and 430 times its volume of ammo- niacal gas. The whole subject of gas absorption has ^^' ^^'^' been investigated by Bunsen, to whose work* the student is referred for further information. The general laws of gas absorption are the following : — I. I^or the same gas, the same liquid, and the same temperature, the weight of gas absorbed is propoi'tional to the pressure. This may also be expressed by saying that at all pressures the volume dissolved is the same ; or that the density of the gas absorbed is in a constant relation with that of the external gas which is not absorbed. Accordingly, when the pressure diminishes, the quantity of dissolved gas decreases. If a solution of gas be placed under the air-pump and a vacuum created, the gas obeys its expansive force and escapes with effer- vescence. II. The quantity of gas absorbed is greater when the temperature is lower-, that is to say, when the elastic force of the gas is less. III. The quantity of gas which a liquid can dissolve is independent of the nature and of the quantity of other gases which it may already hold in solution. In every gaseous mixture each gas exercises the same pressure as it would if its volume occupied the whole space ; and the total pressure is equal to the sum of the individual pressures. When a liquid is in contact with a gaseous mixture, it absorbs a certain part of each gas, but less than it would if the whole space were occupied by each gas. The quantity of each gas dissolved is proportional to the pressure which the unabsorbed * Gasometric Methods, by R. Bunsen, translated by Prof. Roscoe. 176] A rchimedes' Principle applied to Gases. m gas exercises alone. For instance, oxygen forms only about I the quantity of air ; and water, under ordinary conditions, absorbs exactly the same quantity of oxygen as it would if the atmosphere were entirely formed of this gas under a pressure equal to \ that of the atmosphere. t CHAPTER III. PRESSURE ON BODIES IN AIR. BALLOONS. 176. Archimedes' principle applied to g:ases. — The pressure exerted by gases on bodies immersed in them is transmitted equally in all direc- tions, as has been shown by the experiment with the Magdeburg hemi- spheres. It therefore follows that all which has been said about the equilibrium of bodies in hquids applies to bodies in air ; they lose a part of their weight equal to that of the air which they displace. The loss of weight in air is demon- strated by means of the baroscope, which consists of a scalebeam, at one of whose extremities a small leaden weight is supported, and at the other there is a hollow copper sphere (fig. 125). In the air they exactly balance one another; but when they are placed under the receiver of the air pump and a vacuum is produced, the sphere sinks; thereby showing that in reality it is heavier than the small leaden weight. Before the air is exhausted each body is buoyed' up by the weight of the air which it dis- places. But as the sphere is much the larger of the two, its weight undergoes most apparent diminution, and thus, though in reality the heavier body, it is balanced by the small leaden weight. It may be proved by means of the same apparatus that this loss is equal to the weight of the displaced air. Suppose the volume of the sphere is 10 cubic inches. The weight of this volume of air is 3-1 grains. If now this weight be added to the leaden weight, it will overbalance the sphere in air, but will exactly balance it in vacuo. The principle of Archimedes is true for bodies in air ; all that has been said about bodies immersed in liquids applies to them, that is, that when a body is heavier than air, it will sink, owing to the excess of its weight over the buoyancy. If it is as heavy as air, its weight will exactly counter- balance the buoyancy, and the body will float in the atmosphere. If the body is lighter than air, the buoyancy of the air will prevail, and the body Fig. 138 On Gases. [176- will rise in the atmosphere until it reaches a layer of the same density as its own. The force of the ascent is equal to the excess of the buoyancy over the weight of the body. This is the reason why smoke, vapours, clouds, and air balloons rise in the air. * , AIR BALLOONS. 177. Air balloons. — Air balloons are hollow spheres made of some light impermeable material, which, when filled with heated air, with hydrogen gas, or with coal gas, rise in the air in virtue of their relative lightness. They were invented by the brothers Mongolfier, of Annonay, and the first experiment was made at that place in June 1783. Their balloon was a sphere of 40 yards in circumference, and weighed 500 pounds. At the lower part there was an aperture, and a sort of boat was suspended, in which fire was lighted to heat the internal air. The balloon rose to a height of 2,200 yards, and then descended without any accident. Charles, a professor of physics in Paris, substituted hydrogen for hot air. He himself ascended in a balloon of this kind in December 1783. The use of hot air balloons was entirely given up in consequence of the serious accidents to which they were liable. Since then, the art of ballooning has been greatly extended, and many ascents have been made. That which Gay-Lussac made in 1804 was the most remarkable for the facts with which it has enriched science, and for the height which he attained — 23,000 feet above the sea level. At this height the barometer descended to I2"6 inches, and the thermometer which was 31° C. on the ground, was 9 degrees below zero. In these high regions, the dryness was such on the day of Gay-Lussac's ascent, that hygrometric substances, such as paper, parchment, etc., became dried and crumpled as if they had been placed near the fire. The respi- ration and circulation of the blood were accelerated in consequence of the great rarefaction of the air. Gay-Lussac's pulse made 120 pulsations in a minute, instead of 66, the normal number. At this great height the sky had a very dark blue tint, and an absolute silence prevailed. One of the most remarkable of recent ascents was made by Mr. Glaisher and Mr. Coxwell, in a large balloon belonging to the latter. This was filled with 90,000 cubic feet of coal gas (sp. gr. 0-37 to o'33) ; the weight of the load was 600 pounds. The ascent took place at i p.m. on September 5, 1861 ; at i° 28' they had reached a height of 15,750 feet, and in eleven minu^s after a height of 21,000 feet, the temperature being- 10*4; at 1° 50' they were at 26,200 feet, with the thermometer at - 1 5*2° At 1° 52' the height attained was 29,000 feet, and the temperature — i6'0 C. At this height the rarefaction of the air was so great, and the cold so intense, that Mr. Glashier fainted, and could no longer observe. According to an approximate estimation the lowest barometric height they attained was 7 inches, which would correspond to an elevation of 36,000 to 37,000 feet. 1 78. Construction and managrement of balloons. — A balloon is made of long bands of silk sewn together and covered with caoutchouc varnish, -178] A ir Balloons. 139 which renders it air-tight. At the top there is a safety valve closed by a spring which the aeronaut can open at pleasure by means of a cord. A light wicker-work boat is suspended by means of cords to a net-work, which entirely covers the balloon. A balloon of the ordinary dimensions, which can carry three persons, is about 16 yards high, 12 yards in diameter, and its volume when it is quite full is about 680 cubic yards. The balloon itself weighs 200 pounds ; the accessories, such as the rope and boat, 100 pounds. The balloon is filled either with hydrogen or with coal gas. Although the latter is heavier than the former, it is generally preferred, because it is cheaper and more easily obtained. It is passed into the balloon from the gas reservoir by means of a flexible pipe. It is important not to fill the balloon quite full, for the atmos- pheric pressure diminishes as it rises (fig. 126), and the gas inside expand- ing in consequence of its elastic force, tends to burst it. It is sufficient for the ascent if the weight of the dis- placed air exceeds that of the balloon by 8 or 10 pounds. And this force remains constant so long as the balloon is not quite distended by the dilata- tion of the air in the interior. If the atmospheric pressure, for example has diminished to one half, the gas in the balloon according to Boyle's volume of the air displaced is therefore twice as great ; but since its density has become only one-half, the weight, and consequently the upward buoyancy, are the same. When once the balloon is completely dilated, if it continue to rise the force of the ascent decreases, for the volume of the displaced air remains the same, but its density di- minishes, and a time arrives at which the buoyancy is equal to the weight of tlie balloon. The balloon can now only take a horizontal direction, carried by the currents of air which prevail in the atmosphere. The aeronaut knows by the barometer whether he is ascend- ing or descending ; and by the same means he determines the height which he has reached. A long flag fixed to the boat would indicate, by the position it takes either above or below, whether the balloon is descending or ascendino-. Fig. 126. 40 On Gases [178- At the in 1794, battle of a captive When the aeronaut wishes to descend, he opens the valve at the top of the balloon by means of the cord, which allows gas to escape, and the balloon sinks. If he wants to descend more slowly, or to rise ao-ain he empties out bags of sand, of which there is an ample supply inihe car. The descent is facilitated by means of a grappling iron fixed to the boat. When once this is fixed to any obstacle, the balloon is lowered by pulling the cord. The only practical applications which air balloons have hitherto had _______ have been in military recon- noitring. Fleurus, balloon, that is, one held by a cord, was used, in which there was an observer who reported the movements of the enemy by means of signals. At the battle of Solferino the move- ments and dispositions of the Austrian troops were watched by a captive balloon ; and in the war in America balloons were frequently used, while their importance during the siege of Paris is fresh in all memories. The whole subject of military ballooning has been treated in two papers by Cap- tain Grover and by Captain Beaumont, in a recent volume of the Professional Papers of the Royal Engineers. Many as- cents have recently been made by Mr. Glaisher for the purpose of making meteorological ob- servations in the higher regions of the atmosphere. Air balloons can only be truly useful when they can be guided, and as yet all attempts made with this view have coriapletely failed. There is no other course at pre- sent than tsiWsfe'^lritb^^ until there is a current which has more or less the desired direction. '^ 179. Parachute. — The object of the parachute is to allow the aeronaut to leave the balloon, by giving him the means of lessening the rapidity of his descent. It consists of a large circular piece of cloth ffig. 127^ about 16 feet in diameter, and which by the resistance of the air spreads out like a gigantic umbrella. In the centre there is an aperture, through which the air compressed by the rapidity of the descent makes its escape ; for otherwise oscillations might be produced, which, when com- municated to the boat, would be dangerous. In '^g. 126 there is a parachute attached to the net-work of the balloon Fig. 127. -181] Air Pump. 141 by means of a cord which passes round a pulley, and is fixed at the other end to the boat. When the cord is cut the parachute sinks, at first very rapidly, but more slowly as it becomes distended, as represented in the figure. 1 80. Calculation of the weight which a balloon can raise. — To calculate the weight which can be raised by a balloon of given dimensions, let us suppose it perfectly spherical, and premise that the formulae which express the volume and the superficies in terms of the radius are V = ~ — and S = \-k^ ; tt being the ratio of the circumference to the diameter, and equal to 3-1416. The radius R being measured in feet, let p be, in pounds, the weight of a square foot of the material of which the balloon is constructed ; let P be the weight of the car and the accessories a the weight in pounds of a cubic foot of air at zero, and under the pressure 076, and a' the weight of the same volume under the same con- dition of the gas with which the balloon is inflated (144). Then the total weight of the envelope in pounds will be "4irR2/ ; that of the gas will be ^^^"^'j and that of the displaced air 4!:5!^. If X be the weight which the balloon can support, we have , x = 4iR!_^-4':^'-4.R!/^-p. 3 3 Whence But, as we have before seen (178), in order that the balloon may rise, the weights must be less by 8 or 10 pounds than that given by this equation. CHAPTER IV. APPARATUS FOUNDED ON THE PROPERTIES OF AlR. 181. Air pump. — The air pump is an instrument by which a vacuum can be produced in a given space, or rather by which air can be greatly rarefied, for an absolute vacuum cannot be produced by its means. It was invented by Otto von Guericke in 1650, a few years after the inven- tion of the barometer. The air pump, as now usually constructed, may be described as follows : In fig. 128, which shows the general arrangement, E is the receive7%\r\. which the vacuum is to be produced. It is a bell glass, resting on a plate D, of thick glass ground perfectly smooth. In the centre of D, at C, there is an opening by which a communication is made between the interior of the receiver and of the cyHnders P, P. This communication is effected by a tube or pipe passing through the body of the plate A, and then branching off at right angles, as shown by Kco Kcs, in fig 129, which 142 On Gases. [181- represents a horizontal section of the machine. In the cyHnders — which are commonly of glass, and which are firmly cemented to the plate A — are two pistons, P and Q, fitting air-tight. Each piston is moved by a rack, working with a pinion, H, turned by a handle, M. This is shown more plainly in fig. 1 30, which represents a vertical section of the machine through the cylinders : here H is the pinion, and MN the handle. When M is forced down one piston is raised, and the other depressed. When M's action is reversed, the former piston is depressed, and the latter raised. ♦ The action of the machine is this : Each cylinder is fitted with a valve so contrived that when its piston is raised, communication is opened between the cyhnder and the receiver : when it is depressed the corn- Fig. 128. munication is closed. Now if P were simply raised, a vacuum would be formed below P ; but as a communication is opened with the receiver E, the air in E expands so as to fill both the receiver and the cylinder. As soon as the piston begins to descend, the communication is closed, and none of the air in the cylinder returns to the receiver, but, by means of properly constructed valves, escapes into the atmosphere. Consequently the rarefaction which the air in the receiver has undergone is permanent. By the next stroke a further rarefaction is produced : and so on, at each succeeding stroke. It is plain that when the rarefaction has proceeded to a considerable extent the atmospheric pressure on the top of P will be very great, but it -181] Air Pump. 143 will be very nearly balanced by the atmospheric pressure on the top ot the other piston. Consequently the experimenter will have to overcome Fig. 132. Fig. 129. Fig. 130. Fig. 131 This is the reason why two The 130. only the difference of the two pressures, cylinders are employed. To explain the action of the valves we must go into particulars, general arrangement of the interior of the cylinders is shown in fig. Fig. 133 shows the section of the piston in detail. The piston is formed of two brass discs (X and V), screwed to one another, and compressing between them a series of leathern discs Z, whose diameters are slightly greater than those of the brass discs. The leather is thoroughly saturated with oil, so as to slide air- tight, though with but little friction, within the cylinder. To the centre of the upper disc is screwed a piece, B, to which the rack H is riveted. The piece B is pierced so as to put the interior of the cylinder into communication with the external air. This communication is closed by a valve /, held down by a delicate spring, r. When the piston is moved downward the air below the piston is compressed until it forces up / and escapes. The instant the action is reversed, the valve / falls, and is held down by the spring, and the pressure of the external air, which is thereby kept from coming in. The communication between the cylinder below Fig. 133. the piston and the receiver is opened and closed by the valve marked o in fig. 130, and sg in fig. 133. The rod sg 144 On Gases. [181- passing through the piston is held by friction, and is raised with it ; but is kept from being Hfted through more than a very small distance by the top of the cylinder, while the piston, in continuing its upward motion, slides over sg. When the piston descends it brings the valve with it, which at once cuts off the communication between the cylinder and the receiver. 182. Air pump g:augre. — When the pump has been worked sometime, the pressure in the receiver is indicated by the difference of level of the mercury in the two legs of a glass tube bent like a syphon, one of which is opened, and the other closed like the barometer. This little apparatus, which is called \};\& gauge, '\s fixed to an upright scale, and placed under a small bell jar, which communicates with the receiver E by a stop- cock, A, inserted in the tube leading from the orifice C to the cylinders, fig. 128. Before commencing to exhaust the air in the receiver, its elastic force exceeds the weight of the column of mercury, which is in the closed branch and which consequently remains full. But as the pump is worked, the elastic force soon diminishes, and is unable to support the weight of the mercury, which sinks and tends to stand at the same level in both legs. If an absolute vacuum could be produced, they would be exactly on the same level, for there would be no pressure either on the one side or the other. But with the very best machines the level is always about a thirtieth of an inch higher in the closed branch, which indicates that the vacuum is not absolute, for the elastic force of the residue is equal to the pressure of a column of mercury of that height. Practically the machine can never give an absolute vacuum, for, as we have seen, the air becomes ultimately so rarefied that, when the pistons are at the bottom of the cylinder, its elastic force cannot overcome the pressure on the valves in the inside of the piston, which, therefore, do not open. Theoretically an absolute vacuum is also impossible ; for, since the volume of each cylinder is, say, ^^ that of the receiver, only ^j of the air in the receiver is extracted at each stroke of the piston, and consequently it is impossible to exhaust all the air which it contains. The theoretical degree of exhaustion after a given number of strokes is easily calculated as follows : — Let A denote the volume of the receiver, including in that term the pipe ; B the volume of the cylinder between the highest and lowest positions of the piston ; and assume for the sake of distinctness that there is only one cyhnder ; then the air which occupied A before the piston is lifted occupies A + B after it is lifted, and consequently if D , is the density at the end of the first stroke and D the original density, we must have ' A + B If Dg is the density at the end of the second stroke, we have for just the same reason ' 'A+B Va+B/ -183] Air Pump. 145 Now this reasoning will apply to 71 strokes ; consequently D„ = D ( — : — ) . If there are two equal cylinders, the same formula holds, but in this case, in counting 71, upstrokes and downstrokes equally reckon as one. It is obvious that the exhaustion is never complete, since D„ can be zero only when 71 is infinite. However, no very great number of strokes is required to render the exhaustion virtually complete even if A is several times greater than B. Thus if A = 10 B, a hundred strokes will reduce the density from D to 0-0004 D ; that is, if the initial pressure is 30 in., the pressure at the end of 100 strokes is 0*012 of an inch. . Practically, however, a limit is placed on the rarefaction that can be produced by any given air pump ; for, as we have seen, the air becomes ultimately so rarefied that, when the pistons are at the bottom of the cylinder, its elastic force cannot overcome the pressure on the valves in the inside of the piston ; they therefore do not open, and there is no further action of the pump. 183. Boubly-exhaustingr stopcock. — M. Babinet has invented an im- proved stopcock, by which the exhaustion of the air can be carried to a very high degree. This stopcock is placed in the fork of the pipe leading from the receiver to the two cylinders ; it is perforated by several channels, which are successively used by turning it into two different positions. Fig. 129 represents a horizontal section of the stop- cock R, in such a position that, by its central opening and two lateral openings, it forms a communication between the orifice K of the plate, and the two valves o and s. The machine then works as has been described. In fig. 132 the stopcock has been turned a quarter, and the transversal channel db, which was horizontal in fig. 129, is now vertical, and its extremities are closed by the side of the hole in which the stopcock works. But a second channel, which was closed before, and which has taken the place of the first, now places the right cylinder alo7ie in communication with the receiver by the channel cbs (fig. 132), and it further connects the right with the left cylinder by a channel aeo (fig. 132), or aico (fig. 131). This channel passes from a central opening a, placed at the base of the right cylinder, across the stopcock to the valve ^, of the other cylinder, as represented in figs. 131 and 132 : but this channel is closed by the stopcock when it is in its first position, as is seen in figs. 129 and 130. The right piston in rising exhausts the air of the receiver, but when it descends the exhausted air is driven into the left cylinder through the orifice a, the channel io^ and the valve o (fig. 131), which is open. When the same piston rises, that of the left sinks ; but the air which is above it does not return into the right cylinder, because the valve o is now closed. As the right cylinder continues to exhaust the air in the re- ceiver, and to force it into the left cylinder, the air accumulates here, and ultimately acquires sufficient tension to raise the valve of the piston Q, which was impossible before the stopcock was turned, for it is only when the valves in the piston no longer open, that a quarter of a turn is given to the stopcock. 146 On Gases. [184- 184. Siancbi's air pump. — M. Bianchi has invented an air pump which has several advantages. It is made entirely of iron, and it has only one cylinder, which oscillates on a horizontal axis fixed at its base, as seen in fig. 1 34. A horizontal shaft, with heavy fly-wheel, V, works in a frame, and is turned by a handle, M. A crank, m, which is joined to the top of the piston-rod, is fixed to the same shaft, and consequently at every revolution of the wheel the cyHnder makes two oscillations. Fig- 134- In some cases, as in that shown in the figure, the crank and the fly- wheel are on parallel axes connected by a pair of cog-wheels. The modi- fication in the action produced by this arrangement is as follows : — If the cog-wheel on the former axis has twice as many teeth as that on the latter axis, the pressure which raises the piston is doubled ; an advantage which is counterbalanced by the inconvenience that now the piston will make one oscillation for one revolution of the fly-wheel. -185] Air Pump. U7 The machine is double acting ; that is the piston PP (fig. 135) pro- duces a vacuum both in ascending and descending. This is effected by the following arrangements : — In the piston there is a valve, b, opening upwards as in the ordinary machine. The piston rod AA is hollow, and in the inside there is a copper tube, X, by which the air makes its escape through the valve b. At the top of the cylinder there is a second valve a, opening upwards. An iron rod, D, works with gentle friction in the piston, and terminates at its ends in two conical valves, s and s\ which fit into the openings of the tube BC leading to the receiver. Let us suppose the piston descends. The valve s' is then closed, and the valve s being open, the air of the receiver passes in the space above the piston, while the air in the space below the piston undergoes com- pression, and raising the valve, escapes by the tube X, which commu- nicates with the atmosphere. When the piston ascends, the exhaustion takes place through s', and the valve s being closed, the com- pressed air escapes by the valves. The machine has a stopcock for double exhaustion, similar to that already described (183). It is also oiled in an ingenious manner. A cup, E, round the rod is filled with oil, which passes into the annular space between the rod AA and the tube X ; it passes then into a tube 00, in the piston, and forced by the atmospheric pressure, is uniformly distributed en the sur- face of the piston. The apparatus is of iron, and can consequently be made of much greater dimensions than the ordinary machine. A va- cuum can also be produced with it in far less time and in appa- ratus of greater size than usual. 185. Sprengrel's air pump. — Sprengel has devised a form of air pump which depends on the principle of converting the space to be exhausted into a Torri- cellian vacuum. The idea and construction of the apparatus are thus described by the inventor. If an aperture be made in the top of a barometer tube, the mercury sinks and draws in air ; if the experiment be so arranged as to allow air to enter along with mercury 148 On Gases. [185- and if the supply of air be limited while that of mercury is unlimited, the air will be carried away, and a vacuum produced. The following is the simplest form of the apparatus in which this action is realised. In fig. 136 cd\s a glass tube longer .than a barometer, open at both ends, and connected by means of india-rubber tubing with a funnel, A, filled with mercury and supported by a stand. Mercury is allowed to fall in this tube at a rate regulated by a clamp at c ; the lower end of the tube cd fits in the flask B, which has a spout at the side a little higher than the lower end of cd ; the upper part has a branch at x to which a receiver R can be tightly fixed. When the clamp at c is opened, the first portion of mercury which runs out closes the tube and prevents air from en- tering below. As the mercury is allowed to run down, the exhaus- tion begins, and the whole length of the tube from x to d \s filled with cylinders of air and mercury having a downward motion. Air and mercury escape through the spout of the bulb B which is above the basin A, where the mercury is collected. It is poured back from time to time into the funnel A, to be repassed through the tube until the exhaustion is complete. As this point is approached, the en- closed air between the mercury cylinders is seen to diminish, until the lower part of cd forms a con- tinuous column of mercury about 30 inches high. Towards this stage of the process a noise is heard like that of a water hammer when shaken ; the operation is com- pleted when the column of mercury encloses no air, and a drop of mer- cury falls on the top of the column without enclosing the slightest air bubble. The height of the column then represents the height of the column of mercury in the baro- meter ; in other words it is a baro- meter whose Torricellian vacuum is the receiver R. This apparatus has been used with great success in experiments in which a very complete exhaustion is required, as in the preparation of Geissler's It may be advantageously combined Fig. 136 tubes. (See Book X. Chapter VI.) with an exhausting syringe which first removes the greater part of the air, the exhaustion being then completed as above. -187] M or r en's Mercury Pump. 149 186. Aspirating- actions of currents of air. — When a jet of liquid or of a gas passes through air it carries the surrounding air along with it ; fresh air rushes in to supply its place, comes also in contact with the jet, and is in like manner carried away. Thus then there is a continual rarefac- tion of the air around the jet, in consequence of which it exerts an aspiratory action. This phenomenon may be well illustrated by means of an apparatus represented in fig. 137, the analogy of which to the experiment described (203) will be at once evident. It consists of a wide glass tube in the two ends of | ^-^-^^^^_ ^^ which are fitted two small tubes ab and c ! g ;^£^g^^l^ -b_ cd\ in the bottom is a manometer tube '^ ^^U^^^^^briH^^M containing a coloured liquid. On blowing ^ through the narrow tube the liquid at A ^^hw^^^^ is seen to rise. If on the contrary the 1 wide tube be blown into, a depression is ^ i^^p To this class of phenomena belongs ^^ the following experiment, which is a simple Pig j-^^ modification by Faraday of one originally described by Clement and Desormes. Holding one hand horizontal, the palm downwards and the fingers closed you blow through the space be- tween the index and middle finger. If a piece of light paper of 2 or 3 square inches, is held against the aperture it does not fall as long as the blowing continues. The old water bellows still used in mountainous places where there is a continuous fall, is a further application of the principle. Water falling from a reservoir down a narrow tube divides and carries air along with it ; and if there are apertures in the side through which air can enter, this also is carried along, and becomes accumulated in a reservoir placed below from which by means of a lateral tube it can be directed into the hearth of a forge. By the locomotive stea7npip3 a jet of steam entering the chimney of the locomotive carries the air away, so that fresh air must arrive through the fire and thus the draught be kept up. In Giffard's injector water is pumped by means of a jet of steam into the boiler of a steam engine. 187. Morren's mercury pump. — Figs. 138 and 139 represent a mercu- rial air pump, which is an improvement by Alvergniat, of a form devised by Morren. It consists of two reservoirs, A and B, figs. 138 and 1 39, connected by a barometer tube T, and a long caoutchouc tube C. The reservoir B and the tube T are fixed to a vertical support A, which is movable and open, and can be alternately raised and lowered through a distance of nearly four feet. This is effected by means of a long wire rope, which is fixed at one end to the reservoir A, and passes over two pulleys, a and b, the latter of which is turned by a handle. Above the reservoir B is a three-way cock ;/ ; to this is attached a tube ^ over H — /z', that is to say, to h + h'. _ In the suction and force pump it is readily seen that the pressure which the piston supports is also equal to the weight of a column of water, the base of which is the section of the piston, and the height that to which the water is raised. 198, Fire engrine. — The fire engine is a force pump in which a steady jet is obtained by the aid of an air chamber, and also by two pumps working alternately (fig. 1 53). The two pumps in and n, worked by the same lever PO, are immersed in a tank, and which is kept filled with water as long as the pump works. From the arrangement of the valves it will be seen, that when one pump n draws water from the tank, the other Fig. 153- m forces it into the air chamber R ; whence, by an orifice Z, it passes into the delivery tube, by which it can be sent in any direction. Without the air chamber the jet would be intermittent. For as the velocity of water on entering the reservoir is less than on emerging, the level of the water rises above the orifice Z, compressing the air which fills the reservoir. Hence, whenever the pistons stop, the air thus compressed reacting on the liquid forces it out during its momentary stoppage, and thus keeps up a constant flow. 199. Velocity of efflux. Torricelli's theorem. — Let us imagine an aperture made in the bottom of any vessel, and consider the case of a particle of liquid on the surface, without reference to those which are beneath. If this particle fell freely, it would have a velocity on reaching i6o On Gases. [199 the orifice equal to that of any other body falling through the distance between the level of the liquid and the orifice. This, from the laws of falling bodies, is s/2gh, in which g is the accelerating force of gravity, and // the height. If the liquid be maintained at the same level, for instance, by a stream of water running into the vessel sufficient to replace what has escaped, the particles will follow one another with the same velocity, and will issue in the form of a stream. Since pressure is transmitted equally in all directions, a Hquid would issue from an orifice in the side with the same velocity provided the depth were the same. The law of the velocity of efflux was discovered by Torricelli. It may be enunciated as follows : The velocity of efflux is the velocity which a freely falling body would have on reachi?ig the orifice after having started from a state of rest at the surface. It is algebraically expressed by the formula v = ^/7.gh. It follows directly from this law, that the velocity of efflux depends on the depth of the orifice below the surface, and not on the nature of the liquid. Through orifices of equal size and of the same depth, water and mercury would issue with the same velocity, for although the density of the latter liquid is greater, the weight of the column, and consequently the pressure, is greater too. It follows further that the velocities of efflux are directly proportional to the square roots of the depths of the orifices. Water would issue from an orifice coo inches below the surface with ten times the velocity with which it would issue from one an inch below the surface. The quantities of water which issue from orifices of different areas are very nearly proportional to the size of the orifice, provided the level remains constant. 200. Direction of the jet from lateral orifices. — From the principle of the equal transmission of pressure, water issues from an orifice in the side of a vessel with the same velocity as from an aperture in the bottom of a vessel at the same depth. Each particle of a jet issuing from the side of a vessel begins to move horizontally with the velocity above mentioned, but it is at once drawn downward by the force of gravity, in the same manner as a bullet fired from a gun, with its axis horizontal. 'It is well known that the bullet describes a para- bola with a vertical axis, the vertex being the muzzle of the gun. Now since each particle of the jet moves in the same curve, the jet itself takes the parabolic form, as shown in fig. 154. Fig. 154. It may be remarked, that in every parabola there is a certain point called the focus, and that the distance from the vertex to the focus fixes the magnitude of a parabola in much the same manner as the -203] Quantity of Efflux. i6i distance from the centre to the circumference fixes the magnitude of a circle. Now it is easily capable of proof that the focus is as much below, as the surface of the water is above, the orifice. Accordingly, the jets~~^ formed by water coming from orifices at different depths below . the surface take different forms, as shown in fig. 1 54. 201. Heigrtit of tlie jet. — If a jet issuing from an orifice in a vertical direction has the same velocity as a body would have which fell from the surface of the liquid to that orifice, the jet ought to rise to the level of the liquid. It does not, however, reach this ; for the particles which fall hinder it. But by inclining the jet at a small angle with the vertical, it reaches about j^ths of the theoretical height, the difference being due to friction and to the resistance of the air. By experiments of this nature the truth of Torricelli's law has been demonstrated. 202. Quantity of efflux. Vena contracta. — If we suppose the sides of a vessel containing water to be thin, and the orifice to be a small circle whose area is A, we might think that the quantity of water E discharged in a second would be given by the expression A^2gh, since each particle has, on the average, a velocity equal to V2ghj and particles issue from each point of the orifice. But this is by no means the case. This may be explained by reference to fig. 155, in which AB represents an orifice in the bottom of a vessel — what is true in this case being equally true of an orifice in the side of the vessel. Every particle above AB endeavours to pass out of the vessel, and in so doing exerts a pressure on those near it. Those that issue near A and B exert pressures in the directions MM and NN ; those near the centre of the orifice in the direction RQ, those in the intermediate parts in the directions PQ, PQ. In consequence, the water within the space PQP is unable to escape, and that which does escape, instead of assuming a cylindrical form, at first contracts, and takes the form of a truncated cone. It is found that the escaping jet con- tinues to contract, until at a distance from the orifice about equal to the diameter of the orifice. This part of the jet is called the vena contracta. It is found that the area of its smallest section is abotit | or 0*62 of that of the orifice. Accordingly, the true value of the efflux per second is given approximately by the formula ^^ ^ ■? n E = o-62AV^, ==V\j^#== or the actual value of E is about 0"62 of its theoretical a??io7int. 203. Influence of tubes on the quantity of efflux. — ^ , The result given in the last article has reference to an { aperture in a thin wall. If a cylindrical or conical efflux- | tube or ajutage is fitted to the aperture, the amount of Y\g. 155. the efflux is considerably increased, and in some cases falls but a little short of its theoretical amount. A short cylindrical ajutage, whose length is from two to three times its diameter, has been found to increase the efflux per second to about O'ZiKsJ^gh. In this case, the water on entering the ajutage forms a con- tracted vein (fig. 157), just as it would do on issuing freely into the air ; 62 On Gases. [203- Fig. 156. but afterwards it expands, and, in consequence of the adhesion of the water to the interior surface of the tube, has, on leaving the ajutage, a section greater than that of the contracted vein. The contraction of the jet within the ajutage causes a partial vacuum. If an aperture is made in the ajutage, near the point of greatest con- traction, and fitted with a vertical tube, the, other end of which dips into water (fig. 156), it is found that water rises in the vertical tube, thereby proving the formation of a partial vacuum. If the ajutage has the form of a conic frustrum whose larger end is at the aperture, if the dimensions are properly chosen, the efflux in a second may be raised to o-()2 A ^2gh. If the smaller end of a frustrum of a cone of suitable dimensions be fitted to the orifice, the efflux may be still further increased, and fall very little short of the theoretical amount. When the adjutage has more than a certain length, a considerable diminution takes place in the amount of the efflux : for example, if its length is 48 times its diameter, the efflux is reduced to 0-62, A ^2gk. This arises from the fact, that, when water passes along cylindrical tubes, the resistance increases with the length. The resistance which gives rise to this result is called hydraulic frictio7i ; it is independent of the material of the tube, provided it be not roughened ; but depends in a considerable degree on the viscosity of the liquid ; for instance, ice-cold water experiences a greater resistance than lukewarm water. The velocity of efflux through capillary ajutages have been found by Poiseuille to be proportioned to the heights and not to the square roots, a striking exception from Torricelli's theorem. 204. Form of the jet. — After the contracted vein, the jet has the form of a solid rod for a short distance, but then begins to separate into drops which present a peculiar appearance. They seem to form a series of ventral and nodal segments (fig. 157). The ventral segments consist of drops extended in a horizontal direction, and the nodal segments in a longitudinal direction. And as the ventral and nodal segments have re- spectively a fixed position, each drop must alternately become elongated and flattened while it is falling (fig. 158). Between any two drops there are smaller ones, so that the whole jet has a tube-like appearance. If the aperture is not circular the form of the jet undergoes curious changes. 205. Hydraulic tourniquet. — If water be contained in a vessel, and an aperture made in one of the sides, the pressure at this point is removed, for it is expended in forcing out the water ; but it remains on the other side ; and if the vessel were moveable in a horizontal direction, it would move in a direction opposite that of the issuing jet. This is illustrated by the apparatus known as the hydraulic iourniquetj or Barker's inill{^%. 159). 206] Hydraulic Tourniquet. 163 It consists of a glass vessel, M, containing water, and capable of moving about its vertical axis. At the lower part there is a tube, C, bent horizon- tally in opposite directions at the two ends. If the vessel were full of water and the tubes closed, the pressures on the sides of C would balance each other, being equal and acting in contrary directions ; but, being open, the water runs out, the pressure is not exerted on the open part, but only on the opposite side, as shown in the figure A. And this pressure, not 'I 7;^ ''0: I Fig- 157- Fig. 158. being neutralised by an opposite pressure, imparts a rotatory motion in the direction of the arrow, the velocity of which increases with the height of the liquid and the size of the aperture. The same principle may-be illustrated by the following experiment. A tall cylinder containing water and provided with a lateral stopcock near the bottom is placed on a light shallow dish on water, so that it easily floats. On opening the stopcock so as to allow water to flow out, the vessel is observed to move in a direction diametrically opposite to that in which the water is issuing. Segner's water-wheel and the reaction machine depend on this prin- ciple. Rotating fireworks also act on the same principle ; that is, an unbalanced reaction from the heated gases which issue from openings in them gives them motion in the opposite direction. 206. IVater-wlieels. Turbines. — When water is continuously flowing from a higher to a lower level, it may be used as a motive power. This is effected by means of water-wheels ; that is, wheels provided with buckets or float-boards at the circumference, and on which the water acts either by pressure or by impact. 164 On Gases. [206- Water-wheels turn in a vertical plane round a horizontal axis, and are of two principal kinds, 7indershot and overshot. In undershot wheels the float-boards are at right angles to the circum- ference of the wheel. The lowest float-boards are immersed in the water, which flows with a velocity depending on the height of the fall. Such wheels are applicable where the quantity of water is great, but the fall in- considerable. Overshot wheels are used with a small quantity of water which has a high fall, as with small mountain streams. On the circumference of the wheel there are buckets of a peculiar shape. The water falls into the buckets on the upper part of the wheel, which is thus moved by the weight of the water, and as each bucket arrives at the lowest point of re- volution it discharges all the water, and ascends empty. The turbine is a horizontal water-wheel, and is similar in principle to the hydraulic tourniquet. But instead of the horizontal tubes there is a horizontal drum, containing curved vertical walls ; the water, in issuing from the turbine, pressing against these walls, exerts a reaction, and turns the whole wheel about a vertical axis. Turbines have the advantage of being of small bulk for their power, and equally efficient for the highest and the lowest falls. 207. mxariotte's bottle, its use. — Mariotte's bottle presents many curious effects of the pressure of the atmosphere, and furnishes a means of obtaining a constant flow of water. It consists of a large narrow- mouthed bottle, in the neck of which there is a tightly-fitting cork (fig. 160). Through this a tube passes open at both ends. In the sides of the bottle there are three tubulures, each with a narrow orifice, and which can be closed at will. The bottle and the tube being quite filled with water, let us consider what will be the effect of opening successively one of the tubu- lures, a. b, and c, supposing, as represented in the figure, that the lower extremity of ^ is be- tween the tubulures b and c. i. If the tubulure b is open the water flows out, and the surface sinks in the tube g until it is on the same level as b, when the flow stops. This flow arises from the excess of pressure at the point e over that at b. The pressure at e is the same as the pressure of the atmosphere. But when once the level is the same at b and at e, the efflux ceases, for the atmospheric pressure on all points of the same horizontal layer, be, is the same (95). ii. If now the tubulure b is closed, and a opened, no efflux takes place ; on the contrary, air enters by the orifice a, and water ascends in the tube g, as high as the layer ad, and then equilibrium is established. iii. If the orifices a and b are closed, and c opened, an efflux having constant velocity takes place, as long as the level of the water is not -207] Mariotte's Bottle. 165 below the open end, /, of the tube. Air enters bubble by bubble at /, and takes the place of the water which has flowed out. In order to show that the efflux at the orifice c is constant, it is neces^ sary to demonstrate that the pressure on the horizontal layer ch is always equal to that of the atmosphere in addition to the pressure of the column ///. Now suppose that the level of the water has sunk to the layer ad The air which has penetrated into the flask supports a pressure equal to that of the atmosphere diminished by that of the column of liquid /;;, or H — /«. In virtue of its elasticity this pressure is transmitted to the layer ch. But this layer further supports the weight of a column of water, /;;/, so that the pressure at rn is really /w + H — /«, or H -h w;/, that is to say, H + hi. In the same manner it may be shown that this pressure is the same when the level sinks to b, and so on as long as the level is higher than the aperture /. The pressure on the layer ch is therefore constant, and consequently the velocity of the efflux. But when once the level is below the point /, the pressure decreases, and with it the velocity. To obtain a constant flow by means of Mariotte's bottle, it is filled with water, and the orifice which is below the tube / is opened. The rapidity of the flow is proportional to the square root of the height hi. 1 66 ' Acoustics, [208 4 BOOK V. ACOUSTICS. CHAPTER I. PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND. 2o3. Object of acoustics. — The study of sounds, and that of the vibrations of elastic bodies, form the object of acoustics. Music considers sounds with reference to the pleasurable feelings they are calculated to excite. Acoustics is concerned with the questions of the production, transmission, and comparison of sounds ; to which may be added, the physiological question of the perception of sounds. 209. Sound and noise. — Sound is a peculiar sensation excited in the organ of hearing by the vibratory motion of bodies, when this motion is transmitted to the ear through an elastic medium. All sounds are not identical ; they present differences by which they may be distinguished, compared, and their relations determined. Sounds are distinguished from noises. Sound properly so called, or musical sound, is that which produces a continuous sensation, and the musical value of which can be determined : while noise is either a sound of too short a duration to be determined, like the report of a cannon, or else it is a confused mixture of many discordant sounds, like the rolling of thunder or the noise of the waves. Nevertheless, the difference be- tween sound and noise is by no means precise ; Savart has shown that there are relations of height in the case of noise, as well as in that of sound ; and there are said to be certain ears sufficiently well organised to determine the musical value of the sound produced by a carriage rolling on the pavement. 210. Cause of sound. — Sound is always the result of rapid oscillations imparted to the molecules of elastic bodies, when the state of equilibrium of these bodies has been disturbed either by a shock or by friction. Such bodies tend to regain their first position of equilibrium, but only reach it after performing, on each side of that position, very rapid vibratory move- ments, the amplitude of which quickly decreases. A body which produces a sound is called a sonorous body. As under- stood in England and Germany, a vibration comprises a motion to and fro ; in France, on the contrary, a vibration means a movement to or fro. The French vibrations are with us semi-vibrations, an oscillation or vi- -213] Propagation of Sound. 167 bration is the movement of the vibrating molecule in only one direction : a double or complete vibration comprises the oscillation both backwards and forwards. Vibrations are very readily observed. If a light powder is sprinkled on a body which is in the act of yielding a musical sound, a bell jar held horizontally in the hand, for example, a rapid motion is imparted to the powder which renders visible the vibrations of the body ; and in the same manner, if a stretched cord be smartly pulled and let go its vibrations are apparent to the eye. 211. Sounds not propagrated in vacuo.— The vibrations of elastic bodies can only produce the sensation of sound in us by the intervention of a medium interposed between the ear and the sonorous body, and vibrating with it. This medium is usually the air, but all gases, vapours, liquids, and solids also transmit sounds. The following experiment shows that the presence of a ponderable medium is necessary for the propagation of sound. A small metallic bell, which is continually struck by a small hammer by means of clockwork, or an ordinary musical box, is placed under the receiver of the air-pump (fig. 161). As long as the receiver is full of air at the ordinary pressure, the sound is trans- mitted, but in proportion as the air is exhausted the sound becomes feebler, and is imperceptible in a vacuum. To ensure the success of the experi- ment, the bellwork or musical box must be placed on wadding ; for otherwise the vibrations would be transmitted to the air through the plate of the machine. 212. Sound is propagrated in all elastic bodies. — If, in the above experi- ment, after the vacuum has been made, any vapour or gas be admitted, the sound of the bell will be heard, showing that sound is propagated in this medium as in air. Sound is also propagated, in liquids. When two bodies strike against each other under water, the shock is distinctly heard. And a diver at the bottom of the water can hear the sound of voices on the bank. The conductibility of solids is such, that the faint scratching of a pen at the end of a long piece of wood is heard at the other end. The earth conducts sound so well, that at night, when the ear is applied to the ground, the steps of horses or any other noise at great distances is heard. 213. Propagration of sound in the air. — In order to simplify the theory of the propagation of sound in the air, we shall first consider the case in which it is propagated in a cylindrical tube of indefinite length. Let MN, fig. 162, be a tube filled with air at a constant pressure and temperature, and let P be a piston oscillating rapidly from A to a. When Fig. 161. 1 68 Acoustics. [213- the piston passes from A to ^ it compresses the air in the tube. But in consequence of the great compressibiHty, the condensation of the air does Fig. 162. not take place at once throughout the whole length of the tube, but solely within a certain length, aW, which is called the condensed wave. If the tube MN be supposed to be divided into lengths equal to «H, and each of these lengths divided into layers parallel to the piston, it may be shown by calculation, that when the first layer of the wave d\i\. comes to rest, the motion is communicated to the first layer of the second wave HH', and so on from layer to layer in all parts of H'H'^, WW. The condensed wave advances in the tube, each of its parts having successively the same degree of velocity and condensation. When the piston returns in the direction ^A, a vacuum is produced behind it, which causes an expansion of the air in contact with its pos- terior face. The next layer expanding in turn brings the first to its original state of condensation, and so on from layer to layer. Thus when the piston has returned to A, an expatided wave is produced of the same length as the condensed wave, and directly following it in the tube where they are propagated together, the corresponding layers of the two waves possessing equal and contrary velocities. The whole of a condensed and expanded wave forms an undulation; that is, an undulation comprehends that part of the column of air affected during the backward and forward motion of the piston. The length of an undulation is the space which sound traverses during a complete vi- bration of the body which produces it. This length is less in proportion as the vibrations are more rapid. It is important to remark that if we consider a single row of particles, which when at rest occupy a line parallel to the axis of the cylinder, for instance, those along AH^' (fig. 162), we shall find they will have respec- tively at the same instant all the various velocities which the piston has had successively while oscillating from Kio a and back to A. So that if in fig. 26 AH' represents the length of one undulation, the curved line H'PQA will represent the various velocities which all the points in the line AH' have simultaneoiisly : for instance, at the instant the piston has returned to A, the particle at M will be moving to the right with a velo- city represented by QM, the particle at N will be moving to the left with a velocity represented by PN, and so on of the other particles. When an undulatory motion is transmitted through a medium, the motions of any two particles are said to be in the same phase when those particles move with equal velocities in the same direction ; the motions are said to be in opposite phases when the particles move with the same velocities in opposite directions. It is plain, from an inspection of fig. 26, -214] Intensity of Sound. 1 69 that when any two particles are separated by a distance equal to half an undulation, their motions are always in opposite phases, but if their dis- tance equals the length of a complete undulation their motions are in the same phase. A little consideration will show that in the conde^ised wave the con- densation will be greatest at the middle of the wave, and likewise that the expanded wave will be most rarefied at its middle. It is an easy transition from the theory of the motion of sonorous waves in a cylinder to that of their motion in an unenclosed medium. It is simply necessary to apply, in all directions, to each molecule of the vibrating body, what has been said about a piston movable in a tube. A series of spherical waves alternately condensed and rarefied is pro- duced around each centre of disturbance. As these waves are contained within two concentrical spherical surfaces, whose radii gradually increase, while the length of the undulation remains the same, their mass increases with the distance from the centre of disturbance, so that the amplitude of the vibration of the molecules gradually lessens, and the intensity of the sound diminishes. It is these spherical waves, alternately condensed and expanded, which in being propagated transmit sound. If many points are disturbed at the same time, a system of waves is produced around each point. But all these waves are transmitted one through the other without modifying either their lengths or their velocities. Sometimes condensed or expanded waves coincide with others of the same nature to produce an effect equal to their sum ; sometimes they meet and produce an effect equal to their difference. If the- surface of still water be disturbed at two or more points, the co;^e^istence of waves becomes sensible to the eye. 214. Catdises wbicli influence the intensity of sound.. — Many causes modify t^ force or the ititeiisity of the sound. These are, the distance of the>^norous body, the amplitude of the vibrations, the density of the air aj/'the place where the sound is produced, the direction of the currents of air, and, lastly, the neighbourhood of other sonorous bodies. i. The intensity of sound is inversely as. the square of the distance of the sonorotis body from the ear. This law has been deduced by calculation, bat it may be also demonstrated experimentally. Let us suppose several sounds of equal intensity — for instance, bells of the same kind, struck by hammers of the same weight, falling from equal heights. If four of these bells are placed at a distance of 20 yardls from the ear, and one at a distance of 10 yards, it is fau,n,d that the single bell produces/a sound of the same intensity as the four bjells struck simultaneoiisly. Coj|lsequently, for'.double the distance the- intengity of the sound is only one /ourth. l^he distance at which sounds can be heard depends on thfeir intensity. The f-eport of a volcano at St. Vincent was heard at Demerfira, 300 miles off, an'd the firing at Waterloo was heard at Dover. ii. The ititensity of the sound increases with the amplitude of the vibra- tions of the sonorous body. The connection between the intensity of the sound and the amplitude of the vibrations is readily observed by means of vibrating cords. For if the cords are^ somewhat long, the oscillations are I 170 Acoustics. [214- perceptible to the eye, and it is seen that the sound is feebler in propor- tion as the amphtude of the oscillations decreases. iii. The intensity of soimd depends on tJie density of the air in the place in which it is prodicced. As we have already seen (202), when an alarum moved by clockwork is placed under the bell-jar of the air pump, the sound becomes weaker in proportion as the air is rarefied. In hydrogen, which is about j^th the density of air, sounds are much feebler, although the pressure is the same. In carbonic acid on the con- trary, whose density is 1*529, sounds are more intense. On high moun- tains, where the air is much rarefied, it is necessary to speak with some effort in order to be heard, and the discharge of a gun produces only a feeble sound. The ticking of a watch is heard in water at a distance of 23 feet, in oil of 161, in alcohol of 13, and in air of only 10 feet. iv. The ititensity of sound is modified by the motion of the atmosphere^ and the direction of the wind. In calm weather sound is always better propagated than when there is wind ;.in the latter case, for an equal dis- tance, sound is more intense in the direction of the wind than in the con- trary direction. V. Lastly, sound is strengthened by the proximity of a sojtorous body. A string made to vibrate in free air and not near a sounding body has but a very feeble sound ; but when it vibrates above a sounding-box, as in the case of the violin, guitar, or violoncello, its sound is much more intense. This arises from the fact that the box and the air which it con- tains vibrate in unison with the strjxig:. — Hen^g^e use of sounding-boxes in stringed instruments. Fig. 163. 215. Apparatd^o streng-then sound. — The apparatus refffesented in fig. 163 was used by S^art to show the influence of boxesjil^trengthening sound. It consists of aSumnispherical brass vesspli ; . . . 1664 „ ,0^W -218] Velocity of Sound in Gases. 173 218. Formulae for calculating- tlie velocity- of sound in grases. — For calculating the velocity of sound in gases Newton gave a rule equiva- lent to the formula '-y e in which v represents the velocity of the sound or the distance it travels in a second, e the elasticity of the gas, and d its density. This formula expresses that the velocity of the propagation of sound in gases is directly as the square root of the elasticity of the gas, and in- versely as the square root of its density. It follows that the velocity of sound is the same under any pressure, for although the elasticity increases with greater pressure, the density increases in the same ratio. At Quito, where the mean pressure is only 21*8 inches, the velocity is the same as at the sea level, provided the temperature is the same. If g be the force of gravity, h the barometric height reduced to the temperature zero, and r the density of mercury, also at zero, then for a gas under the atmospheric pressure, and for zero, e =gho ; Newton's formula accordingly becomes / gh^ Now if we suppose the temperature of a gas to increase from 0° to /°, its volume will increase from unity at zero to i ■{■ at aX t, a being the coefficient of expansion of the gas. But the density varies inversely as the volume, therefore d becomes d-i-{i + at). Hence y^:^(.-'). The values of v, obtained by this formula, are less than the experimen- tal results. Laplace assigned as a reason for this discrepancy the heat produced by pressure in the condensed waves ; and, by considerations based on this idea, Poisson and Biot have found that Newton's formula ought to be written "^ = ^ ^-(i'^^^)-,; ^ being the specific heat of the gas for a constant pressure, and d its specific heat for a constant volume (see Book VI.). When thus modified the results calculated by the for- mula agree with the experimental results. The physical reason for introducing the constant -^ into the equation c for the velocity of sound may be understood from the following con- siderations. We have already seen that sound is propagated in air by a series of alternate condensations and rarefactions of the layers. At each condensation heat is evolved, and this heat increases the elasticity, and thus the rapidity, with which each condensed layer acts on the next; but, in the rarefaction of each layer, the same amount of heat disappears as was developed by the condensation, and its elasticity is diminished by the cooling. The effect of this diminished elasticity of the cooled layer is 1/4 Acoustics, [218- the same as if the elasticity of an adjacent wave had been increased, and the rapidity with which this latter would expand upon the dilated wave would be greater. Thus, while the average temperature of the air is unaltered, both the heating which increases the elasticity and the chilling which diminishes it concur in increasing velocity. Knowing the velocity of sound, we can calculate approximately the distance at which it is produced. Light travels with such velocity that the flash or the smoke accompanying the report of a gun may be con- sidered to be seen simultaneously with the explosion. Counting then the number of seconds which elapse between seeing the flash and hear- ing the sound, and multiplying this number by 1125, we get the distance in feet at which the gun is discharged. In the same way the distance of thunder may be estimated. 219. Velocity of sound in various grases. — Approximately the same results have been obtained for the velocity of sound in air, by another method by which the velocity in other gases could be determined. As the wave length ^, is the distance which sound travels during the time of one oscillation, that is n of a second, the velocity of sound or the distance traversed in a second is v = n\. Now the length of an open pipe is half the wave length of the fundamental note of that pipe ; and that of a closed pipe is a quarter of the wave length (259). Hence if we know the number of vibrations of the note emitted by any particular pipe, which can be easily ascertained by means of the syren, and we know the length of this pipe, we can calculate v. Taking the temperature into account, Wertheim found 1086 feet for the velocity of sound at zero. Further, since indifferent gases which have the same elasticity, but differ in density, the velocity of sound varies inversely as the square root of the density, knowing the velocity of sound in air, we may calculate it for other gases ; thus, in hydrogen it will be This number cannot be quite accurate, for the coefficient — differs somewhat in different gases. And when pipes were sounded with different gases, and the number of vibrations of the notes multiplied with twice the length of the pipe, numbers were obtained which differed from those calculated by the above formula. When, however, the calcu- lation was made, introducing for each gas the specia value of — , the theoretical results agreed very well with the observed ones. By the above method the following values have been obtained : — Carbonic acid 856 ft. in a second. Oxygen 1040 „ Air 1093 „ Carbonic oxide 1106 „ Hydrogen . 4163 „ -221] Velocity of Sound in Liquids and in Solids. 1 75 220. Boppler's principle. — When a sounding body approaches the ear, the tone perceived is somewhat higher than the true one ; but if the source of sound recedes from the ear, the tone perceived is lower. The truth of this, which is known as Dopplefs principle, will be apparent from the following considerations : — When the source of sound and the ear are at rest, the ear perceives n waves in a second ; but if the ear ap- proaches the sound, or vice versa, it perceives more ; just as a ship meets more waves when it ploughs through them than if it is at rest. Conversely, the ear receives a smaller number when it recedes from the source of sound. The effect in the first case is as if the sounding body emitted more vibrations in a second than it really does, and in the second case fewer. Hence in the first case the note appears higher ; in the second case lower. If the distance which the ear traverses in a second towards the source of sound (supposed to be stationary) is s feet, and the wave length of the particular tone is A feet, then there are — waves in a second ; or also — , . \ c for X = — , where c is the velocity of sound (216). Hence the ear receives not only the 11 original waves, but also in addition. Therefore the number of vibrations which the ear actually perceives is , US / J \ c c for an ear which approaches a tone ; and by similar reasoning it is , lis , s ^ n' = n — -^ - n (i — _) c c for an ear receding from a tone. To test Doppler's theory Buys Ballot stationed trumpeters on the Utrecht railway, and also upon locomotives, and had the height of the approaching or receding tones compared with stationary ones by musicians. He thus found both the principle and the formula fully confirmed. 221. Velocity of sound in liquids and in solids.— The velocity of sound in water was investigated in 1827 by Colladon and Sturm. They moored two boats at a known distance in the lake of Geneva. The first supported a bell immersed in water, and a bent lever provided at one end with a hammer which struck the bell, and at the other with a lighted wick, ' so arranged that it ignited some powder the moment the hammer struck the bell. To the second boat was affixed an ear-trumpet, the bell of which was in water, while the mouth was applied to the ear of the observer, so that he could measure the time between the flash of light and the arrival of sound by the water. By this method the velocity was found to be 4708 feet in a second at the temperature 8'i°, or four times as great as in air. The velocity of sound, which is different in different liquids, can be calculated by a formula analogous to that given above (219) as applicable 176 Acoustics. [221- to gases. In this way are obtained the number given in the following table. As in the case of gases, the velocity varies with the temperature, which is therefore appended in each case : — River water (Seine) . '. . I3°C. = 4714 ft. in a second J» J5 5> • • • 30 = 5013 Artificial sea-water . 20 = 4761 Solution of common salt . 18 = 5132 „ „ chloride of calcium . 23 - 6493 Absolute alcohol . . 23 = 3804 Turpentine . . . > . 24 = 3976 Ether = 3801 As a general rule, this elasticity of solids, as compared with the density, is greater than that of liquids, and consequently the propagation of sound is more rapid. The difference is well seen in an experiment by M. Biot, who found that when a bell was struck by a hammer, at one end of an iron tube 3 1 20 feet long, two sounds were distinctly heard at the other end. The first of these was transmitted by the tube itself with a velocity x\ and the second by the enclosed air with a known velocity a. The interval between the sounds was 2-5 seconds. The value of :r, obtained from the equation 3I20 _3I20_ u X shows that the velocity of sound in the tube is about 9 times as great as that in air. To this class of phenomena belongs the fact that if the ear is held against a rock in which a blasting is being made at a distance, two distinct reports are heard, one transmitted through the rock to the ear, and the other transmitted through the air. The velocity of sound in other solids has also been determined theo- retically by Wertheim, by means of their coefficient of elasticity. The following table gives the velocity, expressed in feet per second : — Lead . . . ' . Gold .... Silver. Copper Steel wire . Iron .... The velocity in the direction of the fibres was greater than across them. A direct method of determining the velocity of sound in solids, gases, and vapours will be described further on. 222. Reflection of sound.— So long as sonorous waves are not ob- structed in their motion, they are propagated in the form of concentric spheres ; but, when they meet with an obstacle, they follow the general law of elastic bodies , that is, they return upon themselves, forming new concentric waves, which seem to emanate from a second centre on the 4030 Pine . 1 0900 5717 Oak . . 12622 8553 Ash . . 13314 1 1666 . Elm . . 13516 15470 Fir . . 15218 16822 Aspen . . 16677 223] Echoes and Resonances. 177 other side of the obstacle. This phenomenon constitutes the reflection of sound. Fig. 164 represents a series of incident waves reflected from an ob- stacle, PQ. Taking, forexample, the incident wave MCDN, emitted from the centre A, the corresponding reflected wave is represented by the arc, CKD, of a circle, whose centre a is as far beyond the obstacle PQ as A is before it. If any point, C, of the reflecting surface be joined to the sonorous centre, and if the perpendicular CH be let fall on the surface of this body, the angle ACH is called the ajigle of incidence, and the angle BCH, formed by the prolongation of ^C is the angle of rejiection. The reflection of sound is subject to the two following laws : — I. The angle of reflection is equal to the afigle of incidence. II. The incident sonorous ray and the reflected ray are i7i the same plave perpendicular to the reflecting surface. From these laws it follows that the wave which in the figure is pro- pagated in the direction AC, takes the direction CB after reflection, so that an observer placed at B hears, besides the sound proceeding from the point A, a second sound, which appears to come from C. The laws of the reflection of sound are the same as those for light and radiant heat, and may be demonstrated by similar experiments. One of the simplest of these is made with conjugate mirrors (see chapter on Radiant Heat) ; if in the focus of one of these mirrors a watch is placed the ear placed in the focus of the second mirror hears the ticking very distinctly, even when the mirrors are at a distance of 12 or 13 yards. 223. Echoes and resonances. — An echo is the repetition of a sound in the air, caused by its reflection from some obstacle. A very sharp quick sound can produce an echo when the reflecting surface is 55 feet distant, but for articulate sounds at least double that distance is necessary, for it may be easily shown that no one can pro- nounce or hear distinctly more than five syllables in a second. Now, as the velocity of sound at ordinary temperatures may be taken at 11 25 feet in a second, in a fifth of that time sound would travel 225 feet. If the I 3 178 Acoustics. [223- reflecting surface is 112*5 feet distant in going and returning, sound would travel through 225 feet. The time which elapses between the articu- lated and the reflected sound would, therefore, be a fifth of a secondj the two sounds would not interfere, and the reflected sound would be dis- tinctly heard. A person speaking with a loud voice in front of a reflector, at a distance of 112-5 f^^t» can only distinguish the last reflected syllable : such an echo is said to be monosyllabic. If the reflector were at a dis- tance of two or three times 112-5 ^^^^y the echo would be dissyllabic, trisyllabic, and so on. When the distance of the reflecting surface is less than 112-5 f^^^ ^^^ direct and the reflected sound are confounded. They cannot be heard separately but the sound is strengthened. This is what is called reso- naiice, and is often observed in large rooms. Bare walls are very reso- nant ; but tapestry and hangings, which are bad reflectors, deaden the sound- Multiple echoes are those which repeat the same sound several times : this is the case when two opposite surfaces (for example, two parallel walls) successively reflect sound. There are echoes which repeat the same sound 20 or 30 times. Ah echo in the chateau of Simonetta, in Italy, repeats a sound 30 times. At Woodstock there is one which repeats from 17 to 20 syllables. As the laws of reflection of sound are the same as those of light and heat, curved surfaces produce acoustic foci like the luminous and calorific foci produced by concave reflectors. If a person standing under the arch of a bridge speaks with his face turned towards one of the piers, the sound is reproduced near the other pier with such distinctness that a conversation can be kept up in a low tone, which is not heard by any one standing in the intermediate spaces. There is a square room with an elliptical ceiling, on the ground floor ot the Conservatoire des Arts et Metiers, in Paris, which presents this phenomenon in a remarkable degree when persons stand in the two foci of the ellipse. It is not merely by solid surfaces, such as walls, rocks, ship's sails, etc., that sound is reflected. It is also reflected by clouds, and it has even been shown by direct experiment that a sound in passing from a gaseous medium of one density into another is reflected at the surface as it would be against a sohd surface. Whispering galleries are formed of smooth walls having a continuous curved form. The mouth of the speaker is presented at one point, and the ear of the hearer at another and distant point. In this case, the sound is successively reflected from one point to the other until it reaches the ear. Different parts of the earth's surface are unequally heated by the sun, owing to the shadows of trees, evaporation of water, and other causes, so that in the atmosphere there are numerous ascending and descending currents of air of different density. Whenever a sonorous wave passes from a medium of one density into another it undergoes partial reflection,, which, though riot strong enough to form an echo, distinctly weakens HNEk -224] Refraction of Sound. 179 the direct sound. This is doubtless the reason, as Humboldt remarks, why sound travels further at night than at daytime ; even in the South American forests, where the animals, which are silent by day, fill the atmosphere in the night with thousands of confused sounds. It has generally been considered that fog in the atmosphere is a great deadener of sound, it being a mixture of air and globules, of water, at each of the innumerable surfaces of contact a portion of the vibration is lost. The evidence as to the influence of this property is conflicting ; recent researches of Tyndall show that a white fog, or snow, or hail, are not im- portant obstacles to the transmission of sound, but that aqueous vapour is. Experiments made on a large scale, in order to ascertain ' the best form of fog-signals, gave some remarkable results. On some days which optically were quite clear, certain sounds could not be heard at a distance far inferior to that at which they could be heard even during a thick haze. Tyndall ascribes this result to the presence in the atmosphere of aqueous vapour ; which forms in the air innumerable stride that do not interfere with its optical clearness, but render it acoustically turbid. These conclusions first drawn from observations have been verified by laboratory experiments. Tyndall has shown tliat a medium consisting of alternate layers of a light and heavy gas deadens sound, and also that a medium consisting of alternate strata of heated and ordinary air exerts a similar influence. The same is the case with an atmosphere containing the vapours of volatile liquids. So long as the continuity of air is pre- served, sound has great power of passing through the interstices of solids ; thus it will pass through twelve folds of a dry silk handkerchief, but is stopped by a single layer if it is wetted. 224. Refraction of sound. — It will be found in the sequel that refrac- tion is the change of direction which light and heat experience on passing from one medium to another, Sondhauss has found that sonorous waves are refracted like light and heat. He constructed gas lenses, by filHng spherical or lenticular collodion envelopes with carbonic acid. With envelopes of paper or of goldbeater's skin the refraction of sound is not perceptible. Sondhauss cut equal segments out of a large collodion balloon, and fastened them on the two sides of a sheet iron ring a foot in diameter, so as to form a hollow biconvex lens about 4 inches thick in the centre. This was filled with carbonic acid, and a watch was placed in the direc- tion of the axis : the point was then sought, on the other side of the lens at which the sound was most distinctly heard. It was found that when the ear was removed from the axis, the sound was scarcely perceptible ; but that at a certain point on the axial line it was very distinctly heard. Consequently, the sonorous waves in passing from the lens had converged towards the axis, their direction had been changed ; in other words, they had been refracted. The refraction of sound may be easily demonstrated by means of one of the very thin india-rubber balloons used as children's toys, inflated by i8o Acoustics. [224- carbonic acid. If the balloon be filled with hydrogen, no focus is detected ; it acts like a convex lens, and the divergence of the rays is increased instead of their being converged to the ear. 225. Speaking: trumpet. Ear trumpet. — These instruments are based both on the reflection of sound and on its conductibility in tubes. The speaking trumpet, as its name implies, is used to render the voice audible at great distances. It consists of a slightly conical tin or brass tube (fig. 165), very much wider at one end (which is called the bell), and Fig. 165. provided with a mouthpiece at the other. The larger the dimensions of this instrument the greater is the distance at which the voice is heard. Its action is usually ascribed to the successive reflections of sonorous waves from the sides of the tube, by which the waves tend more and more to pass in a direction parallel to the axis of the instrument. It has, however, been objected to this explanation, that the sounds emitted by the speaking trumpet are not stronger solely in the direction of the axis, but in all directions, that the bell would not tend to produce parallelism in the sonorous wave, whereas it certainly exerts considerable influence in strengthening the sound. It must be said that no satisfactory explana- tion has been n-iven of the effect of the bell. The ear trumpet is used by persons who are hard of hearing. It is essentially an inverted speaking trumpet, and consists of a conical metallic tube, one of whose extremities, terminating in a bell, receives the sound, while the other end is introduced into the ear. This instrument is the reverse of the speaking trumpet. The bell serves as a mouthpiece ; that is, it receives the sound coming from the mouth of the person who speaks. These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves which would become greatly developed, are concentrated on the auditory apparatus, and produce a far greater effect than divergent waves would have done. FJg. 166, Fig. 167. 226. Stetboscope. — One of the most useful applications of acoustical principles is the stethoscope. Figs. 166, 167 represent an improved form V -227] Measurement of the Number of Vibrations. i8i of this instrument devised by Konig. Two sheets of caoutchouc, c and a^ are fixed to the circular edge of a hollow metal hemisphere ; the edge is provided with a stopcock, so that the plates can be inflated, and then present the appearance of a double convex lens as represented in section in fig. 1 66. To a tubulure on the hemisphere is fixed a caoutchouc tube terminated by horn or ivory, o^ which is placed in the ear (fig. 167). When the membrane of the stethoscope is applied to the chest of a sick person the beating of the heart and the sounds of respiration are trans- mitted to the air in the chamber CA, and from thence to the ear by means of the flexible tube. If several tubes are fixed to the instrument as many observers may simultaneously auscultate the same patient. CHAPTER II. MEASUREMENT OF THE NUMBER OF VIBRATIONS. 227. Savart's apparatus. — Savarfs tocthed wheels so called from the name of its inventor, is an apparatus by which the absolute number of vibrations corresponding to a given note can be determined. It consists of a sohd oak frame in which there are two wheels, A and B (fig. 168); e Ik Fig. i68j the larger wheel. A, is connected with tlr?tDothed wheel by means of a strap and a multiplying wheel, thereby causing the toothed wheel to revolve with great velocity ; a card, E, is fixed on the frame, and, in revolving, the toothed wheel strikes against it, and causes it to vibrate. The card being struck by each tooth, makes as many vibrations as there are teeth. At the side of the apparatus there is an indicator, H, which gives the number of revolutions of the wheel, and consequently the number of vibrations in a given time. When the wheel is moved slowly, the separate shocks against the card are distinctly heard ; but if the velocity is gradually increased, the l82 Acoustics. [227- sound becomes higher and higher. Having obtained the sound whose number of vibrations is to be determined, the revolution of the wheel is continued with the same velocity for a certain number of seconds. The number of turns of the toothed wheel B is then read off on the indicator, and this multiplied by the number of teeth in the wheel gives the total number of vibrations. Dividing this by the corresponding number of seconds, the quotient gives the number of vibrations per second for the given sound. 228. Syren. — The syren is an apparatus which, like Savart's wheel, is used to measure the number of vibrations of a body in a given time. The name ' syren ' was given to it by its inventor, Cagniard Latour, because it yields sounds under water. It is made entirely of brass. Fig. 169 represents it fixed on the table of a bellows, by which a continuous current of air can be sent through it. Figs. 170 and 171 show the internal details. The lower part consists of Fig. 169. Fig. 171. a cylindrical box, O, closed by a fixed plate, B. On this plate a vertical rod, T, rests, to which is fixed a disc, A, moving with the rod. In the plate B there are equidistant circular holes, and in the disc A are an equal number of holes of the same size, and the same distance from the centre as those of the plate. These holes are not perpendicular to the disc ; they are all inclined to the same extent in the same direction in the plate, and are inclined to the same extent in the opposite direction in the disc, so that when they are opposite each other they have the appearance represented in mu, fig. 171. Consequently, when a current of air from the bellows reaches the hole m, it strikes obliquely against the sides of the hole n, and imparts to the disc A a rotatory motion in the direction nA. For the sake of simplicity, let us first suppose that in the movable disc A there are eighteen holes, and in the fixed plate B only one, which -229] Measurement of the Number of Vibrations. 183 faces one of the upper holes.— The wind from the bellows striking against the sides of the latter, the movable disc begins to rotate, and the space between two of its consecutive holes closes the hole in the lower plate. But as the disc continues to turn from its acquired velocity, two holes are again opposite each other, a new impulse is produced, and so on. During a complete revolution of the disc the lower hole is eighteen times open and eighteen times closed. A series of effluxes and stoppages is thus produced, which makes the air vibrate, and ultimately produces a sound when the successive impulses are sufficiently rapid. If the fixed plate, like the moving disc, had eighteen holes, each hole would separately produce the same effect as a separate one, the sound would be eighteen times as intense, but the number of vibrations would not be in- creased. In order to know the number of vibrations corresponding to the sound produced, it is necessary to know the number of revolutions of the disc A in a second. For this purpose an endless screw on the rod T transmits the motion to a wheel, a, with 100 teeth. On this wheel, which moves by one tooth for every turn of the disc, there is a catch, P, which at each complete revolution moves one tooth of a second wheel, b (fig. 170). On the axis of these wheels there are two needles, which move round dials represented in fig. 169. One of these indices gives the number of turns of the disc A, the other the number of hundreds of turns. By means of two screws, D and C, the wheel a can be uncoupled from the endless screw. Since the sound rises in proportion to the velocity of the disc A, the wind is forced until the desired sound is produced. The same current is kept up for a certain time, two minutes for example, and the number of turns read off. This number multiplied by 18, and divided by 120, indi- cates the number of vibrations in a second. With the same velocity the syren gives the same sound in air as in water ; the same is the case with all gases ; and it appears, therefore, that any given sound depends on the number of vibrations, and not on the nature of the sounding body. The buzzing and humming noise of certain insects is not vocal, but is produced by very rapid flapping of the wings against the air or the body. The syren has been ingeniously applied to count the velocity of the undu- lations thus produced, which is effected by bringing it into unison with the sound. It has thus been found that the wings of a gnat flap at the rate of 15,000 times in a second. 229. Bellows. — In acoustics a bdlows is an apparatus by which wind instruments, such as the syren and organ pipes, are worked. Between the four legs of a table there is a pair of bellows, S (fig. 172), which is worked by means of a pedal, P. D is a reservoir of flexible leather, in which is stored the air forced in by the bellows. If this reservoir is pressed by means of weights on a rod, T, moved by the hand, the air is driven through a pipe, E, into a chest, C, fixed on the table. In this chest there are small holes closed by leather valves, which can be opened 1 84 Acoustics. {229^ by pressing on keys in front ot the box. The syren or sounding pipe is placed in one of these holes. Fig. 172. 230. Ziimit of perceptible sounds. — Before Savart's researches, physicists assumed that the ear could not perceive a sound when the number of vibrations was below 16 for deep sounds, or above 9,000 for acute sounds. But he showed that these limits were too close, and that the faculty of perceiving sounds depends rather on their intensity than on their height ; so that when extremely acute sounds are not heard, it arises from the fact that they have not been produced with sufficient intensity to affect the organ of hearing. By increasing the diameter of the toothed wheel, and consequently the amplitude and intensity of the vibrations, Savart pushed the limit of acute sounds to 24,000 vibrations in a second. For deep sounds, he substituted for the toothed wheel an iron bar about two feet long, which revolved on a horizontal axis between two thin wooden plates, about 0*08 of an inch from the bar. As often as the bar passed, a grave sound was produced, due to the displacement of the air. As the motion became accelerated, the sound became continuous, very grave and deafening. By this means Savart found, that with 7 to 8 vibrations in a second, the ear perceived a distinct but very deep sound. M. Despretz, however, who has investigated the same subject, disputes Savart's results as to the limits of deep sounds, and holds that no sound is -231] Measurement of the Number of Vibrations. 185 audible that is made by less than 16 vibrations per second. Helmholtz holds that the perception of a sound begins at 30 vibrations, and only has a definite musical value when the number is more than 40. Below 30 the impression of a number of separate beats is produced. On the other hand, acute sounds are audible up to those corresponding to 38,000 vibra- tions in a second. The discordant results obtained by these and other observers for the limit of audibility of higher notes, are no doubt due to the circumstance that different observers have different capacities for the perception of sounds. 231. Bubaxnel's graphic method. — When the syren or Savart's wheel is used to determine the exact number of vibrations corresponding to a given sound, it is necessary to bring the sound which they produce into unison with the given sound, and this cannot be done exactly unless the experimenter have a practised ear. M. Duhamel's graphic method is very simple and exact, and free from this difficulty. It consists in fixing a fine point to the body emitting the sound, and causing it to trace the vibrations on a properly prepared surface. The apparatus consists of a wood or metal cylinder. A, fig. 173, fixed Fig. 1 73. to a vertical axis, O, and turned by a handle. The lower part of the axis is a screw working in a fixed nut, so that, according as the handle is turned from left to right, or from right to left, the cylinder is raised or depressed. Round the cyHnder is rolled a sheet of paper covered with an inadhesive film of lampblack. On this film the vibrations register themselves. 1 86 Acoustics. [231- This is effected as follows : Suppose the body emitting the note to be a steel rod. It is held firmly at one end, and carries at the other a fine point which grazes the surfaces of the cylinder. If the rod is made to vibrate and the cylinder is at rest, the point would describe a short line ; but if the cylinder is turned, the point produces an iindulati?ig trace, containing as many undulations as the point has made vibrations. Con- sequently the number of vibrations can be counted. It remains only to determine the time in which the vibrations were made. There are several ways of doing this. The simplest is to compare the curve traced by the vibrating rod with that traced by a tuning-fork (237)5 which gives a known number of vibrations per second — for example, 500. One prong of the fork is furnished with a point, which is placed in contact with the lampblack. The fork and the rod are then set vibrating together, and each produces its own undulating trace. When the paper is unrolled, it is easy by counting the number of vibrations each has made in the same distance to determine the number of vibrations made per second by the elastic rod. Suppose, for instance, that the tuning-fork made 150 vibrations, while the rod made 165 vibrations. Now we already know that the tuning-fork makes one vibration in the j^oo part of a second, and therefore 150 vibrations in §|§ of a second. But in the same time the rod makes 165 vibrations; therefore it makes one vibration in the ^ — ^- of a second, and hence 500 X 165 it makes per second 5QO ^ LJ or 550 vibrations. • 150 CHAPTER III. THE PHYSICAL THEORY OF MUSIC. 232. Properties of musical tones. — A simple musical tone results from a continuous rapid isochronous vibration, provided the number of the vibrations falls within the very wide limits mentioned in the last chapter (230). Musical tones are in most cases compound. The dis- _,-^ ttnction between a simple and a compound musical tone will be explained later in the chapter. The tone yielded by a tuning-fork furnished with a proper resonance box is simple ; that yielded by a wide-stopped organ pipe, or by a flute, is nearly simple ; that yielded by a musical string is compound. Musical tones have three leading qualities, namely, /zV^/^, intensity, and timbre or colour. i. The pitch of a musical tone is determined by the number of vibra- tions per second yielded by the body producing the tone. ii. The intensity of the tone depends on the extent of the vibrations. It is greater when the extent is greater, and less when it is less. It is, in -234] Physical Theory of Music, 187 fact, nearly or exactly proportional to the square of the extent or amplitude of the vibrations which produce the tone. iii. The timb?'e is that peculiar quality of tone which distinguishes a note when sounded on one instrument from the same note when sounded on another. Thus when the C of the treble stave is sounded on a violin, and on a flute, the two notes will have the same pitch, that is, are produced by the same number of vibrations per second, and they may have the same intensity, and yet the two tones will have very distinct qualities, that is, their timbre is different. The cause of the peculiar timbre of tones will be considered later in the chapter. 233. Musical intervals. — Let us suppose that a musical tone, which for the sake of future reference we will denote by the letter C, is pro- duced by m vibrations per second ; and let us further suppose that any other musical tone, X, is produced by 71 vibrations per second, ti being greater than m ; then the interval from the note C to the note X is the ratio 71 ; /;?, the interval between two notes being obtained by division^ not by subtraction. Although two or more tones may be separately musical, it by no means follows that when sounded together they produce a pleasurable sensation. On the contrary, unless they are concordant^ the result is harsh, and usually unpleasing. We have therefore to enquire what notes are fit to be sounded together. Now when musical tones are compared, it is found that if they are separated by an interval of 2 : I, 4 : I, etc., they so closely resemble one another that they may for most purposes of music be considered as the same tone. Thus, sup- pose c to stand for a musical note produced by 2ni vibrations per second, then C and c so closely resemble one another as to be called in music by the same name. The interval from C to f resonators act on manometric flames (262) ; the sounds thus become visible, and may be shown to a large auditory. It consists of an iron frame (fig. 177) on which are fixed in two parallel lines fourteen resonators tuned so as to give the notes from F^ to c^^, that is to say, four octaves and a half ; or notes of which the highest give the lower harmonics of the primary. On the right is a chamber, C, which is supplied with coal gas by the caoutchouc tube, D, and on which are placed eight gas jets, each provided with a manometric capsule (251, 263). Each jet is connected with the chamber C by a special caoutchouc tube, while behind the apparatus a second tube connects the same jet to one of the resonators. On the right of the jets is a system of rotating mirrors identical with that described. These details being understood, suppose the largest resonator on the right tuned to resound with the note i, and seven others with the harmonics of this note. Let the sound i be produced in part of this apparatus ; if it is simple, the lower resonator alone answers, and the corresponding flame is alone dentated ; but if the fundamental note is accompanied by one or more of its harmonics, the corresponding resonators speak at the same time, which is recognised by the dentation of their flames ; and thus the constituents of each sound may be detected. 243. Synthesis of sounds. — Not only has Helmholtz succeeded in decomposing sounds into their constituents ; he has verified the result of his analysis by performing the reverse operation, the synthesis ; that is, he has reproduced a given sound by combining the individual sounds of K 194 Acoustics. [243- which his resonators had shown that it was composed. The apparatus which he used for this purpose consists of eleven tuning-forks, the first of which yields the fundamental note of 256 vibrations, or C, nine others its harmonics, while the eleventh serves as make and break to cause the Fig. 177. diapasons to vibrate by means of electro-magnets. Each diapason has a special electro-magnet, arid moreover a resonator, which strengthens it. All these diapasons and their accessories are arranged in parallel lines of five (fig. 178), the first comprising the fundamental note and its uneven harmonics, 3, 5, 7, and 9 ; the second the even harmonics, 2, 4, 6, 8 and 10 ; beyond, there is the diapason break K arranged horizontally. One of its limbs is provided with a platinum point which grazes the surface of mercury contained in a small cup, the bottom of which is connected, by a copper wire, with an electro-magnet placed in front of the diapason. The apparatus being thus arranged, a wire from a voltaic battery is connected with the binding screw, c, and this with the electro-magnet, E ; which in turn is connected with those of the nine following diapasons. -243] Synthesis of Sounds. 195 and then with the diapason K itself. So long as the diapason does not vibrate, the current does not pass, for the platinum point does not dip in the^, mercury cup which is connected with the other pole of the battery. But when the diapason is made to vibrate by means of a bow, the current passes. Owing to their elasticity, the limbs of the tuning-fork soon revert to their original position, the point is no longer in the mercury, the current is broken, and so on at each double vibration of the diapason. This intermittence of the current being transmitted to all the other electro-magnets, they are alternately active and inactive. Hence they communicate to all the diapasons by their attraction the same number of vibrations. This is the case with the diapason i, which is tuned in unison Fig. 178. with the diapason break ; but the diapason 3 being tuned to make three times as many vibrations, makes three vibrations at each break of the current ; that is to say, the electro-magnet only attracts it at every third vibration ; in like manner, diapason b only receives a fresh impulse every five vibrations, and so on. The following is the working of the apparatus. The resonator of each diapason is closed by a clapper O (fig. 179), so that the sounds made by the diapasons are scarcely perceptible when the clappers are lowered. Each of these is fixed to the end of a bent lever, the shorter arm of which is worked by a cord a, which is connected with one of the keys of a key- board placed in front of the apparatus (fig. 178). When a key is depressed, the cord m.oves the lever, which raises the clapper, and the resonator then acts by strengthening its diapason. Hence by depressing any keys, we may add to the fundamental sounds any of the nine primary 196 Acoustics. [243 harmonics, and thus reproduce the sounds, the composition of which has been determined by analysis. Thus by depressing all the keys at once we obtain the sound of an open pipe in unison with the deepest diapason. By depressing the key of the fundamental notes and those of its uneven harmonics, we obtain the sound of a closed pipe. 244. Results of Helmboltz's researches. — By both his analytical and synthetical investigations into sounds of the most kinds, those from various musical instruments, the human voice, and even noises, Helm- holtz has fully succeeded in explaining the different timbre or quality of these sounds. It is due to the different intensities of the harmonics which accompany the primary tones of those sounds. The leading results of these researches into the colour of sounds may be thus stated : i. Simple tones, as those produced by a tuning-fork with a resonance box, and by wide covered pipes, are soft and agreeable without any rough- ness, but weak, and in the deeper notes dull. ii. Musical sounds accompanied by a series of harmonics, say up to the sixth, in moderate strength are full and musical. In comparison with simple tones they are grander, richer, and more sonorous. Such are the sounds of open organ pipes, of the pianoforte, etc. iii. If only the uneven harmonics are present, as in the case of narrow covered pipes, of pianoforte strings struck in the middle, clarionets, etc. the sound becomes indistinct : and when a greater number of harmonics are audible, the .sound acquires a nasal character. iv. If the harmonics beyond the sixth and seventh are very distinct, the sound becomes sharp and rough. If less strong, the harmonics are not prejudicial to the musical usefulness of the notes. On the contrary, they are useful as imparting character and expression to the music. Of this kind are most stringed instruments, and most pipes furnished with tongues, etc. Sounds in which harmonics are particularly strong acquire thereby a peculiarly penetrating character ; such are those yielded by brass instruments. -246] Physical Theory of Music. 1 97 V. To form a given vowel sound one or more characteristic notes which are always the same must be added. These change with the syllable pronounced, but depend neither on the height of the note, nor on the" person who emits them. A popular but adequate account of Helmholtz's principal results will be found in Helmholtz's ' Popular Scientific Lectures/ Longman's, 1873. 245. Froduction and perception of sounds. — Vocal sounds originate in the larynx in consequence of air being forced through a slit formed of two membranes called the vocal chords. These can be tightened or relaxed by means of certain muscles, and thus high or low notes can be produced. The notes produced by men are deeper than those of women or boys, because in them the larynx is longer and the vocal chords larger and thicker ; hence, though equally elastic, they vibrate less swiftly. Chest notes are due to the fact that the whole membrane vibrates, while the falsetto is produced by a vibration of the extreme edges only. The ordinary compass of the voice is within two octaves, though this is exceeded by some celebrated singers. Catalani, for instance, is said to ^ave had a range of 3^ octaves. / The wave length of the sounds emitted by a man's voice in ordinary / conversation is from 8 feet to 12 feet and that of women's voice is from 2 sV feet to 4 feet in a second. 1^ — ^^ The sound of the human voice is very complex and rich in harmonics, / for the mouth and the various cavities opening into the mouth act as resonators ; as the note changes with their extent, with the degree to which the mouth is opened and the shape given to it, certain harmonics are strengthened or not, and thus the voice acquires different timbre. Without giving an account of the anatomy of the ear we may state succinctly how Helmholtz explains the perception by the ear of the most complicated sounds. The recent observations of M. Corti have shown that the inner membrane of the cochlea is lined with about 3,000 extremely minute fibres which are the termination of the acoustic nerve. Each of these, which are called CortVs Jibres, seems to be tuned for a particular note as if it were a small resonator. It thus only vibrates in unison with this note, and is deaf for all others. Hence each simple note only causes one fibre to vibrate, while compound notes cause several : just as when we sing with a piano, only the fundamental note and its harmonics vibrate. 'Hence, however complex external sounds may be, these microscopic fibres can analyse it and reveal the constituents of which it is formed. 246. Beats. — When two simple tones are sounded together, it is 'in many cases found that they alternately strengthen and weaken one an- other. When this is so, they are said to beat with one another. This may be explained as follows : Suppose AB, in fig. 180, to be a row of particles transmitting the sound : suppose the vibrations producing the one tone to be indicated by the continuous curved line ; then, on the one hand, the ordinates of the different points of AB give the velocities with which those points are simultaneoiisly moving, and on the other hand, each point 198 Acotistics. [246- vvill have successively the different velocities represented by the successive ordinates. In hke manner let the dotted line show the vibrations which produce the second tone. And, for the sake of distinctness, suppose the number of vibrations in a second producing the former tone to be to that producing the latter in the ratio of 3 : 2. Now let us consider any point which when at rest occupies the position N ; draw the ordinate cutting the former curve in P and the latter in O. If the tones were sounded separately, the velocity of N at a given distance produced by the former tone would be PN, and that of N at the same instant produced by the latter tone would be ON. Consequently, as they are sounded together, the actual velocity of N at the given instant is the sum of these, or PN + QN. If at the same instant we consider the point n, its velocity will consist of pn and nq jointly, but as these are in opposite directions, its actual amount will he pn — nq. Hence the actual velocity resulting from the coexistence of the two tones will be indicated by the curve in fig. 181, Fig. 180. ^.4:^^^ A whose ordinates equal the (algebraical) sum of the corresponding oj^i- nates of the two curves in fig. 180; that is, if AN, A«, . . . represent equal distances in both figures, the curve is described by taking RN equal to PN + QN, rn equal to pn — qn, and so on. This curve shows by its successive ordinates the simultaneous velocities of the different particles of AB, and the successive velocities communicated to the drum of the ear. An inspection of the figure will show that the velocities are first great, then small, then great, and so on, the drum being first moved rapidly for a short time, then for a short time nearly brought to rest, and so on. In short, the effect of the beating of tones on the air as compared with that of a continuous tone is strictly analogous to the effect produced on the eye by a flickering as compared with a steady light. It may be proved that when two simple tones are produced by m and n double vibrations per second, they produce ;//—;/ beats per second ; thus, if C is produced by 128, and D by 144 double vibrations per second, they will on being sounded together produce 16 beats per second. It has been ascertained that the beats produced by two tones are not audible unless the ratio m : n\s less than the ratio 6 : 5. Hence, in the case represented by fig. 181, though the alternations of intensity exist, they would not be audible. Also, if the tones have very different intensities, the intensity of the beat is very much disguised. It is found that when beats are fewer than 10 per second or more than 70 per second they are disagreeable, but not to the extent of producing -248] Physical Theory of Music. 1 99 discord. Beats from 10 to 70 per second may be regarded as the source of all discord in music, the maximum of dissonance being attained when about 30 beats are produced in a second. For example, if c and B are sounded together, the effect is very discordant, the interval between those notes being 16 : 15, so that the beats are audible, and the number of beats per second being 16. On the other hand, if C, E, and G are sounded together there is no dissonance, but if C, E, G, B are sounded together the discord is very marked, since C produces c, which is discordant with B. It will be remarked that C, E, G is a major triad, while E, G, B is a minor triad. A compound musical tone, being composed of simple tones represented by 1,2, 3, 4, 5, 6, 7, etc., does not give rise to any simple tones capable of producing an audible beat up to the seventh — the sixth and seventh are the first that produce an audible beat. It is for this reason that there is no trace of roughness in a compound tone, unless the seventh harmonic be audible. If we were to represent graphically a compound tone, we should proceed to construct a curve out of simple tones of different intensities in the same manner as fig. 181 is constructed from two simple tones of equal intensity represented by fig. 180. It is evident that the resulting curve will take different forms according to the presence or absence of different har- monics and their different intensities ; in other words, the colour of the notes produced by different instruments will depend upon the for7n of the vibrations producing the sound. 247. Combinational tones. — Besides the beats produced when two musical notes are sounded together, there is another and distinct pheno- menon, which may be thus described : Suppose two simple tones to be simultaneously produced by vibrations of finite extent, and of ti and m vibrations per second. It has been shown by Helmholtz that they generate a series of other tones. The principal one of these, which may be called the differential tone, is produced by n — m vibrations per second. Its intensity is generally very small, but it is distinctly audible in beats. It has been called the grave harmonic, as generally its pitch is much lower than that of the notes by which it is generated. It has been supposed to be caused by the beats becoming too numerous to be distinguished, and coalescing into a continuous sound, and this sup- position was countenanced by the fact that its pitch is the same as the beat number. The supposition is shown to be erroneous, first, by the existence of the differential tones for intervals that do not beat, and secondly, by the fact that, under certain circumstances, both the beats and the differential tones may be heard together. 248. The physical constitution of musical chords. — Let us sup- pose two compound tones to be sounded together, say C and G, then we obtain two series of tones each consisting of a primary and its harmonics namely, denoting C by 4, the two series, 4, 8, 12, 16, . . . and 6, 12, 18, 24, etc. Now, if instead of producing the two notes C and G, we had sounded the octave below C, we should have produced the series, 2, 4, 6, 8, 10, 12, 14, 16, 18, etc. It is plain that the two former series 200 Acoustics. [248- when joined differ from the last in the following respects : {a) The primary tone 2 is omitted, {b) In the case of the last series, the con- secutive tones continually decrease in intensity, whereas in the two former series, 4 and 6 are of the same intensity, 8 is of lower intensity, but the two 12's will strengthen each other, and so on. {c) Certain of the har- monics of the primary 3 are omitted ; for example, 10, 14, etc., do not occur in either of the two former series. In spite of these differences, however, the two compound notes affect the ear in a manner very closely re- sembling a single compound tone ; in short, they coalesce into a single tone with an artificial colour. It may be added that in the case above taken C and G produce as a combination tone 2 (that is, 6 — 4), so that, strictly speaking, the 2 is not wanted m the series produced by C and G, only it exists in very diminished intensity. The same explanation will apply to all possible chords ; for. example, in the case of the major chord, C, E, G, we have a tone of artificial colour expressed by the series of simple tones, 4, 5, 6, 8, 10, 12, 15, 16, 18, etc., together with the combination tones, I, I, 2. It will be remarked that in the whole of this series there are no dissonant tones introduced, except 15, 16, and 16, 18, and this dissonance will be inappreciably slight, since 15 is the third harmonic of 5, and the 16 the fourth harmonic of 4, so that their intensities will be different, as also will be the intensities of 16 and 18. On the other hand, nearly all the tones which form a natural compound tone are present, namely, there are i, 2, 4, 5, 6, 8, 10, 12, etc., in place of i, 2, 3, 4, 5, 6, 7, 8, 9, 10, II, 12, etc. In short, the major triad differs only from a nattirat compound tone in that it consists of a series of simple tones of different intensities, and omits those which by beating with its' neighbour- ing tone would produce dissonance, for example, 7, which would beat with 6 and 8 ; 9, which would beat with 8 and 10 ; and 11, which would beat with 10 and 12. It is this circumstance which renders the major chord of such great importance in harmony. If the constituents of the minor chord are similarly discussed, namely, three compound tones whose primaries are proportional to 10, 12, 15, it will be found to differ from the major chord in the following principal respects : (a) The primary of the natural tone to which it approximates is very much deeper than that of the corresponding major chord, {b) It introduces the differ- ential tones, 2, 3, 5, which form a major chord. Now it has already been remarked that when a major and minor chord are sounded together, they are distinctly dissonant ; for example, when C, E, G, A, are sounded together. Accordingly, the fact of the differential tones forming a major chord shows that an elementary dissonance exists in every minor chord. 251] Vibrations of Strings. 201 J CHAPTER \W.\ VIBRATIONS OF STRETCHED STRINGS, AND ,0F COLUMNS OF AIR. I meant the string of a .ched by a certain force, The vibrations which 'ongitiiditial, but prac- ■sat vibrations may be 249. Vibrations of strings. — By a string musical instrument, such as a viohn, which is stj and is commonly of catgut or is a metallic wii strings experience may be either transversat o\ tically the former are alone important. Transi produced by drawing a bow across the string, as in the case of the violin ; or by striking the string, as in the case of the pianoforte ; or by pulling it transversely, and then letting it go suddenly, as in the case of the guitar and the harp. 250. Sonometer. — The sonometer is an apparatus by which the trans- verse vibrations of strings may be studied. It is also called monochord, because it has generally only one string. In addition to the string, it consists of a thin wooden box to strengthen the sound ; on this there are two fixed bridges, A and D (fig. 182), over which passes the string, which Fig. 182. is usually a metallic wire. This is fastened at one end, and stretched at the other by a weight, P, which can be increased at will. By means of a third movable bridge, B, the length of that portion of the wire which is to be put in vibration can be altered at pleasure. 251. Xiaws of tlie transverse vibrations of stringrs. — If / be the length of a string, that is, the vibrating part between two bridges, A and B (fig. 182), r the radius of the string, d its density, P the stretching weight, and n the number of vibrations per second, it is found by calcu- lation that 2rts/ ^g being the ratio of the circumference to the diameter, g the acceleration of gravity. The above formula expresses the following laws : — I. The stretching weight or tension beiftg constajtt, the number of vibrations in a second is inversely as the length. II. The number of vibrations in a second is inversely as the diameter of the string. K3 202 Acoustics. [251- III. The number of vibrations in a second is directly as t^ie square root of the stretching weight or tension. IV. The number of vibrations in a second of a string is inversely as the square root of its density. These laws are applied in the construction of stringed instruments, in which the length, diameter, tension, and substance of the strings are so chosen, that given notes may be produced from them. 252. Experimental verification of tbe laws of tlie transverse vibration of string-s. — Law of the lengths. In order to prove this law, we may call to mind that the relative numbers of vibrations of the notes of the gamut are CDEFGAB c T J^liSlls^ ^843238"' If now the entire length of the sonometer be made to vibrate, and then, by means of the bridge B, the lengths f , |, f , |, f, {■., |, which are the inverse of the above numbers, be successively made to vibrate, all the notes of the gamut are successively obtained, which proves the first law. Law of the diameters. This law is verified by stretching upon the sono- meter two cords of the same material, the diameters of which are as 3 to 2, for instance. When these are made to vibrate, the second cord gives the fifth above the other ; which shows that it makes three vibrations while the first makes two. Law of the tensions. Having placed on the sonometer two identical strings, they are stretched by weights which are as 4 : 9. The second now gives the fifth of the first, from which it is concluded that the numbers of their vibrations are as 2 : 3, that is, as the square roots of the tensions. If the two weights are as 16 to 25, the major third or | would be obtained. Law of the densities. Two strings of the same radius but different densities are fixed on the sonometer. Having been subjected to the same stretching weight, the position of the movable bridge on the denser one is altered until it is in unison with the other string. If then d and d' are the densities of the two strings, and / and I' the lengths which vibrate in unison, we find - ■=."^1—^. But as we know from the first ^ law that / \j d ^= ~ , we have — = -'^, , which verifies this law. /' n n sjd 253. iTodes and loops.— Let us suppose the string AD (fig. 182) to begin vibrating, the ends A and D being fixed, and while it is doing .so. let a point, B, be brought to rest by a stop, and let us suppose DB to be one- third part of AD. The part DB must now vibrate about B and D as fixed points in the manner indicated by the continuous and dotted lines ; now all parts of the same string tend to make a vibration in the same time ; accordingly the part between A and B will not perform a single vibration, but will divide into two at the point C, and vibrate in the manner shown in the figure. If BD were one-fourth part of AD (fig. 1 83), the part AD would be subdivided at C and Q' into three vibrating portions each equal to BD. The points B, C, C are called nodes or nodal 255] Wind Instruments. 203 points ; the middle point of the part of the string between any two conse- cutive nodes is called a loop or a ventral segment. It will be remarked that the ratio of BD : BA must be that of some two whole numbers, for example, i : 2, i : 3, 2 : 3, etc., otherwise the nodes cannot be formed, since the two portions of the string cannot then be made to vibrate in the same time, and the vibrations will interfere with and soon destroy one another. If now we refer to fig. 183, the existence of the node at C can be easily proved by bending some Hght pieces of paper, and placing them on the Fig. 183. Fig. 184. String. Say three pieces, one at C and the others respectively midway between B and C, and between C and A. The one at C experiences only a very slight motion, and remains in its place, thereby proving the exist- ence of a node at C ; the other two are violently shaken, and in most cases thrown off the string. When a musical string vibrates between fixed points A and B, its motion is not quite so simple as might be inferred from the above description. In point of fact, partial vibrations are soon produced, and superimposed upon the primary vibrations. The partial vibrations cor- respond to the half, third, fourth, etc. parts of the string. It is by these partial vibrations that the harm.onics are produced which accompany the primary note due to the primary vibrations. 254. iVind instruments. — In the cases hitherto considered the sound results from the vibrations of solid bodies, and the air only serves as a vehicle for transmitting them. In wind instruments on the contrary, when the sides of the tube are of adequate thickness, the enclosed column of air is the sonorous body. In fact, the substance of the tubes is without influence on the primary tone; with equal dimensions it is the same whether the tubes are of glass, of wood, or of metal. These different ma- terials simply do no more than give rise to different harmonics, and impart a different quality to the compound tone produced. In reference to the manner in which the air in tubes is made to vibrate wind instruments are divided into 7noutk instruments and reed instru- ments. 255. Mouth instruments.— In mouth instruments all parts of the mouthpiece are fixed. Fig. 185 represents the mouthpiece of an organ 204 Acoustics. [255^ Fig. 1 86. pipe, and fig. i86 that of a whistle, or of a flageolet. In both figures, the aperture ib is called the mouth ; it is here that air enters the pipe : b and o are the lips, the upper one of which is bevelled. The mouthpiece is fixed at one end of a tube, the other end of which may be either opened or closed. In fig. 185 the tube can be fitted on a wind-chest by means of the foot P. When a rapid current of air enters by the mouth, it strikes against the upper lip, and a shock is produced which causes the air to issue from bo in an intermittent manner. In this way, pulsations are produced which, transmitted to the air in the pipe, make it vibrate, and a sound is the result. In order that a pure note may be produced, there must be a certain relation between the form of the lips and the magnitude of the mouth ; the tube also ought to have a great length in comparison with its diameter. The number of vibrations depends in general on the dimensions of the pipe, and the velocity of the current of air. 256. Reed instruments. — In reed instruments a simple elastic tongue sets the air in vibration. The tongue, which is either of metal or of wood, is moved by a current of air. The mouthpieces of the oboe, the bassoon, the clarionet, the child's trumpet, are different applications of the reed, which, it may be remarked, is seen in its simplest form in the Jew's harp. Some organ pipes are reed pipes, others are mouth pipes. Fig. 187 represents a model of a reed pipe as com- monly shown in lectures. It is fixed on the wind-chest O of a bellows, and the vibra- tions of the reed can be seen through a piece of glass, E, fitting into the sides. A wooden horn, H, strengthens the sound. Fig. 137. Fig. 188. Fig. 189. Y\g. 188 shows the reed, out of the pipe. It consists of four pieces: ist, a rectangular wooden tube closed below and open above at ; 2nd, a copper plate cc forming one side of the tube, and in which there is a longitudinal aperture. -258] Mouth and Reed Instruments. 205 through which air passes from the tube MN to the orifice o ; 3rd, a thin elastic plate, i, called the tongue^ which is fixed at its upper end, and which grazes the edge of the longitudinal aperture, nearly closing it ; 4th, a curved wire, r, which presses against the tongue, and can be moved up and down. It thus regulates the length of the tongue, and deter- mines the pitch of the note. It is by this wire that reed pipes are tuned. The reed being replaced in the pipe MN, when a current of air enters by the foot P, the tongue is compressed, it bends inwards, and affords a passage to air, which escapes by the orifice o. But, being elastic, the tongue regains its original position, and performing a series of oscillations successively opens and closes the orifice. In this way sonorous waves result and produce a note, whose pitch increases with the velocity of the current. In this reed the tongue vibrates alternately before and behind the aper- ture, and just escapes grazing the edges, as is seen in the harmonium, con- certina, etc. ; such a reed is called 2. free reed. But there are other reeds called beatifig reeds, in which the tongue, which is larger than the orifice, strikes against the edges at each oscillation. The reed of the clarionet, represented in fig. 189, is an example of this ; it is kept in its place by the pressure of the lips. The reeds of the hautboy and bassoon are also of this kind. 257. Of the tones produced by the same pipe. — Daniel Bernouilli discovered that the same organ pipe can be made to yield a succession of tones by properly varying the force of the current of air. The results he arrived at may be thus stated : — = i. If the pipe is open at the end opposite to the mouthpiece, then, de- noting the primary tone by I, we can, by gradually increasing the force of the current of air, obtain successively the tones 2, 3, 4, 5, etc., that is to say, the harmonics of the primary tone. ii. If the pipe is closed at the end opposite to the mouthpiece, then, denoting the primary tone by l, we can, by gradually increasing the force of the current of air, obtain successively the tones 3, 5, 7, etc., that is to say, the uneven harinonics of the primary tone. It must be added that if a closed and an open pipe are to yield the same primary tone, the closed pipe must be half the length of the open pipe, if in other respects they are the same. In any case it is impossible to produce from the given pipe a tone not included in the above series respectively. ^ Although the above laws are enunciated with reference to an organ ^ipe, they are of course true of any other pipe of uniform section. ^58. On the nodes and loops of an orgran pipe. — The vibrations of the air producing a musical tone take place in a direction parallel to the axis of the pipe — not transversely as in the case of the portions of a vibrating spring. In the former case, however, as well as in the latter, the phenomena of nodes and loops may be produced. But now by a 7iode must be understood a section of the column of air contained in the pipe, where the particles remain at rest, but where there are rapid alternations of condensation and rarefaction. By a loop or ventral segment must be 206 Acoustics. [258- iinderstood a section of the column of air contained in the pipe where the vibrations of the particles of air have the greatest amplitudes, and where there is no change of density. The sections of the column of air are, of course, made at right angles to its axis. When the column of air is divided into several vibrating portions, it is found that the distance between any two consecutive loops is constant, and that it is bisected by a node. We can now consider separately the cases of the open and closed pipes. i. In the case of a stopped pipe, the bottom is always a node, for the layer of air in contact with it is necessarily at rest, and only undergoes variations in density. At the mouthpiece, on the contrary, where the air has a constant density, that of the atmosphere, and the vibration is at its maximum, there is always a loop. In any stopped pipe there is at least f ¥ ¥ u V N V N V / Fig. 190. Fig. i9i. Fig. 192. Fig. 193. Fig. 194- Fig. 195 one node and one loop (fig. 190) ; the pipe then yields its fundamental note, and the distance VN from the loop to the node is equal to half a condensed or rarefied wave length. If the current of air be forced, the mouthpiece always remains a loop, and the bottom a node, the column divides into three equal parts (fig. 191) and an intermediate node and loop are formed. The sound produced is the first harmonic. When the second harmonic (5) is produced, there are two intermediate nodes and two loops, and the tube is then sub- divided into five equal parts (fig. 192), and so on. ii. In the case of the open pipe, whatever tone it produces, there must be a loop at each end, since the enclosed column of air is in contact with the external air at those points. When the primary tone is produced, there will be a loop at each end, and a node at the middle section of the pipe, the nodes and loops dividing the column into tivo equal parts (fig. 193). When the first harmonic (2) is produced, there will be a loop -258] Nodes and Loops of an Organ Pip£. 207 at each end, and a loop in the middle, the column being divided 'mXofoiir equal parts by the alternate loops and nodes (fig. 194). When the second harmonic (3) is produced, the column of air will be divided into six equal parts by the alternate nodes and loops, and so on (fig. 195). It will be remarked that the successive modes of division of the vibrating column are the only ones compatible with the alternate recurrence at equal in- tervals of nodes and loops, and with the occurrence of a loop at each end of the pipe. There are several experiments by which the existence of nodes and loops can be shown. o {d) If a fine membrane is stretched over a pasteboard ring, and has sprinkled on it some fine sand, it can be gradually let down a tube, as shown in fig. 198. Now suppose the tube to be producing a musical note. As the membrane descends, it will be set in vibration by the vibrating air. But when it reaches a node it will cease to vibrate, for there the air is- at rest. Consequently the grains of sand, too, will be at rest, and their quiescence will indicate the position of the node. On the other 2o8 Acoustics. [258 hand, when the membrane reaches a loop, that is, a point where the am- phtude of the vibrations of the air attains a maximum, it will be violently agitated, as will be shown by the agitation of the grains of sand. And thus the positions of the loops can be rendered manifest. {b) Again, suppose a pipe to be constructed "Avith holes bored in one of its sides, and these covered by little doors which can be opened and shut, as shown m fig. 196. Let us suppose the little doors to be shut and the pipe to be caused to produce such a tone that the nodes are at N and N' and the loops at V, Y', Y^\ At the latter points the density is that of the external air, and consequently if the door at V is opened no change is produced in the note. At the former points N and N' there are alter- nately condensation and rarefaction taking place. If now the door at N' is opened, this alternation of density is no longer possible, for the density at this open point must be the same as that of the external air, and consequently N^ becomes a loop and a note yielded by the tube is changed. The change of notes produced by changing the fingering of the flute is, of course, one form of this experi- ment. {c) Suppose A, in fig. 197, to be a pipe emitting a certain note, and suppose P to be a plug, fitting the tube, fastened to the end of a long rod by which it can be forced down the tube. Now when the plug is inserted, whatever be its position, there will be a node in contact with it. Consequently, as it is gradually forced down, the note yielded by the pipe will keep on r^. .. changing. But every time it reaches a position fe;,f-^] which was occupied by a node before its inser- I tion, the note becomes the same as the note BiiAiiiiMii originally yielded. For now the column of air vibrates in exactly the same manner as it did before the plug was put in. {a) Y\g. 1 99 shows another mode of illustrating the same point, which is identical in principle with Konig's manometric flames. The figure represents an organ pipe, on one side of which is a chest, P, filled with coal gas, by means of the tube S. The gas from the chest comes out in three jets, A, B, C, and is then ignited. The manner in which the gas passes from the chest to the point of ignition is shown '^' '^^' in the smallest figure, which is an enlarged section of A. A circular hole is bored in the side of the pipe and covered with a membrane, r. A piece of wood is fitted into the hole so as to leave a small space between it and the membrane. The gas passes from the chest, in the direction indicated by the arrow, into the space between the membrane and the piece of wood, and so out of the tube 7?i, at the mouth of which it is ignited. Now suppose the pipe to be caused to II fl 260] Nodes and Loops of mi Organ Pipe. 209 yield its primary note, then as it is an uncovered pipe there ought to be a node at B, its middle point. Consequently there ought to be rapid changes of density at B ; these would cause the membrane r to vibrate,^ and thereby blow out the flame w, and this is what actually happens. If by increasing the force of the wind the octave to the primary note is produced, B will be a loop, and A and C nodes. Consequently the flames at A and C will now be extinguished, as is, in point of fact, the case. But at B, there being no change of density, the membrane is unmoved, and the flame continues to burn steadily. By each and all of these experiments it is shown that in a given pipe, whether open or closed, there are always a certain number of nodes, and midway between any two consecutive nodes there is always a loop or ventral segment. 259. Forznulse relative to tbe number of vibrations produced by a musical pipe. — It follows from what has been said that the column of air in stopped pipes is always divided by the nodes and loops into an uneven number of parts which are equal to each other, and each of which is a quarter of a complete vibration (figs. 190, 191, and 192) while in an open pipe it is divided into an even number of such parts (figs. 193, 194, 195). If L be the length of the pipe, / the wave length of the sound which it emits, and/ any whole number, then for stopped pipes we have L = (2/ + i) - ; and for open pipes L = 2/ - =^ . Replacing in each of 4 42 these formulas / by its value - (237), we haveL = (2/ +1) — and L = n 4.n y , ?— ; from which for stopped pipes we have n = I p -^ ^v ^^^ ^^^ open 7.n rr tr r 4L ' ones Ji= ^ — 2 L If, in the first formula, we give to p the successive values o, i, 2, 3, 4, etc., we have ;^ = -^, ?^, i-^ ; that is the fundamental sound and 4L 4L 4L all its uneven harmonics ; and in the formula for the open pipe we get similarly —,^' ^, etc., that is the fundamental note and all its har- 2 L 2 L 2 L monies even and uneven. 260. Explanation of tbe existence of nodes and loops In a musical pipe.— The existence of nodes and loops is to be explained by the co- A . , - ^^C — ^S^i^ ^-^— -^ ff existence in the same pipe of two equal waves travelling m contrary directions. Let A be a point from which a series of waves sets out towards B, and 210 A coiistics. [260- let the length of these waves, whether of condensation or rarefaction, be AC, CD, DB. And let B be the point from which the series of exactly equal waves sets out towards A. It must be borne in mind that in the case of a wave of condensation originating at A, the particles move in the direction A to B, but in a wave of condensation originating at B they move in the direction B to A. Now let us suppose that condensation at C, caused by the wave from A, begins at the same instant that condensa- tion caused by the wave from B begins at D. Consequently, restricting our attention to the particles in the line CD, at any instant the velocities of the particles in CD due to the former w^ave will be represented by the ordinates of the curve SPRT, while those due to the wave from B will be represented by the co-ordinates of the curve TQrS. Then, since the waves travel with the same velocity and are at C and D respectively at the same instant, we must have, for any subsequent instant, CR equal to Dr. If, therefore, N is the middle point between C and D, we must have rN equal to RN, and consequently PN equal to ON, that is to say, if the particle at N transmitted only one vibration, its motion at each instant would be in the opposite phase to that of its motion if it transmitted only the other vibration. In other words, the particle N will at every instant tend to be moved with equal velocity in opposite directions by the two waves, and therefore will be pennaneritly at rest. That point is therefore a node. In like manner there is a node at N' midway between A and C, and also at N'^ midway between B and D. In regard to the motion of the remaining particles, it is plain that their respective velocities will be the (algebraical) sum of the velocities they would at each instant receive from the waves separately. Hence at the instant indicated by the diagram they are given by the ordinates of the curve HNK. This curve will change from instant to instant, and at the end of the time occupied by the passage of a wave of condensation (or of rarefaction) from C to D will occupy the position shown by the dotted line Ji^k. Hence it is evident that particles near N have but small changes of velocity, whilst those near C and D experience large changes of velocity. If the curve HK were produced both ways, it would always pass through W and N^' ; the part, however, between N and N' would some- times be on one side and sometimes on the other side of AB. Hence all the particles between W and N have, simultaneously, first a motion in the direction A to B, and then a motion in the direction B to A, those particles near C having the greatest amplitude of vibrations. Hence near N and W there will be alternately the greatest condensation and rarefaction. This explanation apphes to the case in which AB is the axis of an open [organ pipe, A being the end where the mouthpiece is situated. The ^aves from B have their origin in the reflection of the series of waves from A. In the particular case considered, the note yielded by the pipe that indicated by 3, that is, the fifth above the octave to the primary [ote. A similar explanation can obviously be applied to all other cases, id whether the end be opened or closed. But in the latter case the series of waves from the closed end must commence at a point distant from the -261] Ktindfs Determination of the Velocity of Sound. 2 1 1 mouthpiece by a space equal to one-half, or three halves, or five halves, etc. of the length of a wave of condensation or expansion, 261. Kundt's determination of the velocity of sound. — Kundt has devised a method of determining the velocity of sound in solids and in gases which can be easily performed by means of simple apparatus, and is capable of great accuracy. A glass tube © BB, about two yards long, and two inches in the clear, is closed at one end by a movable stopper b ; the other end is fitted with a cork KK, which tightly grasps a glass tube AA, of smaller dimensions. This is closed at one end by a piston a which moves with gentle friction in the outer tube BB. Then by rubbing the free end of the tube AA with a wet cloth, it produces longitudinal vibrations, and these transmit their motion to the air in the part ab. If the tube ab contain some lycopodium powder, this is set in active vibra- tion and then arranges itself in small patches in a certain definite order as represiented in the figure ; the nature and arrangement of which depend on the vibrating part of the rod and the tube. When the length of the column of air is an exact multiple of the wave length the heaps are not dis- tinct. These heaps represent the nodes, and the mean distance d between them can be measured with great accuracy. This distance represents the distance between two nodes, which is half a wave length ; that is the wave length of the sound in air is id. If the rod has the length s and is grasped in the middle by the cork KK, from the law of the longitudinal vi- brations of rods, (265) the wave length of the sound it then emits is twice its length or 2 s. That is the wave length of the vibrating column of air is to that in the rod as 2d : is. As the velocity of sound in any body is equal to the wave length in that body multiplied by the number of vibrations in a second ; and since the number of vibrations is here the same in both cases, for the tone is the same, the velocity of sound in the glass is to the velocity of sound in air as 7.sn : idn^ that is as s : d. Thus when the glass tube was clamped in the middle by KK, so that the length ab was equal to half the length of the tube Art, the number of the ventral segments was eight. This corresponds to a ratio of wave length of i to 16 : in other words the velocity of sound in glass is 16 times that in air. The method is capable of great extension. By means of the stopcock different gases could be introduced instead of air, and corre- sponding differences found for the length of the ventral segments ; from which, by a simple calculation the corresponding velocities were found. Thus the velocities of sound in carbonic acid, coal gas, and hydrogen, were found to be respectively o-8, i'6, and 3*56 that of air, or, nearly as the inverse square of the densities. So also by varying the material of the rod A a, different velocities 212 Acoustics. [261- are obtained. Thus the velocity in steel was found to be 15 "24, and that in brass 10*87 that of air. 262. Chemical harmonicon.— The air in an open tube may be made to give a sound by means of a luminous jet of hydrogen, coal gas, etc. When a glass tube about 12 inches long is held over a lighted jet of hydrogen (fig. 202), a note is produced, which, if the tube is in a certain position, is the fundamental note of the tube. The sounds, doubtless, arise from the successive explosions produced by the periodic combinations of the atmospheric oxygen with the issuing jet of hydrogen. The apparatus is called the chemical harmonicon. The phenomena of the chemical harmonicon and of singing flames have been investigated by Prof. Tyndal!, whose Lectures on Soujid con- tain a number of very beautiful experiments on this subject. The note depends on the size of the flame and the length of the tube : with along tube, by varying the position of the jet in the tube, the series of notes in the ratio 1.2:3:4:5 is obtained. If, while the tube emits a certain sound, the voice or the (syren 229) be gradually raised to the same height, as soon as the note is nearly in unison with the har- monicon, the flame becomes agitated, jumps up and down, and is finally steady when the two sounds are in unison. If the tone of the syren is gradually heightened, the pulsations again commence ; they are the optical expressions of the beats (246) which occur near perfect unison. If, while the jet burns in the tube and produces a note, the position of the tube is slightly altered, a point is reached at which no sound is heard. If now the voice, or the syren, or the tuning-fork, be pitched at the note produced by the jet, it begins to sing, and continues to sing even after the syren is silent. A mere noise, or shouting at an incorrect pitch, affects the flame, but does not cause it to sing. 263. stringred instruinents< — Stringed musical instruments depend on the production of transverse vibrations. In some, such as the piano, the sounds are constant, and each note requires a separate string ; in others, such as the violin and guitar, the sounds are varied by the finger- ing, and can be produced by fewer strings. In the piano the vibrations of the strings are produced by the stroke of the hammer, which is moved by a series of bent levers communicating with the keys. The sound is strengthened by the vibrations of the air in the sounding board on which the strings are stretched. Whenever a key is struck, a damper is raised which falls when the finger is removed from the key and stops the vibrations of the corresponding strings. By means Fig. 202. -264] Wwd InsU'uments. 2 1 3 of a pedal all the dampers can be simultaneously raised, and the vibra- tions then last for some time. The harp is a sort of transition from the instruments with constant to those with variable sounds. Its strings correspond to the natural notes of the scale : by means of the pedals the lengths of the vibrating parts can be changed, so as to produce sharps and flats. The sound is strengthened by the sounding box, and by the vibrations of all the strings harmonic with those played. In the violin and guitar each string can give a great number of sounds according to the length of the vibrating part, which is determined by the pressure of the fingers of the left hand while the right hand plays the bow, or the strings themselves. In both these instruments the vibrations are communicated to the upper face of the sounding box, by means of the bridge over which the strings pass. These vibrations are communicated from the upper to the lower face of the box, either by the sides or by an intermediate piece called the sound post. The air in the interior is set in vibration by both faces, and the strengthening of the sound is produced by all these simultaneous vibrations. The value of the instrument con- sists in the perfection with which all possible sounds are intensified, which depends essentially on the quality of the wood, and the relative arrangement of the parts. 264. IVind instruments. — All wind instruments may be referred to the different types of sounding tubes which have been described. In some, such as the organ, the notes 2.xq fixed, and require a separate pipe for each note ; in others the notes are variable, and are produced by only one tube : the flute, horn, etc. are of this class. In the organ the pipes are of various kinds, namely, mouth pipes, open and stopped, and reed pipes with apertures of various shapes. By means of stops the organist can produce any note by both kinds of pipe. In th^fiute, the mouthpiece consists of a simple lateral circular aper- ture ; the current of air is directed by means of the lips, so that it grazes the edge of the aperture. The holes at different distances are closed either by the fingers or by keys ; when one of the holes is opened, a loop is produced in the corresponding layer of air, which modifies the distri- bution of nodes and loops in the interior, and thus alters the note. The whistling of a key is similarly produced. The pandtTaji pipe consists of tubes of different sizes corresponding to the different notes of the gamut. In the trumpet, the horn, the trombone, cornet-h-piston, and ophicleide, the lips form the reed, and vibrate in the mouthpiece. In the horn, different notes are produced by altering the distance of the lips. In the trombone, one part of the tube slides within the other, and the performer can alter at will the length of the tube, and thus produce higher or lower notes. In the cornet-a-piston the tube forms several convolutions ; pistons placed at different distances can, when played, cut off communi- cation with other parj;s of the tube, and thus alter the length of the vibrating column of air. \/ 214 A coiistics. [265- CHAPTER V. VIBRATIONS OF RODS, PLATES, AND MEMBRANES. 265. Vibrations of rods. — Rods and narrow plates of wood, of glass, and especially of tempered steel, vibrate in virtue .of their elasticity ; like strings they have two kinds of vibrations, longitudinal and transverse. The latter are produced by fixing the rods at one end, and passing a bow over the free part.. Longitudinal vibrations are produced by fixing the rod at any part, and rubbing it in the direction of its length with a piece of cloth sprinkled with resin. But in the latter case the sound is only produced when the point of the rod at which it has been fixed is some aliquot part of its length, as a half, a third, or a quarter. It is shown by calculation that the nuniber of transverse vibrations made in a given time by rods and thin plates of the same kind is directly as their thickness, and inversely as the square of their length. The width of the plate does not affect the number of vibrations. A wide plate, how- ever, requires a greater force to set it in motion than a narrow one. It is, of course, understood that one end of the vibrating plate is held firmly. The laws of the longitudinal vi- brations of strings, are expressed in the formula ;z = _i /^^ in 2.rl V -nd which «, r, /, d, and g, have all the same meaning as in the formula for the transverse vibrations, while O is the coefficient of elasticity of the string, the number which ex- presses the weight by which the cord must be stretched in order to elongate by its own length. Fig. 203 represents an instru- ment invented by Marloye, and known as Marloye's harp, based on the longitudinal vibration of rods. It consists of a solid wooden pedestal in which are fixed twenty thin deal rods, some coloured and others white. They are of such a length that the white rods give the diatonic scale, while the coloured Y\a- 203 °^^^ Si'^^ th^ semitones, and com- plete the chromatic scale. The in- strument is played by rubbing the rods in the direction of their length between the finger and thumb, which have been previously covered -266] Vibrations of Rods and Plates. 215 with powdered resin. The notes produced resemble t"hose of a pan- daean pipe. The timing-fork, the triangle, and musical boxes are examples of the transverse vibrations of rods. In musical boxes small plates of steel of different dimensions are fixed on a rod, like the teeth of a comb. A cylinder whose axis is parallel to this rod, and whose surface is studded with steel teeth, arranged in a certain order, is placed near the plates. By means of a clockwork motion, the cylinder rotates, and the teeth striking the steel plate set them in vibration, producing a tune, which depends on the arrangement of the teeth on the cylinder. If a given rod be clamped either in the middle, or at both ends, the wave length of the note produced by making it vibrate longitudinally, is double its own length, and if it be clamped at one end only and made to vibrate longitudinally, the wave length of the sound is four times its own length. Thus the former case is analogous to an open pipe, and the latter to a stopped pipe in respect of the sounds produced. 266. Vibrations of plates. — In order to make a plate vibrate, it is fixed in the centre (fig. 204), and a bow rapidly drawn across one of the Fig. 205. edges ; or else it is fixed at any point of its surface, and caused to vibrate by rapidly drawing a string covered with resin against the edges of a central hole (fig. 205). Vibrating plates contain nodal lines (253), which vary in number and position according to the form of the plates, their elasticity, the mode of excitation, and the number of vibrations. These nodal lines may be made visible by covering the plate with fine sand before it is made to vibrate. As soon as the vibrations commence, the sand leaves the vibrating parts, and accumulates on the nodal lines, as seen in figs. 204 and 205. The position of the nodal lines may be determined by touching the 2i6 Acoustics. [267- points at which it is desired to produce them. Their number increases with the number of vibrations, that is, as the note given by the plates is higher. The nodal lines always possess great symmetry of form, and the same form is always produced on the same plate under the same con- ditions. They were discovered by Chladni. The vibrations of plates are governed by the following law : — /;/ plates of the same kind and shape ^ and giving the same system of nodal lines, the ntwiber of vibrations per second is directly as the thickftess of the plates, and inversely as their area. Go7igs and cymbals are examples of instruments in which sounds are produced by the vibration of metallic plates. The glass harmotiicon depends on the vibrations of glass plates. 267. Vibrations of xuembranes, — In consequence of their inflexibility membranes cannot vibrate unless they are stretched, like the skin of a drum. The sound they give is more acute in proportion as they are smaller and more tightly stretched. To obtain vibrating membranes, Savart fastened gold-beater's skin on wooden frames. Fig. 206. In the drum, the skins are stretched on the ends of a cylindrical box. When one end is struck, if communicates its vibrations to the internal column of air, and the sound is thus considerably strengthened. The cords stretched against the lower skin strike against it when it vibrates, and produce the sound characteristic of the drum. Membranes either vibrate by direct percussion, as in the drum, or they rhay be set in vibration by the vibrations of the air, as Savart has observed, provided these vibrations are sufficiently intense. Fig. 206 shows a mem- brane vibrating under the influence of the vibrations in the air caused by a sounding bell. Fine sand strewn on the membrane shows the formation of nodal lines just as upon plates. There are numerous instances in which solid bodies are set in vibration by the vibrations of the air. The condition most favourable for the pro- duction of this phenomenon is, that the body to be set in vibration is under such conditions that it can readily produce vibrations of the same dura- tion as those transmitted to it by the air. The following are some of these phenomena : If two violoncello strings tuned in unison are stretched on the same -268] Methods of Studying Vibratory Motions. 2 1 7 sound-box, as soon as one of them is sounded, the other is set in vibration. This is also the case if the interval of the strings is an octave, or a perfect _^ fifth. A violin string may also be made to vibrate by sounding a tuning- fork. Two large glasses are taken of the same shape, and as nearly as pos- sible of the same dimensions and weight, and are brought in unison b'y pouring into them proper quantities of water. If now one of them is sounded, the other begins to vibrate, even if it is at some distance, but if water be added to the latter, it ceases to vibrate. Breguet found that if two clocks, whose time was not very different, were fixed on the same metallic support,, they soon attained exactly the same time. Membranes are eminently fitted for taking up the vibrations of the air, on account of their small mass, their large surface, and the readiness with which they subdivide. With a pretty strong whistle, nodal lines may be produced in a membrane stretched on a frame, even at the distant end of a large room. The phenomenon so easily produced in easily-moved bodies is also found in large and less elastic masses ; all the pillars and walls of a church vibrate more or less while the bells are being rung. ' chAPTER Vl. GRAPHICAL METHOD OF STUDYING VIBRATORY MOTIONS. 268. AK. Ziissajous' xnetbod of making- vibrations apparent. — The method of M. Lissajous exhibits the vibratory motion of bodies either directly or by projection on a screen. It has also the great advantage that the vibratory motions of two sounding bodies may be compared without the aid of the ear, so as to obtain the exact relation between them. This method, which depends on the persistence of visual sensations on the retina, consists in fixing a small mirror on the vibrating body, so as to vibrate with it, and impart to a luminous ray a vibratory motion similar to its own. M. Lissajous uses tuning-forks, and fixes to one of the prongs a small metallic mirror, in (fig. 207), and to the other a counterpoise, ;/, which is necessary to make the tuning-fork vibrate regularly for a long time. At a few yards' distance from the mirror there is a lamp surrounded by a dark chimney, in which is a small hole, giving a single luminous point. The tuning-fork being at rest, the eye is placed so that the luminous point is seen at 0. The tuning-fork is then made to vibrate, and the image elon- gates so as to form a persistent image, oi, which -diminishes in proportion as the amplitude of the oscillation decreases. If, during the oscillation of the mirror, it is made to rotate by rotating the tuning-fork on its axis, a sinuous line, oix, is produced instead of the straight line oi. These dif- ferent effects are explained by the successive displacements of the luminous pencil, and by the duration of these luminous impressions on the eye after L 2l8 Acoustics. [268- the cause has ceased, a phenomenon to which we shall revert in treating of vision. '■VXAAJ, |.- rwiViihi Fig. 207. N LAMBERT Fig. 208, If, instead of viewing these effects directly, they are projected on the screen, the experiment is arranged as shown in fig. 208, the pencil reflected -270] Optical Combination of Vibratory Motions, 219 from the vibrating mirror is reflected a second time from a fixed mirror, rn, which sends it towards an achromatic lens, /, placed so as to project the images on the screen. 269. Combination of two vibratory motions in tbe same direction. — M. Lissajous has resolved the problem of the optical combination of Fig. 209. two vibratory motions — vibrating at first in the same direction, and then at right angles to each other. Fig. 209 represents the experiment as arranged for combining two parallel motions. Two tuning-forks provided with mirrors are so arranged that the light reflected from one of them reaches the other, which is almost parallel to it, and is then sent towards a screen after having passed through a lens. If now the first tuning-fork alone vibrates, the image on the screen is the same as in figure 209 ; but if they both vibrate, supposing they are in unison, the elongation increases or diminishes according as the simultaneous motions imparted to the image by the vibrations of the mirrors do or do not coincide. If the tuning-forks pass their position of equilibrium in the same time, and in the same direction, the image attains its maximum ; and the image is at its minimum when they pass at the same time but in opposite direc- tions. Between these two extreme cases the amplitude of the image varies according to the time which elapses between the exact instant at which the tuning-forks pass through their position of rest respectively. The ratio of this time to the time of a double vibration is called a differ- ence of phase of the vibration. If the tuning-forks are exactly in unison, the luminous appearance on the screen experiences a gradual diminution of length in proportion as the amplitude of the vibration diminishes ; but if the pitch of one is very little altered, the magnitude of the image varies periodically, and, while the beats resulting from the imperfect harmony are distinctly heard, the eyes see the concomitant pulsations of the image. 270. Optical combination of two vibratory motions at rig-bt ang^les to eacb other. — The optical combination of two rectangular vibratory motions is effected as shown in the figure 210, that is, by means of two 220 A cons tics. [270- tuning-forks, one of which is horizontal and the other vertical, and both provided with mirrors. If the horizontal fork first vibrates alone, a hori- zontal luminous outline is seen on the screen, while the vibration of the other produces a vertical image. If both tuning-forks vibrate simul- taneously the two motions combine, and the reflected pencil describes a more or less complex curve, the form of which depends on the number of vibrations of the two tuning-forks in a given time. This curve gives a valuable means of comparing the number of vibrations of two sounding bodies. Fig. 211 show^s the luminous image on the screen when the tuning-forks are in unison, that is, when the number of vibrations is equal. Thefractions below each curve indicate the differences of phase between them. The initial form of the curve is determined by the difference of phase. The curve retains exactly the same form when the tuning-forks are in unison, provided that the amplitudes of the two rectangular vibra- tions decrease in the same ratio. 271] Optical Combination of Vibratory Motions. 22* If the tuning-forks are not quite in unison, the initial difference of phase is not preserved, and the curve passes through all its variations. Fig. 212 represents the different appearances of the luminous image when the difference between the tuning-forks is an octave ; that is, when Fig. 212. the numbers of their vibrations are as i : 2 ; and fig. 213 gives the series of curves when the numbers of the vibrations are as 3 : 4. It will be seen that the curves are more complex when the ratios or the numbers of vibrations are less simple. M. Lissajous has examined these curves theoretically {Annales de Physique et de CJiiiiiie^ 1857), and has calculated their general equations. When these experiments are made with a Duboscq's photo-electrical apparatus instead of an ordinary lamp, the phenomena are remarkably brilliant. 271. Zieon Scott's Phonautogrrapli.— This beautiful apparatus pos- ■ sesses the great advantage of being able to register not only the vibra- tions produced by solid bodies, but also those produced by wind instru- ments, by the voice in singing, and even by any noise whatsoever, for instance,''that of thunder, or the report of a cannon. It consists of an 222 Acoustics » [271- ellipsoidal barrel, AB, about a foot and a half long and a foot in its greatest diameter, made of plaster of Paris. The end A is open, but the end B is closed by a solid bottom, to the middle of which is fitted a brass tube, rt, bent at an elbow and terminated by a ring on which is fixed a flexible membrane which by means of a second ring can be stretched to the required amount. Near the centre of the membrane, fixed by sealing- wax, is a hog's bristle which acts as a style, and, of course, shares the Fig. 214. movements of the membrane. In order that the style might not be at a node, M. Scott fitted the stretching ring with a moveable piece, /, which he calls a subdivider, and which, being made to touch the membrane first at one point and then at another, enables the experimenter to alter the arrangements of the nodal lines at will. By means of the subdivider the point is made to coincide with a loop, that is, a point where the vibrations of the membrane are at a maximum. When a sound is produced near the apparatus, the air in the ellipsoid, the membrane, and the style will vibrate in unison with it, and it only remains to trace on a sensitive surface the vibrations of the style, and to fix them. For this purpose there is placed in front of the membrane a copper cylinder, C, turning round a horizontal axis by means of a handle, in. On the prolonged axis of the cylinder a screw is cut which works in a nut ; consequently, when the handle is turned, the cylinder gradually advances in the direction of its axis. Round the cylinder is wrapped a sheet of paper, covered with a thin layer of lampblack. The apparatus is used by bringing the prepared paper into contact -271] The P hoiiaiitograph. 223 with the point of the style, and then setting the cylinder in motion round its axis. So long as no sound is heard the style remains at rest, and merely removes the lampblack along a Hne which is a helix on the cylinder, but which becomes straight when the paper is unwrapp>ed. But when a sound is heard, the membrane and the style vibrate in unison, and the line traced out is no longer straight, but undulates ; each undula- tion corresponding to a double vibration of the style^ Co-nsequently, the figures thus obtained faithfully denote the number, amplitude, and iso- chronism of the vibrations. Fig. 215 shows the trace produced when a simple note is sung, and strengthened by means of its upper octave. The latter note is represented by the curve of lesser amplitude. Fig. 216 represents the sound produced Fig. 215. Fig. 216. Fig. 217. Fig. 21 jointly by two pipes whose notes differ by an octave. Fig. 217 in its lower line represents the rolling sound of the letter R when pronounced with a ring ; and fig. 218 on its lower Hne represents the sound produced by a tin plate when struck with the finger. The upper lines of figs. 217 and 218 are the same, and represent the perfectly isochronous vibrations of a tuning-fork placed near the ellipsoid. These lines were traced by a fine point on one branch of the fork, which was thus found to make exactly 500 vibrations per second. In conse- quence, each undulation of the upper line corresponds to the s^^th part of a second ; and thus these lines become very exact means of measuring short intervals of time. For example, in fig. 217, each of the separate 224 Acoustics. [271- shocks producing the rolling sound of the letter R corresponds to about 1 8 double vibrations of the tuning-fork, and consequently lasts about -^^^ or about ^-^Xh of a second. 272. K6nlg:'s znanoznetric flames. — Konig's method consists in trans- mitting the movement of the sonorous waves which constitute a sound to gas flames, which, by their pulsations, indicate the nature of the sounds. For this purpose a metallic capsule, represented in section at A, fig. 219 Fig. 219. is divided into two compartments by a thin membrane of caoutchouc ; on the right of the figure is a gas jet, and below it a tube conveying coal gas; on the left is a tubulure, to which may be attached a caoutchouc tube. The other end of this may be placed at the node of an organ pipe (258) or it terminates in a mouth-piece, in front of which a given note may be sung ; this is the arrangement represented in fig. 219. When the sound waves enter the capsule by the mouth-piece and the tube, the membrane yielding to the condensation and rarefaction of the waves, the coal gas in the compartment on the right is alternately con- tracted and expanded, and hence are produced alternations in the length of the flame, which are, however, scarcely perceptible when the flame is observed directly. But to render them distinct they are received on a mirror with four faces, M, which may be turned by two cog-wheels and a handle. As long as the flame burns steadily there appears in the mirror, when turned, a continuous band of light. But if the capsule is connected with a sounding tube yielding the fundamental note, the image of the -272] Kdnigs M alio metric Flames. 22 1; flame takes the form represented in figure 220, and that of figure 221 if the sound yields the octave. If the two sounds reach the capsule simul- taneously the flame has the appearance of fig. 222: in that case, however Fig. 220. Fig. 221 the tube leading to the capsule must be connected by a T-pipe with two sounding tubes, one giving the fundamental note, and the other the Fig. 222. Fig. 223. octave. If one gives the fundamental note and the other the third, the. flame has the appearance of figure 223. 226 Acoustics. [272- If the vowel E be sung in front of the mouth-piece first upon c, and then upon c'^ the turning mirror gives the flames represented in figs. Fig. 224. Fig. 225. 224 and 225 ; and by singing the vowel O on the same notes the figs. 226 and 227. Fig. 226. Fig. 227. ■273] Heat, 227 CHAPTER I. PRELIMINARY IDEAS. THERMOMETERS. 273. Heat. Hypothesis as to its nature. — In ordinary language the term heat is used not only to express a particular sensation, but also to describe that particular state or condition of matter which produces this sensation. Besides producing this sensation, heat acts variously upon bodies ; it melts ice, boils water, makes metals red-hot, produces elec- trical currents, decomposes compound bodies, and so forth. Two theories as to the cause of heat have been propounded ; these are the theory of emission and the theory of undulation. On the first theory, heat is caused by a subtle imponderable fluid, which surrounds the molecules of bodies, and which can pass from one body to another. These heat atmospheres, which thus surround the molecules, exert a repelling influence on each other, in consequence of which heat acts in opposition to the force of cohesion. The entrance of this sub- stance into our bodies produces the sensation of warmth, its egress the sensation of cold. On the second hypothesis the heat of a body is caused by an ex- tremely rapid oscillating or vibratory motion of its molecules ; and the hottest bodies are those in which the vibrations have the greatest velocity and the greatest amplitude. At any given time the whole of the mole- cules of a body possess a sum of vis viva which is the heat they contain. To increase their temperature is to increase their vis viva ; to lower their temperature is to decrease their vis viva. Hence, on this view, heat is not a substance but a condition of 7natter, and a condition which can be transferred from one body to another. When a heated body is placed in contact with a cooler one the former cedes more molecular motion than it receives ; but the loss of the former is the equivalent of the gain of the latter. It is also assumed that there is an imponderable elastic ether, which pervades all matter and infinite space. A hot body sets this in rapid vibration, and the vibrations of this ether being communicated to material objects set them in more rapid vibration, that is, increase their 228 On Heat, [273- temperature. Here we have an analogy with sound ; a sounding body is in a state of vibration, and its vibrations are transmitted by atmo- spheric air to the auditory apparatus in which is produced the sensation of sound. This hypothesis as to the nature of heat is now admitted by the most distinguished physicists. It affords a better explanation of all the pheno- mena of heat than any other theory ; and it reveals an intimate connec- tion between heat and light. It will be subsequently seen that by the friction of bodies against each other an indefinite quantity of heat is produced. Experiment has shown that there is an exact equivalence between the motion thus destroyed and the heat produced. These and many other facts are utterly inexplicable on the assumption that heat is a substance, and not a form of motion. In what follows, however, the phenomena of heat will be considered, as far as possible, independently of either hypothesis ; but we shall sub- sequently return to the reasons for the adoption of the latter hypothesis. Assuming that the heat of bodies is due to the motion of their particles, we may admit the following explanation as to the nature of this motion in the various forms of matter. In solids the molecules have a kind of vibratory motion about certain fixed positions. This motion is probably very complex ; the constituents of the molecule may oscillate about each other, besides the oscillation of the molecule as a whole, and this latter again may be a to-and-fro motion, or it may be a rotatory motion about the centre. In the liquid state the molecules have no fixed positions. They can rotate about their centres of gravity, and the centre of gravity itself may move. But the repellent action of the motion, compared with the mutual attraction of the molecules is not sufficient to separate the molecules from each other. A molecule no longer adheres to particular adjacent ones ; but it does not spontaneously leave them except to come into the same relation to fresh ones as to its previous adjacent ones. Thus in a liquid there is a vibratory, rotatory, and progressive motion. In \)ciQ gaseous state the molecules are entirely without the sphere of their mutual attraction. They fly forward in straight lines according to the ordinary laws of motion, until they impinge against other molecules, or against a fixed envelope which they cannot penetrate, and then return in an opposite direction, with, in the main, their original velocity. The perfection of the gaseous state implies that the space actually occupied by the molecules of the gas be infinitely small compared with the entire volume of the gas ; that the time occupied by the impact of a molecule either against another molecule or against the sides of the vessel ht in- finitely small in comparison with the interval between any two impacts ; and that the influence of molecular attraction be infinitely small. When these conditions are not fulfilled the gas partakes more or less of the nature of a liquid, and exhibits certain deviations from Boyle's law. This is the case with all gases ; to a very slight extent with uncondensible gases, but to a far greater extent with vapours and condensible gases, especially near their points of liquefaction. -275] General Effects of Heat. 229 274. General effects of heat. — The general effects of heat upon bodies may be classed under three heads. One portion is expended in raising, the temperature of the body, that is, in increasing the vis viva of its molecules. In the second place, the molecules of bodies have a certain attraction for each other, owing to which is due their relative positions ; hence a second portion of heat is consumed in augmenting the ampli- tude of the oscillations, by which an increase of volume is produced, or in completely altering the relative positions of the molecules by which a change of state is effected. These two effects are classed as internal "duork. Thirdly, since bodies are surrounded by atmospheric air which exerts a certain pressure on their surface, this has to be overcome or lifted through a certain distance. The heat or work required for this is called the external work. If O units of heat are imparted to a body, and if A be the quantity of heat which is equivalent to the unit of work ; then if W is the amount of heat which serves to increase the temperature, I that required to alter the position of the molecules, and if L be the equivalent of the external work, then Q = A(W + I + L). 275. Expansion. — All bodies expand by the action of heat. As a general rule, gases are the most expansible, then liquids, and lastly solids. In solids which have definite figures, we can either consider the expan- sion in one dimension, or the linear expansion ; in two dimensions, the supe7'ficial expansion ; or in three dimensions, the (;;//^zV<2/ expansion or the expansion of volume, although one of these never takes place without the other. As Hquids and gases have no definite figures, the expansions of volume have in them alone to be considered. To show the linear expansion of solids, the apparatus represented in fig. 228 may be used. A metal rod, A, is fixed at one end by a screw Fig. 228. B, while the other end presses against the short arm ot an index, K which moves on a scale. Below the rod there is a sort of cylindrical lamp in which alcohol is burned. The needle K is at first at the zero point, but as the rod becomes heated, it expands, and moves the needle alonof the scale. 230 On Heat. [275- The cubical expansion of solids is shown by a Gravesande^s ring. It consists of a brass ball a (fig. 229), which at the ordinary temperature passes freely through a ring, ;«, almost of the same diameter. But when the ball has been heated, it expands and no longer passes through the ring. In order to show the expansion of liquids, a large glass bulb provided with a capillary stem is used (fig. 230). If the bulb and a part of the Fig. 229. Fig. 230. Fig. 231 Stem contain some coloured liquid, the liquid rapidly rises in the stem when heat is applied, and the expansion thus observed in far greater than in the case of solids. The same apparatus may be used for showing the expansion of gases. Being filled with air, a small thread of mercury is introduced into the capillary tube to serve as index (fig. 231). When the globe is heated in the slightest degree, even by approaching the hand, the expansion is so great that the index is driven to the end of the tube, and is finally expelled. Hence, even for a very small degree of heat, gases are highly expansible. In these different experiments the bodies contract on cooling, and when they have attained their former temperature they resume their original volume. Certain metals, however, especially zinc, form an ex- ception to this rule, and it appears to be also the case with some kinds of glass. MEASUREMENT OF TEMPERATURE. THERMOMETRY. 276. Temperature. — The temper attire or hotness of a body, indepen- dently of any hypothesis as to the nature of heat, may be defined as being -278] Thermometers. 231 the greater or less extent to which it tends to impart sensible heat to othen bodies. The temperature of a body must not be confounded with thfr quantity of heat it possesses ; a body may have a high temperature and yet have a very small quantity of heat, and conversely a low temperature and yet possess a large amount of heat. If a cup of water be taken from a bucketful, both will indicate the same temperature, yet the quantities they possess will be different. This subject of the quantity of heat will be afterwards more fully explained in the chapter on Specific Heat. 277. TYiemioTaeteT^.— Therfnometers are instruments for measuring temperatures. Owing to the imperfections of our senses we are unable to measure temperatures by the sensation of heat or cold which they produce in us, and for this purpose recourse must be had to the physical action of heat on , bodies. These actions are of various kinds, but the expansion of bodies has been selected as the easiest to observe. But heat also produces electrical phenomena in bodies ; and on these the most delicate methods of observing temperatures have been based, as we shall see in a subsequent chapter. Liquids are best suited for the construction of thermometers — the ex- pansion of solids being too small, and that of gases too great. Mercury and alcohol are the only liquids used — the former because it only boils at a very high temperature, and the latter because it does not solidify at the greatest known cold. The mercurial thermometer is the most extensively used. It consists of a capillary glass tube, at the end of which is blown the bulb, a cylin- drical or spherical reservoir. Both the bulb and a part of the stem are filled with mercury, and the expansion is measured by a scale graduated either on. the stem itself, or on a frame to which it is attached. Besides the manufacture of the bulb, the construction of the thermo- meter comprises three operations : the calibration of the tube, or its division into parts of equal capacity, the introduction of the mercury into the reservoir, and the graduation. 278. Division of the tube into parts of equal capacity. — As the indications of the thermometer are only correct when the divisions of the scale correspond to equal expansions of the mercury in the reservoir, the scale must be graduated so as to indicate parts of equal capacity in the tube. If the tube were quite cylindrical, and of the same diameter throughout, it would only be necessary to divide it into equal lengths. But as the diameter of glass tubes is usually greater at one end than another, parts of equal capacity in the tube are represented by unequal lengths of the scale. In order, therefore, to select a tube of uniform calibre, a thread of mercury about an inch long is introduced into the capillary tube, and moved in different positions in the tube, care being taken to keep it at the same temperature. If the thread is of the same length in every part of the tube, it shows that the capacity is everywhere the same ; but if the thread occupies different lengths the tube is rejected, and another one sought. 232 On Heat. [279- 279. Filling: tlie thermometer.— In order to fill the thermometer with mercury, a small funnel, C (fig. 232), is blown on at the top, and is filled, with mercury ; the tube is then slightly inclined, and the air in the bulb expanded by heating it with a spirit lamp. The expanded air partially escapes by the funrtel, and on cooling, the air which remains contracts, and a portion of the mercury passes into the bulb D. The bulb is then again warmed, and allowed to cool, a fresh quantity of mercury enters, and so on, until the bulb and part of the tube are full of mercury. The mercury is then heated to boihng ; the mercurial vapours in escaping carry with them the air and moisture which remain in the tube. The tube, being full of the expanded mercury and of mercurial vapour, is hermetically sealed at one end. When the thermometer is cold, the mercury ought to fill the bulb and a portion of the stem. 280. Graduation of the thermometer. — The thermometer being filled, it requires to be gra- duated, that is, to be provided with a scale to which variations of temperature can be referred. And, first of all, two points must be fixed which represent identical temperatures and which can always be easily produced. Experiment has shown that ice always melts at the same point whatever be the degree of heat, and that distilled water under the same pressure, and in a vessel of the same kind, always boils at the same temperature. Consequently, for the first fixed point, or zero, the temperature of melting ice has been taken ; and for a second fixed point, the temperature of boiling water in a metallic vessel under the normal atmospheric pressure of 760 millimetres. This interval of temperature, that is, the range from zero to the boiling point, is taken as the unit for comparing temperatures ; just as a certain length, a foot or a metre for instance, is used as a basis for comparing lengths. 281. Determination of the fixed points. — To obtain zero, snow or pounded ice is placed in a vessel, in the bottom of which is an aperture by which water escapes (fig. 233). The bulb and a part of the stem of the thermometer are immersed in this for about a quarter of an hour, and a mark made at the level of the mercury which represents zero. The second fixed point is determined by means of the apparatus re- presented in the figures 234 and 235, of which 235 represents a vertical section. In both, the same letters designate the same parts. The whole of the apparatus is of copper. A central tube, A, open at both ends, is fixed on a cylindrical vessel containing water ; a second tube, B, con- centric with the first, and surrounding it, is fixed on the same vessel, M. Fig. 235 -281] Graduation of the Thermometer. 233 In this second cylinder, which is closed at both ends, there are three tubulures, a^ E, D. . A cork, in which is the thermometer /, fits in a. To E a glass tube, containing mercury, is attached, which serves as a manometer for measuring the pressure of the vapour in the apparatus. D is an escape tube for the vapotir and condensed water. The apparatus is placed on a furnace and heated till the water boils ; the vapour produced in M rises in the tube A, and passing through the two tubes in the direction of the arrows, escapes by the tubulure D. The thermometer / being thus surrounded with vapour, the mercury expands and when it has become stationary, the point at which it stops is marked. This is the point sought for. The object of the second case, B, is to avoid the cooling of the central tubulure by its contact with the air. The determination of the point 100 (see next article) would seem to require that the height ot the barometer during the experiment should be 760 millimetres, for when the barometric height is greater or less than this quantity, water boils either above or below 100 degrees. But the Fig. 233. \ Fig. 234. Fig. 235 point 100 may always be exactly obtained, by making a correction in- troduced by M. Biot. He found that, for every 27 millimetres' difference in height of the barometer, there was a difference in the boiling point of I degree. If, for example, the height of the barometer is 778— that is 234 On Heat. [281- I 1 8 millimetres, or two-thirds of 27, above 760— water would boil at 100 degrees and two-thirds. Consequently, loof would have to be marked aj the point at which the mercury stops, Gay-Lussac observed that water boils at a somewhat higher tem- perature in a glass than in a metal vessel : and as the boiling point is raised by any salts which are dissolved, it has been assumed that it was necessary to use a metal vessel and distilled water in fixing the boiling point. M. Rudberg has, however, shown that these latter precautions are superfluous. The nature of the vessel, and salts dissolved in ordinary water, influence the temperature of boiling water, but not that of the vapour which is formed. That is to say, that if the temperature of boil- ing water from any of the above causes is higher than 100 degrees, the temperature of the vapour does not exceed 100, provided the pressure is not more than 760 millimetres. Consequently, the higher point may be (g) determined in a vessel of any material, provided the thermo- meter is quite surrounded by vapour, and does not dip in the water. Even with distilled water, the bulb of the thermometer must not dip in the liquid ; for it is only the upper layer that really has the temperature of 100 degrees, since the temperature in- creases from layer to layer towards the bottom in consequence of the increased pressure. 282. Construction of tbe scale. — Just as the foot-rule which is adopted as the unit of comparison for length is divided into a number of equal divisions called inches for the purpose of having a smaller unit of comparison, so likewise the unit of comparison of temperatures, the range from zero to the boiling point, must be divided into a number of parts of equal capacity called degrees. There are three modes in which this is done. On the Continent, and more especially in France, this space is divided into 100 parts, and this division is called the Cetitigrade or Celsius scale; the latter being the name of the inventor. The Centigrade thermometer is almost exclusively adopted in foreign scientific works, and as its use is gradually extending in this country, it has been and will be adopted in this book. The degrees are designated by a small cipher placed a little above on the right of the number which marks the temperature, and to indicate temperatures below zero the mihus sign is placed before them. Thus, —15° signifies 15 degrees below zero. In accurate thermometers the scale is marked on the stem itself (fig. 235). It cannot be displaced, and its length remains fixed, as glass has very little expansibihty. The graduation is effected by covering the stem with a thin layer of wax, and then marking the divisions of the scale, as well as the corresponding numbers, with a steel point. The thermometer is then exposed for about ten minutes to the vapours of hydrofluoric acid, which attacks the glass where the wax has been removed. The rest of the wax is then removed, and the stem is found to be permanently etched. Fig. 236. -282] Construction of the Therino7neter Scale. 235 Besides the Centigrade scale two others are frequently used — Fahren- heit's scale and Reaionur^s scale. In Reaumur's scale the fixed points are the same as on the Centi- grade scale, but the distance between them is divided into 80 degrees, instead of into 100, That is to say, 80 degrees Reaumur are equal to 100 degrees Centigrade ; one degree Reaumur is equal to ^^^ or | of a degree Centigrade, and one degree Centigrade equals y^o^o *^^ I degrees Reaumur. Consequently, to convert any number of Reaumur's degrees into Centigrade degrees (20 for example), it is merely necessary to multiply them by f (which gives 25). Similarly, Centigrade degrees are converted into Rdaumur by multiplying them by f . The thermometric scale invented by Fahrenheit in 17 14 is still much used in England, and also in Holland and North America. The higher fixed point is like that of the other scales, the temperature of boiling water, but the null point or zero is the temperature obtained by mixing equal weights of sal-ammoniac and snow, and the interval between the two points is divided into 212 degrees. The zero was selected because the temperature was the lowest then known, and was thought to repre- sent absolute cold. When Fahrenheit's thermometer is placed in melting ice it stands at 32 degrees, and, therefore, 100 degrees on the Centigrade scale are equal to 1 80 degrees on the Fahrenheit scale, and thus i degree Centigrade is equal to | of a degree Fahrenheit, and inversely i degree Fahrenheit is equal to | of a degree Centigrade. If it be required to convert a certain number of Fahrenheit degrees (95 for example) into Centigrade degrees, the number 32 must first be sub- tracted, in order that the degrees may count from the same part of the scale. The remainder in the example is thus 63, and as i degree Fah- renheit is equal to | of a degree Centigrade, 63 degrees are equal to 63 + 1 or 35 degrees Centigrade. If F be the given temperature in Fahrenheit degrees and C the corre- sponding temperature in Centigrade degrees, the former may be converted into the latter by means of the formula (F. = 32)f = C, and conversely. Centigrade degrees may be converted into Fahrenheit by means of the formula fC. + 32 = F. These formulas are applicable to all temperatures of the two scales, pro- vided the signs are taken into account. Thus, to convert the temperature of 5 degrees Fahrenheit into Centigrade degrees, we have (5-32)1 = :::^^^ = -15 c. In like manner we have, for converting Reaumur into Fahrenheit degrees, the formula |R. + 33 = F, and conversely, for changing Fahrenheit into Rdaumur degrees, the formula CF.-32)| = R. 236 On Heat [283- 283. Displacement of zero. — Thermometers, even when constructed with the greatest care, are subject to a source of error which must be taken into account : this is, that in course of time the zero tends to rise, the displacement sometimes extending to as much as 2 degrees ; so that when the thermometer is immersed in melting ice it no longer sinks to zero. This is generally attributed to a diminution of the volume of the reservoir and also of the stem, occasioned by the pressure of the atmosphere. It is usual with very delicate thermometers to fill them two or three years before they are graduated. Besides this slow displacement, there are often variations in the position of the zero, when the thermometer has been exposed to high temperatures, caused by the fact that the bulb and stem do not contract on cooling to their original volume (275), and hence it is necessary to verify the position of zero when a thermometer is used for delicate determinations. Regnault has found that some mercurial thermometers, which agree at 0° and at 100°, differ between these points, and that these differences frequently amount to several degrees. Regnault thinks that this is due to the unequal expansion of different kinds of glass. 284. limits to tbe employment of mercurial thermometers. — Of all thermometers in which liquids are used, the one with mercury is the most useful, because this liquid expands most regularly, and is easily obtained pure, and because its expansion between —36° and 100° is 7'cgular, that is proportional to the degree of heat. It also has the advantage of having a very low specific heat. But for temperatures below —36° C. the alcohol thermometer must be used, for mercury solidifies at —40° C. Above 100 degrees the coefficient of expansion increases and the indications of the mercurial thermometers are only approximate, the error arising sometimes to several degrees. Mercurial thermometers also cannot be used for temperatures above 350°, for this is the boiling point of mercury. 285. Alcohol thermometer. — The alcohol thermometer differs from the mercurial thermometer in being filled with coloured alcohol. But as the expansion of liquids is less regular in proportion as they are near the boiling point, alcohol which boils at 78° C, expands very irregularly. tTence, alcohol thermometers are usually graduated by placing them in baths at different temperatures together with a standard mercurial thermometer, and marking on the alcohol thermometer the temperature indicated by the mercurial thermometer. In this manner the alcohol thermometer is comparable with the mercurial one ; that is to say, it indicates the same temperatures under the same conditions. The alcohol thermometer is especially used for low temperatures, for it does not solidify at the greatest known cold. 286. Conditions of the delicacy of a thermometer. — A thermometer may be delicate in two ways: — i, When it indicates very small changes of temperature. 2. When it quickly assumes the temperature of the surrounding medium. The first object is attained by having a very narrow capillary tube and -288] Differential Thermometer. 237 a very large bulb ; the expansion of the mercury on the stem is then limited to a small number of degrees, the 10 to 20 or 20 to 30 for instance so that each degree occupies a great length on the stem, and can be sub- divided into very small fractions. The second kind of delicacy is obtained by making the bulb very small, for then it rapidly assumes the tempera- ture of the liquid in which it is placed. A good mercurial thermometer should answer to the following tests : When its bulb and stem, to the top of the column of mercury, are im- mersed in melting ice, the top of the mercury should exactly indicate o°C. ; and when suspended with its bulb and scale immersed in the steam of water boiling in a metal vessel (as in fig. 234), the barometer standing at 760 mm., the mercury should be stationary at 100° C. When the instru- ment is inverted, the mercury should fill the tube, and fall with a metallic click, thus showing the complete exclusion of air. The value of the de- grees should be uniform : to ascertain this, a little cylinder of mercury may be detached from the column by a slight jerk, and on inclining the tube it may be made to pass from one portion of the bore to another. If the scale be properly graduated, the column will occupy an equal number of degrees in all parts of the tube. 287. Differential thermometer.— Sir John Leslie constructed a thermometer for showing the difference of temperature of two neigh- bouring places, from which it has received the name differetitial ther- mometer. A modified form of it is that devised by Matthiesson (fig. 237), which has the advantage of being available for indicating the temperature of liquids. It consists of a bent glass tube, each end i of which is bent twice, and terminates in a bulb ; the bulbs being pendant can be readily immersed in a liquid. The bend contains some coloured liquid, and in atube which connects the two limbs is a stopcock, by which the liquid in each hmb is easily brought to the same level. The whole is supported by a frame. When one of the bulbs is at a higher temperature than the other, the liquid in the stem is depressed, and rises in the other stem. The instrument is now only used as a thermoscope^ that is to indicate a difference of temperature between the two bulbs and not to measure its amount. 288. Sregruet's metallic ther- mometer. — Breguet invented a thermometer founded on the unequal expansion of metals, and remark- 238 On Heat. [288- able for its delicacy. It consists of three strips of platinum, gold, and silver, which are passed through a rolling mill so as to form a very thin metallic ribbon. This is then coiled in a spiral form, as seen in fig. 238, and one end being fixed to a support, a light needle is fixed to the other, v/hich is free to move round a graduated scale. Silver, which is the most expansible of the metals, forms the internal face of the spiral, and platinum the external. When the temperature rises, the silver expands more than gold or platinum, the spiral un- winds itself, and the needle moves from left to right of the above figure. The contrary effect is produced when the temperature sinks. The gold is placed between the other two metals, because its expansibility is interme- diate between that of the silver and the platinum. Were these two metals employed alone, their rapid unequal expansion might cause a fracture. Breguet's thermometer is graduated in Centigrade degrees, by comparing it with a standard mercurial thermo- meter. 289. Rutberford's xnaxixuum and xuinimuzu thermometers.— It is ne- cessary, in meteorological observations, to know the highest temperature of the day and the lowest temperature of the night. Ordinary thermometers could only give these indications by a continuous observation, which would be impracticable. Several instruments have accordingly been in- vented for this purpose, the simplest of which is Rutherford's. On a rectangular piece of plate-glass (fig. 239) two thermometers are fixed, Pig. 238. ^ Fig. 239. whose stems are bent horizontally. The one. A, is a mercurial, and the other, B, an alcohol thermometer. In A there is a small piece of iron wire, A, moving freely in the tube, which serves as an index. The ther- mometer being placed horizontally, when the temperature rises the mer- 291] Different Remarkable Temperatures. 239 cury pushes the index before it. But as soon as the mercury contracts the index remains in that part of the tube to which it has been moved, for there is no adhesion between the iron and the mercury. In this way the index registers the highest temperature which has been attained ; in the figure this is 31°. In the minimum thermometer there is a small hollow glass tube which serves as index. When it is at the end of the column of liquid, and the temperature falls, the column contracts, and carries the index with it, in consequence of adhesion, until it has reached the greatest contraction. When the temperature rises the alcohol ex- pands, and passing between the sides of the tube and the index, does not displace B. The position of the index gives therefore the lowest temper- ature which has been reached : in the figure this was 9^ degrees below zero. 290. Pyrometers. — The name pyrometers is given to instruments for measuring temperatures so high that mercurial thermometers could not be used. The older contrivances for this purpose, Wedgewood's, DanielFs (which in principle resembled the apparatus in fig. 228), Brongniart's, etc., are gone entirely out of use. None of them gives an exact measure of temperature. The arrangements now used for the purpose are either based on the expansion of gases and vapours, or on the electrical proper- ties of bodies, and will be subsequently described. 291. Different remarkable temperatures. — The following table gives some of the most remarkable points of temperature. It may be observed, that it is easier to produce very high temperatures than very low de- grees of cold. Greatest artificial cold produced by a bath of bisulphide of carbon and liquid nitrous acid — 140° C. Greatest cold produced by ether and liquid carbonic acid — no Greatest natural cold recorded Mercury freezes Mixture of snow and salt . Ice melts .... Greatest density of water . Mean temperature of London Blood heat Water boils Mercury boils . Red heat (just visible) (Daniell) Silver melts . . . „ Cast iron melts . . „ Highest heat of wind furnace „ in Arctic expeditions - 49 - 39'4 - 20 o + 4 9'9 36-6 100 350 526 1000 1530 1800 240 On Heat. [292- CHAPTER II. EXPANSION OF SOLIDS. 292. Xtinear expansion and cubical expansion. Coefficients of expansion. — It has been already explained that in solid bodies the ex- pansion may be according to three dimensions — linear, superficial, and cubical. The coefficient of litiear expansion is the elongation of the unit of length of a body when its temperature rises from zero to one degree ; the coeffi- cient of superficial expansion is the increase of the surfsice in being heated from zero to i degree, and the coefficient of cubical expansion is the in- crease of the unit of volume under the same circumstances. These coefficients vary with different bodies, but for the same body the coefficient of cubical expansion is three times that of the linear expansion ^ as is seen from the following considerations. Suppose a cube, the length of whose side is i at zero. Let k be the elongation of this side in passing from zero to i degree, its length at i degree will be i + >^, and the volume of the cube, which was i at zero, will be (i + k)"^, or 1 + 3^^ + 3/^^ + J^. But as the elongation k is always a very small fraction (see table, art. 294), its square ^^, and its cube P, are so small that they may be neglected, and the value at i degree becomes very nearly i + 3-^. Consequently, the in- crease of volume is 3/^', or thrice the coefficient of linear expansion. In the same manner it may be shown that the coefficient of superficial expansion is double the coefficient of linear expansion. 293. Measurement of the coefficient of linear expansion. Iiavoisier and liaplace's method. — The apparatus used by Lavoisier and Laplace for determining the coefficients of linear expansion (fig. 240) consists of a Fig. 240. brass trough, placed on a furnace between four stone supports. On the two supports, on the right hand, there is a horizontal axis, at the end of which is a telescope ; on the middle of this axis, and at right angles to it, is fixed a glass rod, turning with it, as does also the telescope. The other two supports are joined by a cross piece of iron, to which another glass rod is fixed, also at right angles. The trough, which contains oil or water, is heated by a furnace not represented in the figure, and the bar whose expansion is to be determined is placed in it. -294] Expansion of Solids. 241 Fig. 241 represents a section of the apparatus ; G is the telescope, KH the bar, whose ends press against the two glass rods F and D. As the rod F is fixed, the bar can only expand in the direction KH, and in order to eliminate the effects of friction it rests on two glass rollers. Lastly, the telescope has a cross-view in the eyepiece, which, when the Fig. 241 telescope moves, indicates the depression by the'corresponding number of divisions on a vertical scale AB, at a distance of 220 yards. The trough is first filled with ice, and the bar being at zero, the division on the scale AB, corresponding to the wire of the telescope, is read off. The ice having been removed, the trough is filled with oil or water, which is heated to a given temperature. The bar then expands, and when its temperature has become stationary, which is determined by means of thermometers, the division of the scale, seen through the telescope, is read off. From these data the elongation of the bar is determined ; for since it has become longer by a quantity, CH, and the optical axis of the tele- scope has become inclined in the direction GB, the two triangles, GHC and ABG, are similar, for they have the sides at right angles each to each, so that = .-:— . In the same way, if HC were another elonga- AB AG tion, and AB' a corresponding deviation, there would still be HC^_GH AB' AG ' from which it follows that the ratio between the elongation of the bar and C H the deflection of the telescope is constant, for it is always equal to -—, * A preliminary measurement had shown that this ratio was yij' Con- HG AB sequently, = =^r whence HC=- — ; that is, the total elongation of AB '**' 744 the bar is obtained by dividing the length on the scale traversed by the cross wire by 744. Dividing this elongation by the length of the bar, and then by the temperature of the bath, the quotient is the dilatation for the unit of length and for a single degree — in other words, the coefficient of linear dilatation. 294. Roy and Ramsden's method. — Lavoisier and Laplace's method is founded on an artifice which is frequently adopted in physical deter- minations, and which consists in amplifying by a known amount dimen- sions which, in themselves, are too small to be easily measured. Unfor- tunately this plan is often more fallacious than profitable, for it is first necessary to determine the ratio of the motion measured to that on which 242 On Heat. [294- it depends. In the present case it is necessary to know the lengths ot the arms of the lever in the apparatus, But this preliminary operation may introduce errors of such importance as partially to counterbalance the advantage of great delicacy. The following method, which was used by General Roy in 1787, and which was devised by Ramsden, depends on another principle. It measures the elongations directly, and without amphfying them, but it measures them by means of a micrometer, which indicates very small displacements. The apparatus (fig. 242) consists of three parallel metal troughs about 6 feet long. In the middle one there is a bar of the body whose expan- Fig. 242. sion is to be determined, and in the two others are cast-iron bars 01 exactly the same length as this bar. Rods are fixed vertically on both ends of these three bars. On the rods in the troughs A and B there are rings with cross-wires like those of a telescope. On the rods in the trough C are small telescopes also provided with cross-wires. The trough being filled with ice, and all three bars at zero, the points of intersection of the wires in the disc, and of the wires in the telescope, are all in a line at each end of the bar. The temperature in the middle trough is then raised to 100° C. by means of spirit lamps placed beneath the trough ; the bar expands, but as it is in contact with the end of a screw, rt, fixed on the side, all the elongation takes place in the direction ;/;«, and as the cross-wire n remains in position, the cross-wir^ in is moved towards B by a quantity equal to the elongation. But since the screw a is attached to the bar, by turning it slowly from right to left, the bar is moved in the direction inn, and the cross-wire in regains its original position. To effect this, the screw has been turned by a quantity exactly equal to the elongation of the bar, and as this advance of the -295] Expansion of Solids. 243 screw is readily deduced from the number of turns of its tlwead (11), the total expansion of the bar is obtained, which, divided by the temperature of the bath, and this quotient by the length of the bar at zero, gives the coefficient of linear expansion. Coefficieiits of linear expansion for 1° between 0° and 100° C. White glass . . . o-oockx)86j3 Copper 0-000017182 Platinum .... 0-000008842 Bronze ..... 0-000018167 Untempered steel . 0-000010788 Brass 0-000018782 Cast iron .... 0-000011250 Silver 0-000019097 Wrought iron . . . 0-000012204 Tin 0-000021730 Tempered steel . . 0-000012395 Lead 0-000028575 Gold 0-000014660 Zinc 0-000029417 From what has been said about the linear expansion (292), the co- efficients of cubical expansion of solids are obtained by multiplying those of linear expansion by three. The coefficients of the expansion of the metals vary with their physical condition, being different for the same metal according as it has been cast or hammered and rolled, hardened or annealed. As a general rule, operations which increase the density increase also the rate of expansion. But even for substances in apparently the same condition, different ob- servers have found very unequal amounts of expansions ;, this may arise in the case of compound substances, such as glass, brass, or steel, from a want of uniformity in chemical composition, and in. simple bodies from slight differences of physical state. The expansion of amorphous solids, and of those- which crystallise in the regular system, is the same for all dimensions,, unless they are sub- ject to a strain in some particular direction. A fragjnent of such a sub- stance varies in bulk, but retains the same shape. Crystals not belonging to the regular system exhibit, when heated, an. unequal expansion in the direction of their different axes, in consequence, of which the magnitude of their angles, and therefore their form, is altered. In the dimetric system the expansion is the same in the direction of the two equal axes, but different in the third. In crystals belonging to the hexagonal system the expansion is the same in the direction of the three secondary axes, but different from that according to the principal one. In the trimetric system it is different in all three directions. To the general law that all bodies expand by heat there is an impor- tant exception in the case of iodide of silver, which contracts somewhat when heated. It has a negative coefficient of expansion the value of which is 0-00000139. 295. The coefficients of expansion increase with the temperature. — According to Dr. Matthiessen, who determined the expansion of the metals and alloys by weighing them in water at different temperatures, the coefficients of expansion are not quite regular between 0° and 100°. He found the following values for the linear expansion between 0° and 100°:— M 2' 244 On Heat. [295- Zinc . . . L,= Lo (i +0-00002741 / + 0-0000000235 /') Lead . . L^ = L^ (i + 0-00002726 / + 0-0000000074 i) Silver . . Li = Lo (i +0-00001809 / + 0-0000000135 f^) Copper . , L, = Lq (i + 0-00001408 / + 0-0000000264 f^) Gold . . L, = Lo (i +0-00001358 / + 0-0000000I 12 Z'^) The same authority has found that alloys expand very nearly according to the following law : — ' The coefficients of expansion of an alloy are equal to the mean of the coefficients of expansion of the volumes of the metals composing it.' 296. Formulae relative to the expansion of solids. — Let / be the length of a bar at zero, /' its length at the temperature f C, and « its coefficient of linear expansion. The tables usually give the expansion for 1° between 0° and 100°, as in article 294, or for 100° ; in this latter case n is obtained by dividing the number by 100. The relation existing'between the above quantities is expressed by a few simple formulas. The elongation corresponding to /° is / times a or nt for a single unit of length, or oil for / units. The length of the bar which is / at zero is /+ atl at /", consequently, r^l+atl=l{l+at) This formula gives the length of a body I' at /°, knowing its length /at zero, and the coefficient of expansion a ; and by simple algebraical trans- formations, we can obtain from it formula: for the length at zero, knowing the length /' at t°, and also for finding a the coefficient of linear expan- sion, knowing the lengths /' and / at i° and zero respectively. It is obvious that the formulae for cubical expansion are entirely analo- gous to the preceding. The following are examples of the application of these formulas : — A metal bar has a length /' at i'°, what will be its length / at /° ? From the above formula we first get the length of the given bar at zero, which is ; by means of the same formula we pass from zero to I + at f° in multiplying by i + at', which gives for the desired length the formula 1+at The density of a body being d at zero, required its density d' at t°. If I be the volume of the body at zero, and D its coefficient of cubical expansion, the volume at t will be i + D/, and as the density of a body is in inverse ratio of the volume which the body assumes in expanding, we get the inverse proportion, d' : d=\ : i + D/, d' \ ^' d ^ . ; or d d i + D^' i + D/ Consequently, when a body is heated from o to /°, its density, and therefore its weight for an equal volume, is inversely as the binomial ex- pression, I + D/. -297] Application of the Expansion of Solids. J45 297. Applications of tbe expansion of solids.— In the arts we meet with numerous examples of the influence of expansion, (i.) The bars of furnaces must not be fitted tightly at their extremities, but must, at least, be free at one end, otherwise, in expanding, they would split the masonry. (ii.) In making railways a small space is left between the successive rails, for if they touched, the force of expansion would cause them to curve or would break the chairs, (iii.) Water pipes are fitted to one another by means of telescopic joints, which allow room for expansion, (iv.) If a glass is heated or cooled too rapidly it cracks ; this arises from the fact that glass is a bad conductor of heat, the sides become unequally heated, and consequently unequally expanded, which causes a fracture. "When bodies have been heated to a high temperature, the force pro- duced by their contraction on cooling is very considerable ; it is equal to the force which is needed to compress or expand the material to the same extent by mechanical means. Ac- cording to Barlow a bar of malleable iron a square inch in section is stretched 10000^^ of its length by a weight of a ton ; the same increase is experienced by about 9° C. A difference of 45° C. between the cold of winter and the heat of summer is not unfrequently experienced in this country. In that range, a wrought iron bar ten inches long will vary in length by ^^gth of an inch and will exert a strain, if its ends are securely fastened, of fifty tons. It has been calculated from Joule's data that the force exerted by heat in ex- panding a pound of iron between 0° and 100° during which it increases about olo^^ of its bulk, is equal to 16,000 foot pounds; that is, it could raise a weight of 7 tons through a height of one foot. (i.) An application of this contractile force is seen in the mode of securing the tires on wheels. The tire being made red hot, and thus considerably expanded, is placed on the circumference of the wheel and then cooled. The tire, when cold, em- braces the wheel with such force as not only to secure itself on the rim, but also to press home the joints of the spokes into the felloes and nave, (ii.) Another inter- esting application was made in the case of a gallery at the Conservatoire des Arts et Metiers in Paris, the walls of which had begun to bulge outwards. Iron bars were passed across the building and screwed into plates on the outside of the walls. Each alternate bar was then heated by means of rig- 243- 246 On Heat. [297 o ^ lamps, and when the bar had expanded it was screwed up. The bars being then allowed to cool contracted, and in so doing drew the walls together. The same operation was performed on the other bars. 298. Compensation pendulum. — An important application of the expansion of metals has been made in the cofupensation pendulum. This is a pendulum in which the elongation, when the teipperature rises, is so compensated that the distance between the centre of suspension and the centre of oscillation (76) remains constant, which, from the laws of the pendulum ^^'j), is necessary for isochronous oscillations, and in order that the pendulum may be used as a regulator of clocks. In fig. 243, which represents the gridiron pendulum, one of the com- monest forms of compensation pendulum, the ball, L, instead of being supported by a single rod, is supported by a framework, consisting of alternate rods of steel and brass. In the figure, the shaded rods represent steel ; including a small steel rod, b^ which supports the whole of the apparatus, there are six of them. The rest of the rods, four in number, are of brass. The rod /, which supports the ball, is fixed at its upper end to a horizontal cross-piece ; at its lower end it is free, and passes through the two circular holes in the lower horizontal cross-pieces. Now it is easy to see from the manner in which the vertical rods are fixed to the cross-pieces, that the elongation of the steel rods can only take place in a downward direction, and that of the brass rods in an up- ward direction. Consequently in order that the pendulum may remain of the same length, it is necessary that the elongation of the brass rods shall tend to make the ball rise by exactly the same quantity that the elonga- tion of the steel rod tends to lower it : a result which is attained when the sum of the lengths of the steel rods A is to the sum of the lengths of the brass rods B in the inverse ratio of the coefficients of expansion of steel and brass, a and b, that is, in the proportion A : B = ^ : «. The elongation of the rod may also be compensated for by means of coviperisating strips. These consist of two blades of copper and iron soldered together and fixed to the pendulum rod, as represented in fig. 244. The copper blade, which is more expansible, is below the iron. .^ V. Fig. 244. Fig. 245. Fig. 246. When the temperature sinks, the pendulum rod becomes shorter, and the ball rises. But at the same time the compensating strips become curved, as seen in fig. 245, in consequence of the copper contracting more than -299] Expansion of Liquids. 247 the iron, and two metallic balls at their extremities become lower. If they have the proper size in reference to the pendulum ball, the parts which tend to approach the centre of suspension compensate those which tend to remove from it, and the centre of oscillation is not displaced. If the temperature rises the pendulum ball descends, but at the same time the small balls ascend, as shown in fig. 246, so that there is always compen- sation. One of the most simple compensating pendulums is the mercury peit- dulu77i, invented by an English watchmaker, Graham. The ball of the pendulum, instead of being solid, consists of a glass cylinder, containing pure mercury, which is placed in a sort of stirrup, supported by a steel rod. when the temperature rises the rod and stirrup become longer, and thus lower the centre of gravity ; but at the same time the mercury ex- pands, and, rising in the cylinder, produces an inverse effect, and as mer- cury is much more expansible than steel, a compensation may be effected without making the mercurial vessel of undue dimensions. The same principle is applied in the compensating balances of chrono- meters. The motion here is regulated by a balance or wheel, furnished with a spiral spring, and the time of the chronometer depends on the force of the spring, the mass of the balance, and on its circumference. Now when the temperature rises the circumference increases, and the chronometer goes slower ; and to prevent this, part of the mass must be brought nearer the axis. On the circumference of the balance compen- sating strips are fixed, of which the more expansible metal is on the outside, and at the end of these are small masses of metal which play the same part as the balls in the above case. When the radius is expanded by heat, the small masses are brought nearer the centre in con- sequence of the curvature of the strips ; and as they can be fixed in any position, they are easily arranged so as to compensate for the expansion of the balance. CHAPTER III. EXPANSION OF LIQUIDS. 299. Apparent and real expansion. — If a flask of thin glass, provided with a capillary stem, the flask and part of the stem being filled with some coloured liquid, be immersed in hot water, fig. 247, the column of liquid in the stem at first sinks from b to a, but then immediately after rises, and continues to do so until the liquid inside has the same tempe- rature as the hot water. This first sinking of the liquid is not due to its contraction ; it arises from the expansion of the glass, which becomes heated before the heat can reach the liquid ; but the expansion of the liquid soon exceeds that of the glass, and the liquid ascends. Hence in the case of liquids we must distinguish between the appar- ent and the real or absolute expansion. The apparent expansion is that which is actually observed when liquids contained in vessels are heated : 248 On Heat. [299 Fig. 247. the absolute expansion is that which would be observed if the vessel did not expand ; or, as this is never the case, it is the apparent expansion corrected for the simultaneous expansion of the containing vessel. As has been already stated, the cubical expansion of liquids is alone considered ; and as in the case of solids, the coefficient of expatisio7t of a liquid is the increase of the unit of volume for a single degree, but a distinction is here made between the coefficient of absolute expansion and the coefficient oj appareftt expajision. Of the many methods which have been employed for determining these two coefficients, we shall describe that of Dulong and Petit. 300. Coefficient of the absolute ex- pansion of mercury. — In order to deter- mine the coefficient of obsolute expansion of mercury, the influence of the envelope must be eliminated. Dulong and Petit's method depends'on the hydrostatical prin- ciple that, in two communicating vessels, the heights of two columns of liquid in equilibrium are inversely as their densities (104), a principle in- dependent of the diameters of the vessels, and therefore of their expansions. The apparatus consists of two glass tubes, A and B (fig. 248), joined by a capillary tube, and kept vertical on an iron support, KM, the horizon- tality of which is adjusted by means of two levelling screws and two spirit levels, m and n. Each of the tubes is surrounded by a metal case, of which the smaller, D, is filled with ice ; the other, E, containing oil, can be heated by the furnace, which is represented in section so as to show the case. Mercury is poured into the tubes A and B ; it remains at the same level in both as long as they are at the same temperature, but rises in B in proportion as it is heated, and expands. Let h and d be the height and density of the mercury in the leg A, at the temperature zero, and h' and d! the same quantities in the leg B. From the hydrostatical principle previously cited we have had hd=h'd' . Now from the problem in article 296, d' = - — =^, D being the coefficient of ab- solute expansion of mercury ; substituting this value of d' in the equation, we have — - =}id. from which we get D = — ~ -. i + D/ ' ^ ht The coefficient of absolute expansion of mercury is obtained from this formula, knowing the heights h' and h, and the temperature / of the bath in which the tube B is immersed. In Dulong and Petit's experiment this temperature was measured by a weight thermometer, P (302), the mercury of which overflowed into the basin, C, and by means of an air thermometer, T (311) ; the heights h' and h were measured by a catheto- meter, K (85). 301] Expansion of Liquids. 249 Dulong and Petit found by this method that the coefficient of absolute expansion of mercury, between 0° and 100° C. is ^^. But they found that the coefficient increased with the temperature. Between 100° and 200° it is 5/25, and betwen 200° and 300° it is ~-^. The same observa- tion has been made in reference to other Hquids, showing that their ex- Fig. 248. pansion is not regular. It has beea found that this expansion is less regular in proportion as liquids are near a change in their state of aggre- gation, that is, approach their freezing or boiling points. Dulong and Petit found that the expansion of mercury between — 36° and 100° is prac- tically quite uniform. Regnault, who has determined this important physical constant, has found that the mean coefficient between 0° and 100° is 55^^85 between 100° and 200°, 53^^, and between 200° and 300°, t^^^^. 301. Coefficient of tbe apparent expansion of mercury. — The co- efficient of apparent expansion of a liquid varies with the na- ture of the envelope. That of mercury in glass was deter- mined by means of the appa- ratus represented in figure 249. It consists of a glass cyhnder ^ ^is-:^^:,^^^^^^^ to which is joined a bent capil- Pj^ ,^ lary glass tube, open at the end. The apparatus is weighed first empty, and then when filled with mer- cury at zero ; the difference gives the weight of the mercury, P. It is then raised to a known temperature, / ; the mercury expands, a certain M3 250 Oh Heat. [301- ^- ^ quantity passes out, which is received in the capsule and weighed. If the weight of this mercury be p, that of the mercury remaining in the ap- paratus will be P— ^ When the temperature is again zero, the mercury in cooling produces an empty space in the vessel, which represents the contraction of the weight of mercury P —p, from f to zero, or, what is the same thing, the expansion of the same weight from o to t°, that is, the weight p repre- sents the expansion of the weight P — /, for f. If this weight expands n glass by a quantity p for f^ a single unit of weight would expand ^ for /°'and ^^— ^- for a single degree ; consequently, for D', (P -p) (P -p)t the coefficient of apparent expansion of mercury in glass, we have D' = ?- . Dulong and Petit found the coefficient of apparent expan- sion of mercury in glass to be g^^^. 302. VTeigrbt thermometer. — The apparatus represented in fig. 249 is called the weight thentiometer, because the temperature can be deduced from the weight of mercury which overflows. The above experiments have placed the coefficient of apparent expan- K. from which sion at g^— ; we have therefore the equation we get t- {Y-p)t ' a formula which gives the temperature / when the ^^ 6480/ weights P and p are known. 303. Coefficient of tbe expansion of g-lass. — As the absolute expansion of a liquid is the apparent expansion ^///j- the expansion due to the enve- lope, the coefficient of the cubical expansion of glass has been obtained by taking the difference between the coefficient of absolute expansion of mercury in glass and that of its apparent expansion. That is, the coeffi- \Vient of cubical expansion of glass is 5^8 -6180 =18^00=0-002584. Regnault has found that the coefficient of expansion varies with different kinds of glass, and further with the shape of the vessels. For ordinary chemical glass tubes, the coefficient is 0*0000254. 304. Coefficients of expansion of various liquids. — The apparent e^^pansion of liquids may be determined by means of the weight thermo- meter, and the absolute expansion is obtainedby adding to this coefficient the expansion of the glass. Totat apparent expansions 0/ liquids between 0° and 100° C. Mercury .... 0-01543 Oil of turpentine . . 0-07 Distilled water . . . 0-0466 Ether . . . 0-07 Water saturated with salt . 0*05 Fixed oils . . o-o8 Sulphuric acid . . , 0-06 Nitric acid . . .011 Hydrochloric acid . . o-o6 Alcohol . . o-ii6 The coefficient of apparent expansion for 1° C. is obtained by dividing these numbers by 100 ; but the number thus obtained does not represent -306] Force exerted by Liquids in expanding. 251 the mean coefficient of expansion of liquids, for the expansion of these bodies increases gradually from zero. The expansion of mercury is prac- tically constant between — 36° and 100° C, while water contracts from zero to 4°, and then expands. For many physical experiments a knowledge of the exact expansion of water is of great importance. This physical constant was determined with great care by Dr. Matthiessen, who found that between 4° and 32^ it may be expressed by the formula V/= I —0-00000253 (/ — 4) + 0*0000008389 (/-4)2 + 0-00000007173 (/ — 4)3; and between 30° and 100° by Nt = 0-999695 + 0-0000054724/2 + o-oooooooi 1 26/^ Many liquids, with low boiling points, especially condensed gases, have very high coefficients of expansion. Thilorier found that liquid carbonic acid expands four times as much as air. Drion has recently confirmed this observation, and has obtained analogous results with chloride of ethyle, liquid sulphurous acid, and liquid hyponitrous acid. 305. Correction of tbe barometric beigrtat. — It has been already ex- plained under the Barometer (159), that, in order to make the indications of this instrument comparable in different places and at different times, they must be reduced to a uniform temperature, which is that of melting ice The correction is made in the following manner : — Let H be the barometric height at /°, and k its height at zero, d the density of mercury at zero, and d its density at /°. The heights H and k df h are inversely as the densities d and d'\ that is, ^ = -j- If we call H d I the volume of mercury at zero, its volume at f will be i + D/, D beiil the coefficient of absolute expansion of mercury. But these volumes, i + D/ and i, are inversely as the densities d and d' \ that is, _ = — ^— — Consequently, / ^ = — -, whence h = —- . Replacing d \^T>t ^ ^' H i+D/ i + D/ ^ ^ D by its value rh^^^ we have h = ~— = -i-^— . ^ '''' I . 1 5508 + / 5508 In this calculation, the coefficient of absolute expansion of mercury is taken, and not that of apparent expansion ; for the value H is the same as if the glass did not expand, the barometric height being independent of the diameter of the tube, and therefore of its expansion. 306. Porce exerted by liquids in expanding:. — The force which liquids exert in expanding is very great, and equal to that which would be required in order to bring the expanded liquid back to its original volume. Now we know what an enormous force is required to com- press a liquid to even a very small extent. Thus between 0° and 10°, mercury expands by 0-0017905 of its volume at 0°; its compressibility is 0-00000295 of its volume for one atmosphere ; hence a pressure of more 252 On Heat. [306- than 600 atmospheres would be requisite to prevent mercury expanding when heated from 0° to 10°. 307. nxaximum density of water. — Water presents the remarkable phenomenon that when its temperature sinks it contracts up to 4° ; but from that point, although the cooling continues, it expands up to the freezing point, so that 4° represent the point of greatest contraction of water. Many methods have been used to determine the maximum density of water. Hope made the following experiment. He took a deep vessel, perforated by two lateral apertures, in which he fixed thermometers, and having filled the vessel with water at 0°, he placed it in a room at a tem- perature of 1 5°. As the layers of liquid at the sides of the vessel became heated they sank to the bottom, and the lower thermometer marked 4° while that of the upper one was still at zero. Hope then made the inverse experiment : having filled the vessel with water at 1 5°, he placed it in a room at zero. The lower thermometer having sunk to 4° re- mained stationary for some time, while the upper one cooled down until it reached zero. Both these experiments prave that water is heavier at 4° than at 0°, for in both cases it sinks to the lower part of the vessel. This last experiment maybe adapted for lecture illustration by using a cylinder containing water at 15° C, partially surrounded by a jacket con- taining bruised ice (fig. 250). Hallstrom made a determination of the maximum density of water in the following manner. He took a glass bulb, loaded with sand, and weighed it in water of different temperatures. Allowing for the expansion of glass, he found that 4'i° was the tempera- ture at which it lost most weight and consequently this was the temperature of the maximum density of water. Despretz arrived at the temperature 4° by another method. He took a water thermometer, that is to say a bulbed tube containing water, and placing it in a bath, the temperature of which was indicated by an ordinary mercury thermometer, found that the water contracted to the greatest extent at 4°, and that this is therefore the point of greatest density. This phenomenon is of great importance in the economy of nature. In winter the temperature of lakes and rivers falls from being in contact with the cold air, and from other causes, such as radiation. The colder water sinks to the bottom, and a continual series of currents goes on until the whole has a temperature of 4°. The cooling on the surface still ccntinues, but the cooled layers being lighter remain on the surface. Fig. 250. 308] Expansion of Gases. 253 and ultimately freeze. The ice formed thus protects the water below, which remains at a temperature of 4°, even in the most severe winters, a temperatvire at which fishes and other inhabitants of the waters are not destroyed. The following table of the density of water at various temperatures is based on several sets of observations : — Density of water between 0° and 30°. Tempe- ratures Densities Tempe- ratures Densities" Tempe- ratures Densities 0-99988 II 0-99965 22 0-99785 I 0-99993 12 0-99955 23 0-99762 2 0-99997 13 0-99943 24 0-99738 3 0-99999 14 099930 25 0-99704 4 i-ooooo 15 0-99915 26 0-99089 5 099999 16 0-99900 27 0-99662 6 0-99997 17 0-99884 28 0-99635 7 0-99994 18 0-99800 29 0-99607 8 0-99988 19 0-99847 30 0-99579 9 1-99982 20 0-99807 10 0-99974 21 0-99806 ! CHAPTER IV. ■ EXPANSION AND DENSITY OF GASES. 308. Gay-Aussac's method. — Gases are the most expansible of all bodies, and at the same time the most regular in their expansion. The co- efficients of expansion, too, of the several gases differ only by very small quantities. The cubical expansion of gases need alone be considered. Gay-Lussac first determined the coefficient of the expansion of gases by means of the apparatus represented in fig. 251. In a rectangular metal bath, about 16 inches long, was fitted an air thermometer, which consisted of a capillary tube, AB, with a bulb. A, at one end. The tube was divided into parts of equal capacity, and the contents of the bulb ascertained in terms of these parts. This was effected by weighing the bulb and tube full of mercury at zero, and then heating slightly to expel a small quantity of mercury, which was weighed. The apparatus being again cooled down to zero, the vacant space in the tube corresponded to the weight of mercury which had overflowed; the volume of mercury remaining in the apparatus, and consequently the volume of the bulb, was determined by calculations analogous to those made for the piezometer (94). In order to fill the thermometer with dry air it was first filled with mercury, which was boiled in the bulb itself. A tube, C, filled with 254 On Heat, [308 chloride of calcium, was then fixed on to its end by means of a cork. A fine platinum wire having then been introduced into the stem A B, through the tube C, and the apparatus being slightly inclined and agitated from time to time, air entered, having been previously well dried by passing Fig. 251. through the chloride ot calcium tube. The whole of the mercury was displaced, with the exception of a small thread, which remained in the tube AB as an index. The air thermometer was then placed in the box filled with melting ice, the index moved towards A, and the point was noted at which it became stationary. This gave the volume of air at zero ; for the capacity of the bulb was known. Water or oil was then substituted for the ice, and the bath successively heated to different temperatures. The air ex- panded and moved the index from A towards B. The position of the index in each case was noted, and the corresponding temperature was indicated by means of the thermometers D and E. Assuming that the atmospheric pressure did not vary during the experiment, and neglecting the expansion of the glass as being too small in comparison with that of the air, the total expansion of the air is obtained by subtracting from its volume at a given temperature, its volume at zero. Dividing this by a given temperature, and then by the nurn- ber of units contained in the volume at zero, the quotient is the coefficient of expansion for a single unit of volume and a single degree ; that is, the coefficient of expansion. It will be seen, further on, how corrections for pressure and temperature may be introduced. By this method Gay-Lussac found that the coefficient of expansion of air was 00037 5 ; and he enunciated the two following laws in reference to the expansion of gases : — I. All gases have the same coefficient of expansion as air. II. This coefficient is the same whatever be the pressure supported by the gas. These simple laws are not, however, rigorously exact (310) ; they only express the expansion of gases in an approximate manner. -310] Expansion of Gases. 255 309. Problems on the expansion of erases. — Many of the problems relative to the expansion of gases are similar to those on the expansion of liquids. With obvious modifications, they are solved in a similar manner. In most cases the pressure of the atmosphere must betaken into account in considering the expansion of gases. The following is an example of the manner in which this correction is made : — i. The volume of a gas at /°, and under the pressure H, is V ; what will be the volume V of the same gas at zero, and under the normal pres- sure 760 millimetres ? Here there are two corrections to be made ; one relative to the tem- perature, and the other to the pressure. It is quite immaterial which is taken first. If a be the coefficient of cubical expansion for a single degree, by reasoning similar to that in the case of hnear expansion (296), the volume of the gas at zero, but still under the pressure H, will be This pressure is reduced to the pressure 760, in accordance with I + (it Boyle's law (166), by putting V + 76o= ^' xH; I +r / whence V = 750 (i +tt/) ii. A volume of gas weighs P' at t° ; what will be its weight at zero ,^ Let P be the desired weight, a the coefficient of expansion of the gas ^' its density at /°, and d its density at zero. As the weights of equal V df volumes are proportional to the densities, we have - = -. If i be the volume of a gas at zero, its volume at t will be i + ot\ but as the densities are inversely as the volumes, - = d I + 0/ and therefore P i+a/' whence P = P'(i+n/). P From this equation we get P'' = , which gives the weight at /, 1+0/ knowing the weight at zero, and which further shows that the weight P' is inversely as the binomial of expansion i + at. 310. Regrnault's metbod — M. Regnault used successively four dif- ferent methods for determining the expansion of gases. In some of them the pressure was constant and the volume variable, as in Gay-Lussac's method ; in others the volume remained the same while the pressure varied. The first method will be described. It is the same as that used by Rudberg and Dulong, but is distinguished by the care with which all sources of error are avoided. 256 On Heat, [310- The apparatus consisted of a pretty large cylindrical reservoir, B (fig. 252), terminating in a bent capillary tube. In order to fill the reservoir Fig. 252. with dry air, it was placed in a hot water bath, and the capillary tube connected by a caoutchouc tube with a series of drying tubes. These tubes were joined to a small air pump, P, by which a vacuum could be produced in the reservoir while at a temperature of 100° The reservoir was first exhausted, and air afterwards admitted slowly ; this operation was repeated a great many times, so that the air in the reservoir became quite dry, for the moisture adhering to the sides passed ofi" in vapour at 100°, and the air which entered became dry in its passage through the U tubes. The reservoir was then kept for half an hour at the temperature of boiling water ; the air pump having been detached, the drying tubes were then disconnected, and the end of the tube hermetically sealed, the height, H, of the barometer being noted. When the reservoir B was cool, it was placed in the apparatus represented in fig. 253. It was there quite surrounded with ice, and the end of the tube dipped in the mercury bath, C. After the air in the reservoir B had sunk to zero, the point b was broken off by means of a forceps ; the air in the interior became con- densed by atmospheric pressure, the mercury rising to a height oQx. In order to measure the height of this column, G^) (3) from which the value of a is deduced. The means of a great number of experiments between zero and 100° and for pressures between 300 millimetres and 500 milHmetres, gave the following numbers for the coefficients of expansion for a single degree : Air 0-003667 Carbonic acid .... 0-003710 Hydrogen 6-003661 Nitrous oxide .... 0-003719 Nitrogen 0-003661 Cyanogen 0*003877 Carbonic oxide . . . o-cxy^SGj Sulphurous acid ... 0-003903 These numbers, with which the results obtained by Magnus closely agree, show that the coefficients of expansion of the permanent gases differ very little ; but that they are somewhat greater in the case of the conden- 258 Ott Heat. [310- sible gases, such as carbonic and sulphurous acids. Regnault has further found that, at the same temperature, the coefficient of expansion of any gas increases with the pressure which it supports. Thus, while the co- efficient of expansion of air under a pressure of i lo™™ is 0-003648, under a pressure of 3655™™ or nearly five atmospheres it is 0*003709. The number found by Regnault for the coefficient of the expansion ot air, 0-003667, is equal to ^=^3 nearly; and if we take the coefficient of expansion at 0-0036666 ... it may be represented by the fraction — lo, which is very convenient for purposes of calculation. 311. Air thermometer. — The aif- thermometer is based on the ex- pansion of air. When it is used to measure small differences of tempe- rature, it has the same form as the tube used by Gay-Lussac in deter- mining the expansion of air (fig. 251), that is, a capillary tube with a bulb at the end. The reservoir being filled with dry air, an index of coloured sillphuric acid is passed into the tube ; the apparatus is then graduated in Centigrade degrees by comparing the positions of the index with the indications of a mercurial thermometer. Of course the end of the tube must remain open ; otherwise, the air above the index condensing or ex- panding at the same time as that in the bulb, the index would remain stationary. A correction must be made at each observation for the at- mospheric pressure. When considerable variations of temperature are to be measured, the tube has a form like that used in Regnault's experiments (fig. 252 and 253). By experiments made as described in article 310, P, P', H, H', and h, may be found, and the coefficients a and I being known, the tem- perature t to which the tube has been raised is readily deduced from the equation (3). Regnault's researches show that the air and the mercurial thermometer agree up to 260°, but above that point mercuiy expands relatively more than air. In cases where very high temperatures are to be measured the reser- voir is made of platinum. The use of an air thermometer is seen in Dulong and Petit's experiment (300) ; it was by such an apparatus that Pouillet measured the temperature corresponding to the colours which metals take when heated in a fire, and found them to be as follows : — Incipient red . . . 525°C. Dark orange . . . iioo°C. Dull red .... 700 White .... 1300 Cherry red . .. . 900 Dazzling white . . . 1500 In the measurement of high temperatures Deville and Troost have used with advantage, the vapour of iodine instead of air, and as platinum has been found to be permeable to gases at high temperature, they have employed porcelain instead of that metal. 312. Density of grases.— The relative density of a gas, or its specific gravity, is the ratio of the weight of a certain volume of the gas to that of the same volume of air ; both the gas and the air being at zero and at a pressure of 760 millimetres. In order, therefore, to find the specific gravity of a gas, it is necessary -312] Density of Gases. ^59 to determine the weight of a certain volume of this gas at a pressure of 760 millimetres, and a temperature of zero, and then the weight of the same volume of air under the same conditions. For this purpose a large globe of about two gallons capacity is used, the neck of which is pro- vided with a stopcock, which can be screwed to the air pump. The globe is first weighed empty, and then full of air, and afterwards full of the gas in question. The weights of the gas and of the air are obtained by subtracting the weight of the exhausted globe from the weight of the globes filled, respectively, with air and gas. The quotient, obtained by dividing the latter by the former, gives the specific gravity of the gas. It is difficult to make these determinations at the same temperature and pressure, and therefore all the weights are reduced to zero and the normal pressure of 760 millimetres. The gases are dried by causing them to pass through drying tubes before they enter the globe, and air must also be passed over potash to free it from carbonic acid. And as even the best air pumps never pro- duce a perfect vacuum, it is necessary to exhaust the globe until the manometer in each case marks the same pressure. The globe having been exhausted, dried air is allowed to enter, and the process is repeated several times until the globe is perfectly dried. It is then finally exhausted until the residual tension, in millimetres, is e. The weight of the exhausted globe is p. Air, which has been dried and purified by passing through potash and chloride of calcium tubes, is then allowed to enter slowly. The weight of the globe full of air is P. If H is the barometric height in millimetres, and f the temperature at the time of weighing, P —p is the weight of the globe full of air at the tempe- rature /, and the pressure H — ^. To reduce this weight to the pressure 760 millimetres and the tempera- ture zero, let a be the coefficient of the expansion of air, and -^'~^' (P-/)(i+«/) P-/ 313. Regrnault's metbod of determining- the density of grases,— ^M. Regnault has so modified the above method that many of the corrections may be dispensed with. The globe in which the gas is weighed is sus- pended from one pan of a balance, and is counterpoised by means of a second globe of the same dimensions, and hermetically sealed, suspended from the other. These two globes expanding at the same time always displace the same quantity of air, and consequently variations in the temperature and pressure of the atmosphere do not influence the weighing. The globe, too, is filled with the air or with the gas, at the temperature of zero. This is effected by placing it in a vessel full of ice, as shown in fig. 254. It is then connected with a three-way cock, Fig- 254 A, by which it may be connected either with an air-pump, or with the tubes M and N, which are connected with the reservoir of gas. The tubes M and N contain substances by which their action on the gas dry and purify it. The stopcock A being so turned that the globe is only connected with the air pump, a vacuum is produced; by means of the same cock, the connection with the machine being cut off, but established between M and N, the gas soon fills the globe. But as the exhaustion could not -314] Density of Gases. 261 have been complete, and some air must have been left, the globe is again exhausted and the air allowed to enter, and the process repeated until it is thought all air is removed. The globe being once more produced, a differential barometer (fig. 113), connected with the apparatus by the tube E, indicates the pressure of the residual rarefied gas e. Closing the cock B and detaching A, the globe is removed from the ice, and after being cleaned is weighed. This gives the weight of the empty globe / ; it is again replaced in the ice, the stopcock A adjusted, and the gas allowed to enter, care being taken to leave the stopcocks open long enough to allow the gas in the globe to acquire the pressure of the atmosphere, which is marked by the barometer H. The stopcock B is then closed, A removed, and the globe weighed with the same precautions as before. This gives the weight Pj of the gas. The same operations are then repeated on this globe with air, and two corresponding weights p and P are obtained. The only correction necessary is to reduce the weights in the two cases to the standard pressure by the method described in the preceding paragraph. The correction for temperature is not needed, as the gas is at the temperature of melting ice. The ratio of the weight of the gas to that of the air is thus obtained by the formula p-p 314. Bensity of grases which attack metals. — For gases which attack the ordinary metals, such as chlorine, a metal stopcock cannot be used, and vessels with ground glass stoppers are substituted. The gas is introduced by a bent glass tube, the vessel being held either upright or inverted, according as the gas is heavier or lighter than air ; when the vessel is supposed to be full, the tube is withdrawn, the stopper inserted, and the weight taken. This gives the weight of the vessel and gas. If the capacity of the vessel be measured by means of water, the weight of the air which it contains is deduced, for the density of air at 0° C. and 760 millimetres pressure is y}^ that of distilled water under the same cir- cumstances. The weight of the vessel full of air, less the weight of the contained air, gives the weight of the vessel itself From these three data — the weight of the vessel full of the gas, the weight of the air which it contains, and the weight of the vessel alone — the specific gravity of the gas is readily deduced, the necessary corrections being made for tempe- rature and pressure. Dcfisity of gases at zero aiid at a pressure of 'j^yo" millimetres^ that of air being taken as unity. Air . . . I -OOGO Nitrogen . ■ 0-9714 Hydrogen . . 0-0693 Binoxide of nitrogen . 1-0360 Marsh gas . . 0-5590 Oxygen . . 1-1057 Ammoniacal gas . 0-5367 Sulphuretted hydrogen . 1-1912 Carbonic oxide . . 0-9670 Hydrochloric acid . . 1-2540 262 On HeaL [314- Density of gases at zero — continued. Protoxide of nitrogen . 1-5270 Sulphurous acid . . 2-2474 Carbonic acid . . . J -5291 Chlorine .... 3*4400 Cyanogen .... i-86oo Hydriodic acid . . . 4*4430 Regnault has furnished the following determinations of the weight of a litre of the most important gases at 0° C.-and 760 mm.: — Air . . . 1-293187 grms. Nitrogen . . 1-256167 grms. Oxygen . . 1*429802 Carbonic acid . 1-9774 14 Hydrogen . . 0*089578 CHAPT^K^f ' - CHANGES OF CONtkJTION. VAPOURS. 315. Fusion. Its laws. — The only phenomena of heat with which we have hitherto been engaged have been those of expansion. In the case of solids it is easy to see that this expansion is limited. For in proportion as a body absorbs a larger quantity of heat, the repulsive force between the molecules is increased, and ultimately a point is reached at which the molecular attraction is not sufficient to retain the body in the solid state. A new phenomenon is then produced : fusion takes place ; that is, the body passes from the solid into the liquid state. Some substances, however, such as paper, wood, wool, and certain salts, do not fuse at a high temperature, but are decomposed. Many bodies have long been considered refractory \ that is, incapable of fusion ; but, in proportion as it has been possible to produce higher temperatures, their number has diminished. Gaudin has succeeded in fusing rock crystal by means of a lamp fed by a jet of oxygen ; and more recently Despretz, by combining the effects of the sun, the voltaic battery, and the oxy-hydro- gen blow-pipe, has melted alumina and magnesia, and softened carbon, so as to be flexible, which is a condition near that of fusion. It has been experimentally found that the fusion of bodies is governed by the two following laws : — I. Every substance begins to fuse at a certain temper attire^ which is in- variable for each substance if the pressure be constant. II. Whatever be the intensity of the source of heat, from the 7noment fusion cojnmences, the temperature of the body ceases to rise, and remains constant until the fusion is complete. Fusing points of certain substances. Mercury . . . . — 38-8° Phosphorus . . . -44 Bromine . . . . — 12-5° Spermaceti . . . -49 Ice o Potassium . . . • ^S Butter . . . . . + 33 Margaric acid . . . S7 316] ^ Changes of Condition. * Fusing point of certain sul^stances — continued. V Stearine White wax . Wood's fusible metal Stearic acid . Sodium Rose's fusible metal Sulphur Tin . 60 Bismuth 65 Cadmium . 68 Lead . 70 Zinc . 90 Antimony . 94 Silver . 114 Gold . 228 Iron . 263 264 321 335 422 450 1000 1250 1500 Some substances pass from the solid to the liquid state without showing any definite melting point ; for example, glass and iron become gra- dually softer and softer when heated and pass by imperceptible stages from the solid to the liquid condition. This intermediate condition is spoken of as the state oivitreoits fusion. Such substances may be said to melt at the lowest temperature at w4iich perceptible softening occurs, and to be fully melted when the further elevation of temperature does not make them more fluid ; but no precise temperature can be given as their melting points. 316. Influence of pressure on the melting: point. — Thomson and Clausius have deduced from the principles of the mechanical theory of heat that, with an increase of pressure, the melting point of a body must be raised* All bodies which expand on passing from the solid to the liquid state have to perform external work — namely, to raise the power of the atmo- sphere by the amount of this expansion. Under ordinary circumstances, the amount of external work which solids and liquids thus perform is so small that it may be neglected. But if the external pressure be increased, the power of overcoming it can only be obtained by an increase of vis viva of the molecules. This increase can do more work ; the tempera- ture of fusion as well as the heat of fusion are both increased. Thus Bunsen found that spermaceti, which melts at 48° under a pressure of I atmosphere, melis at 51° under a pressure of 156 atmospheres. Hopkins found that spermaceti melted at 60° under a pressure of 519 atmospheres, and at 80° under 792 atmospheres ; the melting point of sulphur under these pressures was respectively 135^^ and 141°. But in the case of those bodies which contract on passing from the solid to the liquid state, and of which water is the best example, the reverse is the case. Melting ice has no external work to perform, since it has no external pressure to raise ; on the contrary, in melting it assimilates external work which, transformed into heat, renders a smaller quantity of heat necessary ; the external work acts in the same direction as the internal heat — namely, in breaking up the crystalline aggregates. Yet these differences of temperature must be but small, for the molecular forces in solids preponderate far oveir the external pressure ; the internal work is far greater than the external. Sir W. Thomson found that pressures of S'l and i6-8 atmospheres low^ered the melting point of ice by 0-059^ and 0-126°" respectively. These 264 ♦» On Heat. [316- results justify the theoretical previsions of Prof. T. Thomson, according to which an increase of pressure of 7t atmospheres lowers the melting point of ice by 0-0074;^° C. 317. Alloys. Fluxes. — Alloys are generally more fusible than either of the metals of which they are composed ; for instance, an alloy of five parts of tin and one of lead fuses at 194°. The alloy known as Rosens fusible metal, which consists of 4 parts of bismuth, i part of lead, and i of tin, melts at 94°, and an alloy of i or 2 parts of cadmium with 2 parts of tin, 4 parts of lead, and 7 or 8 parts of bismuth, known as Wood's fusible metal, melts between 66° and 71° C. Fusible alloys are of extended use in soldering and in taking casts. Steel melts at a lower temperature than iron, though it contains carbon, which is almost completely in- fusible. Mixtures of the fatty acids melt at lower temperatures than the pure acids. A mixture of the chlorides of potassium and of sodium fuses at a lower temperature than either of its constituents ; the same is the case with a mixture of the carbonates of potassium and sodium, especially when they are mixed in the proportion of their chemical equivalents. An application of this property is met with in the case oi fluxes, which are much used in metallurgical operations. They consist of substances which, when added to an ore, partly by their chemical action, help the reduction of the substance to the metallic state, and, partly by presenting a readily fusible medium, promote the formation of a regulus. 318. Ziatent heat. — Since, during the passage of a body from the soHd to the liquid state, the temperature remains constant until the fusion is complete, whatever be the intensity of the source of heat, it must be con- cluded that, in changing their condition, bodies absorb a considerable amount of heat, the only effect of which is to maintain them in the liquid state. This heat, which is not indicated by the thermometer, is called latent heat or latent heat of fusion, an expression which, though not in strict accordance with modern ideas, is convenient from the fact of its universal recognition and employment (432). An idea of what is meant by latent heat may be obtained from the fol- lowing experiment. If a pound of water at 80° is mixed with a pound of water at zero, the temperature of the mixture is 40°. But if a pound of pounded ice at zero is mixed with a pound of water at 80°, the ice melts, and two pounds of water at zero are obtained. Consequently, the mere change of a pound of ice to a pound of water at the same temperature re- quires as much heat as will raise a pound of water through 80°. This quantity of heat represents the latent heat of the fusion of ice, or the latent heat of water. Every liquid has its own latent heat, and in the chapter on Calorimetry we shall show how this is determined. 319. Solution. — A body is said to dissolve when it becomes liquid in consequence of an affinity between its molecules, and those of a liquid. Gum arabic, sugar, and most salts dissolve in water. During solution, as well as during fusion, a certain quantity of heat -322] Solidification. 265 always becomes latent, and hence it is that the solution of a substance usually produces a diminution of temperature. In certain cases, however, — instead of the temperature being lowered, it actually rises, as when caustic potass is dissolved in water. This depends upon the fact that two simul- taneous and contrary phenomena are produced. The first is the passage from the solid to the liquid condition, which always lowers the tempera- ture. The second is the chemical combination of the body dissolved with the liquid, and which, as in the case of all chemical combinations, pro- duces an increase of temperature. Consequently, as the one or the other of these effects predominates, or as they are equal, the temperature either rises, or sinks, or remains constant. 320. Solidification. — Solidification or congelation is the passage of a body from the liquid to the solid state. This phenomenon is regulated by the two following laws : — I. Every body, tinder the same pressure , solidifies at a fixed temper a- ture, which is the same as that of fusion. II. From the cojnmencement to the etidofthe solidification, the tempera- ture of a liquid 7'emains constant. Certain bodies, more especially some of the fats, present an exception to the first law, in so far that by repeated fusions they seem to undergo a molecular change which alters their melting point. The secoifd law is a consequence of the fact that the latent heat ab- sorbed during fusion becomes free at the moment of solidification. Many liquids, such as alcohol, ether, and bisulphide of carbon, do not solidify even at the lowest known temperature. But M. Despretz, by the cold produced by a mixture of liquid protoxide of nitrogen, solid carbonic acid, and ether, has reduced alcohol to such a consistence that the.vessel containing it could be inverted without losing the liquid. 321. Crystallisation. — Generally speaking, bodies which pass slowly from the liquid to the solid state assume regular geometrical forms, such as the cube, prisms, rhombohedra, &c. ; these are called crystals. If the crystals are formed from a body in fusion, such as sulphur or bismuth, the crystallisation is said to take place by the dry way. But if the crys- tallisation takes place owing to the slow evaporation of a solution of a salt, it is said to be by the moist way. Snow, ice, and many salts present examples of crystallisation. 322. Retardation of the point of solidification. — The freezing point of pure water can be diminished by several degrees, if the water be pre- viously freed from air by boiling and be then kept in a perfectly still place. In fact it may be cooled to — 15° C, and even lower, without freezing. But when it is slightly agitated, the liquid at once solidifies. The smaller the quantity of Hquid the lower the temperature to which it can be cooled, and the greater the mechanical disturbance it supports without freezing, Fournet has observed the frequent occurrence of mists formed of particles of liquid matter suspended in an atmosphere whose temperature is 10° or even 15° below zero. A very rapid agitation also prevents the formation of ice. The same is the case with all actions which, hindering the molecules in theirmove- A— ./^ 266 On Heat [322- ments, do not permit them to arrange themselves in the conditions neces- sary for the sohd state. M. Despretz was able to lower the temperature of water contained in fine capillary tubes to — 20° without their solidi- fying. This experiment shows how it is that plants in many cases do not become frozen, as the sap is contained in very fine capillary vessels. Finally, M. Mousson has found that a powerful pressure not only retards the freezing of water, but prevents its complete solidification. In this case the pressure opposes the tendency of the water to expand on freezing and thus virtually lowers the point of solidification. If water contains salts or other foreign bodies its freezing point is low- ered. Sea water freezes at —2-5° to —3° C. ; the ice which forms is quite pure, and a saturated solution remains. In Finland, advantage is taken of this property to concentrate sea water for the purpose of extracting salt from it. If water contains alcohol, precisely analogous phenomena are observed ; the ice formed is pure, and practically all the alcohol is con- tained in the residue. Dufour has observed some very curious cases of liquids cooled out of contact with solid bodies. His mode of experimenting was to place the liquid in another of the same specific gravity but of lower melting point, and in which it is insoluble. Spheres of water for instance, suspended in a mixture of chloroform and oil, usually solidified between— 4° and — 12°, while some smaller globules cooled down to — 18° or. — 20°. Con- tact with a fragment of ice immediately set up congelation. Globules of sulphur (which solidifies at 1 1 5°) remained liquid at 40° ; and globules of phosphorus (solidifying point 42°) at 20°. When a liquid solidifies after being cooled below its normal freezing point, the solidification takes place very rapidly, and is accompanied by a disengagement of heat, which is sufficient to raise its temperature from the point at which solidification begins up to its ordinary freezing point. This is well seen in the case of hyposulphite of sodium, which melts in its own water of crystallisation at 45°, and when carefully cooled will remain liquid at the ordinary temperature of the atmosphere. If it then be made to solidify by agitation, or by adding a small fragment of the solid salt, the rise of temperature is distinctly felt by the hand. In this case the heat which had become latent in the process of liquefaction again becomes free, and a portion of the substance remains melted ; for it is kept liquid by the heat of sohdification of that which has solidified. 323. Cbangre of volume on solidification and liquefaction. — The rate of expansion of bodies generally increases as they approach their melting points, and is in most cases followed by a further expansion at the moment of liquefaction, so that the liquid occupies a greater volume than the solid from which it is formed. Phosphorus, for instance, increases about 3-4 per cent, on liquefaction ; that is, 100 volumes of solid phos- phorus at 44° (the melting point) become 103-4 at the same temperature when melted. Sulphur expands about 5 per cent, on liquefying, and stearic acid about 1 1 per cent. Water presents a remarkable exception ; it expands on the moment of solidifying, or contracts on melting, by about ten per cent. One volume of -324] Freezing Mixtures. 267 ice at 0° gives 0-9178 of water at 0°, or i volume of water at 0° gives :-io2 of ice at the same temperature. In consequence of this expansion, ice floats on the surface of water. According to Dufour the specific gravity of ice is 0-9178 ; Bunsen found for ice which had been freed from water by boiling the somewhat smaller number 0-91674. The increase of volume in the formation of ice is accompanied by an expansive force which sometimes produces powerful mechanical effects, of which the bursting of water-pipes and the breaking of jugs containing water are familiar examples. The splitting of stones, rocks, and the swelling up of moist ground during frost, are caused by the fact that water penetrates into the pores and there becomes frozen ; in short, the great expansion of water on freezing is the most active and powerful agent of disintegration on the earth's surface. The expansive force of ice was strikingly shown by some experiments of Major Williams, in Canada. Having quite filled a 13-inch iron bomb- shell with water, he firmly closed the touch- hole with an iron plug weighing three pounds, and exposed it in this state to the frost. After some time the iron plug was forced out with a loud explosion, and thrown to a distance of 415 feet, and a cylinder of ice 8 inches long issued from the opening. In another case the shell burst before the plug was driven out, and in this case a sheet of ice spread out all round the crack. It is pos- sible that under the great pressure some of the water still remained liquid up to the time at which the resistance was overcome ; that it then issued from the shell in a liquid state, but at a temperature below 0°, and there- fore instantly began to solidify when the pressure was removed, and thus retained the shape of the orifice whence it issued. Cast-iron, bismuth, and antimony expand on solidifying like water, and can thus be used for casting ; but gold, silver, and copper contract, and hence coins of these metals cannot be cast, but must be stamped with a die. 324. Freezingr mixtures. — The absorption of heat in the passage of bodies from the solid to the liquid state has been used to produce artificial cold. This is effected by mixing together bodies which have an affinity for each other, and of which one at least is solid, such as water and a salt, ice and a salt, or an acid and a salt. Chemical affinity accelerates the fusion : the portion which melts robs the rest of the mixture of a large i quantity of sensible heat, which thus becomes latent. In many cases a very considerable diminution of temperature is produced. The following table gives the names of the substances mixed, their pro- portions, and the corresponding diminutions of temperature : — i Substances ^^'"'^ Reduction of Substances by weight. temperature. Sulphate of sodium . . . 8 . TT J ui • J _ h . . . -h 10" to Hydrochloric acid Pounded ice or snow . Common salt Sulphate of sodium . Dilute nitric acid j} . . . +10° to -18= H . . . +io°to -19= 26S On Heat. [324- 071 Heat. Substances. Sulphate of sodium . Nitrate of ammonium . Dilute nitric acid Phosphate of sodium . Dilute nitric acid Parts by weight. . 6- . 5 ■ . . . 4J • 9". . 4J ' ' Reduction of temperature. . +10° to -2 . + 10° to -2 26° 29° If the substances taken be themselves first previously cooled down, a still more considerable diminution of temperature is occasioned. Freezing mixtures are frequently used in chemistry, in physics, and in domestic economy. The portable ice-making machines which have come into use during the last i&'N years consist of a cylindrical metallic vessel divided into four concentric compartments. In the central one is placed the water to be frozen ; in the next there is the freezing mixture, which usually consists of sulphate of sodium and hydrochloric acid ; 6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in an hour. The third compartment also contains water, and the outside one contains some badly-conducting substance, such as cotton to prevent the influence- of the external temperature. The best effect is obtained when pretty large quantities (2 or 3 pounds) of the mixture are used, and when they are intimately mixed. It is also advantageous to use the machines for a series of successive operations. VAPOURS. MEASUREMENT OF THEIR TENSION. 325. Vapours. — We have already seen (141) that vapours are the aeriform fluids into which volatile substances, such as ether, alcohol, water, and mercury, are changed by the absorption of heat. Volatile liquids are those which thus possess the property of passing into the aeriform state, dcadi fixed liquids, those which do not form vapours at any temperature without undergoing chemical decomposition, 'such as the fatty oils. There are some solids, such as ice, arsenic, camphor, and in general all odoriferous solid substances, which can directly form vapours without first becoming liquid. Vapours are transparent like gases, and generally colourless : there are only a few coloured liquids, which also give coloured vapours. 326. Vaporisation. — The passage of a liquid into the gaseous state is designated by the general term vaporisation ; the term evaporation espe- cially refers to the slow production of vapour at the free surface of a liquid, and boiling to its rapid production in the mass of the liquid itself. We shall presently see (339) that at the ordinary atmospheric pressure, ebulhtion, like fusion, takes place at a definite temperature. This is not the case with evaporation, which takes place even with the same liquid at very different temperatures, although the formation of a vapour seems to cease below a certain point. Mercury, for example, gives no vapour below— 10°, nor sulphuric acid below 30°. -329] Vapours. 269 » 327. Elastic force of vapours. — Like gases, vapours have a certain elastic force, in virtue of which they exert pressures on the sides ot vessels in which they are contained. The tension of vapours may be demonstrated by the following experiment :— A quantity of mercury is placed in a bent glass tube (fig. 254 rt), the shorter leg of which is closed ; a few drops of ether are then passed into the closed leg, and the tube immersed in a water bath at a temperature of about 45°. The mercury then sinks slowly in the short branch, and the space ab is filled with a gas which has alL the appearance of air, and whose elastic force counter- balances the pressure of the column of mercury cd, and the atmospheric pressure on d. This gas is the vapour of ether. If the water be cooled, or if the tube be removed from the bath, the vapour which fills the space ab disappears, and the drop of ether is reproduced. If, on the contrary, the bath be heated still higher, the level of the mercury descends below b, indicating an increased tension. 328. Formation of vapours in a vacuum. — In the previous experiment the liquid changed very slowly into the vaporous condition ; the same is the case when a liquid is freely exposed to the air. In both cases the atmosphere is an obstacle to the vaporisation. In a vacuum there is no resistance, and the formation of vapours is instantaneous, as is seen in the following experiment : — Four barometer tubes, filled with mercury, are immersed in the same trough (fig. 255). One of them. A, serves as a barometer, and a few drops of water, alcohol, and ether are respectively introduced into the tubes, B, C, D. When the liquids reach the vacuum, a depres- sion of the mercury is at cmce produced And as this depression cannot be produced by the weight of the liquid, which is an infinitely small fraction of the weight of the displaced mercury, it must be due to the formation of some vapour whose elastic force has depressed the mercurial column. The experiment also shows that the depression is not the same in all the tubes ; it is greater in the case of alcohol than of water, and greater with ether than with alcohol. We con/equently obtain the two following laws for the formation of vapours \. In a vaaiutn all volatile liquiiis are instantaneously co?iverted into vapour. 11. At the satne temperature ihe vapours of different liquids have different elastic forces. For example, at 20° the tension of ether vapour is 25 times as great as that of aqueous vapour. 329. Saturated vapours. Maximum of tension. — When a very small quantity of a volatile liquid, such as ether, is introduced into a Fig. 254 a. 70 On Heat, [329- barometer tube, it is at once completely vaporised, and the mercurial column is not depressed to its full extent ; for if some more ether be in- troduced the depression increases. By continuing the addition of ether, it finally ceases to vaporise, and remains in the liquid state. There is, therefore, for a certain temperature, a L limit to the quantity of vapour which can A B E c 10 be formed in a given space. This space 1 jl ■ is accordingly said to be sattu^ated. Jfj Further, when the vaporisation of the ll H j i ether ceases, the depression of the mer ■ MMfc^ curial column stops. And hence there is a limit to the tension of the vapour, a limit which, as we shall presently see (332), varies with the temperature, but which for a given temperature is inde- pendent of the pi'cssure. To show that, in a closed space, satur- ated with vapour and containing liquid in excess, the temperature remaining con- stant, there is a maximum of tension which the vapour cannot exceed, a baro- metric tube is used which dips in a deep bath (fig. 256). This tube is filled with mercury, and then so much ether is added as to be in excess after the Torricellian vacuum is saturated. The height of the mercurial column is next noted by means of the scale graduated on the tube itself. Now, whether the tube be depressed, p.._^ ^ which tends to compress the vapour, or whether it be raised, which tends to ex- pand it, the height of the mercurial column is constant. The tension of the vapour remains constant in the two cases, for the depression neither increases nor diminishes it. Hence it is concluded that when the satu- rated vapour is compressed, a portion returns to the liquid state ; that when, on the other hand, the pressure is diminished, a portion of the ex- cess of liquid vaporises, and the space occupied by the vapour is again saturated ; but in both cases the tension and the density of the vapour remain constant. 330. xron-saturated vapours. — From what has been said, vapours present two very different states, according as they are saturated or not. In the first case, where they are saturated and in contact with the liquid, they differ completely from gases, since for a given temperature they can neither be compressed nor expanded ; their elastic force and their den- sity remain constant. In the second case, on the contrary, where they are not saturated, they exactly resemble gases. For if the experiments (fig. 256) be repeated, only a small quantity of ether being introduced, so that the vapour is 330] Non-saturated Vapours, 271 not saturated, and if the tube be then sh'ghtly raised, the level of the mercury is seen to rise, which shows that the elastic force of the vapour has diminished. Similarly, by immersing the tube still more, the level of the mercury sinks. The vapo.ir consequently behaves just as a gas would Fig. 256. Fig. 257. do; its tension diminishes when the volume increases, and vice versa ; and as in both cases the volume of the vapour is inversely as the pressure, it is concluded that non-saturated vapours obey Boyte's taw. When a non-saturated vapour is heated, its volume increases like that of a gas ; and the number 0-00366, which is the coefficient of the expan- sion of air, may be taken for that of vapours. Hence we see that the physical properties of unsaturated vapours are comparable with those of permanent gases, and that the formulae for the compressibility and expansibility of gases (168 and 309) also apply to unsaturated vapours. But it must not be forgotten that there is always a limit of pressure or of cooling at which unsaturated vapours pass into a state of saturation, and that they have then a maximum of tension and 4-941 millimetres. 2-o8 >j 0-84 » 036 J) "272 On Heat. [330- density which can only be exceeded when the temperature rises while they are in contact with the liquid. 331. Tension of aqueous vapour below zero. — For the sake of measuring the elastic force of aqueous vapour below zero, Gay-Lussac used two barometer tubes filled with mercury, and placed in the same bath (fig. 257). The straight tube A serves as a barometer ; the other B, is iDent, so that part of the Torricellian vacuum can be surrounded by a freezing mixture (324). When a little water is admitted into the bent tube, the level of the mercury sinks below that in the tube A to an extent which varies with the temperature of the freezing mixture. At 0° the depression is „ — 10 „ „ -20° These depressions, which must be due to the tension of aqueous vapour in the space BC, show that even at very low temperatures there is always some aqueous vapour in the atmosphere. Although in the above experiment the part B and the part C are not both immersed in the freezing mixture, we shall presently see that when two communicating vessels are at different temperatures, the tension of the vapour is the same in both, and always corresponds to that of the lowest temperature. That water evaporates even below zero follows from the fact, that wet linen exposed to the air during frost first becomes stiff and then dry, showing that the particles of water evaporate even after the latter has been converted into ice. 332. Tension of aqueous vapour bet\ireen zero and one hundred degrees — i. Dalton^s method. Dalton measured the elastic force of aqueous vapour between 0° and 100° by means of the apparatus repre- sented in fig. 258. Two barometer tubes, A and B, are filled with mer- cury, and inverted in an iron bath full of mercury, and placed on a furnace. The tube A contains a small quantity of water. The tubes are supported in a cylindrical vessel full of water, the temperature of which is indicated by the thermometer. The bath being gradually heated, the water in the cylinder becomes heated too ; the water which is in the tube A vaporises, and in proportion as the tension of its vapour increases, the mercury sinks. The depressions of the mercury corresponding to each degree of the thermometer are indicated on the scale E, and in this manner a table of the elastic forces between zero and 100° has been constructed. ii. RegnauWs ?nethod. — Dalton's method is wanting in precision, for the liquid in the cylinder has not everywhere the same temperature, and consequently the exact temperature of the aqueous vapour is not indicated. Regnault's apparatus is a modification of that of Dalton. The cylindrical vessel is replaced by a large cylindrical zinc drum, MN (fig. 259), in the bottom of which are two tubulures. The tubes A and B pass through these tubulures, and are fixed by caoutchouc collars. The tube containing vapour, B, is connected with a flask, a, by means of a brass three-way 332] Tejision of Aqueous Vapour, 27?> tube, O. The third hmb of this tube is connected with a drying tube, D, containing pumice impregnated with sulphuric acid, which is connected with the air pump. When the flask a contains some water, a small portion is distilled into B by gently heating the flask. Exhausting then by means of the air pump, the water distils continuously from the flask and from the baro- metric tube towards D, which condenses the vapours. After having I Fig. 258. Fig. 259. vaporised some quantity of water, and when it is thought that all the air in the tube is withdrawn, the capillary tube which connects B with the three- way tube is sealed. The tube B being thus closed, it is experimented with, as in Dalton's method. The drum MN, being filled with water, is gently heated by a spirit lamp, which is separated from the tubes by a wooden screen. By means of a stirrer, K, all parts of the liquid are kept at the same temperature. In the side of the drum is a glass window, through which the height of the mercury in the tubes can be read off by means of a cathetometer ; from N3 r^\ 274 On Heat [332 the difference in these heights, reduced to zero, the tension of vapour is deduced. By means of this apparatus, the elastic force of vapour between o° and 50° has been determined with accuracy. 333. Tension of aqueous vapour above one hundred degrees. — Two methods have been employed for determining the tension of aqueous vapour at temperatures above 100°, the one by Dulong and Arago, in 1830, and the other by Regnault, in 1844. Fig. 260 represents a vertical section of the apparatus used by Dulong rijT. "iCo. jind Arago. It consisted of a copper boiler, k, with very thick sides, and of about 20 gallons capacity. Two gun-barrels, a, of which only one is seen in the drawing, were firmly fixed in the sides of the boiler, and plunged in the water. The gun-barrels were closed below, and contained mercury, in which were placed thermometers, /, indicating the tempera- ture of the water, and of the vapour. The tension of the vapour was measured by means of a manometer with compressed air, w, previously graduated (171) and fitted into an iron vessel, d, filled with mercury. In order to see the height of the mercury in the vessel, it was connected above and below with a glass tube, «, in which the level was always the same as in the bath. A copper tube, /, connected the upper part of the vessel, d^ with a vertical tube, r, fitted in the boiler. The tube i and the upper part of the bath d were filled with water, which was kept cool by means of a current of cold water flowing from a reservoir, and circulating through the tube b. The vapour which was disengaged from the tube c exercised a pres- sure on the water of the tube / ; this pressure was transmitted to the water and to the mercury in the bath d, and the mercury rose in the 334] Tension of Aqueous Vapour. 75 manometer. By noting on the manometer the pressures corresponding to each degree of the thermometer, Dulong and Arago were able to make a direct measurement of the tension up to 24 atmospheres, and the tension from thence to 50 atmospheres was determined by calcu- lation. 334. Tension of vapour below^ and above one hundred deg-rees. — Regnault has devised a method by which the tension of vapour may be measured at temperatures either below or above 100°. It depends on the principle that when a liquid boils, the tension of the vapour is equal to the pressure it supports (339). If, therefore, the temperature and the corresponding pressure are known, the question is solved, and the method n;ierely consists in causing water to boil in a vessel under a given pressure, and measuring the corresponding temperature. The apparatus consists of a copper retort, C (fig. 261), hermetically I Fig. 261. sealed, and about two-thirds full of water. In the cover there are four thermometers, two of which just dip into the water, and two descend almost to the bottom. By means of a tube, AB, the retort C is connected with a glass globe, M, of about 6 gallons capacity, and full of air. The tube AB passes through a metallic cylinder, D, through which a current of cold water is constantly flowing from the reservoir E. To the upper part of the globe a tube with two branches is attached, one of which is connected with a manometer, O; the other tube, HH', which is of lead, 2/6 On Heat. [334- can be attached either to an exhausting or a condensing air pump, accord- ing as the air in the globe is to be rarefied or condensed. The reservoir K, in which is the globe, contains water of the temperature of the sur- rounding air. If the elastic force of aqueous vapour below ioo° is to be measured, the end H'' of the leaden pipe is connected with the plate of the air pump, and the air in the globe M, and consequently that in the retort C, is rarefied. The retort being gently heated, the water begins to boil at a temperature below ioo°, in consequence of the diminished pressure. And since the vapour is condensed in the tube AB, which is always cool, the pressure originally indicated by the manometer does not increase, and therefore the tension of the vapour during ebullition remains equal to the pressure on the liquid. A httle air is then allowed to enter ; this alters the pressure, and the liquid boils at a new temperature ; both these are read off, and the ex- periment repeated as often as desired up to ioo°. In order to measure the tension above ioo°, the tube H' is connected with a condensing pump, by means of which the air in the globe M and that in the vessel C are exposed to successive pressures, higher than the atmosphere. The ebullition is retarded (343), and it is only necessary to observe the difference in the height of the mercury in the two tubes of the manometer O, and the corresponding temperature, in order to obtain the tension for a given temperature. The following tables by M. Regnault give the tension of aqueous vapour from - 1° to 101°. Tensions of aqueous vapour from —10° to 101° C. k Tensions 2. S i. 6 in tl Tensions in E 3 Tensions in E 3 Tensions in milli- £ 3 millimetres millimetres millimetres 1 metres ^^ 29° fi!" -10° 2-078 12° 10-457 29-782 85° 433-41 8 2-456 13 1 1 -062 30 31-548 90 525-45 6 2-890 14 11-906 31 33-405 91 545-78 4 3-387 15 12-699 32 35-359 92 566-76 2 3-955 16 13-635 33 37-410 93 588-41 4-600 17 14-421 34 39-565 94 610-74 + I 4-940 18 15-357 35 41-827 95 633-78 2 5-302 19 16-346 40 54-906 96 657-54 3 5-687 20 17-391 45 71-391 97 682-03 4 6-097 21 18-495 50 91-982 98 707-26 5 6-534 22 19-659 55 117-478 98-5 720-15 6 6-998 23 20-888 60 148-791 99-0 733-21 7 7-492 24 22-184 65 186-945 99-5 746-50 8 8-OI7 25 23-550 70 233-093 1 00-0 760-00 9 8-574 26 24-998 75 288-517 100-5 773-71 10 9-165 27 26-505 80 354-643 101 -0 787-63 TI 9-792 28 28-101 -336] Tension of the Vapours of Mixed Liquids. 277 In the second table the numbers were obtained by direct observation up to 24 atmospheres ; the others were calculated by the aid of a formula of interpolation. Tensions in atmospheres from 100° to 230'9°. % Z ^ ■" 1 ^ s 3 II E 1 ^"1 S 2 S s 3 6 s 3 g £ 3 s s 3 S ^ ^^ ^ ^^l E^ J^i E^ ;2;t5 ioo-o° I 170-8° ^ 1 198-8° '5 ' 217-9° 22 1 1 2-2 I* 175-8 9 ! 201-9 16 1 220-3 23 . I20-6 2 180-3 10 ' 204-9 17 222-5 24 133-9 3 184-5 II 207-7 18 2247 25 144-0 4 188-4 12 210-4 19 226-8 26 152-2 5 192-1 13 213-0 20 228-9 27 159-2 6 195-5 14 215-5 21 230-9 28 165-3 7 These tables show that the elastic force increases much more rapidly than the temperature. The law which regulates this increase is not accurately known. 335. Tension of tbe vapours of different liquids. — Regnault has determined the elastic force at various temperatures, of a certain number of liquids which are given in the following table : — Liquids Tempera- tures Tensions in millimetres Liquids Tempera- tures Tensions in millimetres Mercury . • Alcohol . ■ Bisulphide of carbon 50° 100 50 100 -20 60 ICO o-ii 0-74 13 220 1695 43 132 1164 3329 Ether . . ■ Sulphurous . acid Ammonia -20° 60 100 -20 60 -30 30 68 182 1728 4950 479 1165 8124 876 3163 8832 336. Tension of tbe vapours of mixed liquids. — Regnault's experi- ments on the tension of the vapour of mixed liquids prove that (i.) when two liquids exert no solvent action on each other — such as water and bisulphide of carbon, or water and benzole — the tension of the vapour which rises from them is nearly equal to the sum of the tensions of the two separate liquids at the same temperature ; (ii.) with water and ether, which partially dissolve each other, the tension of the mixture is much 278 On Heat. [336- less than the sum of the tensions of the separate liquids, being scarcely equal to that of the ether alone; (iii.) when two liquids dissolve in all proportions, as ether and bisulphide of carbon, or water and alcohol, the tension of the vapour of the mixed liquid is intermediate between the tensions of the separate liquids. Wiillner has shown that the tension of aqueous vapour emitted from a sahne solution, as compared with that of pure water, is diminished by an amount proportional to the quantity of anhydrous salt dissolved, when the salt crystallises without water or yields efflorescent crystals ; when the salt is deliquescent, or has a powerful attraction for water, the reduction of tension is proportional to the quantity of crystallised salt. 337. Tension in two communicating- vessels at different tempera- tures. — When two vessels containing the same liquid, but at different temperatures, are connected with each other, the elastic force is not that corresponding to the mean of the two temperitiires, a^ woiild naturally be supposed. Thus, if there are two globes, fig. 262, one. A, containing water kept at zero by means of melting ice, the other, B, containing water at 100°, the tension, as long as the globes are not connected, is 4 to 6 millimetres in the first, and 760 millimetres in the second. But when they are connected by opening the stopcock C, the vapour in the globe B, from its greater tension, passes into the other globe, and is there con- densed, so that the vapour in B can never reach a higher temperature than that in the globe A. The liquid simply distils from B towards A without any increase of tension. From this experiment the general principle may be deduced that when two vessels containing the same liquid, but at different temperatures, are coJtnected, the tension is identical in both vessels, and is the same as that corresponding to the lower tempe?'atui'e An application of this principle has been made by Watt in the condenser of the steam-engine. -339] Lazvs of Ebullition. 279 r'-^\ I 338. Svaporation. Causes which accelerate it. — Evaporation^ as has been already stated (326), is the slow production of vapour at the surface of a liquid. It is in consequence of this evaporation that wet clothes dry when exposed to the air, and that open vessels containing water become emptied. The vapours which, rising in the atmosphere, condense, and becoming clouds fall as rain, are due to the evaporation from the seas, lakes, rivers, and the soil. Four causes influence the rapidity of the evaporation of a liquid : i. the temperature ; ii. the quantity of the same vapour in the surrounding atmo- sphere ; iii. the renewal of this atmo- sphere ; iv. the extent of the surface of evaporation. Increase of temperature accelerates the evaporation by increasing the elastic force of the vapours. In order to understand the influence of the second cause, it is to be ob- served that no evaporation could take place in a space already saturated with vapour of the same liquid, and that it would reach its maximum in air completely freed from this vapour. It therefore follows that between these two extremes the rapidity of evapo- ration varies according as the surrounding atmosphere is already more or less charged with the same vapour. The effect of the renewal of this atmosphere is similarly explained ; for if the air or gas, which surrounds the liquid, is not renewed, it soon becomes saturated, and evaporation ceases. The influence of the fourth cause is self-evident. 339. I>aws of ebullition. — Ebullition, or boiling is the rapid produc- tion of elastic bubbles of vapour in the mass of a liquid itself. When a liquid, water for example, is heated at the lower part of a vessel, the first bubbles are due to the disengagement of air which had previously been absorbed. Small bubbles of vapour then begin to rise from the heated parts of the sides, but as they pass through the upper layers, the temperature of which is lower, they condense before reaching the surface. The formation and successive condensation of these first bubbles, occasion the singing noticed in liquids before they begin to boil. Lastly, large bubbles rise and burst on the surface, and this constitutes the phenomenon of ebullition (tig. 263). The laws of ebullition have been determined experimentally, and are as follows : — • I. The tempetnture of ebullition, or the boiling point, increases with the pressure. Fig. 263. 28o On Heat. [339 II. For a given pressure ebullition begins at a certain temperature^ which varies in different liquids, but which, for equal pressures, is always the same hi the same liquid. III. Whatever be the intensity of the source of heat, as soon as ebulli- tion begins, the temperature of the liquid remains stationary. YCtik- Sulphurous acid . . -IO° Turpentine . Chloride of ethyle + II Butyric acid . Ether .... yi Phosphorus . Bisulphide of carbon . 48 Strong sulphuric acid Bromine 63 Mercury Alcohol . 78 Sulphur Distilled water . 100 Cadmium Acetig acid . . . . 117 Zinc . . ^ , ^.\ ^-^ '-^. xt tUc- Boiling points under the pressure 760 millimetres. ^ 160° 157 290 325 320 447 860 1040 There are many causes which influence the boiling point of a liquid, such as the substances dissolved, the nature of the vessel, and the pres- sure. We shall illustrate the effects of these different causes, more par- ticularly on water. Kopp has pointed out that in analogous chemical compounds the same difference in chemical composition frequently involves the same difference of boiling points ; and he has endeavoured to show that in a very ex- tensive series of compounds the difference of CH^ is attended by a differ- ence of 19° C. in the boiling point. 340. Theoretical explanation of evaporation and ebullition. — From what has been said about the nature of the motion of the mole- cules in liquids (273), it may readily be conceived that in the great variety of these motions, the case occurs in which by a fortuitous concurrence of the progressive vibratory and rotatory motions a molecule is projected from the surface of the liquid with such force that it overleaps the sphere of the action of its circumjacent molecules before, by their attraction, it has lost its initial velocity ; and that it then flies into the space above the liquid. Let us first suppose this space limited and originally vacuous, it gradually fills with the propelled molecules which act like a gas and in their motion are driven against the sides of the envelope. One of these sides, however, is the surface of the liquid itself, and a molecule when it strikes against this surface will not in general be repelled but be retained by the attraction which the adjacent ones exert. Equilibrium will be established when as many molecules are dispersed in the surrounding space as, on the average, impinge against the surface and are retained by it 'in the unit of time. This state of equihbrium is not, however, one of rest, in which evaporation has ceased, but a condition, in which evaporation and condensation, which are equally strong, continually compensate each other. The density of a vapour depends on the number of molecules which -341] Explanation of Evaporation and Ebullition. 281 are repelled in a given time, and this manifestly depends on the motion of the molecules in the liquid. What has been said respecting the surface of the liquid clearly applies to the other sides of the vessel within which the vapour is formed ; some vapour is condensed, this is subject to evaporation, and a con- dition ultimately occurs in which evaporation and precipitation are equal. The quantity of vapour necessary for this depends on the density of vapour in the closed space, on the temperature of the vapour and the side and on the force with which this attracts the molecules. The maximum will be reached when the sides are covered with a layer of liquid, which then acts like the free surface of a liquid. In the interior of a liquid it may happen that the molecules repel each other with such force as to momentarily destroy the coherence of the mass. The small vacuous space which is thereby formed, is entirely sur- rounded by a medium which does not allow of the passage of the repelled molecules. Hence it cannot increase and maintain itself as a bubble of vapour, unless so many molecules are projected from the inner sides that the internal pressure which thereby results, can balance the external pressure which tends to condense the bubble. The expansive force of the enclosed vapour must therefore be so much the greater, the greater the external pressure on the liquid, and thus we see the dependence of pres- sure on the temperature of boiling. 341. Influence of substances in solution on the boillngr point. — The ebullition of a liquid is the more retarded the greater the quantity of any substance it may contain in solution, provided that the substance be not volatile, or, at all events, be less volatile than the liquid itself. Water which boils at 100° when pure, boils at the following temperatures when saturated with different salts : — Water saturated with common salt . . boils at 109° „ „ nitrate of potassium „ 116 „ „ carbonate of potassium „ 135 „ „ chloride of calcium „ 179 Acids in solution present analogous results ; but substances merely mechanically suspended, such as earthy matters, bran, wooden shavings, etc., do not affect the boiling point. Dissolved air exerts a very marked influence on the boiling point of water. Deluc first observed that water freed from air by ebullition, and placed in a flask with a long neck, could be raised to 112° without boiling. M. Donny found that water deprived of air and sealed up in a long glass tube may be heated at one end as high as 138° without boil- ing, and is then suddenly and violently thrown to the other by a burst of vapour. When a liquid is suspended in another of the same specific gravity, but higher boiling point, with which it does not mix, it may be raised far beyond its boiling point without the formation of a trace of vapour. Dufour has made a number of valuable experiments on this subject ; he 282 Oh Heat. [341- used in the case of water a mixture of oil of cloves and linseed oil ; and placed in it globules of water, and then gradually heated the oil ; in this way ebulhtion rarely set in below iio° or 115°, very commonly globules of 10 millimetres diameter reached a temperature of 120° or 130°, while very small globules of i to 3 millimetres reached the temperature of 175*^, a temperature at which the tension of vapour on a free surface is 8 or 9 atmospheres. At these high temperatures the contact of a solid body, or the produc- tion of gas bubbles in the liquid, occasioned a sudden vaporisation of the globule, accompcinied by a sound like the hissing of a hot iron in water. Saturated aqueous solutions of sulphate of copper, chloride of sodium, etc., remained liquid at a temperature far beyond their boiling point, when immersed in melted stearic acid. In like manner, globules of chloroform (which boils at 61°) suspended in a solution of chloride of zinc could be heated to 97° or 98° without boiling. It is a disputed question as to what is the temperature of the vapour from boiling saturated saline solutions. It has been stated by Rudberg to be that of pure water boiling under the same pressure ; the most recent experiments of Magnus seem to show, however, that this is not the case, but that the vapour of boiling solutions is hotter than that of pure water ; and that the temperature rises as the solutions become more concentrated, and therefore boil at higher temperatures. Nevertheless, the vapour was always found somewhat cooler than the mass of the boihng solution, and the difference was greater at high than at low temperatures. The boiling point of a liquid is usually lowered when it is mixed with a more volatile liquid than itself, but raised when it contains one which is less volatile. Thus a mixture of two parts alcohol and one of water boils at 83°, a mixture of two parts of bisulphide of carbon and one part of ether bcils at 38°. In some cases the boiling point of a mixture is lower than that of either of its constituents. A mixture of water and bisulphide boils at 43°, the boiling point of the latter being 46°. On this depends the following curious experiment. If water and bisulphide of carbon, both at the temperature 45°, are mixed together, the mixture at once begins to boil briskly. 342. Influence of the nature of tlie vessel on tbe boiling: point. — Gay-Lussac observed that water in a glass vessel required a higher temperature for ebullition than in a metal one. Taking the temperature of boiling water in a copper vessel at 100°, its boiling point in a glass vessel was found to be 101° ; and if the glass vessel had been previously cleaned by means of sulphuric acid and of potass, the temperature would rise to 105°, or even to 106°, before ebullition commenced. A piece of metal placed in the bottom of the vessel was always sufficient to lower the temperature to 100°, and at the same time to prevent the violent con- cussions which accompany the ebullition of saline or acid solutions in glass vessels. Whatever be the boiling point of water, the temperature of its vapour is uninfluenced by the substance of the vessels. -343] Iiiflueiice of Pressure on the Boiling Point. 283 343. Influence of pressure on the 1>oillnir point.— We see from the table of tensions (334) that at 100°, the temperature at which water boils under a pressure of 760 millimetres, aqueous vapour has a tension ex- actly equal to this pressure. This principle is general, and may be thus enunciated : A liquid boils when the teiision of its vapour is equal to the pressure it supports. Consequently, as the pressure in- creases or diminishes, the tension of the vapour, and therefore the temperature necessary for ebulli- tion, must increase or diminish. In order to show that the boil- ing point is lower under diminished pressure, a small dish containing water at 30° is placed under the receiver of an air pump, which is then exhausted. The liquid soon begins to boil, the vapour formed being pumped out as rapidly as it is generated. A paradoxical but very simple experiment also well illustrates the dependence of the boiling point on the pressure. In a glass flask, water is boiled for some time, and when all air has been expelled by the steam, the flask is closed by .a cork and inverted as shown in fig. 264. If the bottom is then cooled by a stream of cold water from a sponge, the water begins to boil again. This arises from the condensation of the steam above the surface of the water, by which a partial vacuum is pro- duced. It is in consequence of this diminution of pressure that liquids boil on high mountains at lower temperatures. On Mont Blanc, for example, water boils at 84°, and at Quito at 90?. On the more rapid evaporation of water under feeble pressures is based the use of the air pump in concentrating those solutions which either cannot bear a high degree of heat, or which can be more cheaply evaporated in an exhausted space. Mr. Howard made a most important and useful application of this principle in the manufacture of sugar. The syrup, in his method, is enclosed in an air-tight vessel, which is exhausted by a steam-engme. The evaporation consequently goes on at a lower temperature, which secures the syrup from injury. The same plan is adopted in evaporating the juice of certain plants used in preparing medicinal extracts. On the other hand, ebullition is retarded by increasing the pressure ; under the pressure of two atmospheres, for example, water only boils at i2o°-6. Fig. 264. 284 On Heat. [344- 344. Franklin's experiment. — The influence of pressure on ebullition may further be illustrated by means of an experiment of Franklin's. The apparatus consists of a bulb. «, and a tube, b, joined by a tube of smaller ^^N— — *''''^^^^^'*^*\^^ dimensions (fig. 265). The tube ^'"^ T*^ J) js drawn out, and the appara- tus filled with water, which is then in great part boiled aw^y by means of a spirit lamp. When it has been boiled suffi- ciently long to expel all the air, the tube b is sealed. There is then a vacuum in the apparatus, or rather there is a pressure due to the tension of aqueous vapour, which at ordinary temperatures is very small. Consequently, if the bulb a be placed in the hand, the heat is sufficient to produce a tension Fi^. 265. 345. Measurement of heigrbts by tbe boiling: point. — From the con- nection between the boiling point of water and the pressure, the heights of mountains may be measured by the thermometer instead of by the barometer. Suppose, for example, it is found that water boils on the summit of a mountain at 90°, and at its base at 98° ; at these tempera- tures the elastic force or tension of the vapour is equal to that of the pressure on the liquid, that is, to the pressure of the atmosphere at the two places respectively. Now the tensions of aqueous vapour for various temperatures have been determined, and accordingly the tensions corre- sponding to the above temperatures are sought in the tables. These numbers represent the atmospheric pressures at the two places : in other words, they give the barometric heights, and from these the height of the mountain may be calculated by the method already given (165). An ascent of about 1080 feet produces a diminution of 1° C. in the boiling point. The instruments used for this purpose are called thermo-barometers or hypsometers^ and were first applied by Wollaston. They consist essentially of a small metallic vessel for boiling water, fitted with very delicate thermometers, which are only graduated from 80° to i(X>° ; so that each degree occupying a considerable space on the scale, the loths, and even the looths, of a degree may be estimated, and thus it is possible to determine the height of a place by means of the boiling point to within about 10 feet. 346. Formation of vapour in a closed tube. — We have hitherto considered vapours as being produced in an indefinite space, or where they could expand freely, and it is only under this condition that ebullition can take place. In a closed vessel the vapours produced finding no issue, their tension and their density increase with the temperature, but the rapid disengagement of vapour which constitutes ebullition is impossible. Hence, while the temperature of a liquid in an open vessel can never exceed that of ebullition, in a closed vessel it may t -347] Formation of Vapour ift a closed Space. 285 be much higher. The liquid state, has, nevertheless, a limit ; for, accord- ing to experiments by Cagniard-Latour, if either water, alcohol, or ether be placed in strong glass tubes, which are hermetically sealed after the air has been expelled by boiling, when these tubes are exposed to a sufficient degree of heat, a moment is reached at which the liquid suddenly disappears, and is converted into vapour at 200°, occupying a space less than double its volume in the liquid state, and that the tension was then 38 atmospheres. Alcohol which half fills a tube is converted into vapour at 207° C. If a glass tube about half filled with water, in which some carbonate of soda has been dissolved, to diminish the action of the water in the glass, be heated, it is completely vaporised at about the temperature of melting zinc. When chloride of ethyle was heated in a very thick sealed tube, the upper surface ceased to be distinct at 1 70°, and was replaced by an ill- defined nebulous zone. As the temperature rose this zone increased in width in both directions, becoming at the same time more transparent ; after a time the liquid was completely vaporised, and the tube became transparent and seemingly empty. On cooling, the phenomena were reproduced in the opposite order. Similar appearances were observed on heating ether in a sealed tube at 190°. Andrews has observed that when liquid carbonic acid was heated in a closed tube to 31° C. the surface of demarcation between the liquid and the gas became fainter, lost its curvature, and gradually disappeared. The space was then occupied by a homogeneous fluid, which, when the pressure was suddenly diminished, or the temperature slightly lowered, exhibited a peculiar appearance of moving or flickering striae throughout its whole mass. Above 30° no apparent liquefaction of carbonic anhy^ dride, or separation into two distinct forms of matter, could be effected, not even when the pressure of 400 atmospheres was applied. It would thus seem that there exists for every liquid a temperature, the critical tempera- ture. While below this critical point a sudden transition from gas to liquid is accompanied by a sudden diminution of volume, and liquid and gas are separated by a sharp line of demarcation ; above this critical point the change is connected with a gradual diminution of volume, and is quite imperceptible. The condensation can, indeed, only be recognised by a sudden ebullition when the pressure is lessened. Hence, ordinary condensation is only possible below the critical point, and it is not sur- prising, therefore, that mere pressure, however greatj^ should fail to liquefy many of the bodies which usually exist as gases. 347. Papin's digrester. — Papin, a French physician appears to have been the first to study the effects of the productions of vapour in closed vessels. The apparatus which bears his name consists of a cylindrical iron vessel (fig. 266), provided with a cover, which is firmly fastened down by the screw B. In order to close the vessel hermetically, sheet lead is placed between the edges of the cover and the vessel. At the bottom of a cyhndrical cavity, which traverses the cyhnder S, and the tubulure ^, the cover is perforated by a small orifice in which there is a rod, n. This rod ^86 On Heat, [347- presses against a lever, A, movable at a, and the pressure may be regu- lated by means of a weight movable on this lever. The lever is so weighted, that when the tension in the interior is equal to 6 atmospheres, for example, the valve rises and the vapour escapes. The destruction of the apparatus is thus avoided, and the mechanism has hence received the name of safety valve. The digester is filled about two-thirds with water, and is heated on a furnace. The water may thus be raised to a temperature far above ioo°, and the tension of the vapour increased to several atmospheres, ac- cording to the weight on the lever. We have seen that water boils at much lower temperatures on high mountains (343) ; the temperature of water boiling in open vessels in such localities is not sufficient to soften animal fibre completely and extract the nutriment, and hence Papin's di- gester is used in the preparation of food. Papin's digester is used in extract- ing gelatine. When bones are digested in this apparatus they are soft- ened so that the gelatine which they contain is dissolved. 348. l^atent heat of vapour. — As the temperature of a liquid remains constant during ebullition, whatever be the source of heat (339), it follows that a considerable quantity of heat becomes absorbed in ebullition, the only effect of which is to transform the body from the liquid to the gaseous condition. And conversely when a saturated vapour passes into the state of liquid, it gives out an amount of heat. These phenomena were first observed by Black, and he described them by saying that during vaporisation a quantity of sensible heat became latent, and that the latent heat again became free during condensation. The quantity of heat which a liquid must absorb in passing from the liquid to the gaseous state and which it gives out in passing from the state of vapour to that of liquid, is spoken of as the latent heat of evapo- ration. The analogy of these phenomena to those of fusion will be at once seen ; the modes of determining them will be described in the chapter on Calorimetry ; but the following results, which have been obtained for the latent heats of evaporation of a few liquids, may be here given : — Water .... Alcohol Acetic acid . Ether .... Fig. 266. 536 Bisulphide of carbon . 87 208 Turpentine • 74 102 Bromine .... . 46 90 Iodine . <, . . . 24 -349] Cold due to Evaporation. 287 The meaning of these numbers is, in the case of water, for instance that it requires as much heat to convert a pound of water from the state of Mquid at the boiling point to that of vapour at the same temperature, as would raise a pound of water through 540 degrees, or 540 pounds of water through one degree ; or that the conversion of one pound of vapour of alcohol at 78° into liquid alcohol of the same temperature would heat 208 pounds of water through one degree. Watt, who investigated the subject, found that the whole quantity of heat necessary to raise a given weight of water from zero at any tempera- ture, and theft to evaporate it entirely, is a constant quantity. His experi- ments showed that this quantity is 640. Hence the lower the tempera- ture the greater the latent heat, and, on the other hand, the higher the temperature the less the latent heat. The latent heat of the vapour of water evaporated at 100° would be 540, while at 50° it would be 590. At higher temperatures the latent heat of aqueous vapour would go on dimin- ishing. Water evaporated under a pressure of 15 atmospheres at a tem- perature of 200°, would have a latent heat of 440, and if it could be evaporated at 640° it would have no latent heat at all. Experiments by Southern and Creighton in 1803 led to a different con- clusion : namely, that the latent heat of evaporation isaconstatit quantity for all temperatures, afid that the total quantity of heat fiecessary to evaporate water is the sensible heat plus this co7istant, which they found in round numbers to be 540 ; consequently, to evaporate water at 100^,640 thermal units (418) would be needed, while it would require 200 + 540 = 740 thermal units to evaporate it at 200°. Regnault, who examined this question with great care, arrived at results which differed from both these laws. He found that the total quantity of heat necessary for the evaporation of water increases with the tempej-atnre, and is not constant, as Watt had supposed. It is represented by the formula. Q = 606-5 +0-305 T, in which Q is the total quantity of heat, and T the temperature of the water during evaporation, while the numbers are constant quantities. The total quantity of heat necessary to evaporate water at 100° is 606-5 + (0-305 X 100) =637 ; at 120° it is 643 ; at 150° it is 651 ; and at 180° it is 661. Thus the heat required to raise a pound of water from zero and convert it into steam at 100° represents a mechanical work of 885430 units, which would be sufficient to raise a ton weight through a height of nearly 400 feet. 349. Cold due to evaporation. XtKercury frozen. — Whatever be the temperature at which a vapour is produced, an absorption of heat always takes place. If, therefore, a liquid evaporates, and does not receive from without a quantity of heat equal to that which is expended in producing the vapour, its temperature sinks, and the cooling is greater in proportion as the evaporation is more rapid. Leslie succeeded in freezing water by means of rapid evaporation. 2SS On Heat. [349- Under the receiver ot the air pump is placed a vessel containing strong sulphuric acid, and above it a thin metallic capsule (fig. 267) containing a small quantity of water. By exhausting the receiver the water begins to boil (343), and since the vapours are absorbed by the sulphuric acid as Fig. 268. fast as they are formed, a rapid evaporation is produced, which quickly effects the freezing of the water. This experiment is best performed by using, instead of the thin metallic vessel, a watch-glass, coated with lampblack and resting on a cork. The advantage of this is twofold : firstly, the lampblack is a very bad conductor, and, secondly, it is not moistened by the liquid, which remains in the form of a globule not in contact with the glass. A small porous dish may advantageously be used. The same result is obtained by means of Wollaston's cyrophorus (fig. 268), which consists of a bent glass tube provided with a bulb at each end. The apparatus is prepared by introducing a small quantity of water, which is then boiled so as to expel all air. It is then hermetically sealed, so that on cooling it contains only water and the vapour of water. The water being introduced into the bulb A, the other is immersed in a freezing mixture. The vapours in the tube are thus condensed ; the water in A rapidly yields more. But this rapid production of vapour re- quires a large amount of heat, which is abstracted from the water in A, and its temperature is so much reduced that it freezes. Carre has constructed an apparatus which is based upon Leslie's ex- periment, and by which considerable quantities of water may be frozen in a very short time. It consists of a horizontal brass cylinder, about fifteen inches in length and four in diameter, lined on the inside with an alloy of antimony and lead, so as to resist the action of strong sulphuric acid, with which it is about half filled. In the top of the cylinder, and at one end, is fitted a brass tube, bent twice at right angles, and con- structed in such a manner that a flask containing water can be easily fitted on air-tight. At the other end of the cylinder, also at the top, there is a somewhat wide upright tube B. This is connected with a simple air pump, specially devised for the purpose, and there is an arrangement so I -349] Cold due to Evaporation. 289 that the motion which works the pump works also a stirrer, which keeps the acid in continual agitation. A fresh surface is thus continually ab- sorbing aqueous vapour ; and as the space to be exhausted is small, and the pump very effective, soon after its working commences the water first boils and then freezes. These apparatus have been introduced for indus- trial purposes ; and where there is a continual demand and use for dilute sulphuric acid, there seems no reason why this should not be an econo- mical mode of making ice. By using liquids more volatile than water, more particularly liquid sul- phurous acid, which boils at — 10°, a degree of cold is obtained sufficiently intense to freeze mercury. The experiment may be made by covering the bulb of a thermometer with cotton wool, and after having moistened it with liquid sulphurous acid, placing it under the receiver of the air pump. When a vacuum is produced the mercury is quickly frozen. Thilorier, by directing a jet of liquid carbonic acid on the bulb of an alcohol thermometer, obtained a cold of — 100° without freezing the alco- hol. We have already seen, however (320), that with a mixture of solid carbonic acid, liquid protoxide of nitrogen and ether, M. Despretz obtained a sufficient degree of cold to reduce alcohol to the viscous state. By means of the evaporation of bisulphide of carbon, the formation of ice may be illustrated without the aid of an air pump. A little water is dropped on a board, and a capsule of thin copper foil, containing bi- sulphide of carbon, is placed on the water. The evaporation of the bisulphide is accelerated by means of a pair of bellows, and after a few minutes the water freezes round the capsule, so that the latter adheres to the wood. In like manner, if some water be placed in a test tube which is then dipped in a glass containing some ether, and a current of air be blown through the ether by means of a glass tube fitted to the nozzle of a pair of bellows, the rapid evaporation of the ether very soon freezes the water in the tube. Richardson's apparatus for producing local anaesthesia also depends on the cold produced by the evaporation of ether. The cold produced by evaporation is used in hot climates to cool water by means of alcarrazas. These are porous earthen vessels, through which water percolates, so that on the outside there is a continual evaporation which is accelerated when the vessels are placed in a current of air. For the same reason wine is cooled by wrapping the bottles in wet cloths and placing them in a draught. In Harrison's method of making ice artificially, a steam engine is used to work an air pump, which produces a rapid evaporation of some ether, in which is immersed the vessel containing the water to be frozen. The apparatus is so constructed that the vaporised ether can be condensed and used again. The cooling effect produced by a wind or draught does not necessarily, arise from the wind being cooler, for it may, as shown by the thermo- meter, be actually warmer ; but arises from the rapid evaporation it o 290 On Heat. [349 causes from the surface of the skin. We have the feeling of oppression, even at moderate temperatures, when we are in an atmosphere saturated by moisture, in which no evaporation takes place. , 350. Carre's apparatus for freezing- water. — We have already seen that when any liquid is converted into vapour it absorbs a considerable quantity of sensible heat ; this furnishes a source of cold which is the more abundant the more volatile the liquid and the greater its heat of vaporisation. This property of liquids has been utilised by M. Carre, in freezing water by the distillation of ammonia. The apparatus consists of a cyhn- drical boiler C (figs. 269, 270) and of a slightly conical vessel A, which is Fig. 269. Fig. 270. ^^ freezer. These two vessels are connected by a tube ;;z, and a brace «, binds them firmly. They are made of strong galvanised iron plate, and can resist a pressure of seven atmospheres. The boiler C, which holds about two gallons, is three parts filled with a strong solution of ammonia. In a tubulure in the upper part of the boiler some oil is placed, and in this a thermometer t indicating temperatures from icx)° to 150°. The freezer A consists of two concentric envelopes, in such a manner that its centre being hollow, a metal vessel G, con- taining the water to be frozen, can be placed in this space. Hence only the annular space between the sides of the freezer is in communication with the boiler by means of the tube m. In the upper part of the freezer there is a small tubulure, which can be closed by a metal stopper, and by which the solution of ammonia is introduced. The formation of ice comprehends two distinct operations. In the first, the boiler is placed in a furnace F, and the freezer in a bath of cold -352] Carre's Apparatus for Freezing Water. 291 water of about 1 2° The boiler being heated to 1 30° the ammoniacal gas dissolved in the water of the boiler is disengaged, and, in virtue of its own pressure, is liquefied in the freezer, along with about a tenth of its weight of water. This distillation of C towards A lasts about an hour and a quarter, and when it is finished the second operation commences ; this consists in placing the boiler in the cold-water bath (fig. 270), and the freezer outside, care being taken to surround it with very dry flannel. The vessel G, about three-quarters full of water, is placed in the freezer. As the boiler cools, the ammoniacal gas with which it is filled is again dissolved ; the pressure thus being diminished the ammonia which has been liquefied in it is converted into the gaseous form, and now distils from A towards C, to redissolve in the water which has remained in the boiler. During this distillation the ammonia which is rarefied absorbs a great quantity of heat, which is withdrawn from the vessel G and the water it contains. Hence it is that this water freezes. In order to have better contact between the sides of the vessel G and the freezer, alcohol is poured between them. In about an hour and a quarter a perfectly compact cylindrical block of ice can be taken from the vessel G. This apparatus gives about four pounds of ice in an hour, at a price of about a farthing per pound ; large continuously working apparatus have, however, been constructed, which produce as much as 800 pounds of ice in an hour. LIQUEFACTION OF VAPOURS AND GASES. 351. liiquefaction of vapours. — The liquefaction or condensation of vapours is their passage from the aeriform to the liquid state. Conden- sation may be due to three causes — cooling, compression, or chemical affinity. For the first two causes the vapours must be saturated (330), while the latter produces the liquefaction of the most rarefied vapours. Thus, a large number of salts absorb and condense the aqueous vapour in the atmosphere, however small its quantity. When vapours are condensed, their latent heat becomes free, that is, it affects the thermometer. This is readily seen when a current of steam at 100° is passed into a vessel of water at the ordinary temperature. The liquid becomes rapidly heated, and soon reaches 100°. The quantity of heat given up in liquefaction is equal to the quantity absorbed in pro- ducing the vapour. 352. Blstillatlon. Stills. — Distillation is an operation by which a volatile liquid may be separated from substances which it holds in solu- tion, or by which two liquids of different volatilities may be separated. The operation depends on the transformation of liquids into vapours by the action of heat, and on the condensation of these vapours by cooling. The apparatus used in distillation is called 2l still. Its form may vary greatly, but consists essentially of three parts : ist, the body^ A (fig. 271), a copper vessel containing the liquid, the lower part of which fits in the furnace : 2nd, the head, B, which fits on the body, and from which a lateral tube, C, leads to, 3rd, worm, S, a long spiral tin or copper tube. 292 On Heat. [352- placed in a cistern kept constantly full of cold water. The object of the worm is to condense the vapour, by exposing a greater extent of cold surface. To free ordinary well water from the many impurities which it contains, it is placed in a still and heated. The vapours disengaged are condensed Fig. 272. in the worm, and the distilled water arising from the conden.sation is col- lected in the receiver, D. The vapours in condensing rapidly heat the -354] Determination of the Alcoholic Value of Wines, 293 water in the cistern, which must, therefore, be constantly renewed. For this purpose a continual supply of cold water passes into the bottom of the cistern, while the lighter heated water rises to the surface and escapes by a tube in the top of the cistern. 353. Ibiebigr's condenser. — In distilling smaller quantities of liquids, or in taking the boiling point of a liquid, so as not to lose any of it, the apparatus known as Liebig's condenser is extremely useful. It consists of a glass tube, //, fig. 272, about thirty inches long, fitted in a copper or tin tube by means of perforated corks. A constant supply of cold water from the vessel a passes into the space between the two tubes, being conveyed to the lower part of the condenser by a funnel and tubej^ and flowing out from the upper part of the tube g. The liquid to be distilled is contained in a retort, the neck of which is placed in the tube ; the condensed hquid drops quite cold into a vessel placed to receive it at the other extremity of the condensing tube. 354. Apparatus for determinlngr tbe alcobolic value of wines. — One of the forms of this apparatus consists of a glass flask resting on a tripod, and heated by a spirit lamp (fig. 273). By means of a caout- Fig. 273. chouc tube this is connected with a serpentine placed in a copper vessel filled with cold water, and below which is a test-glass for collecting the distillate. On this are three divisions, one a, which measures the quan- tity of wine taken ; the two others indicating one-half and one-third of this volume. The test-glass is filled with the wine up to a, this is then poured into the flask, which, having been connected with the serpentine, the distilla- tion is commenced. The liquid which distils over is a mixture of alcohol and water ; for ordinary wines, such as clarets and hocks, about one-third is distilled over, and for wines richer in spirit, such as sherries and ports, 294 071 Heat. [354- one-half must be distilled ; experiment has shown that under these cir- cumstances all the alcohol passes over in the distillate. The measure is then filled up with distilled water to a ; this gives the mixture of alcohol and water of the same volume as the wine taken, free from all solid mat- ters, such as sugar, colouring matter, and acid, but containing all the alcohol. The specific gravity of this distillate is then taken by means of an alcoholometer (125), and the number thus obtained corresponds to a certain strength of alcohol as indicated by the tables. 355. Safety tube. — In preparing gases and collecting them overmer-" cury or water, it occasionally happens that these liquids rush back into the generating vessel, and destroy the operation. This arises from an excess of atmospheric pressure over the tension in the vessel. If a gas, sulphurous acid, for example, be generated in the flask m (fig. 274), and be passed into water in the vessel A, as long as the gas is given off freely, its tension ex- ceeds the atmospheric pressure and the weight of the column of water, 071, so that the water in the vessel cannot rise in the tube, and absorption is impossible. But if the ten- sion decreases either through the flask be- coming cooled, or the gas being disengaged too slowly, the external pressure prevails, and when it exceeds the internal tension by more than the weight of the column of water CO. the water rises into the flask and the This accident is prevented by means of safety Fig, 274. operation is spoiled. htbes. These are tubes which prevent absorption by allowing air to enter in proportion as the internal tension decreases. The simplest is a tube Qo, Fig. 275. Fig. 276. fig. 275, passing through the cork which closes the flask M, in which the gas is generated, and dipping in the liquid. When the tension of the gas diminishes in M, the atmospheric pressure on the water in the bath E -356] Liquefaction of Gases. 295 causes it to rise to a certain height in the tube DA ; but this pressure, acting also on the hquid in the tube Co, depresses it to the same extent, assuming that this liquid has the same density a5 the water in E. Now as the distance or is less than the height DH, air enters by the aperture o, before the water in the bath can rise to A, and no absorption takes place. Fig. 276 represents another kind of safety tube. It has a bulb a, con- taining a certain quantity of liquid, as does also id. When the tension of the gas in the retort M exceeds the atmospheric pressure, the level in the leg id rises higher than in the bulb, a ; if the gas has the tension of one atmosphere, the level is the same in the tube as in the bulb. Lastly, if the tension of the gas is less than the atmospheric pressure, the level sinks in the leg di ; and, as care is taken that the height ia is less than bh, as soon as the air which enters through c reaches the curved part /, it raises the column ia, and passes into the retort before the water in the cylinder can reach b ; the tension in the interior is then equal to the ex- terior pressure, and no absorption takes place. 356. Iiiquefaction of g:ases. — We have already seen that^a saturated vapour, the temperature of which is constant, is liquefied by increasing the pressure, and that, the pressure remaining constant, it is brought into the liquid state by diminishing the temperature. Unsaturated vapours behave in all respects like gases. And it is natu- ral to suppose that what are ordinarily called permanejit gases are really unsaturated vapours. For the gaseous form is accidental, and is not inherent in the nature of the substance. At ordinary temperatures sul- phurous acid is a gas, while in countries near the poles it is a liquid ; in temperate climates ether is a Hquid, at a tropical heat it is a gas. And just as unsaturated vapours may be brought to the state of saturation and then liquefied by suitably diminishing the temperature or increasing the pressure, so by the same means gases may be liquefied. But as they are mostly very far removed from this state of saturation, great cold and pressure are required. Some of them may indeed be liquefied either by cold or by pressure ; for the majority, however, both agencies must be simultaneously employed. Few gases can resist these combined actions, and probably those which have not yet been liquefied, hydrogen, oxygen, nitrogen, binoxide of nitro- gen, and carbonic oxide, would become so if submitted to a sufficient degree of cold and pressure. Faraday was the first to liquefy some of the gases. His method consists in enclosing in a bent glass tube (fig. 277) substances by whose chemical action the gas to be liquefied is produced and then sealing the shorter leg. '^' ^'^^' In proportion as the gas is disengaged its pressure increases, and it ulti- mately liquefies and collects in the shorter leg, more especially if its con- densation is assisted by placing the shorter leg in a freezing mixture. A small manometer may be placed in the apparatus to indicate the pressure. 296 On Heat. [356- Cyanogen gas is readily liquefied by heating cyanide of mercury in a bent tube of this description ; and carlDonic acid by heating bicarbonate of sodium ; other gases have been condensed by taking advantage of special reactions, the consideration of which belongs rather to chemistry than to physics. For example, chloride of silver absorbs about 200 times its volume of ammoniacal gas ; when the compound thus formed is placed in a freezing tube and gently heated, while the shorter leg is immersed in a freezing mixture, a quantity of liquid ammoniacal gas speedily collects in the shorter leg. 357. Apparatus to liquefy and soUaify grases. — Thilorier first con- structed an apparatus by which considerable quantities of carbonic acid could be liquefied. Its principle is the same as that used by Faraday in working with glass tubes ; the gas is generated in an iron cylinder, and passes through a metallic tube into another similar cylinder where it con- denses. The use of this apparatus is not free from danger ; many acci- dents have already happened with it, and it has been superseded by an apparatus constructed by Natterer, of Vienna, which is both convenient and safe. A perspective view of the apparatus, as modified by M. Bianchi, is repre- sented in fig. 279, and a section on a larger scale in fig. 278. It consists of a wrought-iron reservoir A, of something less than a quart capacity, which can resist a pressure of more than 600 atmospheres. A small force pump is screwed on the lower part of this reservoir. The piston rod t is moved by the crank rod E, which is worked by the handle M. As the com- pression of the gas and the friction of the piston produce a considerable disengagement of heat, the reservoir A is surrounded by a copper vessel, in which ice or a freezing mixture is placed. The water arising from the melting of the ice passes by a tube, w, into a cylindrical copper case C, which surrounds the force pump, from whence it escapes through the tube n^ and the stopcock 0. The whole arrangement rests on an iron frame, PQ. The gas to be Hquefied is previously collected in air-tight bags, R, from whence it passes into a bottle, V, containing some suitable drying sub- stance ; it then passes into the condensing pump through the vulcanised india-rubber tube H. After the apparatus has been worked for some time the reservoir A can be unscrewed from the pump without any escape of the liquid, for it is closed below by a valve S (fig. 278). In order to collect some of the liquid gas the reservoir is inverted and on turning the stop- cock r, the liquid escapes by a small tubulure x. When carbonic acid has been liquefied, and is allowed to escape into the air, a portion only of the liquid volatilises, in consequence of the heat absorbed by this evaporation ; the rest is so much cooled as to solidify in white flakes like snow or anhydrous phosphoric acid. Solid carbonic acid evaporates very slowly. By means of an alcohol thermometer its temperature has been found to be about —90°. A small quantity placed on the hand does not produce the sensation of such great cold as might be expected. This arises from the imperfect contact. But if the solid be mixed with ether the cold produced is so intense that when 357] Liquefaction of Gases. 297 a little is placed on the skin all the effects of a severe burn are produced. A mixture of these two substances solidifies four times its weight of mer- cury in a few minutes. When a tube containing liquid carbonic acid is placed in this mixture, the liquid becomes solid, and looks like a trans- parent piece of ice. The most remarkable liquefaction obtained by this apparatus is that ot protoxide of nitrogen. The gas once liquefied only evaporates slowly, and Fig. 279. produces a temperature of 88° below zero. Mercury placed in it in small quantities instantly solidifies. The same is the case with water ; it must be added drop by drop, otherwise its latent heat being much greater than that of mercury, the heat given up by the water in solidifying would be sufficient to cause an explosion of the protoxide of nitrogen. Protoxide of nitrogen is readily decomposed by heat, and has the pro- 03 298 On Heat. [357- perty of supporting the combustion of bodies with almost as much bril- liancy as oxygen; and even at low temperatures it preserves this pro- perty. When a piece of incandescent charcoal is thrown on liquid pro- toxide of nitrogen it continues to burn with a brilliant light. The cold produced by the evaporation of ether has been used by MM. Loir and Drion in the liquefaction of gases. By passing a current of air from a blowpipe bellows through several tubes into a few ounces of ether, a temperature of — 34° C, can be reached in five or six minutes, and may be kept up for fifteen or twenty minutes. By evaporating liquid sulphu- rous acid in the same manner a great degree of cold, — 50° C, is obtained. At this temperature ammoniacal gas may be liquefied. By rapidly evaporating liquid ammonia under the air pump, in the presence of sulphuric acid, a temperature of —87° is attained, which is found suffi- cient to liquefy carbonic acid under the ordinary pressure of the atmo- sphere. By means of a bath of ether and of solid carbonic acid, and by using very high pressures, Andrews succeeded in reducing air to -^^ of its bulk oxygen to ^f^, hydrogen to -^-^^ carbonic oxide to gf g, and nitric oxide to ilo of its original volume, but without producing liquefaction. Hydrogen and carbonic oxide departed less from Boyle's law than oxygen and nitric oxide. ^ , . \JL a>/^^^ ■ MIXTURES OF GASES AND VAPOURS. 358. Iiaws of the mixture of g:ases and vapours. — Every mixture of a gas and a vapour obeys the following two laws : — I. The tension J and, consegue7ttly, the quantity of vapour which satu- rates a given space, are the same for the same temperature, whether this space contains a gas or is a vacuum. II. The tension of the mixture of a gas and a vapour is equal to the sum of the tensions which each would possess if it occupied the same space alone. These are known as Dalton^s laws, from their discoverer, and are de- monstrated by the following apparatus, which was invented by Gay- Lussac : — It consists of a glass tube A (fig. 280), to which two stopcocks, b and d, are cemented. The lower stopcock is provided with a tubulure, which connects the tube A with a tube B of smaller diameter. A scale between the two tubes serves to measure the heights of the mercurial columns in these tubes. The tube A is filled with mercury, and the stopcocks b and d are closed. A glass globe, M , filled with dry air or any other gas is screwed on by means of a stopcock in the place of the funnel C. All three stop- cocks are then opened, and a little mercury is allowed to escape, which is replaced by the dry air of the globe. The stopcocks are then closed, and as the air in the tube expands on leaving the globe the pressure on it is less than that of the atmosphere. Mercury is accordingly poured into the tube B until it is at the same level in both tubes. The globe is then removed, and replaced by a funnel C, provided with a stopcock ^ of a 359] Mixtures of Gases and Vapours. 299 peculiar construction. It is not perforated, but has a small cavity, as re- presented in ;/, on the left of the figure. Some of the liquid to be vaporised is poured into C, and the height of the mercury, k, having been noted the stopcock b is opened, and a turned, so that its cavity becomes filled with liquid ; being again turned, the liquid enters the space A and vaporises. The Hquid is allowed to fall drop by drop until the air in the tube is saturated, which is the case when the level k of the mercury ceases to sink (329). As the tension of the vapour produced in the space A is added to that of the air already present, the total volume of gas is increased. It may easily be restored to its original volume by pouring mercury into B. When the mercury in the large tube has been raised to the level k, there is a difference, Ba 418. Calorimetry. Thermal unit. — The object of calorimetry is to measure the quantity of heat which a body parts with or absorbs when its temperature sinks or rises through a certain number of degrees, or when it changes its condition. Quantities of heat may be expressed by any of its directly measurable effects, but the most convenient is the alteration of temperature, and quantities of heat are usually defined by stating the extent to which they are capable of raising a known weight of a known substance, such as water. The unit chosen for comparison, and called the thermal unit, is not everywhere the same. In France it is the quantity of heat necessary to raise the temperature of one kilogramme of water through one degree Centigrade; this is called a <:rt:/^r/^. In this book we shall adopt, as a thermal unit, the quantity of heat necessary to raise one pound of water th?-ough one degree Centigrade : i calorie =^T2 thermal units, and i ther- mal unit = 0-45 calorie. 419. specific beat. — When equal weights of two different substances at the same temperature placed in similar vessels are subjected for the same length of time to the heat of the same lamp, or are placed at the same distance in front of the same fire, it is found that their temperatures will vary considerably ; thus mercury will] be much hotter than water. But as, from the conditions of the experiment, they have each been re- ceiving the same amount of heat, it is clear that the quantity of heat which is sufficient to raise the temperature of mercury through a certain number of degrees will only raise the temperature of the same quantity of water through a less number of degrees ; in other words, that it requires more heat to raise the temperature of water through one degree than it does to raise the temperature of mercury by the same extent. Conversely, if the same quantities of water and of mercury at 100° C. be allowed to cool down to the temperature of the atmosphere, the water will require a much longer time for the purpose than the mercury : hence, in cooling through the same number of degrees, water gives out more heat than does mercury. It is readily seen that all bodies have not the same specific heat. If a pound of mercury at 100° is mixed with a pound of water at zero, the temperature of the mixture will only be about 3°. That is to say, that ,x^^ -420] Calorimetry. Specific Heat. 359 while the mercury has cooled through 97°, the temperature ot the water has only been raised 3°. Consequently the same weight of water requires about 32 times as much heat as mercury does to produce the same eleva- tion of temperature. If similar experiments are made with other substances it will be found that the quantity of heat required to effect a certain change of tempera- ture is different for almost every substance, and we speak of the specific heat or calorific capacity of a body as the quantity of heat which it absorbs when its temperature rises through a given range of temperature, from . zero to 1° for example, compared with the quantity of heat which would be absorbed under the same circumstances, by the same weight of water. In other words, water is taken as the standard for the comparison of specific heats. Thus, to say that the specific heat of lead is 0-0314, means that the quantity of heat which would raise the temperature of any given quantity of lead through 1° C. would only raise the temperature of the same quantity of water through 0-0314. Temperature is the vis viva of the smallest particles of a body ; in bodies of the same temperature the atoms have the same vis viva, the smaller mass of the lighter atoms being compensated by their greater velocity. The heat absorbed by a body not only raises its temperature, that is increases the vis viva of the progressive motion of the atoms, but in overcoming the attraction of the atoms it moves them further apart, and along with the expansion which this represents some external pressure is overcome. In the conception of specific heat is included, not merely that amount of heat which goes to raise the temperature, but also that necessary for the internal work of expansion, and that required for the external work. If these latter could be separated we should get the true heat of tempera- ture, that which is used solely in increasing the vis viva of the atoms. This is sometimes called the tn(e specific heat. Three methods have been employed for determining the specific heats of bodies : (i.) the method of the melting of ice, (ii.) the method ot mixtures, and (iii.) that of cooling. In the latter, the specific heat of a body is determined by the time which it takes to cool through a certain temperature. Previous to describing these methods, it will be convenient to explain the expression for the quantity of heat absorbed or given out by a body of known weight and specific heat, when its temperature rises or falls through a certain number of degrees. 420. Measure of tbe sensible heat absorbed by a body. — Let m be the weight of a body in pounds, c its specific heat, and / its temperature. The quantity of heat necessary to raise a pound of water through one degree being taken as unity, in of these units would be required to raise nt pounds of water through one degree, and to raise it through / degrees, / times as much, or 7nt. As this is the quantity of heat necessary to raise through t degrees in pounds of water whose specific heat is unity, a body of the same weight only of different specific heat, would require intc. Consequently, when a body is heated through / degrees, the quantity of heat which it absorbs is the product of its weight into its temperature 36o 071 Heat. [420- into its specific heat. This principle is the basis of all the formulae for calculating specific heats. If a body is heated or cooled from t' to t degrees, the heat absorbed or disengaged will be represented by the formula 7Jt{f — t)c, or m(t-t')c. 42 T ivcethod of the fusion of ice. — This method of determining specific heats is based on the fact that to melt a pound of ice 80 thermal units are necessary, or more exactly 79"25. Black's calorimeter (fig. 316) consists of a block of ice in which a cavity is made, and which is provided with a cover of ice. The substance whose specific heat is to be determined is heated to a certain tem- perature, and then placed m the cavity which is covered. After some time the body becomes cooled to zero. It is then opened, and both the substance and the cavity wiped dry with a sponge which has been previously weighed. The increase of weight of this sponge obviously represents the ice which has been converted into water. Now, since one pound of ice at 0° in melting to water 0° absorbs 80 thermal units, P pounds absorbs 80 P units. On the other hand this quantity of heat is equal to the heat given out by the body in cooling from t° to zero, which is uitc, fot it may be taken for granted that in Fig. 317- Fig. 318. cooling from t^ to zero a body gives out as much heat as it absorbs in being heated from zero to t°. Consequently from 80P mt' intc = 80 P we have c ■■ -422] Specific Heat. 361 It is difficult to obtain blocks of ice as large and pure as those used by Black in his experiments, and Lavoisier and Laplace have replaced the block of ice by a more complicated apparatus, which is called the ice calorimeter. Fig. 317 gives a perspective view of it, and fig. 318 repre- sents a section. It consists of three concentric tin vessels ; in the central one is placed the body M, whose specific heat is to be determined, while the two others are filled with pounded ice. The ice in the compartment A is melted by the heated body, while the ice in the compartment B cuts off the heating influence of the surrounding atmosphere. The two stop- cocks E and D give issue to the water which arises from the liquefaction of the ice. In order to find the specific heat of a body by this apparatus, its weight m is first determined ; it is then raised to a given temperature, /, by keeping it for some time in an oil or water bath, or in a current of steam. Having been quickly brought into the central compartment, the lids are replaced and covered with ice, as represented in the figure. The water which flows out by the stopcock D is collected. Its weight, P, is manifestly that of the melted ice. The calculation is then made as in the preceding case. There are many objections to the use of this apparatus. From its size it requires some quantity of ice, and a body, M, of large mass ; while the experiment lasts a considerable time. A certain weight of the melted water remains adhering to the ice, so that the water which flows out from D does not exactly represent the weight of the melted ice. 422. Bunsen's ice calorimeter. — On the very con- siderable diminution of volume which ice experiences on passing into water (323), Bunsen has based a calorimeter which is particularly suited when only small quantities of a substance can be used in determinations, A small test tube a (fig. 319) intended to receive the substance experimented upon is fused in the wider tube B. The part ab contains pure freshly boiled-out distilled water, H Kla and the prolongation of this tube BC together with the capillary tube d^ contains pure mercury. This tube d is firmly fixed to the end of the tube C ; it is graduated, and the value of each division of the graduation is specially determined by calibration. When the apparatus is im- mersed in a freezing mixture, the water in the part freezes. Hence, if afterwards while the apparatus is protected against the access of heat from without, a weighed quan- tity of a substance at a given temperature is introduced into the tube, it imparts its heat to this in sinking to zero. ^'^- 3^9- In doing so it melts a certain quantity of ice which is evidenced by a corresponding depression of the mercury in tube d. Thus the weight of ice melted, together with the weight and original temperature of the sub- stance experimented upon, furnish all the data for calculating the specific heat. R 362 On Heat. [422- For this mode of determining the specific heat a new determination of the latent heat of ice was made, and was found to be 80-025. It was also in connection with these experiments that Bunsen made his de- termination of the specific gravity of ice, which he found to be in the mean 0-91674. By the above method Bunsen determined the specific heat of several of the rare metals for which a weight of only a few grains could be used. .__ 423. Method of mixtures. — In determining the specific heat of a solid body by this method, it is weighed and raised to a known tempera- ture, by keeping it, for instance, for some time in a closed place heated by steam ; it is then immersed in a mass of cold water, the weight and temperature of which are known. From the temperature of the water after mixture the specific heat of the body is determined. Let M be the weight of the body, T its temperature, c its specific heat ; and let m be the weight of the cold water, and / its temperature. As soon as the heated body is plunged into the water, the temperature of the latter rises until both are at the same temperature. Let this tem- perature be 9. The heated body has been cooled by T - f^ ; it has, there- fore, lost a quantity of heat, M(T-O)^. The cooHng water has, on the contrary, absorbed a quantity of heat equal to vi{(^-t), for the specific heat of water is unity. Now the quantity of heat given out by the body is manifestly equal to the quantity of heat absorbed by the water ; that is, M (T - {))c = m{9 - 1), from which 7n{Q-t) M(T-9* An example will illustrate the application of this formula. A piece of iron weighing 60 ounces, and at a temperature of 100° C, is immersed in 180 ounces of water, whose temperature is 19° C. After the temperatures have become uniform, that of the cooling water is found to be 22° C. What is the specific heat of the iron } Here the weight of the heated body M is 60, the temperature T is 100°, c is to be determined ; the temperature of mixture, P, is 22°, the weight of the cooling water is 180, and its temperature 19°. Therefore 180(22-19) 9 ^Q.j 60(100^22) 78 °''53. 424. Corrections. — The vessel containing the cooling water is usually a small cylinder of silver or brass, with thin polished sides, and is sup- ported by some badly conducting arrangement. It is obvious that this vessel, which is originally at the temperature of the cooling water, shares its increase of temperature, and in accurate experiments this must be allowed for. The decrease of temperature of the heated body is equal to the increase of temperature of the cooling water, and of the vessel in which it is contained. If the weight of this latter be 7n% and its specific heat c', its temperature, like that of the water is / : consequently the previous equation becomes M^(T - 0) = m{9 - /) + w V( --t)) from which, by obvious transformations, -425] Specific Heat. 363 M(T-(;) * Generally speaking, the value m' c' is put = \i ; that is to say, \i is the weight of water which would absorb the same quantity of heat as the vessel. This is said to be the reduced value in water of the vessel, or the water equivalent. The expression accordingly becomes (;y? + fi)(0-/) M(T- ) • In accurate experiments it is necessary also to allow for the heat ab- sorbed by the glass and mercury of the thermometer, by introducing into the equation their values reduced on the same principle. In order to allow for the loss of heat due to radiation, a prehminary experiment is made with the body whose specific heat is sought, the only object of which is to ascertain approximately the increase of temperature of the cooling water. If this increase be 10°, for example, the tempera- ture of the water is reduced by half this number — that is to say 5° below the temperature of the atmosphere — and the experiment is then carried out in the ordinary manner. By this method of compensation, first introduced by Rumford, the water receives as much heat from the atmosphere during the first part of the, experiment as it loses by radiation during the second part. N. / 425. Reg-nault's apparatus for determining' specific lieats. — Fig. /yi^ represents one of the forms of apparatus used by M. Regnault in de- / termining specific heats by the method of mixtures. The principal part is a water-bath, AA, of which fig. 321 represents a section. It consists of three concentric compartments ; in the central one there is a small basket of brass wire, r, containing fragments of the substance to be determined, in the middle of which is placed a thermo- meter, T. The second compartment is heated by a current of steam coming through the tube ^, from a boiler, B, and passing into a worm, a^ where it is condensed. The third compartment, zV, is an air chamber, to hinder the loss of heat. The water bath AA rests on a chamber, K, with double sides, EE, forming a jacket, which is kept full of cold water, in order to exclude the heat from AA and from the boiler B. The central compartment of the water bath is closed by a damper r, which can be I opened at pleasure, so that the basket c can be lowered into the cham- ber K. On the left of the figure is represented a small and very thin brass vessel D, suspended by silk threads on a small carriage^ which can be moved out of, or into, the chamber K. This vessel which serves as a calorimeter, contains water, in which is immersed a thermometer, t. ^nother thermometer at the side, ^, gives the temperature of the air. ] When the thermometer T shows that the temperature of the substance in the bath is stationary, the screen h is raised, and the vessel D moved to just below the central compartment of the water bath. The damper r is then withdrawn, and the basket c and its contents are lowered into the water of the vessel D, the thermometer T remaining fixed in the cork. 3^4 Oil Heat. [425- The carriage and the vessel D are then moved out, and the water agi- tated until the thermometer T becomes stationary. The temperature which it indicates is i). This temperature known, the rest of the calculation is made in the manner described in art. 424, care being taken to make all the necessary corrections. In determining the specific heat of substances — phosphorus, for instance — which^ could not be heated without causing them to melt, or Fig. 320. undergo some change which would interfere with the accuracy of the result, Regnault adopted an inverse process : he cooled them down to a temperature considerably, below that of the water in the calorimeter, and then observed the diminution in the temperature of the latter, which resulted from immersing the cooled substance in it. To ascertain the specific heat of bodies, such as potassium, where the use of water is quite inapplicable, the determination is made in another liquid, such as turpentine or benzole, the specific heat of which is known. 426. Metbod of coolingr. — Equal weights of different bodies whose specific heats are different, will occupy different times in cooling through the same number of degrees. Dulong and Petit have applied this prin- ciple in determining the specific heats of bodies in the following manner: -428] Specific Heat of Liquids. 365 A small polished silver vessel is filled with the substance in a state of fine powder, and a thermometer placed in the powder, which is pressed down. This vessel is heated to a certain temperature, and is then introduced into a copper vessel, in which it fits hermetically. This copper vessel is ex- hausted, and maintained at the constant temperature of melting ice, and the time noted which the substance takes in falling through a given range of temperature, from 15° to 5° for example. The times which equal weights of different bodies require for cooling through the same range of temperature are directly as their specific heats. Regnault has proved that with solids this method does not give trust- worthy results ; it assumes, which is not quite' the case, that the cooling in all parts is equal, and that all substances part with their heat to the silver case with equal facility. The method may, however, be employed with success in the determination of the specific heat of liquids. In an investigation of the specific heats of various soils, Pfaundler found that a soil of low specific heat heats and cools rapidly, while earth of higher specific heat undergoes slow heating and slow coohng ; that moist earths, rich in humus, have a high specific heat amounting in the case of turf, to as much as 0-5 ; while dry soils free from humus, such as lime and sand, have a low specific heat, not more than about 0'2. 427. Specific heat of liquids. — The specific heat of hquids may be determined either by the method of cooling, by that of mixtures, or by that of the ice calorimeter. In the latter case they are contained in a small metal vessel, or a glass tube, which is placed in the central com- partment (fig. 318), and the experiment then made in the usual manner. It will be seen from the following table that water and oil of turpentine have a much greater specific heat than that of other substances, and more especially than the metals. It is from its great specific heat that water requires a long time in being heated or cooled, and that for the same weight and temperature it absorbs or gives out far more heat than other substances. This double property is applied in the hot water apparatus, of which we shall presently speak, and it plays a most important part in the/^conomy of nature. ./428. 428. XMCean specific beats of solids and liquids between C and 100 / '^^By means of the method of mixture and of that of cooling, M. Regnault has determined the specific heats of a number of bodies. The following table contains the numbers obtained for the bodies usually met with in the arts : — Substances Specific heats Substances Specific heats Water at 0° . . i-ooooo Calcined animal cha rcoal 0-26085 „ 10 . . I -00050 Wood charcoal . 0-24111 » 15 . . roo20o Sulphur . 0-20259 mean between Graphite . 0-20187 „ and 100° . I -00500 Thermometer glass . . 0-19768 Turpentine at 17° . . 0-42590 Phosphorus . 0-18949 Alcohol „ 17° . . 0-61500 Diamond . 0-14687 Ether . 0-51600 Grey iron . 0-12983 Glycerine „ . 0-55500 Steel . 0-11750 366 On Heat. [428- Specific heats Substances Specific heats 0-1I379 Tin . . 0-05623 0-10863 Antimony . 0-05077 0-10696 Mercury . . 0-03332 0-09555 Gold . 0-03244 0-09515 Platinum . 0-03244 0-09391 Bismuth . . 0-03084 0-05701 Substances Iron Nickel Cobalt Zinc Copper Brass Silver These numbers represent the mean specific heats between 0° and loo*^. Dulong and Petit's investigations have, however, shown that the specific heats increase with the temperature. Those of the metals, for instance, are greater between 100° and 200° than between zero and 100°, and are still greater between 200° and 300°. That is to say, a greater amount of heat. is required to raise a body from 200° to 250*^ than from 100° to 150° and still more than from zero to 50°. For silver, the mean specific heat between 0° and 100° is 00557, while between 0° and 200° it is o-o6ii. The specific heat of platinum for any temperature may be expressed by the formula 0-0328 + 0-0000042/, where/ is the temperature; and that of water by the formula i + 0-00004/ + o'oooooo()f^ . The increase of specific heat with the temperature is greater as bodies are nearer their fusing point. Any action which increases the density and molecular aggregation of a body, diminishes its specific heat. The specific heat of copper is diminished by its being hammered, but it regains its original value after the metal has been again heated. The specific heat of a liquid increases with the temperature much more rapidly than that of a solid. Water is, however, an exception ; its specific heat increases less rapidly than does that of solids. A substance in the liquid state has a greater specific heat than when it is sohd ; thus, melted tin has the specific heat 0-0637, while that of solid tin is only 005623. The specific heat of liquid bromine is o-iii, that of sohd bromine being 0-081. The difference in the case of water is greater. Its specific heat is i, that of ice, according to Person, being 0*504. In the gaseous state a body has a higher specific heat than in the liquid state. Pouillet used the specific heat of platinum for measuring high degrees of heat. Supposing 200 ounces of platinum had been heated in a furnace, and had then been placed in 1000 ounces of water, the temperature of which it had raised from 13° to 20°. From the formula we have M =200, m = 1000 ; ^ is 20, and /is 13. The specific heat of platinum is 0-033, ^i^d we have, therefore, from the equation, Mc(T-0 = »2(^-0 ^ _ m{^-t)^'^C^ ^ 7000 +132 ^ 7132 ^ r. o Wc 6-6 6-6^ It is found, however, that the specific heat of platinum at tempera- tures of about 1000 is 0-0373 ; if this value, therefore, be substituted for c in the above equation, 7-46 -429] Diilong and Petit' s Law. 367 By this method, which requires great skill in the experimenter, Pouillet determined a series of high temperatures. He found, for example, the temperature of melting iron to be I5cx)° to 1600° C. 429. I>ulong: and Petit's law. — A knowledge of the specific heat of bodies has become of great importance, in consequence of Dulong and Petit's discovery of the remarkable law, that the product of the specific heat of any element into its atomic weight is a constant number, a law which may also be enunciated by saying that the specific heats of simple bodies are inversely as their atomic weights. Thus, taking the atomic weight of iron at 28, its specific heat 0-11379, and the product 3'i86 ; the atomic weight of nickel is 29-5, its specific heat 0-10863, product 3-204 ; the atomic weight of hydrogen is i, its specific heat 3-2, and the product is 3-2. Regnault, who determined the specific heats of a large number of elements with great care, confirmed Dulong and Petit's law, but he found that the number, instead of being constant, as Dulong and Petit had sup- posed, varies between 2*95 and 3-41. These variations may depend partly on the difficulty of obtaining the elements quite pure, and partly on the errors incidental to the determination of the specific heats, and of the equivalents. But the specific heats of bodies vary with the state of aggre- gation, and also with the limits of the temperature at which they are de- termined. Some, such as potassium, have been determined at tempera- tures very near their fusing points ; others, like platinum, at great dis- tances from these points. And, doubtless, the principal reason of the discrepancies is the fact that the determinations have not been made under identical physical conditions, and at temperatures equally distant from the fusing point. The equivalents of the elements represent the relative weights of equal numbers of atoms of these bodies, and the product/^ of the specific heat c into the equivalent p is the ato7nic specific heat, or the quantity of heat necessary to raise the temperature of the same number of atoms by one degree ; and Dulong and Petit's law may be thus expressed : the sajne quantity of heat is needed to heat a?i atom of all simple bodies to the same extent. The atomic heat of a body, when divided by its specific heat, gives the equivalent of a body. Regnault has even proposed to use this relation as a means of determining the equivalent, and it certainly is of great ser- vice in deciding on the equivalent of a body in cases where the chemical relations permit a choice between two or more numbers. In compound bodies the law also prevails ; the product of the specific heat into the equivalent is an almost constant number, which varies, how- ever, with the different classes of bodies. Thus, for the class of oxides of the general formula RO, it is 11-30; for the sesquioxides R^O^ it is 27-15 ; for the sulphides RS, it is 18-88 ; and for the carbonates RCO^, it is 21-54. The law may be expressed in the following general manner : With compounds of the same formula, and of a similar chemical constitution^ 368 On Heat. [429- the product of the atomic weight into the specific heat is a constant quan- tity. This includes Dulong and Petit's law as a particular case. 430. Specific beat of compound bodies. — In order to deduce the specific heat of the compound from that of its elements, M. Woestyn has made the following hypothesis : he assumes that an element, in entering into combination with others to form a compound body, retains its own specific heat, so that if /, p', p", .... represent the atomic weights of the elements, and P that of the compound ; c, c', c", . . . . C, the cor- responding specific heats, while n, n', n'\ .... are the numbers of atoms of these simple bodies which make up the molecule of the compound, the relation obtains : VZ = npc-,n'p'c'-^n"p"c"+ .... M. Wcestyn has found that the results obtained by calculating, on this hypothesis, the specific heats of the sulphides, iodides, and bromides, agree with experimental results. 431. Specific heat of g-ases. — The specific heat of a gas may be re- ferred either to that of water or to that of air. In the former case, it repre- sents the quantity of heat necessary to raise a given weight of the gas through one degree, as compared with the heat necessary to raise the same weight of water one degree. In the latter case it represents the quantity of heat necessary to raise a given volume of the gas through one degree, compared w^th the quantity necessary for the same volume of air treated in the same manner. De la Roche and Bernard determined the specific heats of gases in refer- ence to water by causing known volumes of a given gas under constant pressure, and at a given temperature, to pass through a spiral glass tube placed in water, Fiom the increase in temperature of this water, and from the other data, the specific heat was determined by a calculation analogous to that given under the method of mixtures. The same physi- cists also determined the specific heats of different gases relatively to that of air, by comparing the quantities of heat which equal volumes of a given gas, and of air at the same pressure and temperature, imparted to equal weights of water. Subsequently to these researches, De la Rive and Marcet have applied the method of cooling to the same determination ; and still more recently Regnault has made a series of investigations on the calorific capacities of gases and vapours, in which he has adopted, but with material improvements, the method of De la Roche and Bernard. He has thus obtained the following results for the specific heats of the various gases and vapours, compared first with an equal weight of water taken as unity ; secondly, with that of an equal volume of air, referred, as before, to its own weight of water taken as unity. Specific heats Equal weights Air . f Oxygen . Simple I Nitrogen . gases i Hydrogen I Chlorine . Equal Equal weights volumes 0-2374 0-2374 0-2175 0-2405 0-2438 0-2370 3-4090 0-2359 0-I2I0 0-2962 -432] Latent Heat of FiLsion. 369 Compound gases Vapours ^ f Binoxide of nitrogen I Carbonic oxide I Carbonic acid . Hydrochloric acid Ammonia . defiant gas 'Water Ether Alcohol . Turpentine j Bisulphide of carbon (^ Benzole Specific heats Equal Equal weights volumes 0-2315 0-2406 0-2450 0-2370 0-2163 0-3307 0-1845 0-2333 0-5083 0-2966 0-4040 0-4106 0-4805 0-2984 0-4810 1-2296 0-4534 O-717I 0-5061 2-3776 0-1570 0-4140 0-3754 I -01 14 In making these determinations the gases were under a constant pres- sure, but variable volume ; that is, the gas as it was heated could expand, and this is called the specific heat imder constant pressiire. But if the gas when being heated is kept at a constant volume, its pressure or elastic force then necessarily increasing, it has a different capacity for heat ; this latter is spoken of as the specific heat under constant votume. That this latter is less than the former is evident from the following considerations : Suppose a given quantity of gas to have had its temperature raised t°, while the pressure remained constant, this increase of temperature will have been accompanied by a certain increase in volume. Supposing now that the gas is so compressed as to restore it to its original volume, the result of this compression will be to raise its temperature again to a certain extent, say t'°. The gas will now be in the same condition as if it had been heated, and not been allowed to expand. Hence, the same quantity of heat which is required to raise the temperature of a given weight of gas, f, while the pressure remains constant and the volume alters, will raise the temperature / + /' degrees if it is kept at a constant volume but variable pressure. The specific heat, therefore, of a gas at constant pressure, c^, is greater than the specific heat under constant C t 4- t' volume, c, and they are to each other as / + /' : /, that is -' = . It is not possible to determine by direct means the specific heat of gases under constant volume with even an approach to accuracy ; and it has always been determined by some indirect method, of which the most ac- curate is based on the theory of the propagation of sound (218). The latest determination made on this basis gives the number 1-414 for the value of -^. c 432. latent heat of ftision.— Black was the first to observe that dur- ing the passage of a body from the solid to the liquid state, a quantity of heat disappears, so far as thermometric effects are concerned, and which is accordingly said to become latent. In one experiment he suspended in a room at the temperature 8-5° two thin glass flasks, one containing water at 0°, and the other the same weight R3 < 370 071 Heat. [432- of ice at o° At the end of half an hour the temperature of the water had risen 4°, that of the ice being unchanged, and it was lo^^ hours before the ice had melted and attained the same temperature. Now the temperature of the room remained constant, and it must be concluded that both vessels received the same amount of heat in the same time. Hence 21 times as much heat was required to melt the ice and raise it to 4° as was sufficient to raise the same weight of water through 4°. So that the total quantity of heat imparted to the ice was 21 x 4 = 84, and as of this only 4 was used in raising the temperature, the remainder, 80, was used in simply melting the ice. He also determined this latent heat by immersing 119 parts of ice at 0° in 135 parts of water at 877° C. He thus obtained 254 parts of water at 11-6° C. Taking into account the heat received by the vessel in which the liquid was placed, he obtained the number 79-44 as the latent heat of liquidity of ice. We may thus say : Water at 0° = Ice at 0° + latent heat of liquefaction. The method which Black adopted is essentially that which is now used for the determination of latent heats of liquids ; it consists in placing the substance under examination at a known temperature in the water (or other liquid) of a calorimeter, the temperattire of which is sufficient to melt the substance if it is solid, and to solidify it if liquid, and when uni- formity of temperature is established in the calorimeter, this temperature is determined. Thus, to take a simple case, suppose it is required to de- termine the latent heat of liquidity of ice. Let M be a certain weight of ice at zero, and m a weight of water at f sufficient to melt the ice. The ice is immersed in the water, and as soon as it has melted the final temperature b° is noted. The water, in cooling from f to fc° has parted with a quantity of heat, m{t — ' ). If x be the latent heat of the ice, it absorbs, in liquefying, a quantity of heat, M;ir; but, besides this, the water which it forms has risen to the temperature f^°, and to do so has required a quantity of heat, represented by M^. We thus get the equation M:r + M0 = m{t - O), from which the value of x is deduced. By this method, and avoiding all sources of error, M M. Desains and De la Provostaye found that the latent heat of the liquefaction of ice is 79*25 ; that is, a pound of ice, in liquefying, absorbs the quantity of heat which would be necessary to raise 7925 pounds of water, 1°, or, what is the same thing, one pound of water from zero to 79*25° This method is thus essentially that of the method of mixtures; the same apparatus may be used, and the same precautions are required in the two cases. In determining the latent heat of liquidity of most solids, the different specific heats of the substance in the sohd and in the liquid state require to be taken into account. In such a case, let ?n be the weight of the water in the calorimeter (the water equivalents of the calorimeter and thermometer supposed to be included); M the weight of the substance operated on; / the original and n the final temperature of the calorimeter ; -433] Latent Heat of Vapours. 371 T the original temperature of the substance ; C its melting (or freezing) point ; C the specifit heat of the substance in the solid state between the- temperature C and ^ ; c\\.s specific heat in the liquid state between the temperatures T and % ; and let L be the latent heat sought. If the experiment be made on a melted substance which gives out heat to the calorimeter and is thereby solidified (it is taken for granted that a body gives out as much heat in sohdifying as it absorbs in liquefying), it is plain that the quantity of heat absorbed by the calorimeter, w(y - /), is made up of three parts : first, the heat lost by the substance in cooling from its original temperature T to the solidifying point % ; secondly, the heat given out in solidification, L ; and, thirdly, the heat it loses in sink- ing from its solidifying point C to the temperature of the water of the calorimeter. That is : ni{B -t) = m[^(T-E)^ + L + fr - ^)cj whence, in{^ - i) -(T-^)c-{^-h)C. M. Person, who has made several researches on this subject, has obtained the following numbers for the latent heats of fusion of several bodies : Water • 79-24 Bismuth . 1264 Nitrate of sodium . 62-97 Sulphur • 9-37 Zinc . . 28-13 Lead .... • 5-37 Silver . . 21-07 Phosphorus • 5-03 Tin . . . . 14-25 D'Arcet's alloy . . 4-50 Cadmium . 13-66 Mercury . 2-83 These numbers represent the number of degrees through which a pound of water would be raised by a pound of the body in question in passing from the liquid to the solid state ; or, what is the same thing, the number of pounds of water that would be raised 1° C. by one of the bodies in solidifying. On modern views the heat expended in melting is consumed in moving the atoms into new positions; the work, or its equivalent in heat required for this, the potential energy they thus acquire, is strictly comparable to the expenditure of work in the process of raising a weight. When the liquid solidifies, it reproduces the heat which had been expended in liquefying the solid ; just as when a stone falls it produces by its impact against the ground the heat, the equivalent -of which in work, had been expended in raising it, and a similar explanation applies to the latent heat of gaseification. 433. determination of tbe latent beat of vapours. — Liquids, as we have seen in passing into the state of vapour, absorb a very considerable quantity of heat, which is termed latent heat of vaporisatio7i. In deter- mining the heat absorbed in liquids, it is assumed that a vapour, in liquefying, gives out as much heat as it had absorbed in becoming con- verted into vapour. The method employed is essentially the same as that for determining 372 On Heat. [433 the specific heat of gases. Fig. 322 represents the apparatus used by M. Despretz. The vapour is produced in a retort, C/ where its tempera- ture is indicated by a thermometer. It passes into a worm immersed in cold water, where it condenses, imparting its latent heat to the condensing water in the vessel B. The con- densed vapour is collected in a vessel. A, and its weight represents the quantity of vapour which has passed through the worm. The ther- mometers in B give the change of temperature. Let M be the weight of the con- densed vapour, T its temperature on entering the worm, which is that of its boiling point, and x the latent heat of vaporisation. Simi- larly, let ni be the weight of the condensing water (comprising the weight of the vessel B and of the worm SS reduced in water), let t° be the temperature of the water at the beginning, and fe° its temperature at the end of the experiment. It is to be observed that, at the commencement of the experiment, the condensed vapour passes out at the temperature /°, while at the conclusion its temperature is 6° ; we may, however, assume that its mean temperature Fig. 322. during the experiment is The vapour M after condensation has therefore parted with a quantity of heat M ( T — "*" _ j c, while the heat disengaged in liquefaction is represented by M^. The quantity of heat absorbed by the cold water, the worm and the vessel is m{ii — t). Therefore, M;ir + M^^T - — -^^ c = m(0 - /), from which x is obtained. M. Despretz found that the latent heat of aqueous vapour at 100° is 540 ; that is, a pound of water at 100° absorbs in vaporising as much heat as would raise 540 pounds of water through 1°. M. Regnault found the number 537, and MM. Favre and Silbermann 538-8. As in the case of the latent heat of water we may say. Steam at 100° = Water at 100° + latent heat of gaseification. In the conversion of a body from the liquid into the gaseous state, as in the analogous process of fusion, one part of the heat is used in increasing the temperature and another in internal work. For vaporisation the greater portion is consumed in the internal work of overcoming the reciprocal attraction of the particles of liquid, and in removing them to the far greater distances apart in which they exist in the gaseous state. In -434] Favre and Silhermanii s Caloi^imeter. '^'ji addition to this there is the external work — namely, that required to over- come the external pressure, usually that of the atmosphere ; and as the increase of volume in vaporisation is considerable, this pressure has to be raised through a greater distance. Vaporisation may take place without having external work to perform, as when it is effected in vacuo ; but whether the evaporation is under a high or under a low pressure, on the surface of a liquid or in the interior, there is" always a great consumption of heat in internal work. ' 434. Favre and Silbermann's calorimeter. — The apparatus (fig. 323) furnishes a very delicate means of determining the calorific capacity of liquids, latent heats of evaporation, and the heat disengaged in chemical actions. The principal part is a spherical iron reservoir, A, full of mercury, of which it holds about 50 pounds, and represents, therefore, a volume of more than half a gallon. On the left there are two tubulures, B, in which are fitted two sheet-iron tubes or 7tiuffles, projecting into the interior of the bulb. Each can be fitted with a glass tube for containing the substance experimented upon. In most cases one muffle and one glass tube are enough ; the two are used when it is desired to compare the quantities of heat produced in two different operations. In a third verticle tubulure, C, there is also a muffle, which can be used for determining calorific capacities by Regnault's method (425), in which case it is placed beneath the r of fig. 320. The tubulure d contains a steel piston ; a rod, turned by a handle, in, and which is provided with a screw thread, transmits a vertical motion to the piston ; but, by a peculiar mechanism, gives it no rotatory motion. In the last tubulure is a glass bulb, a, in which is a long capillary glass tube, bo, divided into parts of equal capacity. It will be seen from this description that the mercury calorimeter is nothing more than a thermometer with a very large bulb and a capillary stem : it is therefore extremely delicate. It differs, however, from a ther- mometer in the fact that the divisions do not indicate the temperature of the mercury in the bulb, but the number of thermal units imparted to it by the substances placed in muffle. This graduation is effected as follows : — By working the piston the mercury can be made to stop at any point of the tube, bo, at which it is desired the graduation should commence. Having then placed in the iron tube a small quantity of mercury, which is not afterwards changed, a thin glass tube, e, is inserted, which is kept fixed against the buoyancy of the mercury by a small wedge not represented in the figure. The tube being thus adjusted, the point of a bulb tube (see fig. 324) is introduced containing water, which is raised to the boihng point : turning the position of the pipette, then, as represented on n', a quantity of the liquid flows into the test tube. The heat which is thus imparted to the mercury makes it expand ; the column of mercury in bo is lengthened by a number of divisions, which we shall call n. If the water poured into the test glass be weighed, and if its temperature be taken when the column ^^is stationary, the product of the 374 On Heat. [434- weight of the water into the number of degrees through which it has fallen indicates the number of thermal units which the water gives up to the entire apparatus (419). Dividing by 71 this number of thermal units, Fig. 323. the quotient gives the number a of thermal units corresponding to a single division of the tube bo. In determining the specific heat of liquids, a given weight M, of the liquid in question is raised to the temperature T, and is poured in the tube C. Calling the specific heat of the liquid C, its final temperature ^, and n the number of divisions by which the mercurial column bo has advanced, we have yicij-^)=nn, from which c= -- ^^— -. The boards represented round the apparatus are hinged so as to form a box, which is lined with eider down or wadding to prevent any loss of heat. It is closed at the top by a board, which is provided with a suitable case, also hned, which fits over the tubulures it falls, or wh, less the labour lost by the friction of the apparatus. This is diminished as far as possible by the use of friction wheels, and its amount is determined by connecting C and D without caus- ing them to pass over A, and then determining the weight necessary to communicate to them a uniform motion. In this way it has been found that a thermal unit — that is, the quantity of heat by which a pound of water is raised through 1° C. — is generated by the expenditure of the same amount of work as would be required to raise 1392 pounds through i foot, or i pound through 1392 feet. This is expressed by saying that the mechanical equivalent of the thermal unit is 1392 foot-pounds. The friction of an iron paddle-wheel in mercury gave 1397 foot-pounds, and that of the friction of two iron plates gave 1395 foot-pounds, as the mechanical equivalent of one thermal unit. In another series of experiments, the air in a receiver was compressed. 404 On Heat. [467- by means of a force pump, both being immersed in a known weight of water at a known temperature. After 300 strokes of the piston, the heat, C, was measured which the water had gained. This heat was due to the compression of the air and to the friction of the piston. To ehminate the latter influence, the experiment was made under the same conditions, but leaving the receiver open. The air was not compressed, and 300 strokes of the piston developed Q' thermal units. Hence C — C^ is the heat pro- duced by the compression of the gas. Representing the foot-pounds ex- W pended in producing this heat by W, we have for the value of the mechanical equivalent E. By this method Joule obtained the number 1442. The mean number which Joule adopted for the mechanical equivalent of one thermal unit on the Centigrade scale is 1390 foot-pounds ; on the Fahrenheit scale it is 772 foot-pounds. The number is called Joule's equivalent. On the metrical system 424 metres is taken as the height through which a kilogramme of water must fall to raise its temperature i degree Centigrade. M. Hirn has made the following determination of the mechanical equi- valent by means of the heat produced by the compression of lead. A large block of sandstone, CD (fig. 339), is suspended vertically by cords ; Fig. 339. its weight is P. E is a piece of lead, fashioned so that its temperature may be determined by the introduction of a thermometer. The weight of this is n, and its specific heat c. AB is a cylinder of cast iron, whose weight is/. If this be raised to A^B^, a height of /z, and allowed to fall again, it compresses the lead, E, against the anvil, CD. It remains to measure on the one hand the work lost, and on the other the heat gained. The hammer AB being raised to a height h, the work of its fall is//z, but as, by its elasticity, it rises again to a height h^ the work is/ {h-h^. The anvil, CD, on the other hand, has been raised to a height H, and has absorbed in so doing PH units of work. The work, W, definitely ab- *♦ -467] Mechanical Equivalent of Heat. 405 sorbed by the lead is p {h-h) - PH. On the other hand, the lead has been heated by 9, it has gained n^V thermal units, c being the specific heat of lead, and the mechanical equivalent is therefore equal to the quotient A series of six experiments gave 1394 as the mechanical equivalent. The following is the method which Mayer employed in calculating the mechanical equivalent of heat. It is taken, with slight modifications, from Prof Tyndall's work on 'Heat,' who, while strictly following Mayer's reasoning, has corrected his data. Let us suppose that a rectangular vessel with a section of a square foot contains at 0° a cubic foot of air under the ordinary atmospheric pressure; and let us suppose that it is enclosed by a piston without weight. Suppose now that the cubic foot of air is heated until its volume is doubled ; from the coefficient of expansion of air we know that this is the case at 273° C. The gas in doubling its volume will have raised the piston through a foot in height ; it will have lifted the atmospheric pressure through this distance. But the atmospheric pressure on a square foot is in round numbers 15 x 144 = 2160 pounds. Hence a cubic foot of air in doubling its volume has lifted a weight of 2160 pounds through a height of a foot. Now a cubic foot of air at zero weighs 1-29 ounces, and the specific heat of air under constant pressure, that is, when it can expand freely, as compared with that of an equal weight of water, is 0*24 ; so that the quantity of heat which will raise 1-29 ounce of air through 273° will only raise 0*24 x 1-29 = 0*3 1 oz. of water through the same temperatue ; but 0-31 oz. of water raised through 273° is equal to 5*29 pounds of water raised through 1° C. That is, the quantity of heat which will double the volume of a cubic foot of air, and in so doing will lift 2160 pounds through a height of a foot, is 5-29 thermal units. Now in the above case the gas has been heated under constant pres- sure, that is, when it could expand freely. If, however, it had been heated under constant volume, its specific heat would have been less in the ratio i : i'4i4 (423), so that the quantity of heat required under these circumstances to raise the temperature of a cubic foot of air would be 5-29 X = 374. Deducting this from 5-29, the difference 1-55 repre- 1-41 sents the weight of water which would have been raised 1° C. by the ex- cess of heat imparted to the air when it could expand freely. But this excess has been consumed in the work of raising 2160 pounds through a foot. Dividing this by 1-55 we have 1393. Hence the heat which will raise a pound of water through 1° C. wiH raise a weight of 1393 pounds through a height of a foot; a numerical value of the mechanical equiva- lent of heat agreeing as closely as can be expected with that which Joule adopted as the most certain of his experimental results. ' The law of the relation of heat to mechanical energy may thus be stated : Heat ami inechanical energy are mutually convertible; and heat requires 4o6 On Heat. [467- for its production^ and prodiises by its disappearance, mechanical energy in the ratio of 1390 foot-pounds for every thermal taiit. A variety of experiments may in like manner be adduced to show that whenever heat disappears work is produced. For example, if in a reser- voir immersed in water the air be compressed to the extent of 10 atmo- spheres : supposing that now, when the compressed air has acquired the temperature of the water, it be allowed to act upon a piston loaded by a weight, the weight is raised. At the same time the water becomes cooler, showing that a certain quantity of heat had disappeared in producing the mechanical effort of raising the weight. This may also be illustrated by the following experiment, due to Prof. Tyndall. A strong metal box is taken, provided with a stopcock, on which can be screwed a small condensing pump. Having compressed the air by its means, as it becomes heated by this process, the box is allowed to stand for some time, until it has acquired the temperature of the surrounding Fig. 340. medium. On opening the stopcock, the air rushes out; it is expelled by the expansive force of the internal air ; in short, the air drives itself out. Work is therefore performed by the gas, and there should be a disap- pearance of heat ; and if the jet of gas be allowed to strike against the thermo-pile, the galvanometer is deflected, and the direction of its deflec- tion indicates a cooling (fig. 340). If, on the contrary, the experiment is made with an ordinary pair of bellows, and the current of air is allowed to strike against the battery, the deflection of the galvanometer'is in the opposite direction, indicating an increase of temperature (fig. 341). In this case the hand of the experi- menter performs the work, which is converted into heat. Joule placed in a calorimeter two equal copper reservoirs, which could be connected 5y a tube. One of these contained air at 22 atmospheres, -468] Mechanical Equivalents of Heat. 407 the other was exhausted. When they were connected, they came into equihbrium under a pressure of 1 1 atmospheres ; but as the gas in expand- ing had done no work, there was no alteration in temperature. When, however, the second reservoir was full of water, the air in entering was fig. 34 obliged to expel it and thus perform work, and the temperature sank, owing to an absorption of heat. For further information the student of this subject is referred to the following works : — Tyndall on Heat as a Mode of Motion, Maxwell on Heat (Longmans), Balfour Stewart on Heat (Macmillan), and Tait on Thermodynamics (Edmonston and Douglas). A condensed, though complete and systematic, account of the dynamical theory of heat is met with in Professor Foster's articles on ' Heat,' in Watts's Dictionary of Chemistry. 468. Dissipation of energry. — Rankine has the following interesting observations on a remarkable consequence of the mutual convertibility which has been shown to exist between heat and other forms of energy. Sir W. Thomson has pointed out the fact, that there exists at least in the present state of the known world a predominating tendency to the conversion of all the other forms of physical energy into heat, and to the uniform diffusion of all heat throughout all matter. The form in which we generally find energy originally collected is that of a store of chemical power consisting of uncombined elements. The combination of these elements produces energy in the form known by the name of electrical currents, part only of which can be employed in analysing chemical compounds, and thus reconverted into a store of chemical power ; the remainder is necessarily converted into heat; apart only of this heat can be employed in analysing compounds or in reproducing electric currents. If the remainder of the heat be employed in expanding an elastic substance, it may be converted entirely into visible motion, or into a store of visible mechanical power, (by raising weights, for example) provided the elastic 4o8 On Heat, [468 substance is enabled to expand until its temperature falls to the point which corresponds to the absolute privation of heat; but unless this condition is fulfilled, a certain proportion only of the heat, depending on the range of temperature through which the elastic body works, can be converted, the rest remaining in the state of heat. On the other hand, al] visible motion is of necessity ultimately converted into heat by the agency of friction. There is then in the present state of the known world, a tendency towards the conversion of all physical energy into the sole form of heat. Heat, moreover, tends to diffuse itself uniformly by conduction and radiation, until all matter shall have acquired the same temperature. There is, consequently, so far as we understand the present condition of the universe, a tendency towards a state in which all physical energy will be in the state of heat, and that heat so diffused, that all matter will be at the same temperature ; so that there will be an end of all physical phenomena. Vast as this speculation may seem, it appears to be soundly based on experimental data, and to truly represent the present condition of the universe as far as we know it. r-/ -469] Transmission, Velocity, and Intensity of Light. 409 n BOOK VII. ON LIGHT. : ,/ ./<^'/7t^ ^^(QHAPTE^ I. / ' TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT. 469. Theories of lig-bt. — Light is the agent v/hich, by its action on the retina, excites in us the sensation of vision. That part of physics which deals with the properties of Hght is known as optics. In order to explain the origin of light, various hypotheses have been made, the most important of which are the R, we have >— and < R. P u 2 436 On Light. [499- iii. When the object coincides with the centre, / = R, and, consequently, /' = R ; that is, the image coincides with the object. iv. When the luminous object is between the centre and the principal focus, ^R ; that is, the image is formed on the other side of the centre. When the object is in the focus, R R / = - , which gives ^' = _- =- 00 ; that is, the image is at an infinite dis- tance, for the reflected rays are parallel to the axis. V. Lastly, if the object is between the principal focus and the mirror, we get p< — ; p' is then negative, because the denominator of the for- mula (4) is negative. Therefore, the distance/' of the mirror from the image must be calculated on the axis in a direction opposite to p. The image is then virtual, and is on the other side of the mirror. Making/' negative in the formula (2), it become? -— - = y.-; in this p p' K form it comprehends all cases of virtual images in concave mirrors. In the case of convex mirrors, the image is always virtual (497) ; P' and R are of the same sign, since the image and the centre are on the same side of the mirror, while the object being on the opposite side, p is of the contrary sign ; hence in the formula (2) we get 1-^=1 (5) . -j P' P V. . ^^' as the formula for convex mirrors. It may also be found directly by the same geometrical considerations as those which have led to the formula (2) for concave mirrors. It must be observed that the preceding formulae are not rigorously true, inasmuch as they depend upon the hypothesis that the lines LM and /M (fig. 374) are equal to LA and A/ ; although this is not true, the error diminishes without limit with the angle MCA : and when this angle does not exceed a few degrees, the error is so small that it may, in practice, be neglected. 500. Calculation of the mag^nitude of imagoes. — By means of the above formulas the magnitude of an image may be calculated, when the distance of the object, its magnitude, and the radius of the mirror are given. For if BD be the object (fig. 375), bd its image, and if the distance -502] Spherical A berration. 437 A and the radius AC be known, Ko can be calculated by means of for- mula (3) of article 498. Ko known, oC can be calculated. But as the tri- angles BCD and dCb are similar, their bases and heights are in the pro- portion ^.^ : BD = C^ : CK, or Length of the image : length of the object = distance from image to centre : distance from the object to centre. 501. Spberical aberration. Caustics. — In the foregoing theory of the foci and images of spherical mirrors, it has already been observed that the reflected rays only pass through a single point when the aperture of the mirror does not exceed 8 or 10 degrees (493). With a larger aper- ture, the rays reflected near the edges meet the axis nearer the mirror than those that are reflected at a small distance from the neighbourhood of the centre of the mirror. Hence arises a want of precision in these images, which is called spherical aberration by reflection, to distinguish it from the spherical aberration by refraction, which occurs in the case of lenses. Every reflected ray cuts the one next to it (fig. 376), and their points of intersection forrn in space a curved surface, which is called the caustic by Fig. 376. reflection. The curve FM represents one of the branches of a section of this surface made by the plane of the paper. When the light of a candle is reflected from the inside of a cup or tumbler, a section of the caustic surface can be seen by partly filling the cup or tumbler with milk. , 502. Applications of mirrors. Heliostat. — The apphcations of plane Y ^ mirrors in domestic economy are well known. Mirrors are also frequently^ y ts.*: used in physical apparatus for sending light in a certain direction. The solar light can only be sent in a constant direction by making the mirror movable. It must have a motion which compensates for the continual change in the direction of the sun's rays produced by the apparent diurnal motion of the sun. This result is obtained by means of a clockwork motion, to which the mirror is fixed, and which causes it to follow the course of the sun. This apparatus is called the heliostat. The reflection of light is also used to measure the angles of crystals by means of the instruments known as 7'eflecting goniometers. Concave spherical mirrors are also often used. They are applied for magnifying mirrors^ as in a shaving mirror. They have been employed for burning mirrors, and are still used in telescopes. They also serve as reflectors, for conveying light to great distances, by placing a luminous object in their principal focus. For this purpose, however, parabohc mirrors are preferable. 438 On Light. [503- Fig. 377- 503, Parabolic mirrors. — Parabolic mirrors are concave mirrors, whose surface is generated by the revolution of the arc of a parabola, AM, about its axis, AX (fig. 377). It has been already stated that in spherical mirrors the rays parallel to the axis converge only approximately to the principal focus, and reciprocally when a source of light is placed in the principal focus of these mirrors, the reflected rays are not exactly parallel to the axis. Parabolic mirrors are free from this defect ; they are more difficult to construct, but are far better for reflectors. It is a well-known property of a para- bola that the right line FM, drawn from the focus F, to any point, M, of the curve, and the line ML, pa- rallel to the axis AF, make equal angles with the tangent TT' at this point. Consequently, all rays parallel to the axis after reflection meet in the focus of the mirror F, and, conversely, when a source of light is placed in the focus, the rays incident on the mirror are reflected exactly parallel to the axis. The light thus reflected tends to main- tain its intensity even at a great distance, for it has been seen (478) that it is the diver- gence of the luminous rays which principally weakens the intensity of light. It is from this property that parabolic mirrors are used in carriage lamps, and in the lamps placed in front of and behind railway trains. These reflectors were for- merly used for lighthouses, but have been replaced by lenticular glasses. When two equal parabolic mirrors are cut by a plane perpendicular to the axis passing through the focus, and are then united at their intersections^ as shown in the figure 378, so that their foci coincide, a system of reflectors is obtained with which a single lamp illuminates in two direc- tions at once. This arrangement is used in lighting staircases. -505] Refraction. 439 CHAPTER III. SINGLE REFRACTION. LENSES. 504. Phenomenon of refraction. — Refraction is the deflection or bending which luminous rays experience in passing obhquely from one medium to another ; for instance, from air into water. We say obliquely, because if the incident ray is perpendicular to the surface separating the two media, it is not deflected, and continues its course in a right line. The incident ray being represented by SO (fig. 379), the refracted ray is the direction OH which hght takes in the second medium ; and of the angles SO A and HOB, which these rays form with the line AB, at right angles to the surface which separates the two media, the first is the atigle of incidence, and the other the angle of refraction. According as the refracted ray ap- proaches or deviates from the normal, the second medium is said to be more or less refringent or refracting than the first. All the light which falls on a refracting surface Fig- 379- does not completely pass into it ; one part is reflected and scattered, while another penetrates into the medium. Analysis shows that the direction of refraction depends on the relative velocity of light in the two media. On the undulatory theory the more highly refracting medium is that in which the velocity of propagation is least. Inuncrystallised media, such as air, Hquids, ordinary glass, the luminous ray is singly refracted ; but in certain crystallised bodies, such as Iceland spar, Selenite, etc., the incident ray gives rise to two refracted rays. The latter phenomenon is called double refraction, and will be discussed in another part of the book. We shall here deal exclusively with single re- fraction. 505. Iiaws of singrle refraction. — When a luminous ray is refracted in passing from one medium into another of a different refractive power, the following laws prevail :— I. Whatever the obliquity of the incident ray, the ratio which the sine of the incident angle bears to the sine of the angle of refraction is constant for the same two media, but varies with different media. II. The incident and the refracted ray are in the same plane which is perpendicular to the surface separating the two media. These have been known as Descartes' laws ; they are, however, really due to Willibrod Snell who discovered them in 1620, and are demonstrated by the same apparatus as that used for the laws of reflection (456). The plane mirror in the centre of the graduated circle is replaced by a semi- cylindrical glass vessel, filled with water to such a height that its level is exactly the height of the centre (fig. 3^0). If the mirror, M, be then so inclined that a reflected ray, MO, is directed towards the centre, it is refracted on passing into the water, but it passes out without refraction 440 On Light [505 because then its direction is at right angles to the curved sides of the vessel. In order to observe the course of the refracted ray, it is re- ceived on a screen, P, which is moved until the image of the aper- ture in the screen N is formed in its centre. In all positions of the screens N and P, the sines of the angles of incidence and refraction are measured by means of two graduated rules, movable so as to be always horizontal, and hence perpendicular to the diameter AD. On reading off the lengths of the sines of the angles MOA and DOP in the scales I and R, the numbers are found to vary with the position of the screens, but their ratio is constant ; that is, if the sine of incidence becomes twice or three times as large, the sine of refrac- tion increases in the same ratio, Fig- 380. which demonstrates the first law. The second law follows from the arrangement of the apparatus, for the plane of the graduated limb is perpendicular to the surface of the liquid in the semi-cylindrical vessel. 506. Index of refraction. — The ratio between the sines of the in- cident and refracted angle is 0.2^^^ index of refraction ox refractive index. It varies with the media ; for example, from air to water it is |, and from air to glass it is |. If the media are considered in an inverse order — that is, if light passes from water to air, or from glass to air— it follows the same course, but in a contrary direction, PO becoming the incident and OM the refracted ray. Consequently, the index of refraction is reversed ; from water to air it is then |, and from glass to air f . 507. Effects produced by refraction. — In consequence of refraction, bodies immersed in a medium more highly refracting than air appear nearer the surface of this medium, but they appear to be more distant if immersed in a less refracting medium. Let L (fig. 381) be an object im- mersed in a mass of water. In passing thence into air, the rays LA, LB . . . diverge from the normal to the point of incidence, and assume the direction AC, BD . . . , the prolongations of which intersect approximately in the point L', placed on the perpendicular L'K. The eye receiving these rays sees the object L at L'. The greater the obliquity of the rays LA, LB . . . the higher the object appears. It is for the same reason that a stick plunged obliquely into water appears bent (fig. 382), the immersed part appearing raised. Owing to an effect of refraction, stars are visible to us even when they are below the horizon. For as the layers of the atmosphere are denser -508] Total Reflection, 441 in proportion as they are nearer the earth, and as the refractive power of a gas increases with its density (518), it follows that on entering the Fig. 382. Fig. 383. atmosphere the luminous rays become bent, as seen in the fig. 383, describing a curve before reaching the eye, so that we see the star at S' along the tangent of this curve instead of at S. In our climate the atmospheric refraction does not raise the stars when on the horizon more than half a degree. Another experimental illustration of the effect of re- fraction is the following : — A coin is placed in an empty porcelain basin and the position of the eye is so adjusted that it is just not visible. If now, the position of the eye remaining unaltered, water be poured into the basin the coin becomes visible. A consideration of fig. 381, will suggest the explanation of this phenomenon. 508. Total reflection. Critical angrle. — When a luminous ray passes from one medium into another which is less refracting, as from water into air, it has been seen that the angle of incidence is less than the angle of refraction. Hence, when light is propagated in a mass of water from S to O (fig. 384), there is always a value of the angle of inci- dence SOB, such that the angle of refraction, AOR, is a right angle, in which case the refracted ray emerges parallel to the surface of the water. This angle, SOB, is called the critical angle ^ since for any greater angle, FOB, the incident ray cannot emerge, but undergoes an internal reflection, which is called total reflection^ because the incident light is entirely reflected. From water to air the critical angle is 48° 35' ; from glass to air, 41° 48'. Fig. 384. Fig. 3S5. The occurrence of this internal reflection may be observed by the following experiment. An object A, is placed before a glass vessel filled U3 442 On Light [608- with water (fig. 385) ; the surface of the liquid is then looked at as shown in the figure, and an image of the object A is seen at a^ formed by the rays reflected at w, in the ordinary manner of a mirror. Similar effects of the total reflection of the images of objects contained in aquaria are frequently observed, and add much to the interest of their appearance. 509. IVEiragre. — The mirage is an optical illusion by which inverted images of distant objects are seen as if below the ground or in the atmosphere. This phenomenon is of most frequent occurrence in hot climates, and more especially on the sandy plains of Egypt. The ground Fig. 3S6. there has often the aspect of a tranquil lake, on which are reflected trees and the surrounding villages. The phenomenon has long been known, but Monge, who accompanied Napoleon's expedition to Egypt, was the first to give an explanation of it. It is a phenomenon of refraction, which results from the unequal density of the different layers of the air when they are expanded by contact with the heated soil. The least dense layers are then the lowest, and a luminous ray from an elevated object, A (fig. 386), traverses layers which are gradually less refracting ; for, as will be shown presently (518), the refracting power of a gas diminishes with lessened density. The angle of incidence accordingly increases from one layer to the other, and ultimately reaches the critical angle, beyond which internal reflec- tion succeeds to refraction (508). The ray then rises, as seen in the figure, and undergoes a series of successive refractions, but in a direction contrary to the first, for it now passes through layers which are gradually more refracting. The luminous ray then reaches the eye with the same direction as if it had proceeded from a point below the ground, and hence it gives ah inverted image of the object, just as if it had been reflected at the point O, from the surface of a tranquillake. ^ Mariners sometimes see images in the air of the shores or of distant vessels. This is due to the same cause as the mirage, but in a contrary -511] Prisms. 443 direction, only occurring when the temperature of the air is above that of the sea, for then the inferior layers of the atmosphere are denser, owing to their contact with the surface of the water. TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA. 510. iw alia wl til parallel faces. — When light traverses a medium with parallel faces the emergent rays are parallel to the incident rays. Let MN (fig. 387) be a glass plate with parallel faces, let SA be the incident and DB the emergent ray, /and r the angles of incidence and of refraction at the entrance of the ray, and, lastly, i' and r' the same angles at 'its emergence. At A the light undergoes a first refraction, the index of which is ^JJLf (482). At D it is refracted a second sm r time, and the index is then ^ — . But sm r' we have seen that the index of refraction of glass to air is the reciprocal of its re- fraction from air to glass ; hence Fig- 387- sm r sm i But as the two normals AG and DE are parallel, the angles r and i' are equal, as being alternate interior angles. As the numerators in the above equation are equal, the denominators must be also equal ; the angles r' and i are therefore equal, and hence DB is parallel to SA. 511. Prism. — Inoptics a/r/Vw is any transparent medium comprised between two plane faces inclined to each other. The intersection of these two faces is the edge of the prism, and their inclination is its refracting angle. Every section perpendicular to the edge is called a principal sectioti. The prisms used for experiments are generally right triangular prisms of glass, as shown in fig. 388, and their principal section is a triangle Fig. Fig. 389- (fig. 389). In this section the point A is called the summit of the prism, and the right line BC is called the base; these expressions have reference to the triangle ABC, and not to the prism. 444 On Light. [512 512. Patb of rays in prisms. Angle of deviation. — When the laws of refraction are known, the path of the rays in a prism is readily deter- mined. Let O be a luminous point (fig. 389) in the same plane as the principal section ABC of a prism, and let OD be an incident ray. This ray is refracted at D, and approaches the normal, because it passes into a more highly refracting medium. At K it experiences a second refrac- tion, but it then deviates from the normal, for it passes into air, which is less refractive than glass. The light is thus refracted twice in the same directio.i, so that the ray is deflected towards the base, and consequently the eye which receives the emergent ray KH sees the object O at O'; that is, objects seen through a prism appear deflected towards its summit. The angle OEO', which the incident and emergent rays form with each other, expresses the deviation of light caused by the prism, and is called the angle of deviation. Besides this, objects seen through a prism appear in all the colours of the rainbow ; this phenomenon will be described under the name of dispersion. This angle increases with the refractive index of the material of the prism, and also witli its refracting angle. It also varies with the angle Fig. 390. Fig. 391. under which the luminous ray enters the prism. The angle of deviation increases up to a certain limit, which is determined by calculation, know- ing the angles of incidence of the ray, and the refracting angle of the prism. That the angle of deviation increases with the refractive index may be shown by means of the polyprism. This name is given to a prism formed of several prisms of the same angle connected at their ends (fig. 390). These prisms are made of substances unequally refringent, such as flint glass, rock crystal, or crown glass. If any object — a line, -514] Prisms. 445 for instance — be looked at through the polyprism, its different parts are seen at unequal heights. The highest portion is that seen through the flint glass, the refractive index of which is greatest ; then the rock crystal ; and so on in the order of the decreasing refractive indices. The prism with variable angle, fig. 391, is used for showing that the angle of deviation increases with the refraciing angle of the prism. It consists of two parallel brass plates, BC and C, fixed on a support. Between these are two glass plates moving, on a hinge, with some friction against the plates, so as to close it. When water is poured into the vessel the angle may be varied at will. If a ray of light, S, be allowed to fall upon one of them, by inclining the other more, the angle of the prism increases, and the deviation of the ray is seen to increase. 513. Application of rlgrht angled prisms in reflectors. — Prisms whose principal section is an isosceles right-angled triangle afford an important application of total reflection (508). For let ABC (fig. 392) be the principal section of such a prism, O a luminous point, and OH a ray at right angles to the face BC. This ray enters the glass without being refracted, and makes with the face AB an angle equal to B, that is to 45 degrees, and there- fore greater than the limiting angle of glass, which is 41° 48' (508). The ray OH undergoes therefore at H total re- ^''*- 39-- flection, which imparts to it a direction HI perpendicular to the second face AC. Thus the hypothenuse surface of this prism produces the effect of the most perfect plane mirror, and an eye placed at I sees at O' the image of the point O. This property of right-angled prisms is frequently used in optical instruments. 514. Conditions of emergence in prisms. — In order that any luminous rays refracted at the first face of a prism may emerge from the second, it is necessary that the refractive angle of the prism be less than twice the critical angle of the substance of which the prism is composed. P'or if LI (fig. 393) be the ray in- cident on the first face, IE the refracted ray, PI and PE the normals, the ray IE can only emerge from the second face when the incident angle lEP is less than the critical angle (508). But as the incident angle LIN increases, the angle EIP also increases, while lEP diminishes. Hence, according as the direction of the ray LI tends to become parallel with the face AB, does this ray tend to emerge at the second face. Let LI be now parallel to AB, the angle r is then equal to the critical Fig. 393- 446 On Light. [514- angle / of the prism, because it has its maximum value. Further, the angle EPK, the exterior angle of the triangle IPE, is equal to r + z'; but the angles EPK and A are equal, because their sides are perpen- dicular, and therefore A = r + i' \ therefore also A = /-i- i\ for in this case r = L Hence, if A = 2/ or is >2/, we shall have i' = 1 ox >/, and there- fore the ray would not emerge at the second face, but would undergo internal reflection, and would emerge at a third face, BC. This would be much more the case with rays whose incide.it angle is less than BIN, because we have already seen that i' continually incrjases. Thus, in the case in which the refracting angle of a prism is equal to 2/ or is greater, no luminous ray could pass through the faces of the refracting angle. As the critical angle of glass is 41° 48', twice this angle is less than 90°, and accordingly, objects cannot be seen through a glass prism whose refracting angle is a right angle. As the critical angle of water is 48° 35' light could pass through a hollow rectangular prism formed of three glass plates and filled with water. If we suppose A to be greater than / and less then 2/, then of rays in- cident at I some within the angle NIB will emerge from AC, others will not emerge, nor will any emerge that are incident within the angle NIA. If we suppose A to have any magnitude less than /, all rays incident at I within the angle NIB will emerge .from AC, as also will some of those incident within the angle NIA. 515. IVXiniinum deviation. — When a pencil of solar light passes through an aperture, A, in the side of a dark chamber (fig. 394), the pencil is projected in a straight line, AC, on a distant screen. But if a vertical prism be interposed between the aperture and the screen, the pencil is deviated towards the base of the prism, and the image is pro- jected at D, at some distance from the point C. If the prism be turned, so that the incident angle decreases, the luminous disc approaches the point C, up to a certain position, E, from which it reverts to its original position even when the prism is rotated in the same direction. Hence there is a deviation, EBC, less than any other. It may be demonstrated [^ ^ is ^^^^'fsmmsm.^ 1 ^^^^t -^ ^ X / ■' 1 \ \ V-^.;^^-:^- Fig. 394- mathematically that this ininiinian deviation takes place when the angles of incidence and of emergence are equal. The angle of minimum deviation may be calculated when the incident angle and the refracting angle of the prism are known. P'or, when the -516] Index of Refraction. 447 deviation is least, as the angle of emergence r' is equal to the incident angle i (fig. 393), r must = i'. But it has been shown above (514) that A = r+/'; consequently, A = 2r (I) If the minimum angle of deviation LDL be called d, this angle being exterior to the triangle DIE, we readily obtain the equation d=i- 7' ' r' — i' = 2i—2r, whence d = 2i~A (2) which gives the angle d, when z and A are known. From the formula (i) and (2) a third may be obtained, which serves to calculate the index of refraction of a prism, when its refracting angle and the minimum deviation are known. The index of refraction it is the ratio of the sines of the angles of incidence and refraction ; hence ft = -^, — ; replacing / and r from their values in the above equations (i) sm r ^ \ / and (2), we get <^) (3) 516. IMCeasurement of the index of refraction in solids. — By means of the preceding formula (3) the refractive index of a solid may be calcu- lated when the angles A and d are known. In order to determine the angle A, the substance is cut in the form of a triangular prism, and the angle measured by means of a goniometer (502). The angle ^is measured in the following manner : a ray, LI, emitted from a distant object (fig. 393), is received on the prism, which is turned Fig- 395. in order to obtain the minimum deviation EDU. By means of a tele- scope with a graduated circle, the angle EDL' is read off, which the refracted ray DE makes with the ray DU, coming directly from the object ; now this is. the angle of minimum deviation, assuming that the object is so distant that the two rays LI and L'D are approximately parallel. These values then only need to be substituted in the equation (3) to give the value of n. This method is due to Newton. Under many circumstances it cannot be employed ; for instance, when the refractive index of a mere drop of fluid is required. In this case, use may be made of a method due to 448 On LigJit. [516- WoUaston, which depends on the determination of the critical angle of the substance. 517. Measurement of the index of refraction of liquids. — M. Biot has applied Newton's method to determining the refractive index of liquids. For this purpose a cylindrical cavity O, of about 075 in. in diameter, is perforated in a glass prism, PQ (fig. 396), from the incident face to the face of emer- gence. This cavity is closed by two plates of glass which are cemented on the sides of this prism. Liquids are introduced through a small stoppered aperture, B. The refract- ing angle and the minimum deviation of the F'S- 396. liquid prism in the cavity O having been determined, their values are introduced into the formula (3), which gives the index. 518. IMCeasurement of the index of refraction of grases, — A method for this purpose founded on that of Newton has been devised by MM. Biot and Arago. The apparatus which they use consists of a glass tube (fig. 397), bevelled at its twc ends, and closed by glass plates, which are at an angle of 143° This tube is connected with a bell-jar, H, in which there is a siphon barometer, and with a stopcock by means of which the apparatus can be exhausted, and different gases introduced. After having exhausted the tube AB, a ray of light, SA is transmitted, which is bent away from the normal through an angle r — i at the first incidence, and towards it through an angle /' — r' at the second. These two deviations being added, the total deviation d \s- r-i^i' -r'. In the case of a minimum deviation, / = ;-^ and r = i\ whence d=A~2i, since r + t' = A (514)- The index from vacuum to air, which is evidently ^!^ ^, has therefore r\ sm t the value sm •r^ (4) Fig. 397. {^) Hence, in order to deduce the refrac- tive index from vacuum into air, which is the absolute index or principal index, it is simply necessary to know the refracting angle A, and the angle of minimum deviation d. To obtain the absolute index of any other gas, after having produced a vacuum, this gas is introduced ; the angles A and a having been mea- -519] Lenses. 449 sured, the above formula gives the index of refraction from gas to air. Dividing the index of refraction from vacuum to air by the index of re- fraction from the gas to air, we obtain the index of refraction from vacuum to the gas, that is, its absolute index. By means of this apparatus Biot and Arago have found that the refrac- tive indices of gases are very small as compared with those of solids and liquids, and that for the same gas the 7'efractive power is proportional to the density ; meaning by the refractive action of a substance the square of its refractive index less unity ; that is, n'^—i. The refractive action divided by the density, or is called the absolute 7'efractive power. Table of the absolute indices of refraction. Diamond . . 2-47 to 275 Plate glass, St. Gobin 1-543 Phosphorus . 2-224 Crown glass I -600 Sulphur . 2-II5 Turpentine . 1-470 Ruby , • 1779 Alcohol 1-374 Bisulphide of carbon . . 1-678 Albumen 1-360 Iceland spar, ordinary ray . 1*654 Ether . 1-358 Iceland spar. extraord nary Crystalline lens 1-384 ray . . • 1-483 Vitreous ., 1-339 Flint glass . • ^SIS Aqueous ,. 1-337 Rock salt . . • I-550 Water . 1-336 ., crystal • . 1-548 Ice . . . 1-310 Refractive indices of gases. Vacuum I -oooooo Carbonic acid . . 1-000449 Hydrogen . 1-000138 Hydrochloric acid . . 1-000449 Oxygen . 1000272 Nitrous oxide . . 1-000503 Air ' . I -000294 Sulphurous acid . . 1-000665 Nitrogen . I -000300 Olefiant gas . . .1 -000678 Ammonia . I -000385 Chlorine . I -000772 LEx^JSES. THEIR EFFECTS. 519. Dififerent kinds of lenses. — Lenses are transparent media, which, from the curvature of their surfaces, have the property of causing the k luminous rays which traverse them either to converge or to diverge. According to their curvature they are either spherical, cylindrical, ellipti- cal, or parabolic. Those used in optics are always spherical. They are commonly made either of crown glass, which is free from lead, or of fli?it glass, which contains lead, and is more refractive than crown glass. The combination of spherical surfaces, either with each other or with plane surfaces, gives rise to six kinds of lenses, sections of which are 450 On Light. [519- represented in fig. 398 ; four are formed by two spherical surfaces, and two by a plane and a spherical surface. A is a double convex, B is a plano-convex, C is a converging concavo- convex, D is a double concave, E is a plano-concave, and F is a diverging concavo-convex. The lens C is also called the converging meniscus, and the lens F the diverging meniscus. v> c 1) Fig. 398. The first three, which are thicker at the centre than at the borders, are converging ; the others, which are thinner in the centre, are diverging. In the first group, the double convex lens only need be considered, and in the second the double concave, as the properties of each of these lenses apply to all those of the same group. ^^ I n lenses whose two surfaces are spherical, the centres for these surfaces are caWedr cenlres of curvature, and the right line which passes through these two centres is the 'princi pal axis. In a plano-concave or plano- convex lens, the principal axis is the perpendicular let fall from the centre of the spherical face on the plane face. In order to compare the path of a luminous ray in a lens with that in a prism, the same hypothesis is made as for curved mirrors (492), that is, the surfaces of these lenses are supposed to be formed of an infinity of small plane surfaces or elements ; the normal at any point is then the perpendicular to the plane of the corresponding element. It is a geo- metrical principle that all the normals to the same spherical surface pass through its centre. On the above hypothesis we can always conceive two plane surfaces at the points of incidence and convergence, which are in- clined to each other, and thus produce the effect of a prism. Pursuing this comparison, the three lenses A, B, and C may be compared to a succession of prisms having their summits outwards, and the lenses D, E, and F to a series having their summits inwards ; from this we see that the first ought to condense the rays, and the latter to disperse them, for we have already seen that when a luminous ray traverses a prism it is deflected towards the base (512). 520. Foci in double convex lenses. — The focus of a lens is the point where the refracted rays, or their prolongations, meet. Double convex lenses have the same kind of foci as concave mirrors ; that is, real foci and v irtuaFfoci. ~ ' Kealjoci. We shall first consider the case in which the luminous rays which fall on the lens are parallel to its principal axis, as shown in the fig. 399. In this case, any incident ray, LB, in approaching the normal of the point of incidence B, and in diverging from it at the point of emer- -520] Convex Lenses. 451 gence D, is twice refracted towards the axis, which it cuts at F. As all rays parallel to the axis are refracted in the same manner, it can be shown by calculation that they all pass very nearly through the point F, so long as the arc DE does not exceed 10° to 12°. This point is called the pruicipal focus, and the distance FA is the principal focal distance. It is constant in the same lens, but varies with the radii of curvature and the Fig. 399- index of refraction. In ordinary lenses, which are of crown glass, and in which the radii of the two surfaces are nearly equal, the principal focus coincides very closely with the centre of curvature. / We shall now consider the case in which the luminous object is outside the principal focus, but so near that all incident rays form a divergent pencil, as shown in fig. 400. The luminous point being at L, by comparing V Fig. 400. the path of a diver^^ing ray, LB, with that of a ray, SB, parallel to the axis, the former is found to make with the normal an angle, LB«, greater than the angle SB;^ : consequently, after traversing the lens, the ray cuts the axis at a point, /, which is more distant than the principal focus F. As all rays from the point L intersect approximately in the same point /, this latter is the conjugate focics of the point L ; this term has the same meaning here as in the cases of mirrors, and expresses the relation existing between the two points L and /, which is of such a nature, that if the luminous point is moved to /, the focus passes to L. According as the object comes nearer the lens, the convergence of the emergent rays decreases, and the focus / becomes more distant ; when the object L coincides with the principal focus, the emergent rays on the other side are parallel to the axis, and there is no focus, or, what is the same thing, it is infinitely distant. ^As the refracted rays are parallel in this 452 On LiorJit. [520 case, the intensity of light only decreases slowly, and a simple lamp can illuminate great distances. It is merely necessary to place it in the focus of a double concave lens, as shown in fig. 401. Fig. 401. N^ Virtual foci. A double convex lens has a virtual focus when the luminous object is placed between the lens and the principal focus, as shown in fig. 402. In this case the incident rays make with the normal greater angles than those made by the rays FI from the principal focus ; hence, when the former rays emerge, they move farther from the axis than the latter, and form a diverging pencil, HK, GM. These rays cannot produce a real focus, but their prolongations intersect in some' point, /, on the axis, and this point is the virtual focus of the pomt L (483)- 521. Foci in double concave lenses. — In double concave lenses there are only virtual foci, whatever the distance of the object. Let S' be any pencil of rays parallel to the axis (fig. 403), any ray, SI, is refracted at the Fig- 403- t^ig- 404- point of incidence I, and approaches the normal CI. At the point of emer- gence it is also refracted, but diverges from the normal GC, so that it is -523] Focus of Lenses. 453 twice refracted in a direction which moves it from the axis CC As the same thing takes place for every other ray, S'KMN, it follows that the rays, aftei^ traversing the lens, form a diverging pencil, GH. MN. Hence there is no real focus, but the prolongations of these rays cut one another in a point, F, which is the principal virtual focus. In the case in which the rays proceed from a point, L (fig. 404), on the axis, it is found by the same construction that a virtual focus is formed at /, which is between the principal focus and the lens. 522. Experimental determination of the principal focus of lenses.— To determine the principal focus of a double convex lens, it may be exposed to the sun's rays so that they are parallel to its axis. The emergent pen- cil being received on a ground glass screen, the point to which the rays converge is readily seen ; it is the principal focus. With a double concave lens, the face ab (tig. 405) is covered with an Fig- 405- opaque substance, such as lampblack, two small apertures, a and^, being left in the same principal section, and at an equal distance from the axis ; a pencil of solar light is then received on the other face, and the screen P, which receives the emergent rays, is moved nearer to or farther from the lens, until A and B, the spots of light from the small apertures a and b^ are distant from each other by twice ab. The distance DI is then equal to the focal distance FD, because the triangles Yab and FAB are similar, 'rrr-523. Optical centre, secondary axis. — In every lens there is a point called the optical ccnfre, which is situated on the axis, and which has the Fig. 406. Fig 407. property that any luminous ray passing through it experiences no angular deviation ; th&t is, that the emergent ray is parallel to the incident ray. The existence of this point may be demonstrated in the following manner : Let two parallel radii of curvature, CA and C'A' (fig! 406) be drawn to 454 On Light. [523- the two surfaces of a double convex lens. Since the two plane elements of the lens A and A' are parallel, as being perpendicular to two parallel right lines, it will be granted that the refracted ray KA, A'K' is pro- pagated in a medium with parallel faces. Hence, a ray which reaches A at such an incHnation, that after refraction it takes the direction AA' will emerge parallel to its first direction (521) ; the point O, at which the right line cuts the axis, is therefore the optical centre. The position of this point may be determined for the case in which the curvature of the two faces is the same, which is the usual condition, by observing that the triangles COA and C'OA^ are equal, and therefore that OC = OC, which gives the point O. If the curvatures are unequal, the triangles COA and Q'OPJ are similar, and either CO or CO may be found, and therefore also the point O. In double concave or concavo-convex lenses the optical centre may be determined by the same construction. In lenses with a plane face this point is at the intersection of the axis by the curved face. __ — Every right line, PP' (fig. 407), which passes through the optical centre -wTthout passing through the centres of curvature, is a secondaiy axis. From the property of the optical centre, every secondary axis represents " a luminous rectilinear ray passing through this point, for from the slight thickness of the lenses, it may be assumed that rays passing through the optical centre are in a right line ; that is, that the small deviation may be neglected which rays experience in tra\ersing a medium with parallel faces (fig. 387). So long as the secondary axes only make a small angle with the prin- cipal axis, all that has hitherto been said about the principal axis is ap- plicable to them ; that is, that rays emitted from a point, P (fig. 407), on the secondary axis PP', nearly converge to a certain point of t,his axis, P', and according as the distance from the point P to the lens is greater or less than the principal focal distance, the focus thus formed will be con- jugate or virtual. This principle is the foundation of what follows as to the formation of images. 524. Formation of imagoes in double convex lenses. — In lenses as well as in mirrors the image of an object is the collection of the foci of its several points ; hence the images furnished by lenses are real or virtual in the same case as the foci, and their construction resolves itself into, determining a series of points, as was the case with mirrors (496). — i— ■ i- -/^^«/ image. Let AB ^fig. 408) be placed beyond the principal focus. If a secondary axis, Ka, be drawn from the outside point A, any ray, AC, from this point, will be twice refracted at C and D, and both times in the same direction, approaching the secondary axis, which it cuts at a. From what has been said in the last paragraph, the other rays from the point A will intersect in the point rt, which is accordingly the conjugate focus of the point A. If the secondary axis be drawn from the point B, it will be seen, in like manner, that the rays from this point intersect in the point b^ and as the points between A and B have their foci between a and b, a real but inverted image of AB will be formed at ab. In order to see this image, it may be received on a white screen, on - 524] Double Convex L enses, 555 which it will be depicted, or the eye may be placed in the path of the rays emerging from it. Conversely, if ab were the luminous or illuminated object which Fig. 408. emitted rays, its image would be formed at AB. Tvvo consequences important for the theoiy of optical instruments follow from this : that 1st, If a?t object J even a very large o?ie, is at a sufficient distance frotn a double convex lens, the real and inverted image which is obtained of it is very small, it is near the prijicipal focjis, but somewhat farther from the lens than this is ; 2nd, If a very small object be placed near the principal focus, but a little before it, the image which is formed is at a great distance, it is much larger, and that in proportion as the object is 7iear the prin- cipal focus. In all cases the object and the image have the same propor- tion as their distances from the lens. These two principles are experimentally confirmed by receiving on a screen the image of a lighted candle, placed successively at various dis- tances from a double convex lens. ii. Virtual ii?iage. There is another case in which the object AB (fig. 409) is placed between the lens and its principal focus. If a secondary axis, Oa Fig. 409. be drawn from the point A, every ray, AC, after having been twice refracted on emerging, diverges from this axis, since the point A is at a less dis- tance than the principal focal distance (520). This ray, continued in an opposite direction, will cut the axis Oa in the point a, which is the virtual focus of the point A. Tracing the secondary axis of the point B, it will be found, in the same manner, that the virtual focus of this point is formed at b. There is, therefore, an image of AB at ab. This is a virtual image, it is erect, and larger than the object. 456 On Light. [524- The magnifying power is greater in proportion as the lens is more con- vex, and the object nearer the principal focus. We shall presently show how the magnifying power may be calculated by means of the formulae relating to lenses (527). Double convex lenses, used in this manner as magnifying glasses, are called simple microscopes. 525. Formation of imagres In double concave lenses. — Double con- cave lenses, like convex mirrors, only give virtual images, whatever the distance of the object. Let AB (fig. 410) be an object placed in front of such a lens. If the secondary axis be drawn from the point A, all rays, AC, AI, from this point are twice refracted in the same direction, diverging from the axis AO ; so that the eye, receiv- ing the emergent rays DE and GH, supposes them to proceed from the point where their pro- longations cut the secondary axis AO in the point a. In like manner. Fig. 410. drawing a secondary axis from the point B, the rays from this point form a pencil of divergent rays, the direction of which, prolonged, intersect in b. Hence the eye sees at ab a virtual image of AB, which is always erect ^ and smaller than the object. 526. Spberical aberration. Caustics. — In the theory of the foci, and of the images formed by different kinds of spherical lenses, it has been hitherto assumed, that the rays emitted from a single point intersect also after refraction in a single point. This is virtually the case with a lens whose aperture — that is, the angle obtained by joining the edges to the principal focus — does not exceed 10° or 12°. Where, however, the aperture is larger, the rays which traverse the lens near the edge are refracted to a point nearer the lens than the rays which pass near the axis. The phenomenon thus produced is named spherical abe?^ration by refraction ; it is analogous to the spherical aberra- tion produced by reflection. The luminous surfaces formed by the inter- section of the refracted rays are termed caustics by i^efraction. Spherical aberration is prejudicial to the sharpness and definition of an image. If a ground glass screen be placed exactly in the focus of a lens, the image of an object will be sharply defined m-the centre, but indistinct at the edges ; and, vice versa, if the image is sharp at the edges, it will be indistinct in the centre. This defect is very objectionable, more especially in lenses used for photography. It is partially obviated by placing before the lenses diaphragms provided with a central aperture called stops, which admit the rays passing near the centre, but cut off those which pass near the edges. Mathematical investigation shows that convex lenses, whose radii of curvature stand in the; ratio expressed by the formula r _ 4 — 211^ + n r 171^ -^ 211 ^ -527] Lenses. 457 are free from spherical aberration ; in which r is the radius of curvature of the foci turned to the parallel rays, and r that of the other face, while n is the refractive index. Spherical aberration is also destroyed by com- bining different lenses of suitable curvature. Lenses which are free from spherical aberration are called aplanatic. 527. Formulae relating- to lenses. — In all lenses, the relation between the distances of the image and object, the radii of curvature, and the re- fractive index, may be expressed by a formula. In the case of a double convex lens, let P be a luminous point, situate on the axis, fig. 411, let PI Fig. 4 be an incident ray, IE its direction within the lens, EP' the emergent ray, so that P' is the conjugate focus of P. Further, let CI and CE be the normals to the points of incidence and emergence, and I PA be put equal to u, EP'A'-/3, ECA' = ;, ICA = o, NIP = /, EIO = r, IEO=/', N'EP' = r'. Because the angle i is the exterior angle of the triangle PIC^, and the angle r' the exterior angle of the triangle CEP', therefore, i = a-vl, and ^ = 7 + i^j whence 2+r' = a + /3-ry-h5 . . . . (l) But at the point I, sin i=^n sin r, and at the point E, sin r' = « sin i (506), n being the refractive index of the lens. Now if the arc AI is only a small number of degrees, these sines may be considered as proportional to the angles i, r, /', and y', whence, in the above formula, we may replace the sines by their angles, which gives i=nr and r'=^ni\ from which i^rv' = 11 (r + i'). Further, because the two triangles I OE and COC have a common equal angle,- O, therefore ^+2' = )' + ^, from which i-\-r' = 7i (y + h). Introducing this value into the equation (i) we obtain, n (y + ^) = a -f /3 + y + ^, from which (« ~ i) -(y + ^) = a 1- /3 . . (2) Let CA' be denoted by R, C'A by R', PA by/, and P^A' hy Z""- Then with centre P and radius PA describe the arc hd, and with centre P' and radius P^'A' describe the arc Aw. Now when an angle at the centre of a circle subtends a certain arc of the circumference^ the quotient of the arc divided by the radius measures the angle ; consequently, Kd Kd ,. h'n A'E R y and AI R'" Therefore by substitution in (2) 4S8 ^ • On Light. [527- Now since the thickness of the lens is very small, and the angles are also small, and Art', AI, A'E, K'n differ but little from coincident straight lines, and are therefore virtually equal ; hence the above equation be- comes («-) r4')=^> (3) This is the formula for double convex lenses ; \i p be = oo, we have p being the principal focal distance. If this be represented by/, we get from which the value of/ is easily deduced. Considered in reference to formula (4), the formula (3) assumes the form p'rr ^=' which is that in which it is usually employed. When the image is virtual p changes its sign, and formula (5) takes the form Tp' f- ^'^ In double concave lenses,^' and/retain the same sign, but that of/ changes ; the formula (5) becomes then p p f The formula (7) may be obtained by the same reasonings as the other. 528. Relative xuagrnitudes of imag-e and object. — From the equality of the triangles AOB, aOb (fig. 408) we get for the relative magnitudes of image and object the proportion -_:=^; whence^ ^-^ where AB = o is the magnitude of the object and ab^\ that of the image ; while p and p^ are their respective distances from the lens. Replacing p^ by its value from the equation — + _ = _,, where the image is real, or from the _ ^P Pi J equation -——»=_, where it is virtual, we shall obtain the different values P Px f of the ratio - for various positions of the object. In the first case we have I / O * p~/ Thus if p>2f^l>o / = 2/ 1=0 p<2/ I>o. 530] Dispersion of Light. 459 In the second case when the image is virtual we shall have I f — = / — , so that in all cases I >0. o f-f 529. ]baryng:o scope. — As an application of lenses may be adduced the laryngoscope^ which is an instrument recently invented to facilitate the investigation of the larynx and the other cavities of the mouth. It con- sists of a plane convex lens L, and a concave reflector M, both fixed to a ring which can be adjusted to any convenient lamp. The flame of the lamp is in the principal focus of the lens, and at the same time is at the Fig. 412. centre of curvature of the reflector. Hence the divergent pencil proceeding from the lamp to the lens is changed after emerging into a parallel pencil. Moreover, the pencil from the lamp impinging upon the mirror, is reflected to the focus of the lens, and traverses the lens forming a second parallel pencil which is supported on the first. This being directed into the mouth of a patient, its condition may be readily observed. CHAPTER IV. DISPERSION AND ACHROMATISM. 530. Decomposition of white lig^ht. Solar spectrum. — The pheno- menon of refraction is by no means so simple as we have hitherto as- sumed ; when white light, or that which reaches us from the sun, passes from one medium into another, // is decomposed into several kinds of lights, a phenomenon to which the name dispersion is given. In order to show that white light is decomposed by refraction, a pencil of solar light, SA (fig. 413), is allowed to pass through a small aperture 460 On Light. [530 in the window shutter of a dark chamber. This pencil tends to form a round and colourless image of the sun at K ; but if a flint glass prism, arranged horizontally, be interposed in its passage, the beam, on emerging from the prism, becomes refracted towards its base, and produces on a distant screen a vertical band rounded at the ends, coloured in all the tints of the rainbow, which is called the solar spectrum, see Plate I. In this spectrum there is, in reality, an inhnity of different tints, which im- perceptibly merge into each other, but it is customary to distinguish seven principal colours. These are violet, indigo, blue, greeii^ yellow, orange, red', they are arranged in this order in the spectrum, the violet being the most refrangible, and the red the least so. They do not all occupy an Fig. 413- equal extent in the spectrum, violet, having the greatest extent, and ' orange the least. With transparent prisms of different substances, or with hollow glass prisms filled with various liquids, spectra are obtained formed of the same colours, and in the same order ; but when the deviation produced is the same, the length ,of the spectrum varies with the substance of which the prism is made. The angle of separation of two selected rays (say in the red and the violet) produced by a prism is called the disper- sion, and the ratio of this angle to the mean deviation of the two rays is called the dispersive power. This ratio is constant for the same sub- stance so long as the refracting angle of the prism is small. For the deviation of the two rays is proportional to the refracting angle ; their difference and their mean \2,ry in the same manner, and, therefore, the ratio of their difference to their mean is constant. For flint glass this is 0-043 '-> for crown gla^s it is 0*0246 ; for the dispersive power of flint is almost double that of crown glass. The spectra which are formed by artificial lights rarely contain all the colours of the solar spe-ctrum ; but their colours are found in the solar spectrum, and in the same or-dier. Their relative intensity is also modi- fied The shade jof coJboTiW which predominates in the flame predominates -532] Pj'odiiction of a Pure Spectrum, 461 also in the spectrum : yellow, red, and green flames produce spectra in which the dominant tint is yellow, red, or green. 531. Production of a pure spectrum. — In the above experiment, when the light is admitted through a wide slit, the spectrum formed is built up of a series of overlapping spectra, and the colours are confused and indistinct. In order to obtain a pure spectrum, the slit in the shutter of the dark room through which light enters, should be from 15 to 25""" in height and from i to 2"*™ in breadth. The sun's rays are directed upon the slit by a mirror, or still better by a heliostat (502). An achromatic double convex lens is placed at a distance from the slit of double its own focal length, which should be about a metre, and a screen is placed at the same distance from the lens. An exact image of the slit is thus formed on the screen (528). If now there is placed near the lens, between it and the screen, a prism with an angle of about 60° and with its refracting edge parallel to the slit, a very beautiful sharp and pure spectrum is formed on the screen. The prism should be free from stride, and should be placed so that it produces the minimum deviation. 532. The colours of the spectrum are. simple, and unequally re- frangrihle. — If one of the colours of the spectrum be isolated by inter- cepting the others by means of a screen, E, as shown in fig. 414, and if Fig. 414. the light thus intercepted be allowed to pass through a second prism, B, a refraction will be observed, but the light remains unchanged ;. that is, the image received on the screen H is violet if the violet pencil has been allowed to pass, blue if the blue pencil, and so on. Hence the colours of the spectrum are simple ; that is, they cannot further be decomposed by the prism. Moreover, the colours of the spectrum are unequally refrangible ; that is, they possess different refractive indices. The elongated shape of the spectrum would be sufficient to prove the unequal refrangibihty of the simple colours, for it is clear that the violet, which is most deflected towards the base of the prism, is also most refrangible, and that red which is least deflected is least refrangible. But the unequal refrangi- bihty of simple colours may be shewn by numerous experiments, of which the two following may be adduced : — i. Two narrow strips of coloured paper, one red and the other violet are fastened close to each other on a sheet of black paper. On looking 462 On Light. [532- at them through a prism, they are seen to be unequally displaced, the red band to a less extent than the violet ; hence the red rays are less refran- gible than the violet. ii. The same conclusion may be drawn from Newton's experiment with crossed prisms. On a prism, A (fig. 415), in a horizontal position, Fig. 415- a pencil of white light, S, is received, which, if it had merely traversed the prism A, would form the spectrum rr, on a distant screen. But if a second prism,' B, be placed in a vertical position behind the first, in such a manner that, the refracted pencil passes through it, the spectrum vr becomes deflected towards the base of the vertical prism : but, instead of being deflected in a direction parallel to itself, as would be the case if the colours of the spectrum were equally refracted, it is obliquely refracted in the direction rV, proving that from red to violet the colours are more and more refrangible. • These difterent experiments show that the refractive index differs in different colours ; even rays which are to perception undistinguishable have not the same refractive index. In the red band, for instance, the rays at the extremity of the spectrum are less refracted than those which are nearer the orange zone. In calculating indices of refraction (506), it is usual to take as the index of any particular substance the refrangibility of the yellow ray in a prism formed of that substance. 533. Re composition of white light. — Not merely can white light be -533] Recoinposition of White Light. 463 resolved into lights of various colours, but by combining the different pencils separated by the prism, white light can be reproduced. This may be effected in various ways : — i. If the spectrum produced by one prism be allowed to fall upon a second prism of the same material, and the same refracting angle as the first, but inverted, as shown in fig. 417, the latter reunites the different colours of the spectrum, and it is seen that the emergent pencil E, which is parallel to the pencil S, is colourless. ii. If the spectrum falls upon a double convex lens (fig. 416), a white image of the sun will be formed on a white screen placed in the focus of the lens ; a glass globe filled with water produces the same effect as the lens. iii. When the spectrum falls upon a concave mirror, a white image is formed on a screen of ground glass placed in its focus (fig. 418). Fig. 419 iv. Light may be recomposed by means of a pretty experiment, which consists in receiving the seven colours of the spectrum on seven small glass mirrors with plane faces, and which can be so inclined in all positions that the reflected light may be transmitted in any given direc- tion (fig. 419). When these mirrors are suitably arranged, the seven reflected pencils may be caused to fall on the ceiling in such a manner as to form seven distinct images — red, orange, yellow, etc. When the mirrors are moved so that the separate images become superposed, a single image is obtained, which is white. v. By means of Newtojis disc, fig. 420, it may be shown that the seven colours of the spectrum form white. This is a cardboard disc of about a foot in diameter ; the centre and the edges are covered with Mack paper, while in the space between there are pasted strips of papers of the colours of the spectrum. They proceed from the centre to the circumference, and 464 On Light. [533 their relative dimensions and tints are such as to represent five spectra (fig. 421). When this disc is rapidly rotated, the efi"ect is the same as if the retina received simultaneously the impression of the seven colours. Fig. 420. If by a mechanical arrangement, a prism, on which the sun's light falls, is made to oscillate rapidly so that the spectrum also oscillates the middle of the spectrum appears white. These latter phenomena depend on the physiological fact, that sensa- tion always lasts a little longer than the impression from which it results. If a new impression is allowed to act, before the sensation arising from the former one has ceased, a sensation is obtained consisting of tAvo im- pressions. And by choosing the time short enough, three, four, or more impressions may be mixed with each other. With a rapid rotation the disc is nearly white. It is not quite so, for the colours cannot be exactly arranged in the same proportions as those in which they exist in the spectrum, and pigment colours are not pure. A similar explanation applies to the experiment of the oscillating prism. 534. ITewton's theory of tlie composition of li^lit. — Newton was the first to decompose white light by the prism, and to recompose it. From the various experiments which we have described, he concluded that white light was not homogeneous, but formed of seven lights unequally refrangible, which he called simple or primitive lights. Owing to their difference in refrangibility they become separated in traversing the prism. The designation of the various colours of the spectrum is to a very great extent arbitrary ; for in strict accuracy, the spectrum is made up of -536] Colour of Bodies. 465 an infinite number of simple colours, which pass into one another by imperceptible gradations of colour and refrangibility. _ 535. Colour of bodies. — The natural colour of bodies results from the fact that of the coloured rays contained in white light, one portion is absorbed at the surface of the body. If the unabsorbed portion traverses the body, it is coloured and transparent ; if, on the contrary, it is reflected it is coloured and opaque. In both cases the colour results from the constituents which have not been absorbed. Those which reflect or transmit all colours in the propoition in which they exist in the spectrum are white ; those which reflect or transmit none are black. JBetween these two limits there are infinite tints according to the greater or less extent to which bodies reflect or transmit some colours and absorb others. Thus a body appears yellow, because it absorbs all colours with the exception of yellow. In like manner, a solution of ammoniacal oxide of copper absorbs preferably the red and yellow rays, transmits the blue rays almost completely, the green and violet less so, hence the light seen through it is blue. Hence bodies have no colour of their own ; with the nature of the incident light the colour of the body changes. Thus, if in a dark room a white body be successively illuminated by each of the colours of the spectrum, it has no special colour but appears red, orange, green, etc., according to the position in which it is placed. If homogeneous light falls upon a body, it appears brighter in the colour of this light, if it does not absorb this colour; but black if it does absorb it. In the light of a lamp fed by spirit in which some common salt is dissolved, everything white and yellow seems bright, while most of the other colours are black. This is well seen in the case of a stick of red sealing-wax viewed in such a light. In the light of lamps and of candles, which from the want of blue rays appear yellow, yellow and white appear the same, and blue seems like green. In bright twilight or in moonshine, the light of gas has a reddish tint. 536. Mixed colours. Complementary colours. — By mixed colours we understand the impression of colour which results from the coincident action of two or more colours on the same position of the retina. This new impression is single ; it cannot be resolved into its components ; in this respect it differs from a complex sound in which the ear by practice can distinguish the constituents. Mixed colours may be produced by causing different parts of the spectrum to cover each other ; they may also be produced by looking in an oblique direction through a vertical glass plate at a coloured surface \ while at the same time, the observer's side of the plate reflects towards his eye light of a different colour. The method of the coloured disc affords another means of producing mixed colours. If in any of the methods by which the impression of mixed spectral colours is produced, One or more colours be suppressed, the residue corresponds to one of the tints of the spectrum ; and the mixture of the colours taken away produces the impression of another spectral colour. Thus, if in fig. 416 the red rays are cut off from the lens L, the light on the focus is no longer white but greenish blue. In like manner if the X3 466 On Light. [536- violet, indigo, and blue of tlie colour disc be suppressed, the rest seems yellow, while the mixture of that which has been taken out is a bluish violet. Hence white can always be compounded of two tints ; and two tints which together give white are called covipleinentary colours. Thus of spectral tints red and greenish yellow are complementary, so are orange and Prussian blue ; yellow and indigo blue ; greenish yellow and violet. A distinction must be made between spectral colours and pigment colours. Thus a mixture of pigment yellow and pigment blue produces green and not white, as is the case when the blue and yellow of the spectrum are mixed. The reason of this is that in the mixture of pigments we have a case of substraction of colours and not of addition. For in the mixture the pigment blue absorbs almost entirely the yellow and red light ; and the pigment yellow absorbs the blue and violet light so that only the green remains. If the complementary spectral colours are mixed in other proportions than is requisite for the production of white, intermediate colours are obtained which lie in the spectrum between the tints of the complementary colours. Thus a mixture of red and greenish blue, in which the former predominates, produces a tint which is nearer orange ; while when the latter is in excess, the tint comes nearer yellow and ultimately green. These colours, however, are not so pure as the corresponding spectral tints. They are less saturated, as it is called ; that is, mixed with white. In the above series are two spectral colours very remote in the spec- trum which have nearly the same complementary colours : these are red, the complementary colour to which is greenish blue, and violet, whose complementary colour is greenish yellow. Now when two pairs of com- plementary colours are mixed together, they must produce white, just as if only two complementary colours were mixed. But a mixture of greenish blue and of greenish yellow is green. Hence it follows that from a mixture of red, green, and violet white must be formed. This may easily be ascertained to be the case, by means of a colour disc on which are these three colours in suitable proportions. From the above facts it follows that from a mixture of red, green, and violet all possible colours may be constructed, and hence these three spectral colours are called t\\e^ fundainetital colours. It must be remarked that the tints resulting from the mixture of these three have never the saturation of the individual spectral colours. We have to discriminate three points in regard to colour. In the first place, the tint or colour proper by which we mean that special property which is due to a definite refrangibility producing it ; secondly, the satu- ration which depends on the greater or less admixture of white light with the colours of the spectrum, these being colours which are fully saturated ; and thirdly, there is the intensity which depends on the amplitude of vibration. 537. Bomog:eneous ligrht. — The light emitted from luminous bodies is seldom or never quite pure, on being examined by the prism it will be - 538] Properties of the Spectrum. • 467 found to contain more than one colour. In optical researches it is fre- quently of great importance to procure homogeneous or monocIu'omatic_ light. Common salt in the flame of a Bunsen's lamp gives a yellow of great purity. For red light, ordinary light is transmitted through glass coloured with suboxide of copper, which absorbs nearly all the rays ex- cepting the red, A very pure blue is obtained by transmitting ordinary light through a glass trough containing an ammoniacal solution of sulphate of copper. 538. Properties of the spectrum. — Besides its luminous properties, the spectrum is found to produce calorific and chemical effects. Lu?ni7ious properties. It appears from the experiments of Fraunhofer and of Herschel, that the light in the yellow part of the spectrum has the greatest intensity, and that in the violet the least. Caloripc effects. It was long known that the various parts of the spectrum differed in their calorific effects. Leshe found that a thermo- meter placed in different parts of the spectrum indicated a higher tem- perature as it moved from violet towards red. Herschel fixed the maximum intensity of the heating effects just outside the red ; Berard in the red itself. Seebeck showed that those different effects depend on the nature of a prism : with a prism of water the greatest caloritic effect is produced in the yellow ; with one of alcohol it is in the orange-yellow ; and with a prism of crown glass it is in the middle of the red. Melloni, by using prisms and lenses of rock salt, and by availing him- self of the extreme delicacy of the thermo-electric apparatus, first made a complete investigation of the calorific properties of the thermal spec- trum. This result led, as we have seen, to the confirmation and extension of Seebeck'? observations. Chemical properties. In numerous phenomena, light acts as a chemical agent. For instance, chloride of silver blackens under the influence of light, transparent phosphorus becomes opaque, vegetable colouring matters fade, hydrogen and chlorine gases, when mixed, combine slowly in diffused Hght, and with explosive violence when exposed to direct sunlight. The chemical action differs in different parts of the spectrum. Scheele found that when chloride of silver was placed in the violet, the action was more energetic than in any other part. Wollaston observed that the action extended beyond the violet, and concluded that, besides the visible rajs there are some invisible and more highly refrangible rays. These are the chemical or actinic rays. Th« researches of Bunsen and Roscoe show that whenever chemical action is induced by light, an absorption of light takes place, preferably of the more refrangible parts of the spectrum. Thus, when chlorine and hydrogen unite, under the action of light, to form hydrochloric acid, light is absorbed, and the quantity of chemically active rays consumed is directly proportional to the amount of chemical action. There is a curious difference in the action of the different rays. Moser placed an engraving on an iodised silver plate, and exposed it to the light until an action had commenced, and then placed it under a violet glass in the sunlight. After a few minutes a picture was seen with great 468 ♦ On Light. [538- distinctness, while when placed under a red or yellow glass, it required a very long time, and was very indistinct. When, however, the iodized silver plate was tirst exposed in a camera obscura to blue light for two minutes, and was then brought under a red or yellow glass, an image quickly appeared, but not when placed under a green glass. It appears as if there are vibrations of a certain velocity which could commence an action, and that there are others which are devoid of the property of commencing, but can continue and complete an action when once set up. Becquerel, who discovered these properties in luminous rays, called the former exciting rays, and the latter contiiiuijig or phosphorogenic rays. The phosphorogenic rays, for instance, have the property of rendering certain objects self-luminous in the dark after they have been exposed for some time to the light. Becquerel found that the phosphorogenic spectrum extended from indigo to beyond the violet. 539. Bark lines of the spectrum. — The colours of the solar spectrum are not continuous. For several grades of refrangibility rays are wanting, and in consequence, throughout the whole extent of the spectrum, there are a great number of very narrow dark lines. To observe them, a pencil of solar rays is admitted into a darkened room, through a narrow slit. At a distance of three or four yards, we look at this slit through a prism of flint glass, which must be very free from flaws, taking care to hold its edge parallel to the slit. We then observe a great number of very delicate dark lines parallel to the edge of the prism, and at very unequal intervals. The existence of the dark lines was first observ^ed by WoUaston in 1802 ; but Fraunhofer, a celebrated optician of Miinich, first studied and gave a detailed description of them. Fraunhofer mapped the lines, and indicated the most marked of them by the letters A, a, B, C, D, E, b., F, G, H ; they are therefore generally known as Fraunhofer's lines. The dark line A (see fig. 2 of Plate I.), is at the extremity and B in the middle of the red ray ; C at the boundary of the red and orange ray ; D is in the yellow ray ; E, in the green ; F, in the blue ; G, in the indigo ; H, in the violet. There are certain other noticeable dark lines, such as <^ in the red, and b in the green. In the case of solar light the positions of the dark lines are fixed and definite ; on this ac- count they are used for obtaining an exact determination of the refractive index (506) of each colour ; for example, the refractive index of the blue ray is, strictly speaking, that of the dark line F. In the spectra of artificial fights, and of the stars, the relative positions of the dark lines are changed. In the electric light the dark lines are replaced by brilliant lines. In coloured flames, that is to say, flames in which certain chemi- cal substances undergo evaporation, the dark lines are replaced by very brilliant lines of light, which differ for different substances. Lastly, of the dark lines, some are constant in position and distinctness, such are Fraunhofer's lines ; but some of the lines only appear as the sun nears the horizon, and others are strengthened. They are also influenced by the state of the atmosphere. The fixed lines are due to the sun ; the -541J FraunJwfer s Lines, 469 variable lines have been proved by Jannsen and Secchi to be due to the aqueous vapour in the air, and are called atmospheric or teliiiric lines. F'raunhofer counted in the spectrum more than 600 dark lines, more or less distinct, distributed irregularly from the extreme red to the extreme violet ray, Brewster counted 2,000. By causing the refracted rays to Fig. 422, pass successively through several analysing prisms, not merely has the existence of 3,000 dark lines been ascertained, but several which had been supposed single have been shown to be double. 540. iLpplications of Fraunhofer's lines. — Subsequently to Fraun- hofer, several physicists studied the dark lines of the spectrum. In 1822 Sir J. Herschel remarked that by volatilising substances in a flame a very delicate means is aflbrded of detecting certain ingredients by the colours they impart to certain of the dark lines of the spectrum ; and Fox Talbot in 1834 suggests optical analysis as probably the most delicate means of detecting minute portions of a substance. To Kirchoff and Bunsen, however is really due the merit of basing on the observation of the lines of the spectrum a method of analysis. They ascertained that the salts of the same metal, when introduced into a flame, always produce lines identical in colour and position, but different in colour, position, or num- ber for different metals, and finally that an exceedingly small quantity of a metal sufflces to disclose its existence. Hence has arisen a new method of analysis, known by the name of spectral a?ialysis. 541. Spectroscope. — The name of spectroscope has been given to the apparatus employed by Kirchhoff and Bunsen for the study of the 4/0 On Light. [541- spectrum. One of the forms of this apparatus is represented in fig. 422 It is composed of three telescopes mounted on a common foot, and whose axes converge towards a prism, P, of flint-glass. The telescope A is the only one which can turn round the prism. It is fixed in any required position by a clamping screw n. The screw-head, ;;/, is used to shift the position of the eye-piece, so that a clear image of the spectrum may be obtained, or in other words, to focus the eyepiece. The screw-head ?i is used to change the inclination of the axis. To explain the use of the telescopes B and C, we must refer to fig. 423, which shows the passage of the light through the apparatus. The rays emitted by the flame G falls on the lens a, and are caused to converge to a point, b, which is the principal focus of a second lens c. Conse- quently the pencil, on leaving the telescope B, is formed of parallel rays. This pencil enters the prism P. On leaving the prism, the light is decomposed, and in this state falls on the lens x. By this lens x, a real and reversed image of , the spectrum is formed at t. This image is seen by the observer through a magnifying glass which forms at ss' a virtual image of the spectrum magnified about eight times. The telescope C serves to measure the relative distances of the lines of the spectrum. For this purpose there is placed at 7n a micrometer Fig, 423- divided into 23 equal parts. The micrometer is formed thus : — A scale of 250 millimetres is divided with great exactness into 25 equal parts. A photographic negative on glass of this scale is taken, reduced to 15 millimetres. The negative is taken because then the scale is light on a dark ground. The sqale is then placed at w. in the principal focus of the lens e : consequently, when the scale is lighted by the candle F, the rays emitted from it leave the lens e in parallel pencils ; a portion of these, being reflected from a face of the prism, passes through the lens X, and forms a perfectly distinct image of the micrometer at z, thereby furnishing the means of measuring exactly the relativ^e distances of the different spectral lines. I -541] Spectroscope. 471 Fig. 424. The micrometric telescope C (fig. 422) is furnished with several adjust- ing screws, /, o^ r\ of these / adjusts the focus; o displaces the micro- meter in the direction of the spectrum laterally ; r raises or lowers the micrometer, which it does by giving ditferent inclinations to the telescope. The opening whereby the light of the flame G enters the telescope B consists of a narrow vertical slit, which can be opened more or less by causing the moveable piece a to ad- vance or recede by means of the screw V (fig. 424). When for pur- poses of comparison two spectra are to be examined simultaneously, there is placed over the upper part of the sht a small prism, whose refracting angle is 60°. Rays from one of the flames, H, fall at right angles on one face of the prism, they then experi- ence total reflection on a second face, and leave the prism by the third face, and in a direction at right angles to that face. By this means they pass into the telescope in a direction parallel to its axis, .without in any degree .nixing with the rays which proceed from the second flame, G. Consequently, the two pencils of rays traverse the prism P (fig. 423), and form two hori- zontal spectra which are viewed simultaneously through the telescope A. In the flames G and H are platinum wires, <;', c . These wires have been dipped beforehand into solution of the salts of the metals on which experiment is to be made; and by the vaporisation of these salts the metals modify the transmitted light, and gave rise to definite lines. Each of the flames H and G is a jet of ordinary gas. The apparatus through which the gas is supplied is known as a Bimseiis burner. The gas comes through the hollow stem k (fig. 422). At the lower part of this there is a lateral orifice to admit air ";o support the combustion of the gas. This orifice can be more or less closed by a small diaphragm, which acts as a regulator. If we allow a moderate amount of air to enter, the gas burns with a luminous flame, and the fines are obscured. But if a strong and steady current of air enters, the carbon is rapidly oxidised, the flarxie loses its brightness, and burns with a pale blue light, but with an intense heat. In this state it no longer yields a spectrum. If, how- ever, a metallic salt is introduced either in a solid state or in a jtate of solution, the spectrum of the metal makes its appearance, and in a fit state for observation. There are three chief types of spectra : the co7itimioiis spectrum, or those furnished by ignited sohds and liquids (fig. i, Plate I.) ; the band or line spectrum, consisting of a number of bright lines, and produced by ignited gases or vapours ; and absorption spectra, or those furnished by the sun or fixed stars. For an explanation of these, see art. 543. Bodies at a red heat give only a small spectrum, extending at most to the orange ; 472 On Light. [541 • as the temperature gradually rises, yelbw, green, blue, and violet success- ively appear, while the intensity of the lower colours increases. Instead of the prism very pure spectra may also be obtained by means of a grating (6io). 542. Experiments witb tlie spectroscope. — The coloured plate at the beginning shows certain spectra observed by means of the spectro- scope. No. I represents the continuous spectrum. No. 2 shows the spectrum of sodium. The spectrum contains neither red, orange, green, blue, nor violet. It is marked by a very brilliant yellow ray in exactly the same position as Fraunhofer's dark line D. Of all metals sodium is that which possesses the greatest spectral sensibility. In fact, it has been ascertained that one two hundred millionth of a grain of sodium is enough to cause the appearance of the yellow line. Consequently, it is very difficult to avoid the appearance of this line. A very little dust scattered in the apartment is enough to produce it, — a circumstance which shows how abundantly sodium is distributed though- out nature. No. 3 is the spectrum of lithium. It is characterised by a well- marked line in the red called Li^/, and by the feebler orange line Li(-\ Nos. 4 and 5 show the spectra of cccsium and rutiidiiun, metals dis- covered by Bunsen and Kirchhoff by means of spectral analysis. The former is distinguished by tw.o blue lines Cs7 and Cs3, the latter by two very brilliant dark red lines Rbv and Rbc^, and by two less intense violet lines RbrandRb^. A third metal, thaltiunr, has been discovered by the same method by Mr. Crookes in England, and independently by M. Lamy in France. Thallium is characterised by a single green line. Still more recently Richter and Reich have discovered a new metal associated with zinc, and which they call indium from a couple of charac- teristic lines which it forms in the indigo. The extreme delicacy of the spectrum reactions, and the ease with which they are produced, constitute them a most valuable help in the quantitative analysis of the alkalies and alkaline earths. It is sufficient to place a small portion of the substance under examination on platinum wire as represented in tig. 424, and compare the spectrum thus obtained either directly with that of another substance, or with the charts in which the positions of the lines produced by the various metals are laid down. With other metals the production of their spectra is more difficult, especially in the case of some of their compounds. The heat of a Bunsen's burner is insurincient to vaporise the metals, and a more intense tempera- ture must be used. 'This is effected by taking electric sparks between wires consisting of the metal whose spectrum is required, and the electric sparks are most conveniently obtained by means of Ruhmkorff's coil. Thus all the metals may be brought within the sphere of spectrum obser- vations. The power of the apparatus has great influence on the nature of the spectrum ; while an apparatus with one prism only gives in a sodium flame the well known yellow line, an apparatus with more prisms resolves it into two or three lines. -542] Experiments with the Spectroscope. 473 It has been observed that the character of the spectrum changes with the temperature; thus chloride of lithium in the flame of a Bunsen's burner gives a single intense peach-coloured line ; in a hotter flame, as that of hydrogen, it gives an additional orange line ; while in the oxy- hydrogen jet or the voltaic arc a broad brilliant blue band comes out in addition. The sodium spectrum produced by a Bunsen's burner con- sists of a single yellow line ; if, by the addition of oxygen, the heat be gra- dually increased, more bright lines appear ; and with the aid of the oxy- hydrogen flame the spectrum is continuous. Sometimes also, in addition to the appearance of new lines, an increase in temperature resolves those bands which exist into a number of fine lines, which in some cases are more and in some less refrangible than the bands from which they are formed. It may be supposed that the glowing vapour found at the low- temperature consists of the oxide of some difficultly reducible metal, whereas at the enormously high temperature of the spark these com- pounds are decomposed, and the true bright lines of the metal are formed. The delicacy of the reaction increases very considerably with the tem- perature. With the exception of the alkalies, it is from 40 to 300 times greater at the temperature of the electric spark than at that of Bunsen's burner. The spectra of the permanent gases are best obtained by taking the electric spark of a Ruhmkorff's coil, or Holtz's apparatus, through glass tubes of a special construction, provided with electrodes of platinum and filled with the gas in question in a state of great attenuation, known as Geissler's tubes ; if the spark be passed through hydrogen, the light emitted is bright red, and its spectrum consists of one bright red, one green, and one blue line No. 7, the first two of which appear to coincide with Fraun- hofer's lines C and F, and the third with a line between F and G, No. 6 represents the spectrum of oxygen. No. 8 is the spectrum of nitrogen. The light of this gas in a Geissler's tube is purple and the spectrum very complicated. If the electric discharge take place through a compound gas or- vapour, the spectra are those of the elementary constituents of the gas. It seems as if at very intense temperatures chemical combination was impossible, and oxygen and hydrogen, chlorine and the metals, could coexist in a separate form, although mechanically mixed with each other. The nature of the spectra of the elementary gases is very materially influenced by alterations of temperature and pressure. Wiillner made a series of very accurate observations on the gases oxygen, hydrogen, and nitrogen. He not only used gases in closed tubes, which by various electrical means he raised to different temperatures ; but in one and the same series of experiments, in which a small inductorium was used, he employed pressures varying from 100 millimetres to a fraction of a milli- metre ; while, in another series, in which a larger apparatus was used, he extended the pressure to 2,000 millimetres. At the lowest pressure of less than one millimetre, the spectrum of hydrogen was found to be green, and consisting of six splendid groups of lines, which at a higher pressure 474 On Light. [542- than I millimetre changed to continuous bands ; at 2 to 3 millimetres the spectrum consisted of the often-mentioned three Hnes, which did not disappear under a higher pressure, but gradually became less brilliant as the continuous spectrum increased in extent and lustre. From this point the light, and therefore the spectrum, became feebler. Using the larger apparatus, the band spectrum appeared only under a higher pressure ; at the highest pressuie of 2,000 millimetres it gave place to the continuous spectrum, since the bright lines continually extended and ultimately merged into each other. 543. Explanation of tbe dark lines of tlie solar spectrum. — It has been already seen that incandescent sodium vapour gives a bright yellow line corresponding to the dark line D of the solar spectrum. Kirchhoff found that, when the brilliant light produced by incandescent lime passes through a flame coloured by sodium in the usual manner, a spectrum is produced in which is a dark line coinciding with the dark line D of the solar spectrum ; what would have been a bright yellow line becomes a dark line when formed on the back ground of the lime light. By allowing in a similar manner the lime light to traverse vapours of potas- sium, barium, strontium, etc., the bright. lines which they would have formed were found to be converted into dark lines : such spectra are called absorption spectra. It appears then that the vapour of sodium has the power of absorbing rays of the same refrangibility as that which it emits. And the same is true of the vapours of potassium, barium, strontium, etc. This absorptive power is by no n>eans an isolated phenomenon. These substances share it, for example, with the vapour of nitrous acid, which Brewster found to possess the following property : when a tube filled with this vapour is placed in the path of the light either of the sun or of a gas flame, and the light is subsequently decomposed by a prism, a spectrum is produced which is full of dark lines (No. 9, Plate I.) ; and Miller showed that iodine and bromine vapour produced analogous effects. Hence the origin of the above phenomenon is, doubtless, the absorption by the sodium vapour of rays of the same kind, that is, as the same re- frangibility, as those which it has itself the power of emitting. Other rays it allows to pass unchanged, but these it either totally or in great part suppresses. Thus the particular lines in the spectrum to which these rays would converge are illuminated only by the feebly luminous sodium flame, and accordingly appear dark by contrast with the other portions of the spectrum which receive light from the powerful flame behind. By replacing one of the flames, G or H (fig. 420), by a ray of solar light reflected from a heliostat, Kirchhoff ascertained by direct comparison that the bright lines which characterise iron correspond to dark lines in the solar spectrum. He also found the same to be the case with sodium, magnesium, calcium, nickel, and some other metals. From these observations we may draw important conclusions with respect to the constitution of the sun. Since the solar spectrum has dark lines where sodium, iron, etc., give bright ones (No. 1 1. Plate I.), it is prob- able that around the solid, or more probably liquid, body of the sun, which -543] Dark Lines of the Solar Spectrum. 475 throws out the hght, there exists a vaporous envelope which, like the sodium flame in the experiment described above, absorbs certain rays, namely, those which the envelope itself emits. Hence those parts of the spectrum which, but for this absorption, would have been illuminated by these particular rays, appear feebly luminous in comparison with the other parts, since they are illuminated only by the light emitted by the envelope, and not by the solar nucleus ; and we are at the same time led to con- clude that in this vapour there exists the metals sodium, iron, etc. Huggins and Miller have applied spectrum analysis to the investigation of the heavenly bodies. The spectra of the moon and planets, whose light is reflected from the sun, give the same lines as those of the sun. Uranus proves an exception to this, and is probably still in a self- luminous condition. The spectra of the fixed stars contain, however, dark lines differing from the solar lines, and from one another. Four distinct types of spectra are distinguished by Pere Secchi. The first embraces the white stars and includes the well-known Sirius and a Lyrae. Their spectra (No. 12, Plate I.) usually contain a number of very fine lines, and always contain four broad dark lines, which coincide with the bright lines of hydrogen. Out of 346 stars 164 were found to belong to this group. The second group embraces those, having spectra intersected by numerous fine lines like those of our sun. About 140 stars, among them Pollux, Capella, (t, Aquilae, belong to this group. The third group embraces the red and orange stars, such as a Orionis, o Pegasi ; the spectra of these (Nos. 13, 14, Plate I.) are divided into eight or ten parallel columnar clusters of dark and bright bands increasing in intensity to the red. Group four is made up of small red stars with spectra, and is con- structed of three bright zones increasing in intensity towards the violet. It would thus appear that these fixed stars, while differing from one another in the matter of which they are composed, are constructed on the same general plan as our sun. Huggins has observed a striking difference in the spectra of the nebulas ; where they can at all be observed, they are found to consist generally of bright lines, like the spectra of the ignited gases, instead of like the spectra of the sun and stars consisting of a bright ground intersected by dark lines. J t is hence probable that the nebulae are masses of glowing gas, and do not consist, like the sun and stars, of a photosphere surrounded by a gaseous atmosphere. One of the most interesting triumphs of spectrum analysis has been the discovery of the true nature of the protuberances., which appear during a solar eclipse as mountains or cloud-shaped luminous objects varying in size, and surrounding the moon's disc. During the eclipse of 1868 it had been ascertained by Jannsen that they emitted certain bright fines coinciding with those of hydrogen. They have, however, been fully understood only since Lockyer and Jannsen have discovered a method of investigating them at any time. The prin- ciple of this method is as follows : — When a line of light admitted through a slit is decomposed by a prism, the length of the spectrum may be increased by passing it through two or more prisms ; as the quantity of light is the same, it is clear that the intensity of the spectrum will be 476 On Light. [543-,— diminished. This is the case with the ordinary sources of light, such as the sun ; if the light be homogeneous, it will be merely deviated, and not reduced in intensity by dispersion. And if the source of light emit lights of both kinds, the image of the slit of light of a definite refrangibility which the mixture may contain will stand out by their superior intensity on the weaker ground of the continuous spectrum. This is the case with the spectrum of the protuberances. Viewed through an ordinary spectro- scope, the light they emit is overshadowed by that of the sun ; but by using prisms of great dispersive power the sun's light becomes weakened, and the spectrum of the protuberances may be secured. Lockyer's researches leave no doubt that they are ignited gas masses, principally of hydrogen. By altering the position of the slit a series of sections of the prominences are obtained by collating which the form of the prominence may be inferred. They are thus found to enclose the sun usually to a depth of about 5,000 miles, but sometimes in enormous local accumula- tions, which reach the height of 70,000 miles. Lockyer has not merely examined these phenomena right on the edge of the sun ; but he has been able to observe them on the disc itself. He has shown that some of these protuberances are the results of sudden outbursts or storms, which move with the enormous velocity of 120 miles in a second. For a fuller account of this branch of Physics, which is incompatible with the limits of this work, the reader is referred to Roscoe's ' Lectures on Spectrum Analysis,' and to the same writer's articles in Watts's '- Dictionary of Chemistry,' or to Schellen's ' Spectrum Analysis,' translated by Lassell. 544. Uses of the spectroscopec — When a liquid placed in a glass tube or in a suitable glass cell is interposed between a source of light and the slit of the spectroscope, on looking through the telescope, the spec- trum observed will in many cases be found to be traversed by dark bands. No 10, Plate I, represents the appearance of the spectrum when a solution of chlorophylle, the green colouring matter of plants, is thus interposed. Both in the red, the yellow and the violet parts dark bands are formed, and the blue gives way to a reddish shimmer. If instead of chlorophylle arterial blood greatly diluted be used, the red of the spec- trum appears brighter, but green and violet are nearly extinguished. As these bands thus differ in different liquids as regards position, breadth, and intensity, in many cases they afford the most suitable means of identifying bodies. Sorby and Browning have devised a combination of the microscope and spectroscope, called the microspectroscope, which renders it possible to examine even very minute traces of substances. This application of the spectroscope has been very useful in inves- tigating substances which have special importance in physiology and pathology ; thus, in examining normal and diseased blood, in detecting albumen in urine, and in ascertaining the rate at which certain substances pass into the various fluids of the system. The characteristic absorption bands which certain liquids, such as wine, beer, etc., present in their normal state, compared with those yielded by adulterated substances furnishes a delicate and certain means of detecting the latter. • ^ — - 5 45] Fluorescence. 477 545. Fluorescence. — Professor Stokes has made the remarkable dis- covery that under certain circumstances the rays of hght are capable of undergoing a change of refrangibility. The discovery originated in the study of a phenomenon observed by Sir J, Herschel, that certain solutions when looked at by transmitted light appear colourless, but when viewed in reflected light present a bluish appearance. Stokes has found that this property which he calls fluorescence, is characteristic of a large class of bodies. The phenomenon is best seen when a solution of sulphate of quinine, • contained in a trough with parallel sides, is placed in different positions in the solar spectrum. No change is observed in the upper part of the spectrum, but from about the middle of the lines G and H (coloured Plate) to some distance beyond the extreme range of the violet, rays of a beau- tiful sky-blue colour are seen to proceed. These invisible ultra-violet rays also become visible when the spectrum is allowed to fall on paper im- pregnated with a solution of cpsculine (a substance extracted from horse chestnut), an alcoholic solution of stramonium, or a plate of canary glass (which is coloured by means of uranium). This change arises from a diminution in the refrangibility of those lays outside the violet, which are ordinarily too refrangible to affect the eye. Glass appears to absorb many of these more refrangible rays, which is not the case nearly to the same extent with quartz. When prisms and troughs formed of plates of quartz are used, a spectrum may be obtained which, outside the line H, is double the length of the visible spectrum. In the spectrum thus made visible dark lines may be seen like those in the ordinary spectrum. The phenomena may be observed without the use of a prism. When an aperture in a dark room is closed by means of a piece of blue glass, and the light is allowed to fall upon a piece of canary glass, it instantly appears self-luminous from the emission of the altered rays. In most cases it is the violet and ultra-violet rays which undergo an alteration of refrangibility, but the phenomenon is not confined to them. A decoction of madder in alum gives yellow and violet light from about the line D to beyond the violet ; an alcoholic solution of chlorophylle gives red light from the line B to the Hmit of the spectrum. In these cases the yellow, the green, and the blue rays experience diminution of refrangibility ; the change never produces more highly refrangible rays. The electric light gives a very remarkable spectrum. With quartz apparatus Stokes obtained a spectrum six or eight times as long as the ordinary one. Several flames of no great illuminating power emit very peculiar light. Characters traced on paper with solution of stramonium, which are almost invisible in daylight, appear instantaneously when illumi- nated by the flame of burning sulphur. Robinson has found that the light of the aurora is peculiarly rich in rays of high refrangibility. If a pencil of rays be allowed to pass through a condensing lens, and be received on a screen within the focus, the bright spot has a red edge, while if the screen is placed beyond the focus the bright spot has a violet edge. 478 On Light. [546- 546. Chromatic aberration. — The various lenses hitherto described (51 ) possess the inconvenience that, when at a certain distance from the eye, they give images with coloured edges. This defect, which is most observable in condensing lenses, is due to the unequal refrangibility of the simple colours (532), and is called chromatic aberration. For, as a lens may be compared to a series of prisms with infinitely small faces, and united at their bases, it not only refracts light, but also decomposes it like a prism. On account of this dispersion, therefore lenses have really a distinct focus for each colour. In condensing lenses, for example, the red rays, which are the least refrangible, form their focus at a point, r, on the axis of the lens (fig. 425), while the violet rays, Fig. 425. which are most refrangible, coincide in the nearer point, v. The foci of the orange, yellow, green, blue, and indigo are between these points. The chromatic aberration is more perceptible in proportion as the lenses are more convex, and as the point at which the rays are incident is further from the axis ; for then the deviation, and therefore the dispersion, are increased. If a pencil graze which has passed through a condensing lens be received on a screen placed at in m within the first distance, a bright spot is seen with a red border, if it is placed ^X s s the bright spot has a violet border. 547. Acbromatism. — By combining prisms which have different re- fracting angles (512), and are formed of substances of unequal dispersive powers (530), white light may be refracted without being dispersed. The same result is obtained by combining lenses of different substances, the curvatures of which are suitably combined. The images of objects viewed through such lenses do not appear coloured, and they are accordingly called achromatic lenses ; achrontatism being the term applied to the phenomenon of the refraction of light without decomposition. By observing the phenomenon of the dispersion of colours in prisms ot water, of oil, ot turpentine, and of crown glass, Newton was led to sup- pose that dispersion was proportional to refraction. He concluded that there could be no refraction without dispersion, and, therefore, that achromatism was impossible. Almost half a century elapsed before this was found to be incorrect. Hall, an Enghsh philosopher, in 1733, was the first to construct achromatic lenses, but he did not publish his dis- covery. It is to Dolland, an optician in London, that we owe the greatest improvement which has been made in optical instruments. He showed -547] Achromatism. ^ 479 in 1757 that by combining two lenses, one a double convex crown glass lens, the other a concavo-convex lens of flint glass (fig. 426), a lens is obtained which is virtually achromatic. To explain this result, let two prisms, BFC and CDF, be joined and turned in a contrary direction, as shown in fig. 427. Let us suppose, in the first case, that both prisms are of the same material, but that the refracting angle of the second, CDF, is less than the refracting angle of the first ; the two prisms will produce the same effect as a single prism, BAF ; that is to say, that white light which traverses it will not only be refracted, but also decomposed. If, on the contrary, the first prism BCF were of crown glass, and the other of flint glass, the dispersion might be destroyed without destroying the refraction. For as flint glass is more dispersive than crown, and as the dispersion produced by a prism dimi- nishes with its refracting angle (530), it follows that by suitably lessening the refracting angle of the flint glass prism CFD, as compared with the refracting angle of the crown glass prism BCF, the dispersive power of Fig. 426. Fig. 427. these prisms maybe equalised ; and as, from their position, the dispersion takes place in a contrary direction, it is neutralised ; that is, the emergent rays EO are parallel, and therefore give white light. Nevertheless, the ratio of the angles BCF and CFD, which is suitable for the parallehsm of the red rays and violet rays, is not so for the intermediate rays, and, consequently, only two of the rays of the spectrum can be exactly com- bined, and the achromatism is not quite perfect. To obtain perfect achromatism, several prisms would be necessary, of unequally dispersive materials, and the angles of which were suitably combined. The refraction is not destroyed at the same time as the dispersion ; that could only happen if the refracting power of a bqdy varied in the same ratio as its dispersive power, which is not the case. Consequently, the emergent ray EO is not exactly parallel to the incident ray, and there is a refraction without appreciable decomposition. Achromatic lenses are made of two lenses of unequally dispersive ma- terials ; one. A, of flint glass, is a diverging concavo-convex (fig, 422) ; the other, B, of crown glass, is double convex, and one of its faces may exactly coincide with the concave face of the first. As with prisms, several lenses would be necessary to obtain perfect achromatism ; but for optical instruments two are sufficient, their curvature being such as to combine the blue and orange rays. 48o On Light. [548- CHAPTER V. OPTICAL INSTRUMENTS. 548. Tbe different kinds of optical instruments. — By the term optical instrument is meant any combination of lenses, or of lenses and mirrors. Optical instruments may be divided into three classes, accord- ing to the ends they are intended to answer, viz.: — i. Microscopes, which are designed to obtain a magnified image of any object whose real dimen- sions are too small to admit of its being seen distinctly by the naked eye. ii. Telescopes, by which very distant objects, whether celestial or terres- trial, may be observed, iii. histruments designed to project on a screen a magnified or diminished image of any object which can thereby be either depicted or rendered visible to a crowd of spectators : such as the camera lucida, the camera obscura, photographic apparatus, the 7nagic lanter?t, the solar microscope, the photo-electric microscope, etc. The two former classes yield virtual images ; the last, with the exception of the camera lucida, yield real images. MICROSCOPES. 549. Tlie simple microscope.— The simple microscope, or jnagnifying glass is merely a convex lens of short focal length, by. means of which we look at objects placed between the lens and its principal focus. Let AB (fig. 428) be the object to be observed placed between the lens and its Fig. 428. principal focus, F. Draw the secondary axes AO and BO, and also from A and B rays parallel to the axis of the lens FO. Now these rays, on passing out of the lens, tend to pass through the second principal focus F', consequently they are divergent with reference to the secondary axes, and therefore, when produced, will cut those axes in A' and B' respec- tively. These points are the virtual foci of A and B respectively. The lens therefore produces at A' B' an erect and magnified virtual image of the object AB. The position and magnitude Df this image depend on the distance of J -560] Optical Instruments. 481 the object from the focus. Thus, if AB is moved to ab nearer the lens, the secondary axes will contain a greater angle, and the image will be formed at a'b', and will be much smaller, and nearer the eye. On the other hand, if the object is moved farther from the lens the angle between the secondary axes is diminished, and their intersection with the pro- longation of the refracted rays taking place beyond A'B', the image is formed farther from the lens, and is larger. In a simple microscope both chromatic aberration and spherical aberration increase with the degree of magnification. We have already seen that the former can be corrected by using achromatic lenses (547), and the latter by using diaphragms, which allow the passage of such rays only as are nearly parallel to the axis, the spherical aberration of these rays being nearly inappreciable. Spherical aberration may be Fig. 429. still further corrected by using two plano-convex lenses, instead of one very convergent lens. When this is done, the plane face of each lens is turned towards the object (fig. 429). Although each lens is less convex than the simple lens which together they replace,'^ yet their joint magnifying power is as great, and with a less amount of. sphei-ical aber- ration, since the first lens draws towards the axis the, ray^which fall on the second lens. This combination of lenses is known as Wollaston's doublet. There are many forms of the simple microscope. One of the best is that represented in fig. 430. On a hori- zontal support, E, which can be raised and lowered by a rack and pinion, there is a black eyepiece, w, in the centre of which is fitted a small con- vex lens. Below this is the stage, which is fixed, and on which the object is placed between glass plates. In order to illuminate the object power- fully, diffused light is reflected from a concave glass mirror, M, so that the reflected rays fall upon the object. ~ — — ^-=-- In using this microscope, the eye ^^' ^^°' is placed very near the lens, which is lowered or raised until the position is found at which the object appears in its greatest distinctness. 550. Conditions of distinctness of tlie imagres. — In order that objects looked at through a microscope should be seen with distinctness Y _ 4^2 On Light, [550 they must have a strong light thrown upon them, but this is by no means enough. It is necessary that the image be formed at a determinate distance from the eye. In fact, there is for each person 2, distance of most distinct vision, a distance, that is to say, at which an object must be placed from an observer's eye, in order to be seen with greatest dis- tinctness. This distance is different for different observers, but ordi- narily is between lo and 12 inches. It is, therefore, at this distance from the eye that the image ought to be formed. Moreover, this is why each observer has to focus the instrument, that is, to adapt the microscope to his own distance of most distinct vision. This is effected by slightly varying the distance from the lens to the object, for we have seen above that a slight displacement of the object causes a great displacement of the image. With a common magnifying glass, such as is held in the hand, the adjustment is effected by merely moving it nearer to or farther from the object. In the microscope the adjustment is effected by means of a rack and pinion, which in the case of the instrument shown in fig. 430 moves the instrument, but moves the object in the case of the instrument depicted in fig. 435. What has been said ?^iovXfocHssi7tg the microscope applies equally to telescopes. In the latter instruments the eyepiece is Fig. 432. generally adjusted with respect to the image formed in the focus of the object glass. 551. Apparent magrnitude of an object. — The apparent magnitude of apparent diameter pf a body is the angle it subtends at the eye of the observer. Thus, if AB is the object, and O the observer's eye (figs. 431, 432), the apparent magnitude of the object is the angle AOB contained by two visual rays drawn from the centre of the pupil to the extremities of the object. In the case of objects seen through optical instruments, the angles which they subtend are so small that the arcs which measure the angles do not differ sensibly from their tangents. The ratio of two such angles is therefore the same as that of their tangents. Hence we deduce the two following principles : — -552] Measure of Magnification. 483 I. When the same object is seen at itmquat distafices, the apparent dia- 7ueter varies rnversely as the distance from the observer's eye. — - II. In the case of two objects seen at the sam'^ distance, the ratio of the apparent diaj?ieters is the sam3 as that of their absolute magnitudes. These principles may be proved as follows : i. In fig. 431, let AB be the object in its first position, and ab the same object in its second position. For the sake of distinctness these are represented in such positions that the line OC passes at right angles through their middle points C and c respectively. It is, however, sufficient that ab and AB should be the bases of isosceles triangles having a common vertex at O. Now by what has been said above, AB is virtually an arc of a circle described with centre O and radius OC ; likewise ab is virtually an arc of a circle whose centre is O and radius O^. Therefore, AOB:^0^ = ^:^'^-= -^^ : ^. OC O^ OC Oc Therefore, AOB varies inversely as OC. ii. Let AB and A'B' be two objects placed at the same perpendicular distance, OC, from the eye, O, of the observer (fig. 332). Then they are virtually arcs of a circle whose centre is O and radius OC. Therefore, AOB : A'OB' = ^^ : ^'^- = AB : A^B, a proportion which expresses the second principle. 552. Measure of magrnification. — In the simple microscope, the mea - sure of the magnification produced is the ratio of the apparent diam.eter of the image to that of the object, both being at the distance of most dis tinct vision.* The same rule holds good for other microscopes. It is however, important to obtain an expression for the magnification depend- ing on data that are of easier determination. * A simpler and more general definition may be stated thus —Let a be the angular magnitude of the object as seen by the naked eye, ^ the angular magnitude of the image, whether real or virtual, actually present to the eye, then the magnification is ^ -r- a. This rule appJies to telescopes., Y2 484 On Light. [552- In fig. 433 let AB be the object, and A'B' its image formed at the dis- tance of most distinct vision. Let a'b' be the projection of AB on A'B'. Then, since the eye is very near the glass, the magnification equals 1^^-, or — ,5-, that is, ^ ^ . But since the triangles A'OB' and AOB a'Ob'^ a'b' AB ^ are similar, A'B' : AB = DO : CO. Now DO is the distance of most distinct vision, and CO is very nearly equal to FO,the focal length of the lens. Therefore the magnification equals the ratio of the distance of most distinct vision to the focal length of the lens. Hence we conclude that the magnification is greater : — ist, as the focal length of the lens is smaller, in other words, as the lens is more convergent ; 2ndly, as the observer's distance of most distinct vision is greater. By changing the lens the magnification can be increased, but only within certain limits if we wish to obtain a distinct image. By means of a simple microscope distinct magnification maybe obtained up to 120 diameters. The magnification we have now considered is linear magnification. Stiperjicial magnification equals the square of the linear magnification : for instance, the former will be i ,600 when the latter is 40. 553. Compound microscope. — The compound microscope in its sim- plest form consists of two condensing lenses : one, with a short focus, is called the object glass ox objective^ because it is turned towards the object ; the other is less condensing, and is called the eyepiece or power, because it is close to the observer's eye. Fig. 434 represents the path of the luminous rays, and the formation of the image in the simplest form of a compound microscope. An object Fig. 434 AB, being placed very near the principal focus of the object glass, M, but a little farther from the glass, a real image, ab, inverted and somewhat magnified, is formed on the other side of the object glass (524). Now the distance of the two lenses M and N, is such that the position of the image, ab, is between the eyepiece N, and its focus, F. From this it follows that for the eye at E, looking at the image through the eyepiece this glass produces the same effect as a simple microscope, and instead of this image, ab, another image, a'b' , is seen, which is virtual, and still more magnified. This second image, although erect as regards the first, is inverted in reference to the object. It may thus be said, that the com- pound microscope is nothing more than a simple microscope applied not to the object, but to its image already magnified by the first lens.' 554. Amici's compound microscope. — The principle of the compound -554] Microscope, 485 microscope has been already (553) explained ; the principal accessories to the instrument remain to be described. Fig. 435 represents a perspective view, and fig. 436 a section of a com- pound microscope. The body of the microscope consists of a series of brass tubes, DD', H, and I, in the former of these is fitted the eyepiece, and in the lower part of the latter the object glass, 0. The tube I moves with gentle friction in the tube DD', which in turn can also be moved in Fig. 435- a larger tube fixed in the ring E. This latter is fixed to a piece, BB, which by means of a very fine screw, worked by the milled head T, can be moved up and down an inner rod r, not represented in the figure. The whole body of the microscope is raised and lowered with the piece BB', so that it can be placed near or far from the object to be examined. Moreover, the rod, t, and all the other pieces of the apparatus rest on a horizontal axis, A, with which they turn under so much friction as to remain fixed in any position in which they may be placed. 486 On Light, [554- The objects to be observed are placed between two glass plates, V, on a stage, R. This is perforated in the centre so that light can be reflected upon it by a concave reflecting glass mirror, M. The mirror is mounted on an articulated support, so that it can be placed in any position what- ever, so as to reflect to the object either the diffused light of the atmo- sphere, or that from a candle or lamp. Between the reflector and the stage is a diaphragm or stop, K, perforated by four holes of different sizes, anyone of which can be placed over the perforation in the stage, and thus the light faUing on the object may be regulated; the light can moreover be regulated by raising by a lever, ;/, the diaphragm, K, which is movable in a slide. Above the diaphragm is a piece, ;;/, to which can be attached either a very small stop, so that only very little light can reach the object, or a condensing lens, which illuminates it strongly, or an oblique prism, represented at X. The rays from the reflector undergo two total reflec- tions in this prism, and emerge by a lenticular face that concentrates them on the object, but in an oblique direction, which in some microscopic ob- servations is an advantage. Objects are generally so transparent that they can be lighted from below ; but where, owing to their opacity, this is not possible, they are lighted from above by means of a condensing lens mounted on a jointed support, and so placed that they receive the diffused light of the atmosphere. Fig. 436 shows the arrangement of the lenses and the path of the rays in the microscope. At is the object glass, consisting of three small condensing lenses, represented on a larger scale at L, on the right of the figure. The effects of these lenses being added to each other they act like a single very powerful condensing lens. The object being placed at /, a very little beyond the principal focus of the system, the emerging rays fall upon a fourth condensing lens, Ji, the use of which will be seen presently (555, 556). Having become more convergent, owing to their pas- sage through the lens, ;/, the rays form at aa' a real and amplified image of the object /. This image is between a fifth condensing lens, O, and the principal focus of this lens. Hence, on looking through this, it acts as a" magnifier (524), and gives at AA', a virtual and highly magnified image of aa', and therefore of the object. The two glasses 71 and O, constitute the eyepiece in the same manner as the three glasses, 0, con- stitute the object glass. The first image, aa', must not merely be formed between the glass, O, and its principal focus, but. at such a distance from this glass that the second image, AA^, is formed at the observer's distance of distinct vision. This result is obtained in moving, by the hand the body, DH, of the microscope in the larger tube fixed to the ring, E, until a tolerably dis- tinct image is obtained ; then turning the milled head, T, in one direction or the other, the piece, BB, and with it the whole microscope, are moved until the image, AA', attains its greatest distinctness, which is the case when the image, aa\ is formed at the distance of distinct vision : a distance which can always be ultimately obtained, for as the object glass ap- proaches or recedes from the object, the image, aa' recedes from or approaches the eyepiece, and at the same time the image, AA'. 565] Achromatism of the Microscope. 487 This operation is called the focussing. In the microscope, where the distance from the object glass to the eyepiece is constant, it is effected by altering their distance from the object. In telescopes, where the objects are inaccessible, the object is effected by varying the distance of the eyepiece and the object glass. The microscope possesses numerous eyepieces and object glasses, by means of which a great variety of magnifying power is obtained. A small magnifying power is also obtained by removing one or two of the lenses of the object glass. The above contains the essential features of the microscope ; it is made in a great variety of forms, which differ mainly in the construction of the stand, the arrangement of the lenses, and in the illumination. For descriptions of these, the student is referred to special works on the microscope. 555. Achromatism of tlie microscope. Campani's eyepiece. — When a compound microscope consists of two single lenses, as in fig. 435, not only is the spherical aberration uncorrected, but also the chromatic aberration, the latter defect causing the images to be surrounded by fringes of the prismatic colours, these fringes being larger as the magnifi- cation is greater. It is with a view to correcting these aberrations that the object glass (see fig. 424) is composed of three achromatic lenses, and the eyepiece of two lenses, ?t and w, for the first of these, n^ would be enough to produce colour unless the magnifying power were low. The effect of this eyepiece in correcting the colour may be explained as follows : — It will be borne in mind that with respect to red rays the focal length of a lens is greater than the focal length of the same lens with reference to the violet rays. In fact, if in the equation (4) (527), we write R' = 00 , we obtain / = n — V which gives the focal length of a plano-convex lens whose refractive Fig. 437- index is ;/. Now, in flint glass, and for the red ray, n—\ equals 0-63, and for the violet ray 71 — i equals 0-67 Let ab be the object, O the object glass which is corrected for colour. Consequently, a pencil of rays falling from ^ on O would converge to a focus. A, without any separation of colours, but falling on ihtjield glass C, the red rays would converge to r, the violet rays to v, and intermediate colours, to intermediate points. In like manner the rays from b, after passing through the field glass, would converge to r', v\ and intermediate points. So that on the whole there would be formed a succession of 488 On Light. [555- coloured images of ab, viz. a red image at rr' , a violet image at vv' ., and between them images of intermediate colours. Let d be the point of the object which is situated on the axis. The rays from d will converge to R, V, and intermediate points. Now suppose the eyeglass O' to be placed in such a manner that R is the principal focus of O' for the red rays, then will V be its principal focus for the violet rays. Consequently, the red rays, after emerging from O', will be parallel to the axis, and so will the violet rays emerging from V, and so of any other colour. Consequently, the colours of ^, which are separated by C, are again combined by O'. The same is very nearly true of r and ?y, and of r' and v'. Hence com- bination of lenses C and O' corrects the chromatic aberration that would be produced by the use of a single eyeglass. Moreover, by drawing the rays towards the axis, it diminishes the spherical aberration, and, as we shall see in the next article, enlarges the field of view. In all eyepieces consisting of two lenses the lens to which the eye is applied is called the eye lens, the one towards the object glass is called thtjield lens. The eyepiece above described was invented by Huyghens, who was not, however, aware of its property of achromatism. He de- signed it for use with the telescope. It was applied to the microscope by Campani. The relation between the focal lengths of the lenses is as follows : — The focal length of the field glass is three times that of the eye lens, and the distance between their centres is half the sum of the focal length. It easily follows from this that the image of the point d would but for the interposition of the field lens, be formed at D, which is so situated that CD is three times DO', then the mean of the coloured images will be formed midway between C and O^ 556. Field of view. — By the field of view of an optical instrument is meant all those points which are visible through the eyepiece.. ; The advantage obtained by the use of an eyepiece in enlarging the/ jfield of Fig- 438. lL^ view will be readily understood by an inspection of the accompanying figure. As before, O is the object glass, C the field lens, O' the eye le^s, and E the eye placed on the axis of the instrument. Let ^z be a point of the object ; if we suppose the field lens removed, the pencil of rays from a would be brought to a focus at A, and none of them would fall on the eye lens O', nor pass into the eye E. Consequently, a is beyond the field of view. But when the field glass C is interposed, the pencil of rays is brought to a focus at A', and emerges from O' into the eye. Conse- quently, a is now within the field of view. It is in this manner that the substitution of an eyepiece for a single eye lens enlarges the field of view. 557] Magnifying Power. Micrometer, 489 557. Magrnifyingr power. Micrometer. — The magnifying power of any optical instrument is the ratio of the magnitude of the image to the magnitude of the object. The magnifying power in a compound micro- scope is the product of the respective magnifying powers of the object glass and of the eyepiece ; that is, if the first of these magnifies 20 times, and the other 10, the total magnifying power is 200. The magnifying power depends on the greater or less convexity of the object glass and of the eyepiece, as well as on the distance between these two glasses, to- gether with the distance of the object from the object glass. A magni- fying power of 1,500 and even upwards has been obtained ; but the image then loses in sharpness what it gains in extent. To obtain precise and well illuminated images, the magnifying power ought not to exceed 500 to 600 diameters, which gives a superficial enlargement 25o,cxx) to 360,000 times that of the object. The magnifying power is determined experimentally by means of the micrometer ; this is a small glass plate, on which, by means of a diamond, a series of lines is drawn at a distance from each other of ^^ or j^^ of a millimetre. The micrometer is placed in front of the object glass, and then instead of viewing directly the rays emerging from the eyepiece, Q, they are received on a piece of glass, A (fig. 439), inclined at an angle of 45°, and the eye is placed above so as to see the image of the micrometer lines which is formed by reflection on a screen, E, on whidr is a scaje divided into millimetres. By counting the number of di^yiSions of scale corresponding to a certain number of lines of the iHiage, the rifa nifying power may be deduced. Thus, if the image occupies a space of 45 millimetres on the scale, and contains 1 5 lines of the micrometer, the dis- tance between each of which shall be assumed at j^5 millimetre, the absolute magnitude of the object will be {^-^ millimetre ; and as the image occupies a space of 45 millimetres, the magnifi- cation will be the quotient of 45 by ~~ or 300. The eye in this experiment ought to be at such a distance from the screen, E, that the screen is distinctly visible : this distance varies with different observers, but is usually 10 to 12 inches. The magnifying power of the micro- scope can also be determined by means of the camera lucida. When once the magnifying power is known, the absolute magnitude of objects placed before the microscope is easily deduced. For, as the magnifying power is nothing more than the quotient of the size of the image by the size of the object, it follows that the size of the image divided by the magnifying power gives the size of the object ; it is in this manner that the diameter of all microscopic objects is determined. Fig- 439- Y 3 490 On Light. [558- TELESCOPES. 558, Astronomical telescope. — 1\it. asironomicaltelescope'xs used for observing the heavenly bodies ; hke the microscope, it consists of a con- densing eyepiece and object glass. The object glass, M (fig. 440), forms Fig. 440. between the eyepiece, N, and its principal focus an inverted image of the heavenly body, and this eyepiece, which acts as a magnifying glass, then gives a virtual and highly magnified image, a'b\ of the image ab. The astronomical telescope appears, therefore, analogous to the microscope ; but the two instruments difter in this respect : that in the microscope, the object being very near the object glass, the image is formed much beyond the principal focus, and is greatly magnified, so that both the object glass and the eyepiece magnify : while in the astronomical telescope, the heavenly body being at a great distance, the incident rays are parallel, and the image formed in the principal focus of the object glass is much smaller than the object. There is, therefore, no magnification except by the eyepiece, and this ought, therefore, to be of very short focal length. Ei£. 441. Fig. 441 shows an astronomical telescope mounted on its stand. Above it there is a small telescope, which is called the finder. Telescopes with -559] Terrestrial Telescope. 49^ a large magnifying power are not convenient for finding a star, as they have but a small field of view : the position of the star is, accordingly, first sought by the finder, which has a much larger field of view, that is, takes in a far greater extent of the heavens : it is then viewed by means of the telescope. ACB The magnification (note, art. 552) equals - 7^-77 (^0- 44°) ; that is, it equals ^, and therefore is approximately equal to --, F beingthe focus of the bO C OF object glass, M, and being supposed very nearly to coincide with the focus of the eyepiece, N ; it may, therefore, be concluded that the magnifying power is greater in proportion as the object glass is less convergent, and the eyepiece more so. When the telescope is used to make an accurate observation of the stars, for example, their zenith distance or their passage over the meridian, a C7'0ss wire is added. This consists of two very fine metal wires or spider threads stretched across a circular aperture in a small metal plate (fig. 442). The wires ought to be placed in the position where the inverted image is produced by the object glass, and the point where the wires cross ought to be on the optical axis ^'^" '*'*^' of the telescope, which thus becomes the line of sight or collimaiion. 559. Terrestrial telescope. — The terrestrial telescope di^trsirom the astronomical telescope in producing images in their right positions. This is effected by means of two condensing glasses, P and O (fig. 443), Fig. 443- placed between the object glass, M, and the eyepiece, R. The object being supposed to be at AB, at a greater distance than can be shown in the drawing, an inverted and much smaller image is formed at ba on the other side of the object glass. But the second lens, P, is at such a distance that its principal focus coincides with the image ab ; from which it follows that the luminous rays which pass through b, for example, after traversing the lens, P, take a direction parallel to the secondary axis, bO (520). Similarly the rays passing by a take a direction parallel to the axis aO. After crossing on H, these various rays traverse a third lens. O, whose principal focus coincides with the point H. The pencil BbH converges towards b\ on a secondary axis O' b', parallel to its direction ; the pencil A^H converging in the same manner at ^ , an erect image of the object, AB, is produced at a' b'. This image is viewed, as in the astronomical telescops, through a condensing eyepiece, R, so placed that . 492 On Light. [559- it acts as a magnifying glass, that is, its distance from the image, a' h\ is less than the principal focal distance ; hence, there is formed, at a' b', a virtual image of a' b', erect, and much magnified. The lenses P and O, which only serve to rectify the position of the image, are fixed in a brass tube, at a constant distance, which is equal to the sum of their principal focal distances. The object glass, M, moves in a tube, and can be moved to or from the lens P, so that the image, ab, is always formed in the focus of the lens whatever be the distance of the object. The distance of the lens, R, may also be varied so that the image a^' b'\ may be formed at the distance of distinct vision. This instrument may also be used as an astronomical telescope by using a different eyepiece ; this must have a much greater magnifying power than the former cases. In the terrestrial telescope the magnifying power is the same as in the astronomical telescope, provided always that the correcting glasses, P and O, have the same convexity. 560. Calilean telescope. — The Galilean Telescope is the simplest of all telescopes, for it only consists of two lenses, namely, an object glass, Fig. 444. M, and a diverging or double concave eyepiece, R (fig. 444), and it gives at once an erect image. Opera glasses are constructed on this principle. If the object be represented by the right line AB, a real but inverted and smaller image would be formed at ba ; but in traversing the eyepiece, R, the rays emitted from the points A and B are refracted, and diverge from the secondary axes bO' and .aO\ which correspond to the points b and a of the image. Hence, these rays produced backward meet their axes in a' and b'\ the eye which receives them sees accordingly an erect and magnified image in a' b', which appears nearer because it is seen under an angle, a' O' b', greater than the angle, AOB, under which the object is seen. The magnifying power is equal to the ratio of the angle a' O' b' to the angle AOB, and is usually from 2 to 4. The distance of the eyepiece R from the image ab is pretty nearly equal to the principal focal distance of this eyepiece ; it follows, therefore, that the distance between the two lenses is the difference between their re- spective focal distances ; hence, Galileo's telescope is very short and port- able. It has the advantage of showing objects in their right position ; and, further, as it has only two lenses, it absorbs very little light : in con- sequence, however, of the divergence of the emergent rays, it has only a small field of view, and in using it the eye must be placed very near the 562] Reflecting Telescopes. 493 eyepiece. The eyepiece can be moved to or from the object glass, so that the image a' b' is always formed at the distance of distinct vision. ^ The opera glass is usually double, so as to produce an image in each eye, by which greater brightness is attained. The time at which telescopes were invented is not known. Some at- tribute their invention to Roger Bacon in the 13th century; others to J. B. Porta at the end of the i6th ; others again to a Dutchman, Jacques Metius, who, in 1609, accidentally found that by combining two glasses, one concave and the other convex, distant objects appeared nearer and much larger. Galileo's was the first telescope directed towards the heavens. By its means Galileo discovered the mountains of the moon, Jupiter's satellites, and the spots on the sun. 561. Reflecting: telescopes, — The telescopes previously described are refractmg or dioptric telescopes. It is, however, only in recent times that it has been possible to construct achromatic lenses of large size ; before this, a concave metallic mirror was used instead of the object glass. Telescopes of this kind are called reflecting or catoptric telescopes. The principal forms are those devised by Gregory, Newton, Herschel, and Cassegrain. 562. The Gregrorlan telescope. — Figure 445 is a representation of Gregory's telescope ; it is mounted on a stand, about which it is mov- Fig. 445. able, and can be inclined at any angle. This mode of mounting is optional ; it may be equatorially mounted. Fig. 446 gives a longitudinal section. It consists of a long brass tube closed at one end by a concave metallic mirror, M, which is perforated in the centre by a round aperture 494 On Light. [562 through which rays reach the eye. There is a second concave metaikOr mirror, N, near the end of the tube; it is somewhat larger than the central aperture in the large mirror, and its radius of curvature is iinici. . S Fig. 446. smaller than that of the large mirror. The axes of both mirrors coi| with the axis of the tube. As the centre of curvature of the large mir/or is at O, and its focus at ab, rays, such as SA, emitted from a heavenly body, are reflected from the mirror, M, and form at ab an inverted and! very small image of the heavenly body. The distance of the mirrors and their curvatures is so arranged that the position of this image is between the centre, 0, and the focus,/, of the small mirror ; hence the rays, after being reflected a second time from the mirror N, form at a' b' a magnified and inverted image oiab^ and therefore in the true position of the heavenly body. This image is viewed through an eyepiece, P, which may either be single or compound, its object being to magnify it again so that it is seen at a" b''. As the objects viewed are not always at the same distance, the focus of the large mirror, and therefore that of the small one, vary in position. And as the distance of distinct vision is not the same with all eyes, the image a" b" ought to be formed at different distances. The required ad- justments may be obtained by bringing the small mirror nearer or farther from the larger one ; this is effected by means of a milled head, A (fig. 445), which turns a rod, and this by a screw moves a piece to which the mirror is fixed. 563. The ITewtonian telescope. — This instrument does not differ much from that of Gregory ; the large mirror is not perforated and there IS a sman^i^ne mirror mc'hped at an angle of 45° towards an eyepiece placed in the side of theJele*(iope. The difficulty of constructing metallic mirrors has caused . t^e scxa^ of Gregorian and Newtonian constructioa J -563] Telescopes. 495 to fall into disuse. Of late, however, the process of silvering glass mirrors has been carried to a high state of perfection, and M. Foucault has applied these mirrors to Newtonian telescopes with great success. His first mirror was only four inches in diameter, but he has successively constructed mirrors of 8, 1 2, and 1 3 inches, and at the time of his death had completed one of 32 inches diameter. Fig. 448 represents a Newtonian telescope mounted on an equatoriaL Fij. 448. stand, and fig. 447 gives a horizontal section of it. This section shows how the luminous rays reflected from the parabolic mirror, M, meet a small rectangular prism, ;//;/, which replaces the inclined plane mirror used in 49^ On Light. [563- the old form of Newtonian telescope. After undergoing a total reflection from ;««, the rays form at ab a very small image of the heavenly body. This image is viewed through an eyepiece with four lenses placed on the side of the telescope, and magnifying from 50 to 800 times, according to the sizeof the silvered mirror. In reflectors the mirror acts as object glass, but there is, of course, no chromatic aberration. The spherical aberration is corrected by the form given to the reflector, which is paraboloid, but slightly modified by trial to suit the eye-piece fitted to the telescope. The mirror once polished is immersed in a silvering liquid, which con- sists essentially of ammoniacal solution of nitrate of silver, to which some reducing agent is added. When a polished glass surface is immersed in this solution, silver is deposited on the surface in the form of a brilliant metallic layer, which adheres so firmly that it can be polished with rouge in the usual manner. These new telescopes with glass mirrors have the advantage over the old ones that they give purer images, they weigh less, and are much shorter, their focal distance being only about six times the diameter of the mirror. These details known, the whole apparatus remains to be described. The body of the telescope (fig. 448) consists of an octagonal wooden tube. The end, G, is 6pen ; the mirror is at the other end. At a certain distance from this end, two axles are fixed, which rest on bearings sup- ported by two wooden uprights, A and B. These are themselves fixed to a table, PO, which turns on a fixed plate, RS, placed exactly parallel to the equator. On the circumference of the turning table there is a brass circle, divided into 360 degrees, and beneath it, but also fixed to the turning table, there is a circular toothed wheel, in which an endless screw, V, works. By moving this in either direction by means of the handle w, the table PQ, and with it the telescope, can be turned. A vernier, x., fixed to the plate RS, gives the fractions of a degree. On the axis of the motion of the telescope there is a graduated circle, O, which serves to measure the declitiation of the star, that is, its angular distance from the equator; while the degrees traced round the table, RS, serve to measure the fight ascension, that is, the angle which the declination circle of the star makes with the declination circle passing through the first point of Aries. In order to fix the telescope in declination, there is a brass plate, E, fixed to the upright ; it is provided with a clamp, in which the limb O works, and which can be screwed tight by means of a screw with a milled head, r. On the side of the apparatus there is the eyepiece, 0, which is mounted on a sliding copperplate, on which there is also the small prism inn, represented in section in fig. 447. To bring the image to the right place, this plate may be moved by means of a rack and a milled head, a. The handle, n, serves to clamp or unclainp the screw, V. The drawing was one taken from a telescope, the mirror of which is only 6^ inches in diameter, and which gives a magnifying power of 1 50 to 200. 564. The Kerscbelian telescope. — SirW. Herschel's telescope, which, I 565] Camera Obscura. A97 until recently, was the most celebrated instrument of modern times, was constructed on a method differing from those described. The mirror was so inclined that the image of the star was formed at ab on the side of the telescope near the eyepiece,^; hence it is termed the/r6';z/7/2V7£/ telescope. As the rays in this telescope only undergo a single reflection, the loss of light is less than in either of the preceding cases, and the image is there- fore brighter. The magnifying power is the quotient of the principal focal distance of the mirror by the focal distance of the eyepiece. Herschel's great telescope was constructed in 1789 ; it was 40 feet in length, the great mirror was 50 inches in diameter. The quantity of light obtained by this instrument was so great as to enable its inventor to use magnifying powers far higher than anything which had hitherto been attempted. Herschel's telescope has been exceeded by one constructed by the late Earl of Rosse. This magnificent instrument has a focal length of 53 feet, the diameter of the speculum being six feet. It is at present used as a Newtonian telescope, but it can also be arranged as a front view telescope. INSTRUMENTS FOR FORMING PICTURES OF OBJECTS. 565. Camera obscura. — The camera obscura (dark chamber) is, as its name implies, a closed space impervious to light. There is, however, a small aperture by which luminous rays enter, as shown in fig. 450. The rays, proceeding from external objects, and entering by this aperture, form on the opposite side an image of the object in its natural colours, but of reduced dimensions, and in an inverted position. Porta, a Neapolitan physician, the inventor of this instrument, found that by fixing a double convex lens in the aperture, and placing a white screen in the focus, the image was much brighter, and more definite. Fig. 450 represents a camera obscura, such as is used for drawing. It consists of a rectangular wooden box, formed of two parts which slide in and out. The luminous rays, R, pass into the box by a lens, B, and form an image on the opposite side, O, which is at the focal distance of the lens. But the rays are reflected from a glass mirror, M, inclined at an angle of 45°, and form an image on the ground glass plate, N. When a piece of On Light. [565- tracing paper is placed on this screei), a drawing of the image is easily made. A wooden door, A, cuts off extraneous light. The box is formed of two parts, sliding one within the other, like the joints of a telescope, so that, by elongating it more or less, the reflected image may be made to fall exactly on the screen, N , at whatever distance the object may be situated. Fig. 451 shows another kind of camera obscura, which is occasionally erected in summer houses. In a brass case, A, there is a tri- angular prism, P (fig. 452), which acts both as condens- ing lens and as mirror. One of its faces is plane, but the others have such curvatures that the combined refrac- tions on entering and emerg- ing from the prism produce the effect of a meniscus lens. Hence rays from an object, AB, after passing into the prism and undergoing total reflection from the face cd^ form at abdi real image of AB. In fig. 451, the small I t'ig- 451 table B corresponds to the focus of the prism in the case A, and an image 566] Camera Obsciira. 499 for.ns on a piece of paper placed on the table. The whole is surrounded by a black curtain, so that the observer can place himself in complete darkness. 566. Camera lucida.— The camera lucida is a small instrument de- pending on internal reflection, and serves for taking an outline of any object. It was invented by Dr. Wollaston, in 1804. It consists of a smal four-sided glass prism, of which fig. 453 gives a section perpendicular to the edges. A is a right angle, and C an angle of 135°; the other angles B and D, a are 67^°. The prism rests on a stand, on [—- which it can be raised or lowered, and turned ^ more or less about an axis parallel to the prismatic edges. When the face, AB, is turned towards the object, the rays from the object fall nearly perpendicular on this face, pass into the prism without any appreciable reifraction, and are totally reflected from BC; for as the line ab is perpendicular to BC, and «L to AB, the angle a«L will equal the an ^^rg?:^j[^ is. it will contain 67^°, and this being greater than the critical ^g^feoYglas^^joS), the ray L?/ will undergo total reflection. The rays i*are again totally reflected from o, and emerge near the summit, D, in a direction ^almost .perpendicular to the face DA, so that the eye which re- ceives the i-ays sees at U an image of the object L. If the outlines of the Fig. 452. (k Fig- 453- Fig. 454- image are traced with a pencil, a very correct design is obtained; but un- fortunately there is a great difficulty in seeing both the image and the point of the pencil, for the rays from the object give an image which is farther from the eye than the pencil. This is corrected by placing be- tween the eye and prism a lens, I, which gives to the rays from the pencil and those from the object the same divergence. In this case, however, it is necessary to place the eye very near the edge of the prism, so that the aperture of the pupil is divided into two parts, one of which sees the image and the other the pencil. Amici's camera lucida, represented in fig. 454, is preferable to that of Wollaston, inasmuch as it allows the eye to change its position to a con- 500 On Light. [566- siderable extent, without ceasing to see the image and the pencil at the same time. It consists of a rectangular glass prism, ABC, having one of its perpendicular faces turned towards the object to be depicted, while the other is at right angles to an inclined plate of glass, mn. The rays, LI, proceeding from the object, and entering the prism, are totally re- flected from its base at D, and emerge in the direction KH. They are then partially reflected from the glass plate mn at H, and form a vertical image of the object, L, which is seen by the eye in the direction OL''. The eye at the same time sees through the glass the point of a pencil applied to the paper, and thus the outline of the picture may be traced with great exactness. 567. IMEagrlc lantern. — This is an apparatus by which a magnified image of small objects may be projected on a white screen in a dark room. It consists of a tin plate box, in which there is a lamp placed in the focus of a concave mirror, A (fig. 456). The reflected rays fall upon a condensing lens, B (fig. 455), which concentrates them on the figure painted on a glass plate, V. There is a double convex lens, C, at a dis- tance from V of rather more than its focal distance, and, consequently, a real and very much magnified image of the figure on the glass is produced on the screen (524). Dissolving views are obtained by arranging two magic lanterns, which are quite alike, with diflerent pictures, in such a manner that both pictures Fig. 455. Fig. 456. are produced on exactly the same part of a screen. The object glasses of both lanterns are closed by screens, which are so arranged that according as one is raised the other is lowered, and vice versa. In this way one picture is gradually seen to change into the other. The magnify.ng power of the magic lantern is obtained by dividing the distance of the lens C from the image by its distance from the object. If the image is 100 or 1,000 times farther from the lens than the object, the image will be 100 or 1,000 times as large. Hence a lens with a very short focus can produce a very large image, provided the screen is sufficiently large. I ■** ^^^ -568] Solar Microscope. 501 568. Solar microscope. — The solar microscope is in reality a magic lantern illuminated by the sun's rays ; it serves to produce highly magnified images of very small objects. It is worked in a dark room ; fig. 457 Fig. 457- represents it fitted in the shutter of a room, and fig. 458 gives the internal details. The sun's rays fall on a plane mirror, M, placed outside the room, and are reflected towards a condensing lens, /, and from thence to a second Fig. 458. lens, (fig. 458), by which they are concentrated at its focus. The object to be magnified is at this point ; it is placed between two glass plates, which, by means of a spring, ;z, are kept in a firm position between two metal plates, ;;z. The object thus strongly illuminated is very near the focus of a system of three condensing lenses, x, which forms upon a screen at a suitable distance an inverted and greatly magnified image, ab. The distance of the lenses, and x^ from the object is regulated by means of screws, C and D. As the direction of the sun's hght is continually varying, the position 502 On Light. [568- of the mirror outside the shutter must also be changed, so that the re- flection is always in the direction of the axis of the microscope. The most exact apparatus for this purpose is the heliostat (502) ; but as this instrument is very expensive, the object is usually attained by inclining the mirror to a greater or less extent by means of an endless screw B, and at the same time turning the mirror itself round the lens, /, by a knob A, which moves in a fixed slide. The solar microscope labours under the objection of concentrating great heat on the object, which soon alters it. This is partially obviated by interposing a layer of a saturated solution of alum, which, being a powerfully athermanous substance (407), cuts off a considerable portion of the heat. The magnifying power of the solar microscope may be deduced experi- mentally by substituting for the object a glass plate marked with lines at a distance of Y(> or, ^^^ of a millimetre. Knowing the distance of these lines on the image, the magnifying power may be calculated. The same method is used with the photoelectric light. According to the magnify- ing power which it is desired to obtain, the objective x is formed of one. two, or three lenses, which are all achromatic. The solar microscope furnishes the means of exhibiting to a large audience many curious phenomena, such for instance, as the circulation of blood in the smaller animals, the crystallisation of salts, the occur- rence of animalculae in water, vinegar, etc. 569. Pbotoelectric microscope. — This is nothing more than the solar microscope, which is illuminated by the electric Hght instead of by the sun's rays. The electric light, by its intensity, its steadiness, and the readiness with which it can be procured at any time of the day, is far preferable to the solar light. The photoelectric microscope alone .will be described here : the electric light will be considered under the head of Galvanism. Fig. 459 represents the arrangement devised by M. Duboscq. A solar microscope, ABD, identical with that already described, is fixed on the outside of a brass box. In the interior are two charcoal points which do not quite touch, the space between them being exactly on the axis of the lenses. The electricity of one end of a powerful battery reaches the charcoal, a, by means of a copper wire, K ; while the electricity from the opposite end of the battery reaches ^ by a second copper wire, H. During the passage of the electricity, a luminous arc is formed between the two ends of the carbons, which gives a most brilliant light, and powerfully illuminates the microscope. This is effected by placing at D in the inside of the tube a condensing lens, whose principal focus corre- sponds to the space between the two charcoals. In this manner the luminous rays, which enter the tubes, D and B, are parallel to their axis, and the same effects are produced as with the ordinary solar microscope ; a magnified image of the object placed between two plates of glass is produced on the screen. In continuing the experiment the two carbons become consumed, and 570] Lighthoitse Lenses. 503 to an unequal extent, a more quickly than c. Hence, their distance increasing, the light becomes weaker, and is ultimately extinguished. In speaking afterwards of this electric light, the working of the apparatus, i''ig- 459- P, which keeps these charcoals at a constant distance, and thus ensures a constant light, will be explained. The part of the apparatus, MN, may be considered as a universal photogenic appaj'atiis. The microscope can be replaced by the head pieces of the phantasmagoria, the polyorama, the megascope, by polarising ap- paratus, etc., and in this manner is admirably adapted for exhibiting optical phenomena to a large auditory. Instead of the electric light, we may use with this apparatus the oxy-hydrogen or Drummond's light, which is obtained by heating a cylinder of lime in the flame produced by the combustion of a mixture of hydrogen and oxygen gases. 570. Kigrbtbouse lenses. — Lenses of large dimensions are very dif- ficult of construction ; they further produce a considerable spherical aber- ration, and their thickness causes the loss of much light. In order to avoid these inconveniences, Echelon lenses have been constructed. They consist of a plano-convex lens, C (figs. 460, and 461), surrounded by a series of annular and concentric segments, A, B, each of which has a 504 Oil LigJit. [570- plane face on the same side as the plane face of the central lens, while the faces on the other side have such a curvature that the foci of the different segments coincide in the same point. These rings form, together with the central lens, a single lens, a section of which is represented in fig. 461. The drawing was made from a lens of about 2 feet in diameter, the segments of which are formed of a single piece of glass ; but with larger lenses, each segment is likewise formed of several pieces. Behind the lens there is a support fixed by three rods, on which a body- Fig. 460 can be placed and submitted to the sun's rays. As the centre of the support coincides with the focus of the lens, the substances placed there are melted and volatilised by the high temperature produced. Gold, platinum, and quartz are rapidly melted. The experiment proves that heat is refracted in the same way as light : for the position of the calor- ific focus is identical with that of the luminous focus. Formerly parabolic mirrors were used in sending the light of beacons and lighthouses to gi'eat distances, but they have been supplanted by the use of lenses of the above construction. -571] PJiGiooraphy. 505 lamp of peculiar construction, which gives as much light as 20 moderators. The light is placed in the principal focus of the lens so that the emergent rays form a parallel beam (fig. 401), which loses intensity only by passing through the atmosphere, and can be seen at a distance of above 40 miles. In order that all points of the horizon may be successively illuminated, the lens is continually moved round the lamp by a clockwork motion, the rate of which varies with different lighthouses. Hence, in different parts, the light alternately appears and disappears after equal intervals of time. These alternations serve to distinguish lighthouses from an accidental fire or a star. By means too of the number of times the light disappears in a given time, and by the colour of the light, sailors are enabled to distinguish the lighthouses from one another, and hence to know their position. Of late years the use of the electric light has been substituted for that of oil lamps; a description of the apparatus will be given in a subsequent chapter. PHOTOGRAPHY. 571 . Dag-uerreotype. — Photography is the art of fixing the images of the camera obscura on substances sensitive to light. The various photo- graphic processes may be classed under three heads : photography on metal, photography on paper, and photography on glass. Wedgwood was the first to suggest the use of chloride of silver in fixing the image, and Davy, by means of the solar microscope, obtained images of small objects on paper impregnated with chloride of silver; but no method was known of preserving the images thus obtained, by preventing the further action of light. Niepce, in 18 14, obtained per- manent images of the camera by coating glass plates with a layer of a varnish composed of bitumen dissolved in oil of lavender. This pro- cess was tedious and inefficient, and it was not until 1839 ^^^^-^ the pro- blem was solved. In that year, Daguerre described a method of fixing the images of the camera, which, with the subsequent improvements of Talbot and Archer, has rendered the art of photography one of the most marvellous discoveries ever made, either as to the beauty and per- fection of the results, or as to the celerity with which they are produced. In Daguerre's process, the Daguerreotype^ the picture is produced on a plate of copper coated with silver. This is first very carefully polished, an operation on which much of the success of the subsequent operations depends. It is then rendered sensitive by exposing it to the action of iodine vapour, which forms a thin layer of iodide of silver on the surface. The plate is now fit to be exposed in the camera ; it is sensitive enough for views which require an exposure of ten minutes in the camera, but when greater rapidity is required, as for portraits, etc., it is further exposed to the action of an accelerator^ such as bromine or hypobromite of calcium. All these operations must be performed in a room lighted by a candle, or by the daylight admitted through yellow glass, which cuts off all chemical rays. The plate is preserved from the action of z 5o6 On Light. [571- light by placing it in a small wooden case provided with a slide on the sensitive side. The third operation consists in exposing the sensitive plate to the action of light, placing it in that position in the camera where the image is produced with greatest delicacy. For photographic purposes a camera obscura of peculiar construction is used. The brass tube, A (fig. 462), l> Fig. 462. contains an achromatic condensing lens, which can be moved by means of a rackwork motion, to which is fitted a milled head, D. At the op- posite end of the box is a ground-glass plate, E, which slides in a groove, B, in which the case containing the plate also fits. The camera being placed in a proper position before the object, the sliding part of the box is adjusted until the image is produced on the glass with the utmost sharpness ; this is the case when the glass slide is exactly in the focus. The final adjustment is made by means of the milled head, D. The glass slide is then replaced by the case containing the sensitive plate ; the slide which protects it is raised ; and the plate exposed for a time, the duration of which varies in different cases, and can only be hit exactly by great practice. The plate is then removed to a dark room. No change is perceptible to the eye, but those parts on which the light has acted have acquired the property of condensing mercury : the plate is next placed in a box and exposed to the action of mercurial vapour at 60 or 70 degrees. The mercury is deposited on the parts affected, in the form of globules imperceptible to the naked eye. The shadows, or those parts on which the light has not acted, remain covered with the layer of iodide of silver. This is removed by treatment with hyposulphite of sodium, which dis- solves iodide of silver without affecting the rest of the plate. The plate is next immersed in a solution of chloride of gold in hyposulphite of sodium, which dissolves the silver, while some gold combines with the mercury and silver of the parts attacked, and greatly increases the intensity of the lustre. Hence the light parts of the image aie those on which the mercury 572] Photography. 507 has been deposited, and the shaded those on which the metal has retained its reflecting lustre. -^ Fig. 463 represents a section of the camera and the object glass. At first it consisted of a double convex lens, but now double achromatic lenses, L L', are used as object glasses. They act more quickly than ob- Fig. 463- jectives with a single lens, have a shorter focus, and can be more easily focussed by moving the lens, L', by means of the rack and pinion, D. 572. Photographs on paper. — In Daguerre's process, which has just been described, the images are produced directly on metal plates. With paper and glass, photographs of two kinds may be obtained : those in which an image is obtained with reversed tints, so that the lightest parts have become the darkest on paper, and vice versa ; and those in which the lights and shades are in their natural position. The former are called negative and the \2XX.^x positive pictures. A negative may be taken either on glass or on paper ; it serves to pro- duce a positive picture. Negatives on glass. — A glass plate of the proper size is carefully cleaned ; collodion impregnated with iodide of potassium is then poured upon it ; and the plate moved about till a layer of collodion of uniform thickness is obtained. The plate is then immersed for about a minute in a bath of nitrate of silver containing 30 grains of the salt in an ounce of water. This operation must be performed in a dark room. The plate is then removed, allowed to drain, and when somewhat dry, placed in the closed frame, and afterwards exposed in the camera, for a shorter time than in the case of a Daguerreotype. On removing the plate to a dark room, no change is visible, but on pouring over it a solution called the developer^ an image gradually appears. The principal substances used for developing are protosulphate of iron and pyrogallic acid. The action of light on iodide of silver appears to produce some molecular change, in virtue ©f which the developers have the property of reducing to the metallic state those parts of the iodide of silver which have been most acted upon by the light. When the picture is sufficiently brought out, water is poured over the plate, in order to prevent the further action of the de- veloper. The parts on which light has not acted are still covered with iodide of silver, which would be affected if the plate were now exposed z 2 5o8 On Light. [672- to the light. It is, accordingly, washed with solution of hyposulphite of sodium, which dissolves the iodide of silver and leaves the image un- altered. The picture is then coated with a thin layer of spirit-varnish, to protect it from mechanical injury. When once the negative is obtained, it may be used for printing an indefinite number of positive pictures. For this purpose, paper is impreg- nated with chloride of silver, by immersing it first in solution of nitrate of silver and then in one of chloride of sodium ; chloride of silver is thus formed on the paper by double decomposition. The negative is placed on a sheet of this paper in a copying frame, and exposed to the action of light for a certain time. The chloride of silver becomes acted upon — the light parts of the negative being most affected, and the dark parts least so. A copy is thus obtained, on which the lights of the negative are replaced by shades, and inversely. In order to fix the picture, it is washed in a solu- tion of hyposulphite of sodium, which dissolves the unaltered chloride of silver. The picture is afterwards immersed in a bath of chloride of gold which gives it tone. 573. Positives on grlass. — Very beautiful positives are obtained by preparing the plates as in the preceding cases ; the exposure in the camera, however, is not nearly so long as for the negatives. The picture is then developed by pouring over it a solution of protosulphate of iron, which produces a negative image ; and by afterwards pouring a solution 6f cyanide of potassium over the plate, this negative is rapidly converted into a positive. It is then washed and dried, and a coating of varnish poured over the picture. 574. Pbotog-raplis on albumenised paper and g^lass. — In some cases, paper impregnated with a solution of albumen containing iodide of potassium is used instead of collodion, over which it has the advantage that it can be prepared for some time before it is used, and that it pro- duces certain effects in the middle tints. It has the disadvantage of not being nearly so sensitive. It requires, therefore, longer exposure, and is unsuitable for portraits, but can be advantageously used for views. CHAPTER VI. THE EYE CONSIDERED AS AN OPTICAL INSTRUMENT. 575. Structure of the human eye. — The eye is the organ of vision — thdt is to say, of the phenomenon by virtue of which the light emitted or reflected from bodies excites in us the sensation which reveals their presence. The eye is placed in a bony cavity called the orbit ; it is maintained in its position by the muscles which serve to move it, by the optic nerve, the conjunctiva, and the eyelids. Its size is much the same in all persons : it is the varying aperture of the eyelids that makes the eye appear larger or smaller. -575] Structure of the Human Eye. 509 Fig. 464 represents a transverse section of the eye from back to front. The general shape is that of a spheroid, the curvature of which is greater in the anterior than in the posterior part. It is composed of the follow- ing parts : the ^^r;/^^,the sclerotica^ the iris^ thepupil^ the aqueous humour^ the crystalline, the vitreous body, the hyaloid membrane, the choroid, the retina, and the optic 7ierve. Cornea. — The cornea, a, is a transparent membrane situated in front of the ball of the eye. In shape it resembles a small watch glass, and it fits into the sclerotica, z; in fact, these membranes are so connected that some anatomists have considered them as one and the same, and have distin- guished them by calling the cornea the transpare7it, and the sclerotica the opaque cornea. Sclerotica.— T\iQ sclerotica, /, ox sclerotic coat, is a membrane which together with the cornea, envelopes all parts of the eye. In front there is an almost circular aperture into which the cornea fits ; a perforation behind gives passage to the optic nerve. Iris. — The iris, d, is an annular, opaque diaphragm, placed between the cornea and the crystalline lens. It constitutes the coloured part of the eye, and is perforated by an aperture called^ the pupil, which in man is circular. In some animals, especially those belonging to the genus felis, it is narrow and elongated in a vertical direction ; in the ruminants it is elongated in a transverse direction. It is a contractile membrane, and its diameter varies in the same individual between o'i2 and 0-28 of an inch ; but these limits may be exceeded. The luminous rays pass into the eye through the pupil. The pupil enlarges in darkness, but contracts under the influence of a bright light. These alterations of contraction and enlargement take place with extreme rapidity ; they are very frequent, and play an important part in the act of vision. The movements of the iris are involuntary. It appears from this description that the iris is a screen with a variable aperture, whose function is to regulate the quantity of light which pene- trates into the eye ; for the size of the pupil diminishes as the intensity 510 On Light. [575- of light increases. The iris serves also to correct the spherical aberration, as it prevents the marginal rays from passing through the edges of the crystalline lens. It thus plays the same part with reference to the eye that a diaphragm does in optical instruments (526). Aqueous huinour. — Between the posterior part of the cornea and the front of the crystalline there is a transparent liquid called the aqueous humour. The space, e, occupied by this humour is divided into two parts by the iris ; the part b, between the cornea and the iris, is called the anterior chamber ; the part c, which is between the iris and the crys- talline, is \hQ posterior chamber. Crystalline lens. — This is a double convex transparent body placed immediately behind the iris ; the inner margin of which is in contact with its anterior surface, though not attached to it. The lens is enclosed in a transparent membrane, called its capsule ; it is less convex on its anterior than on its posterior surface, and is composed of almost con- centric layers, which decrease in density and refracting power from the centre to the circumference. To the anterior surface of the capsule, near its margin, is fixed a firm transparent membrane, which is attached behind to the front of the hyaloid membrane, and is known as the suspensory ligament. This ligament exerts a traction, all round, on the front surface of the lens, and renders it less convex than it would otherwise be, and its relaxation plays an important part in the adaptation of the eye for sight at different distances. Vitreous body. Hyaloid 7nembrane. — The vitreous body, or vitreous humour, is a transparent mass resembling the white of an ^%%, which occupies all the part of the ball of the eye, h, behind the crystalline. The vitreous humour is surrounded by the hyaloid membrane, /, which lines the posterior face of the crystalline capsule, and also the internal face of another membrane called the retina. Retina. Optic nerve. — The retina, ;;?, is a membrane which receives the impression of light, and transmits it to the brain by the intervention of a nerve, n, called the optic nerve, which, proceeding from the brain, penetrates into the eye, and extends over the retina in the form of a nervous network. The nerve fibres themselves are not sensitive to light, but are only stimulated by it indirectly through the intervention of certain structures called the 7'ods aiid cones. Where the optic nerve enters, there are no rods or cones ; this part of the retina therefore is insensitive to light and is called the punctum ccEcum. The only property of the retina and optic nerve is that of receiving and transmitting to the brain the impression of objects. These organs have been cut and pricked without causing any pain to the animals submitted to these experiments ; but there is reason to believe that irritation of the optic nerve causes the sensation of a flash of light. Choroid. — The choroid, k, is a membrane between the retina and the sclerotica. It is completely vascular, and is covered on the internal face by a black substance which resembles the colouring matter of a negro's -578] Path of Rays in the Eye. Sir skin, and which absorbs all rays not intended to co-operate in producing vision. The choroid elongates in front, and forms a series of convoluted folds, called ciliary processes, which penetrate between the iris and the crystal- line capsule to which they adhere, forming round it a disc, resembling a radiated flower. By its vascular tissue, the choroid serves to carry the blood into the interior of the eye, and especially to the ciliary processes. 576. Refractive indices of the transparent media of tbe eye. — The refractive indices from air into the transparent parts of the eye have been determined by Brewster. His results are contained in the following table, compared with water as a standard : — Water . 1-3358 Aqueous humour i'3366 Vitreous humour ........ i'3394 Exterior coating of the crystalline 1*3767 Centre of the crystalline i*399o Mean refraction of the crystalline 1*3839 577. Curvatures and dimensions of various parts of tbe buman eye. Radius of curvature of the sclerotica „ „ cornea „ „ anterior face of the crystalline „ „ posterior face Dianieter of the iris . . . , „ „ pupil ... „ „ crystalline Thickness of the crystalline Distance from the pupil to the cornea Length of the axis of the eye 0-40 to 0-44 in. 0-28 to 0-32 „ 0*28 to 0-40 „ 0-20 to 0*24 „ 0-44 to 0-48 „ 0-12 to 0-28 „ 0-40 „ 0*20 „ o'o8 „ 0-88 to 0-96 „ The curvature of the cornea, according to M. Chossat, is that of an ellipsoid of revolution round its major axis, and the curvature of the crystalline that of an ellipsoid of revolution round its minor axis. 578. Path of rays in the eye. — From what has been said as to the structure of the eye it may be compared to a camera obscura (565), of Fig, 465. which the pupil is the aperture, the crystalline is the condensing lens, and the retina is the screen on which the image is formed. Hence, the effect is the same as when the image of an object placed in front of a 512 On Light, [578- double convex lens is formed in its conjugate focus. Let AB (fig. 465) be an object placed before the eye, and let us consider the rays emitted from any point of the object A. Of all these rays those which are directed towards the pupil are the only ones which penetrate the eye, and are operative in producing vision. These rays, on passing into the aqueous humour, experience a first refraction which brings them near the secondary axis ha, drawn through the optic centre of the crystalline ; they then traverse the crystalline, which again refracts them like a double convex lens, and having experienced a final refraction by the vitreous humour, they meet in a point, a, and form the image of the point A. The rays issuing from the point B form in like manner an image of it at the point b^ so that a very small, real, and inverted image is formed exactly on the retina, provided the eye is in its normal condition. 579. Inversion of imag-es. — In order to show that the images formed on the retina are really inverted, the eye of an albino or any animal with pink eyes may be taken ; this has the advantage that, as the choroid is destitute of pigment, light can traverse it without loss. This is then deprived at its posterior part of the cellular tissue surrounding it, and fixed in a hole in the shutter of a dark room ; by means of a lens it may be seen that the inverted images of external objects are depicted on the retina. The inversion of images in the eye has greatly occupied both physicists and physiologists, and many theories have been proposed to explain how it is that we do not see inverted images of objects. The chief diffi- culty seems to have arisen from the conception of the mind or brain as something behind the eye looking into it and seeing the image upon the retina ; whereas really this image simply causes a stimulation of the optic nerve, which produces some molecular change in some part of the brain, and it is only of this change, and not of the image, as such, that we have any consciousness. The mind has thus no direct cognisance of the image upon the retina, nor of the relative positions of its parts, and sight being supplemented by touch in innumerable cases, it learns from the first to associate the sensations brought about by the stimulation of the retina (although due to an inverted image), with the correct position of the object as taught by touch. 580. Optic axis, optic angrle, visual angrle. — T\\q prvicipal optic axis of an eye is the axis of its figure ; that is to say, the straight line in Fig. 466. reference to which it is symmetrical. In a well-shaped eye it is the straight line passing through the centre of the pupil and of the crystal- -581] Estimation of the Size and Distance of Objects. 5 1 3 line, such as the line Oo (fig. 465). The lines Aa, B5, which are almost rectilinear are secondary axes. The eye sees objects most distinctly in the direction of the principal optic axis. The optic -angle is the angle BAC (fig. 466), formed between the principal optic axes of the two eyes when they are directed towards the same point. This angle is smaller in proportion as the objects are more distant. The visual angle is the angle AOB (fig. 467), under which an object is seen ; that is to say, the angle formed by the secondary axes drawn from the optic centre of the crystalline to the opposite extremities of the object. For the same distance, this angle increases with the magnitude of the object, and for the same object it decreases as the distance increases, as is the case when the object passes from AB to A'B.^ It follows, therefore, that objects appear smaller in proportion as they are more distant ; for as the secondary axes, AO, BO, cross in the centre of the crystalline, the size of the image projected on the retina depends on the size of the visual angle, AOB. 5S1. Estimation of tbe distance and size of objects.— The estima- tion of distance and of size depends on numerous circumstances ; these are — the visual angle, the optic angle, the comparison with objects whose size is familiar to us, the diminution of the precision of the image by the interposition of a more or less vaporous medium. When the size of an object is known, as the figure of a man, the height of a tree or of a house, the distance is estimated by the magnitude of the visual angle under which it is seen. If its size is unknown, it is judged relatively to that of objects which surround it. A colonnade, an avenue of trees, the gas lights on the side of a road, appear to diminish in size in proportion as their distance increases, because the visual angle decreases ; but the habit of seeing the columns, trees, etc., in their proper height, leads our judgment to rectify the im- pression produced by vision. Similarly, although distant mountains are seen under a very small angle, and occupy but a small space in the field of view, our familiarity with the effects of aerial perspective enables us to form a correct idea of their real magnitude. The optic angle is also an essential element in appreciating distance. This angle increasing or diminishing according as objects approach or recede, we move our eyes so as to make their optic axes converge towards the object which we are looking at, and thus obtain an idea of its distance. Nevertheless, it is only by long custom that we can establish a relation between our distance from the objects and the corresponding motion of the eyes. It is a curious fact that persons bom bhnd, and whose sight has Z3 514 On Light. [581- been restored by the operation for cataract, imagine at first that all objects are at the same distance. 582. Distance of distinct vision. — The distance of distinct vision is, as already stated, the distance at which objects must be placed so as to be seen with the greatest distinctness. It varies in different individuals, and in the same individual it is often different in the two eyes. For small objects, such as print, it is from 10 to 12 inches in normal cases. In order to obtain an approximate measurement of the least distance of distinct vision, two small parallel slits are made in a card at a distance of 0*03 of an inch. These apertures are held close before the eye, and when a fine slit in another card is held very near these apertures, the slit is seen double, because the rays of light which have traversed both apertures do not intersect each other on the retina, but behind it. But, if the latter card is ;gradually removed, the distance is ultimately reached at which both images coincide and form one distinct image. Stampfer has con- structed an optometer on this principle. Persons altonism. — Achrofnatopsy, or co/oicr disease, is a curious affection which renders us incapable of distinguishing colours, or at any rate certain colours. In some cases the insensibility is complete, while in others some colours can be very well distinguished. Persons affected in this manner can distinguish the outlines of bodies without difficulty, and they can also discriminate between light and shade, but they are unable to distinguish the different tints. D'H ombres- Firmas cites an instance of a person affected with achro- matopsy, who had painted in a room a landscape of which the ground, trees, houses, and men were all painted blue, and when asked why he had not given each its proper colour, he replied that he wished to assimilate the colour of his drawing to that of his furniture ; now this was red. Achromatopsy is also sometimes called Daltonism, because Dalton, who has carefully described it, was so affected. 596. Opbtbalmoscope. — This instrument, as its name indicates, is de- signed for the examination of the eye, and was invented in 1851 by Prof. iH Oh Li^/iL [986- HelmhoUi. It consists ;— i. Of n concave spherical reflector of glass or metal, M (t\>5:s» 474, 475\ in the middle of which is a suiall hole alnnit a sixth of an inch in diameter. The focal lonj;lh of the ivtloctor is ln)ni vS to 10 inches, a. Oi a converginj>~ achromatic K mh is held in fn>nt o( the eye of the patient. 3. Of several ue ionver>;vni, otheJ'S diveiyent, any one of which can be fixed iu ,1 li.une behind the mirror so as to correct any given imperfection in the o))server's si>»ht. ll the niirror is of silvercd j»lass» it is not necessary that it be pierceii at the centre ; it is sntlicient that the silverinj; at the centre be removcii. To ni.iko uso v>f \hc i>phthabnoscope, the patient is placed in a darkened room, and a Lunp tuinished with a sciX'cn put l)eside him, K. The screen serves to shade the light from his head, and keep it in darkness. Vhc oU- Fif . 474' server A, holdings: in one hand the reflector, employs it to concentiaie the light of the lanvp near the eye B of the patient, and with his other hand holds the achromatic lens in front of the eye. Hy this .ui.u\u:c ment the back of the eye is lis;hted up, and its stntcture can bi^ rUnU discerned. Fig. 475 shoM's how the image of the back of the e>*e is prodnced, which the observer A sees on looking through the hole in the reflector. Let ttfi Fif. 47S. be the part of the retina on which the lij^jht is concentrated, pencils of rays proceeding from ad would form an inverted and av^rial imaj;e of afi at a />'. These pencils, however, on leaving the e\"e, pass through the lens <>, and thus the image n''l>" is in fact formed, inverted, but distinct, and in a position tit for vision. 598] Phosphorescence, 525 III': j^rcat quantity of li^lit concentrated by the ophthalmofcope if apt i<> irniiiic painfully the eye of the patient. There arc, therefore, interpo»ed between the lamp and the reflector coloured glaf»ef, to cut off the irri- tating rayj», viz., the red, yellow, and violet ray». The glawet generally employed arc »taincd green or cobalt blue. liy means of the ophthalmoH<;ope flelmholtz ha» found that in an optical point of view no eye is free from defectu. CHAFfEK VII. SOURCES OF T.TCHT. PHOSPHOR ESCEKC15. 597. VarlotM •onroes at lifbt. — The various source* of light arc the Bun, the start, heat, chemical combination, phosphorescence, electricity, and meteoric phenomena. The last two sources will be treated under the articles Electricity and Meteorology. 'ITie origin of the light emitted by the sun and by the stars is unknbwn ; it is assumed that the ignited envelope hjy which the sun is surrounded is gaseous, because the light of the sun, like that emitted from all gaseous bodies, gives no trace of polarisation in the polarising telescope (Chapter VIII.). As regards the light devebped by heat, Pouillct has observed that bodies begin to be luminous in the dark at a temperature of 500* to 600* ; above that the light ia brighter in proportion as the temperature is higher. The luminous effects witnessed in many chemical combinations are flue to the higli temperatures produced. This is the case with the arti- ficial lights used for illuminations; for as we have already seen, luminous flames are nothing more than gaseous matters containing solids heated to the point of incandescence. 598. Fhospboreseenoe : its soiirce*. — Phosphorescence is the pro- perty which a large nurnljer of substances possess of emitting light when placed under certain conditions. M. liecquerel, who has studied this subject in a very comprehensive manner, and has arrived at some extremely remarkable results, refers the phenomena to five causes: — i. Spontaneous phosphorescence in certain vegetables and animals ; for instance, it is very intense in the glow-worm and in the lampyre, and the brightness of their light appears to depend on their will. In tropical climates the sea is often covered with a bright phosphorescent light due to some extremely sirt^ill zoophytes. These animalcula; emit a luminous matter so subtile that MM. (^uoy and Gaimard, during a voyage under the equator, having placed two in a tumbler c;f water, the liquid imme- diately became luminous throughout its entire mass. ii. Phosphorescence by elevation of temperature. This is best seen in certain species of diamonds and in fluorspar, which, when heated to 300^* or 400'^, suddenly becomes luminous, emitting a bluish light. 526 On Light. [598- iii. Phosphorescence by mechanical effects^ such as friction, percussion, cleavage, etc. : for example, when two crystals of quartz are rubbed against each other in darkness, or when a lump of sugar is broken. iv. Phosphorescence by electricity, like that which results from the friction of mercury against the glass in a barometric tube, and especially from the electric sparks proceeding either from an ordinary electrical machine, or from a Ruhmkorff's coil. V. Phosphorescence by isolation or exposure to the sun. A large number of substances, after having been exposed to the action of solar light, or ot the diffused light of the atmosphere, emit in darkness a phosphorescence, the colour and intensity of which depend on the nature and physical con- dition of these substances. This kind of phosphorescence has been studied by M. Becquerel, an abstract of whose researches is given in the next paragraph. 599. Pbospborescence by isolation. — This was first observed in 1604 in Bolognese phosphorus (sulphide of barium), but M. Ed. Becquerel has also discovered it in a great number of substances. The sulphides of calcium and strontium are those which present it in the highest degree. When well prepared, after being exposed to the light, they are luminous for several hours in darkness. But as this phosphorescence takes place in vacuo as well as in a gaseous medium, it cannot be attributed to a chemical action, but rather to a temporary modification which the body undergoes from the action of light. After the substances above named, the best phosphorescents are the following, in the order in which they are placed : a large number of dia- monds (especially yellow), and most specimens of fluorspar ; then arrago- nite, calcareous concretions, chalk, apatite, heavy spar, dried nitrate of calcium, and dried chloride of calcium, cyanide of calcium, a large num- ber of strontium or barium compounds, magnesium and its carbonate, etc. Besides these a large number of organic substances also become phosphorescent by insolation ; for instance, dry paper, silk, cane-sugar, milk-sugar, amber, the teeth, etc. Becquerel finds that the different spectral rays are not equally well fitted to render substances phosphorescent. The maximum effect takes place in the violet rays, or even a little beyond ; while the light emitted by phosphorescent bodies generally corresponds to rays of a smaller re- frangibility than those of the light received by them, and giving rise to the action. The tint which phosphorescent bodies assume is very variable, and even in the same body it changes with the manner in which it is prepared. In strontium compounds green and blue tints predominate ; and orange, yellow, and green tints in the sulphides of barium. The duration of phosphorescence varies also in different bodies. In the sulphides of calcium and strontium phosphorescence lasts as much as thirty hours ; with other substances it does not exceed a few seconds, or even a fraction of a second. Phosphoroscope. In experimenting with bodies whose phosphorescence lasts a few minutes or even a few seconds, it is simply necessary to ex- i -599] Phosphor oscope. 527 pose them to solar or diffused light for a short time, and then place them in darkness : their luminosity is very apparent, especially if care has pre- viously been taken to close the eyes for a few instants. But in the case of bodies whose phosphorescence lasts only a. very short time, this method is inadequate. M. Becquerel has invented a very ingenious ap- paratus, the phosphoroscope^ by which bodies can be viewed immediately after being exposed to light : the interval which separates the insolation and observation can be made as small as possible, and measured with great precision. This apparatus, which is constructed by M. Duboscq, consists of a closed cylindrical box, AB (fig. 476), of blackened metal ; on the ends there are two apertures opposite each other which have the form of a circular sector. One only of these, o, is seen in the figure. The box is fixed, but it is traversed in the centre by a movable axis, to which are fixed two circular screens, MM and PP, of blackened metal (fig. 477). Each of these screens is perforated by four apertures of the same shape as those in the box ; but while the latter correspond to each other, the apertures of the screens alternate, so that the open parts of the one cor- respond to the closed parts of the other. The two screens, as already mentioned, are placed in the box, and fixed to the axis, which by means of a train of wheels, worked by a handle, can be made to turn with any velocity. In order to investigate the phosphorescence of any body by means of this instrument, the body is placed on a stirrup interposed between the two rotating screens. The light cannot pass' at the same time through the opposite apertures of the sides A and B, because one of the closed parts of the screen MM, or of the screen PP, is always between them. So that when a body, a, is illuminated by light from the other side of the apparatus, it could not be seen by an observer looking at the aperture 0, for then it would be masked by the screen PP. Accordingly, when an observer saw the body a, it would not be illuminated, as the light would be intercepted by the closed parts of the screen MM. The body a would alternately appear and disappear ; it would disappear during the time of its being illuminated, and appear when it was no longer so. The time which elapses between the appearance and disappearance depends on the velocity of rotation of the screens. Suppose, for instance, that they made 150 turns in a second ; as one revolution of the screens is effected in ji^y of a second, there would be four appearances and four disappear- ances during that time. Hence the length of time elapsing between the time of illuminatior o-ooo8 of a second. Observations with the phosphoroscope are made in a dark chamber, the observer being on that side on which is the wheelwork. A ray of solar or of electric light is allowed to fall upon the substance «, and the screens being made to rotate more or less rapidly, the body a appears luminous by transparence in a continuous manner, when the interval between insolation and observation is less than the duration of the phos- phoresence of the body. By experiments of this kind, Becquerel has 528 On Light. [600- found that substances which usually are not phosphorescent become so in the phosphoroscope ; such, for instance, is Iceland spar. Uranium compounds present the most brilliant appearance in this apparatus ; they emit a very bright luminosity when the observer can see them 0*03 or Fig. 476. 0*004 ot a second after insolation. But a large number of bodies present no effect in the phosphoroscope ; for instance, quartz, sulphur, phos- phorus, metals, and liquids. CHAPTER VIII. DOUBLE REFRACTION. INTERFERENCE. POLARISATION. 600. The undulatory theory of ligrht. — It has been already stated (469) that the phenomenon of light is, with good reason, ascribed to undulations propagated through an exceedingly rare medium called the luminiferous ether, which is supposed to pervade all space, and to exist -600] Undidatory Theory of Light. 529 between the molecules of the ordinary forms of matter. In a word, it is held that light is due to the undulations of the ether, just as sound is due to undulations propagated through the air. In the latter case the undulations cause the drum of>the ear to vibrate and produce the sensa- tion of sound. In the former case the undulations cause points of the retina to vibrate and 'produce the sensation of Light. The two. cases difler in this, that in the case of sound there is independent evidence of the existence and vibration of the medium (air) which propagates the undulation ; whereas in the case of light the existence of the medium and its vibrations are assumed, because that supposition connects and explains in the most complete manner a long series of very various phenomena. There is, however, no independent evidence of the existence of the lumi- niferous ether. The analogy between the phenomena of sound and light is very close ; thus, the intensity of a sound is greater as the amplitude of the vibration of each particle of the air is greater, and the intensity of light is greater as the amplitude of the vibration of each particle of the ether is greater. Again, a sound is more acute as the length of each undulation producing the sound is less, or, what comes to the same thing, according as the number of vibrations per minute is greater. In like manner, the colour of light is different according to the length of the undulation producing the light : a red light is due to a comparatively long undulation, and coi^- responds to a deep sound, while a violet light is due to a short undula- tion, and corresponds to an acute soimd. Although the length of the undulations cannot be observed directly, yet they can be inferred from certain phenomena with great exactness. The following table gives the length of the undulations corresponding to the light at the principal dark lines of the spectrum. The lengths are given in decimals of an inch^ Dark Length of Line Undulation B ........ . 0-0000271 C . . . . . .. . . 0*0000258 D . 0-0000244 E . 0-0000207 F . . • • • • • • 0-0000191 G . . ... . . . 0-0000169 H ....... . 0-0000155 It will be remarked that the limits are very narrow within which the lengths of the undulations of the ether must be comprised, if they are to be capable of producing the sensation of light. In this respect light is in marked contrast to sound. For the limits are very wide within which the lengths of the undulations of the air may be comprised when they produce the sensation of sound (230). The undulatory theory readily explains the colours of different bodies. According to that theory, certain bodies have the property of exciting undulations of different lengths, and thus producing light of given colours. A A 530 On Light, [600- White light or daylight results from the coexistence of undulations of all possible lengths. The colour of a body is due to the power it has of extinguishing certain vibrations, and reflecting others ; and the body appears of the colour produced by the coexistence of the reflected vibrations. A body appears white when it reflects all different vibrations in the proportion in which they are present in the spectrum : it appears black when it reflects light in such small quantities as not to affect the eye. A red body is one which has the property of reflecting in predominant strength those vibrations which produce the sensation of red. This is seen in the fact that, when a piece of red paper is held against the daylight, and the re- flected light is caught on a white wall, this also appears red. A piece of red paper in the red part of the spectrum appears of a brighter red, and a piece of blue paper held in the blue part appears a brighter blue ; while a red paper placed in the violet or blue part, appears almost black. In the last case the red paper can only reflect red rays, while it extin- guishes the blue rays, and as the blue of the spectrum is almost free from red, so little is reflected that the paper appears black. The undulatory theory likewise explains the colours of transparent bodies. Thus, a vibrating motion on reaching a body sets it in vibration. So also the vibrations of the luminiferous ether are communicated to the ether in a body, and setting it in motion produce light of different colours. When this motion is transmitted through any body, it is said to be trans- parent or translucent^ according to the different degrees of strength with which this transmission is effected.- In the opposite case it is said to be opaque. When light falls upon a transparent body, the body appears colourless if all the vibrations are transmitted in the proportion in which they exist in the spectrum. But if some of the vibrations are checked or extin- guished, the emergent light will be of the colour produced by the coexist- ence of the unchecked vibrations. Thus, when a piece of blue glass is held before the eye, the vibrations producing red and yellow are extin- guished, and the colour is due to the emergent vibrations which produce blue light. The undulatory theory also accounts for the reflection and refraction of light, as well as other phenomena which are yet to be described. The explanation of the refraction of light is of so much importance that we shall devote to it the following article. 60 1. Pbysical explanation of single refraction. — The explanation of this phenomenon by means of the undulatory theory of light presupposes that of the mode of propagation of a plane wave. Now, if a disturbance originated at any point of the ether, it would be propagated as a spherical wave in all directions round that point with a uniform velocity. If, instead of a single point, we consider the front of a plane wave, it is evident that disturbances originate simultaneously at all points of the front, and that spherical waves proceed from each point with the same uniform velocity. Consequently all these spheres will at any subsequent instant be touched by a plane parallel to the original plane. The dis- -602] Explanation of SirigLe Kef raction. 531 turbances propagated from the points in the first position of the wave will mutually destroy each other, except in the tangent plane ; consequently the wave advances as a plane wave, its successive positions being the successive positions of the tangent plane. If the wave moves in the medium with a velocity v^ it will describe a space vt in a time t. Suppose the plane wave, AC (fig. 478), to move through vacuum and Fig. 478. to meet the plane surface, AB, of an ordinary refracting medium at an angle CAB or I. Suppose the velocity of propagation in vaaio to be 7/, and in the medium to be v'. Now the wave entering the medium at A will, after any time /, be moving partly within and partly without the medium. Suppose PR to be the part outside the medium, draw PN at right angles to AC, then PN equals vt. Now in the same time, /, a spherical wave propagated irom A, will have a radius v't\ if, then, PO is drawn, touching a circle whose centre is A and whose radius AQ equals 7/7, then PQ will be the position of the plane wave within the medium at the instant under consideration. If we denote the angle APQ by R it is plain that Sin I : sin R::PN : AQ::^// : v'twv : v\ But a succession of parallel plane waves will give rise to a pencil of parallel rays at right angles to the waves ; consequently, with respect to any one of these rays, I and R are the angles of incidence and retraction. Therefore the ratio of the sines of those angles is constant and equals V : v', which is the distinctive law of single refraction. Moreover, if /u is the refractive index of the substance, v -^ v' equal //, that is, V equals v' ju. Now, under all circumstances, ^ is greater than i, and therefore v is greater than v^\ a result which coincides with that ob- tained from experiment (476). DOUBLE REFRACTION. 602. Double refraction. — It has been already stated (504), that a large number of crystals possess the property of double refraction, in virtue of which a single incident ray in passing through any one of them is divided into two, or undergoes bifurcation, whence it follows that, when an 071 Light, [602 object is seen through one of these crystals, it appears double. The fact of the existence of double refraction in Iceland spar was first stated by Bartholin in 1669, but the law of double refraction was first enunciated exactly by Huyghens in his treatise on light written in 1678, and published in 1690. Crystals which possess this peculiarity are said to be double refracting. It is found to a greater or less extent in all crystals which do not belong to the cubical system. Bodies which crystallise in this system, and those which, like glass, are destitute of crystallisation, have no double refraction. The property can, however, be imparted to them when they are unequally compressed, or when they are cooled quickly after having been heated, in which state glass is said to be ufimmealed. Of all substances, that which possesses it most remarkably is Iceland spar or carbonate of calcium. In many substances the power of double refraction can hardly be proved to exist directly by the bifurcation of an incident ray ; but its existence is shown indirectly by their being able to depolarise light (625). Fresnel has explained double refraction by assuming that the ether in double refracting bcdies is not equally elastic in all directions ; from which it follows that the vibrations, in certain directions at right angles to each other, are transmitted with unequal velocities ; these directions being dependent on the constitution of the crystal. This hypothesis is confirmed by the property which glass acquires of becoming double re- fracting by being unannealed and by pressure. 603. Uniaxial crystals. — In all double refracting crystals there is one direction, and in some a second direction possessing the following pro- perty. When a point is looked at through the crystal in this particular direction, it does not appear double. The lines fixing these directions are called optic axes ; and sometimes, though not very properly, axes of double refraction. A crystal is called uniaxial when it has one optic axis, that is to say, when there is one direction within the crystal along which a ray of light can proceed without bifurcation. When a crystal has tivo such axes, it is called a Max ial crystal. The uniaxial crystals most frequently used in optical instruments are Iceland spar, quartz, and tourmaline. Iceland spar crystallises in rhom- bohedra, whose faces form with each other angles of 105° 5' or 74° 55'. It has eight solid angles (see fig. 479). Of these two, situated at the extremities of one of the diagonals, are severally contained by three obtuse angles. A line drawn within one of these two angles in such a manner as to be equally incHned to the three edges Fig. 479. containing the angle is called the axis of the crystal. If all the edges of the crystal were equal, the axis of the crystal would coincide with the diagonal, ab. Brewster has shown that in all uniaxial crystals the optic axis coincides with the axis of crystallisation. The principal plane with reference to a point of any face of a crystal, -605] Double Refraction. 533 whether natural or artificial, is a plane drawn through that point at right angles to the face and parallel to the optic axis. If in fig. 479 we suppose the edges of the rhombohedron to be equal, the diagonal plane abed contains the optic axis {ab)^ and is at right angles to the faces aedf and chbg ; consequently, it is parallel to the principal plane at any point of either of those two faces. For this reason abed is often called the principal plane with respect to those faces. 604. Ordinary and extraordinary ray.— Of the two rays into which an incident ray is divided on entering a uniaxial crystal, one is called the ordinary and the other the extraordifiary ray. The ordinary ray follows the laws of single refraction, that is, with respect to that ray the sine of the angle of incidence bears a constant ratio to the sine of the angle of refraction, and the plane of incidence coincides with the plane of refrac- tion. Except in particular positions, the extraordinary ray follows neither of these laws. The images corresponding to the ordinary and extraordi- nary rays are called the ordinary and extraordinary images respectively. If a transparent specimen of Iceland spar be placed over a dot of ink, on a sheet of white paper, the two images will be seen. One of them, the ordinary image, will seem slightly nearer to the eye than the other, the extra- ordinary image. Suppose the spectator to view the dot in a direction at right angles to the paper, then, if the crystal, with the face still on the paper, be turned round, the ordinary image will continue fixed, and the extraordinary image will describe a circle round it, the line joining them being always in the direction of the shorter diagonal of the face of the crystal, supposing its edges to be of equal length. In this case it is found that the angle between the ordinary and extraordinary ray is 6° I2^ 605. The laws of double refraction in a uniaxial crystal. — These phenomena are found to obey the following laws: — i. Whatever be the plane of incidence, the ordinary ray always obeys the two general laws of single refraction (504). The refractive index for the ordinary ray is called the ordinary refractive index. < ii. In every section perpendicular to the optic axis the extraordinary ray also follows the laws of single refraction. Consequently in this plane the extraordinary ray has a constant refractive index, which is called the extraordinary refractive index. iii. In every principal section the extraordinary ray follows the second law only of single refraction, that is, the planes of incidence and refraction coincide, but the ratio of the sines of the angles of incidence and refraction is not constant. iv. The velocities of light along the rays are unequal. It can be shown that the difference between the squares of the reciprocals of the velocities along the ordinary and extraordinary rays is proportional to the square of the sine of the angle between the latter ray and the axis of the crystal. There is an important difference between the velocity of the ray and the velocity of the corresponding plane wave. If the velocities of the plane waves corresponding to the ordinary and extraordinary rays are considered, the difference between the squares of these velocities is pro- portional to the square of the sine of the angle between the axis of the 534 On Light [605- crystal and the normal to that plane wave which corresponds to the ex- traordinary ray. The normal and the ray do not generally coincide. Huyghens gave a very remarkable geometrical construction, by means of which the directions of the refracted rays can be determined when the directions of the incident ray and of the axis are known relatively to the face of the crystal. This construction was- not generally accepted by physicists until Wollaston and subsequently Malus showed its truth by numerous exact measurements. 606. Positive and neg-ative uniaxial crystal. — The term extra- ordinary refractive index has been defined in the last article. For the same crystal its magnitude always differs from that of the ordinary re- fractive index : for example, in Iceland spar the ordinary refractive index is I -654, while the extraordinary refractive index is i'483. In this case the ordinary index exceeds the extraordinary index. When this is the case, the crystal is said to be negative. On the other hand, when the extraordinary index exceeds the ordinary index, the crystal is said to be positive. The following list gives the names of some of the principal uniaxial crystals : — Negative Uniaxial Crystals. Iceland spar Emerald Spathose Iron Apatite Tourmaline Pyromorphite Sapphire Ferrocyanide of potassium Ruby Nitrate of sodium Positive Uniaxial Crystals. Zircon Ice Quartz Titanite Apophyllite Boracite 607. Double refraction in biaxial crystals. — A large number of crystals, including all those belonging to the trimetric, the inonoclittic, and the triclinic systems, possess two optic axes ; in other words, in each of these crystals there are two directions along which a ray of light passes without bifurcation. A line bisecting the acute angle between the optic axes is called the medial line ; one that bisects the obtuse angle is called the supplementary line. It has been found that the medial and supple- mentary lines and a third line at right angles to both are closely related to the fundamental form of the crystal to which the optic axes belong. The acute angle between the optic axes is different in different crystals. The following table gives the magnitude of this angle in the case of certain crystals : — Nitre . . 5° 20' Anhydrite . 28° r Strontianite . . 6 56 Heavy spar . • 37 42 Arragonite . . 18 18 Mica . • 45 Brazilian topaz . 49 50 Kyanite - . 81 48 Sugar . . 50 Epidote . 84 19 Selenite . 60 Sulphate of iron . 90 - 608] Interference of L ight. 535 When a ray of light enters a biaxial crystal, and passes in any direction not coinciding with an optic axis, it undergoes bifurcation ; in this case however, neither ray conforms to the laws of single refraction, but both are extraordinary rays. To this general statement the following exception must be made. In a section of a crystal at right angles to the medial line one ray follows the law of ordinary refraction, and in a section at right angles to the supplementary line the other ray follows the laws of ordinary refraction. INTERFERENCE AND DIFFRACTION. 608. Interference of ligrht.— The name interference is given to the mutual action which two luminous rays exert upon each other when they are emitted from two neighbouring sources, and meet each other under a very small angle. This action may be observed by means of the following experiment. In the shutter of a dark room two very small apertures are made, of the same diameter, at a very small distance from each other. The apertures are closed by pieces of coloured glass — red, for example — by which two pencils of homogeneous light are introduced. These two pencils form two divergent luminous cones, which meet at a certain dis- tance ; they are received on a white screen a little beyond the place at which they meet, and in the segment common to the two discs which form upon this screen some very well-defined alternations of red and black bands are seen. If one of the two apertures be closed, the fringes disappear, and are replaced by an almost uniform red tint. From the fact that the dark fringes disappear when one of the beams is intercepted, it is concluded that they arise from the interference of the two pencils which cross obliquely. This experiment was first made by Grimaldi, but was modified by Young. Grimaldi had drawn from it the conclusion that light added to light produced darkness. The full importance of this principle remained for a long time unrecognised, until these enquiries were resumed by Young and Fresnel, of whom the latter, by a modification of Grimaldi's experi- ment, rendered it an exper-imentum cruets of the truth of the undulatory hypothesis. In Grimaldi's experiment diffraction (609) takes place ; for the luminous rays pass by the edge of the aperture. In Fresnel's experiment the two pencils interfere without the possibility of diffraction. Two plane mirrors, AB and BC (fig. 480), of metal, are arranged close to each other, so as to form a very obtuse angle, ABC, which must be very little less than 180°. A pencil of red light, which passes into the dark chamber, is brought, by means of a lens, L, to a focus F. On diverging from F the rays fall partly on AB, and partly on BC. If BA is produced to P and FPF^ is drawn at right angles to AP, and if PFj is made equal to PF, then the rays which fall on AB will, after reflection, proceed as if they diverged from F^. If a similar construction is made for the rays falling on BC, they will proceed after reflection as if they diverged from F2. A little consideration will show that Fj and Fj are 536 On Light, [608 very near each other. Suppose the reflected rays to fall on a screen SS^ placed nearly at right angles to their directions. Every point of the screen -which receives light from both pencils is illuminated by two rays, viz. one from F^, the other from F.^ ; thus the point H is illuminated by two rays, as also are K and I. Now the combined action of these two ^^^-^;::^ pencils is to form a series of parallel bands alternately hght and dark on the screen at right angles to the plane of the paper. This is the funda- mental phenomenon of interference, and that it results from the joint action of the two pencils is plain, since, if the light which falls upon either of the mirrors is cut off, the dark bands disappear. This remarkable fact is explained in the most satisfactory manner by the undulatory theory of light. The explanation exactly resembles that already given of the formation of nodes and loops by the combined action of two aerial waves (253) ; the only difference being that in that case the vibrating particles were supposed to be particles of air, whereas, in the present case, the vibrating particles are supposed to be those of the luminiferous ether. Consider any point K on the screen, and first let us suppose the distances of K from F^ and F2 to be equal. Then the un- dulations which reach K will always be in th-e same phase, and the particle of ether at K will vibrate as if the light came from one source : the amplitude of the vibration, however, will be increased in exactly the same manner as happens at a loop or ventral point; consequently at K the intensity of the light will be increased.^ And the same will be true for all points on the screen, such that the difference between their dis- tarrces from the two images ec^uals the length of o?i€, two, three, etc., undulations. If, on the other hand, the distances of K from Fj and F'o differ by the length of half an undulatnon, then the two waves would reach K in exactly opposite phases. Consequently, whatever velocity would be communicated at any instant to a particle of ether by the one undulation, an exactly equal and opposite velocity would be commu- -609] Diffraction and Fi'inges. 537 nicated by the other undulation, and the particle would be permanently at rest, or there would be darkness at that point; this result being pro- duced in a manner precisely resembling the formation of a nodal point already explained. The same will be true for all positions of K, such that the differences between its distances from F^ and F^ Fig. 490. Fig. 491 Canada balsam 1*549 is less than the ordinary index of Iceland spar 1-654, but greater than its extraordinary index i'483. Hence, when a luminous ray, SC, fig. 491, enters the prism, the ordinary ray under- goes total reflection on the surface ab, and takes the direction CdO, by which it is refracted out of the crystal ; while the extraordinary ray, Ce, emerges alone. Since the Nicol's prism allows only the extraordinary ray to pass, it may be used, like a tourmaline, as an analyser or as a polariser. 623. Physical theory of polarised Ugrht. — The explanation of the dark bands produced by the interference of light is stated in art. 608 to 548 On Light. [623- resemble exactly that of the formation of nodes and loops given in art. 260. It might hence be supposed that the vibrations producing light are similar to those producing sound. But this is by no means the case. In fact, if art. 614 be examined, it will be found that no assumption is there made as to the direction in v^^hich the vibrating particles move, and accordingly that explanation is equally true whether the particles vibrate in the direction AB, BA, or at right angles to AB. As a matter of fact, the former is the case with the vibrations producing sound, the latter with the vibrations producing light. In other words, the vibrations pro- ducing sound take place in the direction of propagation, the vibrations producing light are transversal to the direction of propagation. This assumption as to the direction of the vibration of the particles of ether producing light is rendered necessary, and is justified by the phe- nomena of polarisation. When a ray of light is polarised, all the particles of ether in that ray vibrate in straight lines parallel to a certain direction in the front of the wave corresponding to the ray. When a ray of light enters a double refracting medium, such as Ice- land spar, it becomes divided into two, as we have already seen. Now it can be shown to be in strict accordance with mechanical principles that, if a medium possesses unequal elasticity in different directions, a plane wave produced by transversal vibrations entering that medium will give rise to two plane waves moving with different velocities within the medium, and the vibi-ations of the particles in front of these waves will be in directions parallel respectively to two lines at right angles to each other. If, as is assumed in the undulatory theory of light, the ether exists in a double refracting crystal in such a state of unequal elasticity, then the two plane waves will be formed as above described, and these having different velocities, will give rise to two rays of unequal refrangibility (compare art. 601). This is the physical account of the phenomenon of double refraction. It will be remarked that the vibra^^ions corresponding to the two rays are transversal, rectilinear, and in directions perpendicular to each other in the rays respectively. Accordingly the same theory accounts for the fact that the two rays are both polarised, and in planes at right angles to each other. It is a point still unsettled whether, when a ray of light is polarised with respect to a given plane, the vibrations take place in directions within or perpendicular to that plane. Fresnel was of the latter opinion. It is, however, convenient in some cases to regard the plane of polarisa- tion as that plane in which the vibrations take place. COLOURS PRODUCED BY THE INTERFERENCE OF POLARISED LIGHT. 624. Ziaws of the interference of polarised rays. — After the dis- covery of polarisation, Fresnel and Arago tried whether polarised rays presented the same phenomena of interference as ordinary rays. They were thus led to the discovery of the following laws in reference to the -625] Colours produced by Intcrfererice of Polarised Light. 549 interference of polarised light, and, at the same time, of the brilliant phenomena of colouration, which will be presently described : — I. When two rays polarised in the same plane interfere with each other, they will produce by their interference fringes of the very same kind as if they were common light. II. When two rays of light are polarised at right angles to each other, they produce no coloured fringes in the same circumstances under which two rays of common light would produce them. When the rays are po- larised in planes inclined to each other at any other angles, they produce fringes of intermediate brightness, and if the angle is made to change, the fringes gradually decrease in brightness from 0° to 90°, and are totally obliterated at the latter angle. III. Two rays originally polarised in planes at right angles to each other may be subsequently brought into the same plane of polarisation without acquiring the power of forming fringes by their interference. IV. Two rays polarised at right angles to each other, and afterwards brought into the same plane of polarisation, produce fringes by their interference like rays of common light, provided they originated in a pencil the whole of which was originally polarised in any one plane. V. In the phenomena of interference produced by rays that have suf- fered double refraction, a difference of half an undulation must be allowed, as one of the pencils is retarded by that quantity from some unknown cause. 625. Sffect produced by causing- a pencil of polarised rays to traverse a double refracting- crystal. — The following important ex- periment may be made most conveniently by Norremberg's apparatus (fig. 487). At g (fig. 488) there is a NicoFs prism. A plate of a double refracting crystal cut parallel to its axis is placed on the disc at ^. In the first place, however, suppose the plate of the crystal to be removed. Then, since the Nicol's prism allows only the extraordinary ray to pass when it is turned so that its principal plane coincides with the plane of reflection, no light will be transmitted (622). Place the plate of doubly refracting crystal, which is supposed to be of moderate thickness, in the path of the reflected ray at e. Light is now transmitted through the Nicol's prism. On turning the plate the intensity of the transmitted light varies ; it reaches its maximum when the principal plane of the plate is inclined at an angle of 45° to the plane of reflection, and dis- appears when these planes either coincide with or are at right angles to eaqh other. The light in this case is white. The interposed plate may be called the depolarising plate. The same or equivalent phenomena are produced when any other analyser is used. Thus, assume the double refracting prism to be used. Suppose the depolarising plate to be re- moved. Then, generally, two rays are transmitted ; but if the principal plane of the analyser is turned into the plane of primitive polarisation, the ordinary ray only is transmitted, and then, when turned through 90°, the extraordinary ray only is transmitted. Let the analyser be turned into the former position, then, when the depolarising plate is interposed, both ordinary and extraordinary rays are seen, and when the depolarising 550 On Light. [625^ plate is slowly turned round, the ordinary and extraordinary rays are seen to vary in intensity, the latter vanishing when the principal plane of the polarising plate either coincides with or is at right angles to the plane of primitive polarisation. 626. S£fect produced wben the plate of crystal is very thin. — In order to exhibit this, take a thin film of selenite or mica between the twentieth and sixtieth of an inch thick, and interpose it as in the last article. If the thickness of the film is uniform, the light now transmitted through the analyser will be no longer white, but of a uniform tint ; the colour of the tint being different for different thicknesses — for instance, red, or green, or blue, or yellow, according to the thickness ; the intensity of the colour depending on the inclination of the principal plane of the film to the plane of reflection, being greatest when the angle of inclina- tion is 45°. Let us now suppose the crystalline film to be fixed in that position in which the light is brightest, and suppose its colour to be red. Let the analyser (the Nicol's prism) be turned round, the colour will grow fainter, and when it has been turned through 45°, the colour disappears, and no light is transmitted; on turning it farther, the complementary colour, green, makes its appearance, and increases in intensity until the analyser has been turned through 90°; after which the intensity dimi- nishes until an angle of 135° is attained, when the light again vanishes, and, on increasing the angle, it changes again into red. Whatever be the colour proper to the plate, the same series of phenomena will be observed, the colour passing into its complementary when the analyser is turned. That the colours are really complementary is proved by using a double refracting prism as analyser. In this case two rays are transmitted, each of which goes through the same changes of colour and intensity as the single ray described above, but whatever be the colour and intensity of the one ray in a given position, the other ray will have the same when the analyser has been turned through an angle of 90°. Consequently, these two rays give simultaneously the appearances which are succes- sively presented in the above case by the same ray at an interval of 90°. If now the two rays are allowed to overlap, they produce white light ; thereby proving their colours to be complementary. Instead of using plates of different thickness to produce different tints, the same plate may be employed inclined at different angles to the polar- ised ray. This causes the ray to traverse the film obliquely, and, in fact, amounts to an alteration in its thickness. With the same substance, but with plates of increasing thickness, the tints follow the laws of the colours of Newton's rings (612). The thick- ness of the depolarising plate must, however, be different from that of the layer of air in the case of Newton's rings to produce corresponding colours. Thus corresponding colours are produced by a plate of mica and a layer of air when the thickness of the former is about 400 times that of the latter. In the case of selenite the thickness is about 230 times, and in the case of Iceland spar about 13 times, that of the cor- responding layer of air. -627] Theory of Depolarisation. 551 627. Tbeory of the pbenoxnena of depolarisation. — The phenomena described in the last articles admit of complete explanation by the undu- latory theory, but not without the aid of abstruse mathematical calcula- tions. What follows will show the nature of the explanation. Let us suppose, for convenience, that in the case of a polarised ray the particles of ether vibrate in the plane of polarisation (see art. 610), and that the analyser is a double refracting prism, with its principal plane in the plane of primitive polarisation ; then the vibrations being wholly in that plane have no resolved part in a plane at right angles to it, and, consequently, no extraordinary ray passes through the analyser ; in other words, only an ordinary ray passes. Now take the depolarising plate cut parallel to the axis, and let it be interposed in such a manner that its principal plane makes any angle, {^^) with the plane of primitive polarisation. The effect of this will be to cause the vibrations of the primitive ray to be resolved in the principal plane, and at right angles to the principal plane, thereby giving rise to an ordinary ray (O), and an extraordinary ray (E), which, however, do not become separated on account of the thinness of the de- polarising plate. They will not form a single plane polarised ray on leaving the plate, since they are unequally retarded in passing through it, and consequently leave it in different phases. Since neither of the planes of polarisation of O and E coincides with the principal plane of the analyser, the vibrations composing them will again be resolved by the analyser into vibrations in and at right angles to the principal plane — viz. O gives rise to O^ and Oe and E gives rise to E^ and Y.e. But the vibrations composing Oo and Y.o being in the same plane give rise to a single ordinary ray, I^, and in like manner Oe and E^ give rise to a single extraordinary ray, \e. Thus the interposition of the depolarising plate restores the extraordinary ray. Suppose the angle to be either 0° or 90". In either case the vibra- tions are transmitted through the depolarising plate without resolution, consequently they remain wholly in the plane of primitive polarisation, and on entering the analyser cannot give rise to an extraordinary ray. If the Nicol's prism is used as an analyser, the ordinary ray is sup- pressed by mechanical means. Consequently only \e will pass through the prism, and that for all values of d except 0° and 90°. A little consideration will show that the joint intensities of all the rays existing at any stage of the above transformations must continue constant, but that the intensities of the individual rays will depend on the magnitude of f^, and when this circumstance is examined in detail, it explains the fact that \e increases in intensity as increases from 0° to 45°, and then decreases in intensity as increases from 45° to 90°. In regard to the colour of the rays, it is to be observed that the formulas for the intensities of \o and \e contain a term depending on the length of the wave and the thickness of the plate. Consequently, when white light is used, the relative intensities of its component colours are changed, and, therefore, \o and \e will each have a prevailing tint, which will be different for different thicknesses of the plate. The tints will, however, be comple- mentary, since, the joint intensities of \o and \e being the same as that of 552 On LighU [627- the original ray, they will, when superimposed, restore all the components of that ray in their original intensities, and therefore produce white light. 628. Coloured ring:s produced by polarised lig-bt in traversing double refractingr films — In the experiments with Norremberg's appa- ratus which have just been described (619), a pencil of parallel rays Fig. 492. *< traverses the film of crystal perpendicularly to its faces, and as all parts of the film act in the same manner, there is everywhere the same tint. But when the incident rays traverse the plate under differeMt obliquities, which comes to the same thing as if they traversed plates differing in thickness, coloured rings are formed similar to Newton's rings. The best method of observing these new phenomena is by means of the tourmaline pincette. This is a small instrument consisting of two tourmalines, cut parallel to the axis, each of them being fitted in a copper disc. These two discs, which are perforated in the centre, and blackened, are mounted in two rings of silvered copper, which is coiled, as shown in the figure, so as to form a spring, and press together the tourmalines. The tourmalines turn with the disc, and may be so arranged that their axes are either perpendicular or parallel. The crystal to be experimented upon being fixed in the centre of a cork disc, is placed between the two tourmalines, and the pincette is held before the eye so as to view diffused light. The tourmaline farthest from the eye acts as polariser, and the other as analyser. If the crystal thus viewed is uniaxial, and cut perpendicularly to the axis, and a homogeneous light — red, for instance — is looked at, a series of alternately dark and red rings are seen. With another simple colour similar rings are obtained, but their diameter decreases with the refrangibility of the colour. On the other hand, the diameters of the rings diminish when the thickness of the plates increases, and beyond a certain thickness no more rings are pro- duced. If, instead of illuminating the rings by homogeneous light, white light be used, as the rings of the different colours produced have not the same diameter, they are partially superposed, and produce very brilliant variegated colours The position of the crystal has no influence on the rings, but this is not the case with the relative position of the two tourmalines. P"or instance, in experimenting on Iceland spar cut perpendicular to the axis, and from I to 20 millimetres in thickness, when the axes of the tourmalines are perpendicular, a beautiful series of rings is seen brilliantly coloured, and traversed by a black cross, as shown in fig. i, Plate II. If the axes of the tourmalines are parallel, the rings have tints complementary to those they had at first, and there is a white cross (fig. 1 1^ Plate II.), instead of a black one. V' -629] Coloured Rings produced hi Biaxial Crystals. 553 In order to understand the formation of these rings when polarised light traverses double refracting films, it must first be premised that these films are traversed by a converging conical pencil, whose summit is the eye of the observer. Hence it follows that the virtual thickness of the film which the rays traverse increases with their divergence ; but for rays of the same obliquity this thickness is the same ; hence there result dif- ferent degrees of retardation of the ordinary with respect to the extra- ordinary ray at different points of the plate, and consequently different colours are produced at different distances from the axis, but the same colours will be produced at the same distance from the axis, and conse- quently the colours are arranged in circles round the axis. The arms of the black cross are parallel to the optic axis of each of the tourmalines, and are due to an absorption of the polarised light in these directions. When the tourmalines are parallel the vibrations are transmitted, and hence the white cross. Analogous effects are produced with all uniaxial crystals ; for instance, tourmahne, emerald, sapphire, beryl, mica, pyromorphite, and ferrocya- nide of potassium. 629. Rings in biaxial crystals. — In biaxial crystals, coloured rings are also produced, but their form is more complicated. The coloured bands, instead of being circular and concentric, have the form of curves, with two centres, the centre of each system corresponding to an axis of the crystal. Figs. 4, 5, and ^, Plate II., represent the curves seen when a plate of either Cerussite, topaz, or nitre, cut perpendicularly to the axis, is placed between the two tourmalines, the plane containing the axes of the crystal being in the plane of primitive polarisation. When the axes of the two tourmalines are at right angles to each other, fig. 4, Plate II. is obtained. On turning the crystal without altering the tourmahnes, fig. 5, Plate II. is seen, which changes into fig. 6, Plate II. when the crystal has been turned through 45°. If the axes of the tourmalines are parallel, the same coloured curves are obtained, but the colours are complementary, and the black cross changes into white. The angle of the optic axis in the case of nitre is only 5" 20', and hence the whole system can be seen at once. But when the angle exceeds 20^ to 25°, the two systems of curves cannot be simultaneously seen. There is then only one dark bar instead of the cross, and the bands are not oval, but circular. Fig. 3, Plate II. represents the phenomenon as seen with arragonite. Herschel, who has carefully measured the rings produced by biaxial crystals, refers them to the kind of curve known in geometry as the lemnis- cate, in strict accordance with the results of the undulatory theory of light. The observation of the system of rings which plates of crystals give in polarised light presents a means of distinguishing between optical uniaxial and optical biaxial crystals, even in cases in which no conclu- sion can be drawn as to the system in which a mineral crystallises from mere morphological reasons. In this way, the optical investiga- tion becomes a valuable aid in mineralogy, as, for example, in the case of r. B 554 On Light. [629- mica, of which there are two mineralogical species, the uniaxial and the biaxial. All the phenomena which have been described are only obtained by means of polarised light. Hence a double refracting film, with either a Nicol's prism or a tourmaline as analyser, may be used to distinguish be- tween polarised and unpolarised light— that is, as a polariscope. 630. Colours produced by compressed or by unannealed ^lass. Ordinary glass is not endowed with the power of double refraction. It Fig- 493- Fig- 494- Fig. 495. n Fig. 496. o Fig. 497. Fig. 498. acquires this property, however, if by any cause its elasticity becomes more modified in one direction than in another. In order to effect this, it may be strongly compressed in a given direction, or it may be curved, or tempered— that is to say, cooled after having been heated. If the glass is then traversed by a beam of polarised light, effects of colour are obtained which are entirely analogous to those described in the case of doubly refracting crystals. They are, however, susceptible of far greater variety, according as the plates of glass have a circular, square, rectangular, or triangular shape, and according to the degree of tension of their particles. When the polariser is a mirror of black glass, on which the light of the sky is incident, and the analyser is a Nicol's prism, through which the glass plates traversed by polarised light are viewed, figs. 493, 494, 496, represent the appearances presented successively, when a square plate of compressed glass is turned in its own plane ; figs. 495 and 498 re- present the appearances produced by a circular plate under the same circumstances ; and fig. 497, that produced when one rectangular plate is superposed on another. This figure also varies when the system of plates is turned. Compressed and curved glasses present phenomena of the same kind, which also vary under the same conditions. -632] Origin of Elliptical and Circular Polarisation. 555 ELLIPTICAT., CIRCULAR, AND ROTATORY POLARISATION. 631. Definition of elliptical and circular polarisation. — In the cases hitherto considered the particles of ether composing a polarised ray- vibrate in parallel straight lines ; to distinguish this case from those we are now to consider such light is frequently called plane polarised light. It sometimes happens thaf the particles of ether describe ellipses round their positions of rest, the planes of the ellipses being perpendicular to the direction of the ray. If the axes of these ellipses are equal and parallel, the ray is said to be elliptically polarised. In this case the particles which , when at rest, occupied a straight line, are, when in motion, arranged in a helix round the line of their original position as an axis, the helix chang- ing from instant to instant. If the axes of the ellipses are equal, they become circles, and the light is said to be circularly polarised. If the minor axes become zero, the ellipses coincide with their major axes, and the light becomes plane polarised. Consequently, plane polarised light and circularly polarised light are particular cases of elliptically polarised light. 632. Tbeory oftbe origrin of elliptical and circular polarisation. — Let us in the first place consider a simple pendulum (51) vibrating in any plane, the arc of vibration being small. Suppose that, when in its lowest position, it received a blow in a direction at right angles to the direction of its motion, such as would make it vibrate in an arc at right angles to its arc of primitive vibration, it follows from the law of the composition of velocities (48) that the joint effect will be to make it vibrate in an arc inclined at a certain angle to the arc of primitive vibra- tion, the magnitude of the angle depending on the magnitude of the blow. If the blow communicated a velocity equal to that with which the body is already moving, the angle would be 45°. Next, suppose the blow to communicate an equal velocity, but to be struck when the body is at its highest point, this will cause the particle to describe a circle, and to move as a conical pendulum (53) If the blow is struck under any other circumstances, the particle will describe an ellipse. Now as the' two blows would produce separately two simple vibrations in direc- tions at right angles to each other, we may state the result arrived at as follows : — If two rectilinear vibrations are superinduced on the same particle in directions at right angles to each other, then : i. If they are in the same or opposite phases, they make the point describe a rectilinear vibration in a direction inclined at a certain angle to either of the original vibrations. 2. But if their phases differ by 90° or a quarter of a vibration, the particle will describe a circle, provided the vibrations are equal. 3. Under other circumstances the particle will describe an ellipse. To apply this to the case of polarised light. Suppose two rays of light polarised in perpendicular planes to coincide, each would separately cause the same particles to vibrate in perpendicular directions. Conse- quently — I. If the vibrations are in the same or opposite phases, the 556 On Light. [632- light resulting from the two rays is plane polarised. 2. If the rays are of equal intensity, and their phases differ by 90°, the resulting light is circularly polarised. 3. Under other circumstances the light is ellipti- cally polarised. As an example, if reference is made to arts. 638 and 639, it will be seen that the rays denoted by O and E are superimposed in the manner above described. Consequently, the light which leaves the depolarising plate is elliptically polarised. If, however, the principal plane of the depolarising plate is turned so as to make an angle of 45° with the plane of primitive polarisation, O and E have equal intensities ; and, if further, the plate is made of a certain thickness, so that the phases of O and E may differ by 90°, or by a quarter of a vibration, the light which emerges from the plate is circularly polarised. This method may be employed to produce circularly polarised light. Circular or elliptical polarisation may be either right-handed or left- haiided^ or what is sometimes called dextrogyrate and IcEvogyrate. If the observer looks along the ray in the direction of propagation, from polar- iser to analyser, then, if the particles move in the same direction as the hands of a watch, with its face to the observer, the polarisation is right- handed. 633. Fresnel's rbomb. — This is a means of obtaining circularly polarised light. We have already seen (632) that, to obtain a ray of circularly polarised light, it is sufficient to de- compose a ray of plane polarised light in such a manner as to produce two rays of light of equal intensity polarised in planes at right angles to each other, and differing in their paths by a quarter of an undulation. Fresnel effected this by means of a rhomb, which has received his name. It is made of glass ; its acute angle is 54°, and its obtuse 126°. If a ray, a, fig. 499, of plane polarised light falls perpendicularly on the face AB, it will undergo two total internal reflections at an angle of about 54°, one at E, Pl^ and the other at F, and will emerge perpendicu- larly. If the plane ABCD be inclined at an angle of 45° to the plane of polarisation, the polarised ray will be divided into two coincident rays, with their planes of polarisation at right angles to each other, and it ap- pears that one of them Idses exactly a quarter of an undulation, so that on emerging from the rhomb the ray is circularly polarised. If the ray emerging as above from Fresnel's rhomb is examined, it will be found to differ from plane polarised light in this, that, when it passes through a double refracting prism, the ordinary and extraordinary rays are of equal intensity in all positions of the prism. Moreover, it differs from ordinary light in this, that if it passed through a second rhomb placed parallel to the first, a second quarter of an undulation will be lost, so that the parts of the original plane polarised ray will differ by half an undulation, and -636] Elliptical Polarisation. Rotatory Polarisation. 557 the emergent ray will be plane polarised ; moreover, the plane of polari- sation will be inclined at an angle of 45° to ABCU, but on the other side from the plane of primitive polarisation. 634. Slliptical polarisation. — Our limits will not allow us to enter into this subject, but we may state that, in addition to the method already mentioned (633), elliptically polarised light is generally obtained when- ever plane polarised light suffers reflection. Polarised light reflected from metals becomes elliptically polarised, the degree of ellipticity depending on the direction of the incident ray, and of its plane of polarisation, as well as on the reflecting substance. When reflected from silver, the po- larisation is almost circular, and from galena almost plane. If elliptically polarised light be analysed by the NicoFs prism, it never vanishes, though at alternate positions it becomes fainter ; it is thus distinguished from plane and from circular polarised light. If analysed by Iceland spar neither image disappears, but they undergo changes in intensity. Light can also be polarised elliptically in Fresnel's rhomb. If the angle between the planes of primitive polarisation and of incidence be any other than 45°, the emergent ray is elliptically polarised. 635. Rotatory polarisation. — Rock crystal or quartz possesses a remarkable property which was long regarded as peculiar to itself among all crystals, though it has been since found to be shared by tartaric acid and its salts, together with some other crystalline bodies. This property is called rotatory polarisation, and may be described as follows : — Let a ray of homogeneous light be polarised and let the analyser, say a Nicol's prism, be turned till the light does not pass through it. Take a thin section of a quartz crystal cut at right angles to its axis, and place it between the polariser and the analyser with its plane at right angles to the rays. The light will now pass through the analyser. The phenomenon is not the same as that previously described (625), for, if the rock crystal is turned round its axis, no effect is pro- duced, and if the analyser is turned, the ray is found to \iQ^ plane polarised in a plane inclined at a certain angle to the plane of primitive polarisa- tion. If the light is red, and the plate i millimetre thick, this angle is about 17°. In some specimens of quartz the plane of polarisation is turned to the right hand, in others to the left hand. Specimens of the former kind are said to be right-handed, those of the latter kind left- handed. This difference corresponds to a difference in crystallographic structure. The property possessed by rock crystal of turning the plane of polarisation through a certain angle was thoroughly investigated by M. Biot, who, amongst other results, arrived at this : — For a given colour the angle through which the plane of polarisation is turned is proportional to the thickness of the quartz. 636. Pbysical explanation of rotatory polarisation. — The explana- tion of the phenomenon described in the last article is as follows : — When a ray of polarised light passes along the axis of the quartz crystal, it is divided into two rays of circular ly polarised light of equal intensity, which pass through the crystal with different velocities. In one the circular polarisation is right-handed, in the other left-handed (632). The existence 558 On Light. [636- of these rays was proved by Fresnel, who succeeded in separating them. On emerging from the crystal, they are compounded into a plane polarised ray, but since they move with unequal velocities within the crystal, they emerge in different phases, and consequently the plane of polarisation will not coincide with the plane of primitive polarisation. This can be readily shown by reasoning similar to that employed in art. 632. The same reasoning will also show that the plane of polarisation will be turned to the right or left, according as the right-handed or left-handed ray moves with the greater velocity. Moreover, the amount of the rotation will depend on the amount of the retardation of the ray whose velocity is least— that is to say, it will depend on the thickness of the plate of quartz. In this manner the phenomena of rotatory polarisation can be completely accounted for. , 637. Coloration produced by rotatory polarisation. — The rotation is different with different colours ; its magnitude depends on the re- frangibility, and is greatest with the most refrangible rays. In the case of red light a plate i millimetre in thickness will rotate the plane 17°, while a plate of the same thickness will rotate it 44° in the case of violet light. Hence with white light there will, in each position of the analysing Nicol's prism, be a greater or less quantity of each colour transmitted. In the case of a right-handed crystal, when the Nicol's prism is turned to the right, the colours will successively appear from the less refrangible to the more so — that is, in the order of the spectrum, from red to violet ; with a left-handed crystal in the reverse order. Obviously in turning the Nicol's prism to the left, the reverse of these results will take place. When a quartz plate cut perpendicularly to the »g- soo. ^^.g ^^^ traversed by a ray of polarised light is looked at through a doubly refracting prism, two brilliantly coloured images are seen, of which the tints are complementary ; for their images are partially superposed, and in this position there is a white light (fig. 500). When the prism is turned from left to right, the two images change colours, and as- sume successively all the colours of the spectrum. This will be understood from what has been said about the different rotation for different colours. Quartz rotates the plane of polarisation for red 1 7° for each millimetre, and for violet 44° ; hence from the great difference of these two angles, when the polarised light which has traversed the quartz plate emerges, the various simple colours which it contains are polarised in different planes. Consequently, when the rays thus trans- mitted by the quartz pass through a double refracting prism, they are each decomposed into two others polarised at right angles to each other : the various simple colours are not divided in the same proportion be- tween the ordinary and extraordinary rays furnished by the prism ; the two images are, therefore, coloured ; but, since those which are wanting in the one occur in the other, the colours of the images are perfectly com- plementary. These phenomena of coloration maybe well seen by means of Norrem- -638] Rotatory Power of Liquids. 559 berg's apparatus (fig. 488). A quartz plate, s, cut at right angles to the axis and fixed in a cork disc, is placed on a screen, e ; the mirror, ;/ (fig. 488), - being then so inclined that a ray of polarised light passes through the quartz, the latter is viewed through a refracting prism, ^ ; when this tube is turned, the cemplementary images furnished by the passage of polarised light through the quartz are seen. 638. Rotatory power of liquids. — Biot has found that a great num- ber of liquids and solutions possess the property ot rotatory polarisation. Fig. 501. He has further observed that the deviation of the plane of polarisation can reveal differences in the composition of bodies where none is ex- hibited by chemical analysis. For instance, uncrystallisable grape-sugar deflects the plane of polarisation to the left, while cane-sugar deflects it to the right, although the chemical composition of the two sugars is the same. The rotatory power of liquids is far less than that of quartz. In con- centrated syrup of cane-sugar, which possesses the rotatory power in the highest degree, the power is ^^\h that of quartz, so that it is necessary to operate upon columns of liquids of considerable length — 8 inches for example. Fig. 501 represents the apparatus devised by Biot for measuring the rotatory power of liquids. On a metal groove,^, fixed to a support, r, is a brass tube 20 centimetres long, in which is contained the liquid expe- rimented upon. This tube, which is tinned inside, is closed at each end by 560 On Light. [638- j^lass plates fastened by screw collars. At 7n is a mirror of black glass, in- clined at the polarising angle to the axis of the tubes bd and rt, so that the ray reflected by the mirror ;;z, in the direction bda, is polarised. In the centre of the graduated circle h, inside the tube <7, and at right angles to the axis bda, is a double refracting achromatic prism, which can be turned about the axis of the apparatus by means of a button n. The latter is fixed to a limb c, on which is a vernier, to indicate the number of degrees turned through. Lastly, from the position of the mirror ?«, the plane of polarisation, St?.N>^^ Fig. 509. not the case, for the key would be again supported if the first magnet were presented to it after the removal of the second bar. The attraction which a magnet exerts upon iron is reciprocal, which is indeed a general principle of all attractions. It is easily verified by pre- senting a mass of iron to a movable magnet, when the latter is attracted. 645. Hypotbesis of two magrnetic fluids. — In order to explain the phenomena of magnetism, the existence of two hypothetical magnetic flicids has been assumed, each of which acts repulsively on itself, but attracts the other fluid. The fluid predominating at the north pole of the magnet is called the north fluid or red magnetism, and that at the south pole, the south fluid or blue magnetism. The term ' fluid ' is apt to puzzle beginners, from its ambiguity. Ordinarily the idea of a liquid is associated with the term a fluid ; hence the use of this term to explain the phenomena of magnetism and electricity has produced a widely prevailing impression of the material nature of these two forces. The word fluid, it must be remembered, embraces gases as well as liquids, and here it must be pictured to the mind as representing an invisible, elastic, gaseous atmo- sphere or shell surrounding the particles of all magnetic substances. It is assumed that, before magnetisation, these fluids are combined round each molecule, and mutually neutralise each other ; they can be separated by the influence of a force greater than that of their mutual attraction, and can arrange themselves round the molecules to which they are attached, but cannot be removed from them. The hypothesis of the two fluids is very convenient in explaining mag- netic phenomena, and will be adhered to in what follows. But it must not be regarded as anything more than an hypothesis, and it will afterwards be shown (826) that magnetic phenomena appear to result from electrical cur- rents, circulating in magnetic bodies ; a mode of view which connects the theory of magnetism with that of electricity. 646. Precise definition of poles. — By the aid of the preceding hypo- thesis we are enabled to obtain a clearer idea of the distribution of the magnetism in a magnetised bar, and to account for the circumstance that there is no free magnetism in the middle of the bar, and that it is strongest at the poles. If AB (fig. 5 10) represent a magnet, then the alternate black -646] Definition of Poles. 569 and white spaces may be taken to represent the position of the magnetic fluids in a series of particles after magnetisation ; in accordance with what has been said, the white spaces, representing the south fluid, all point in one direction, and the north fluid in the opposite direction. The last half Fig. 510. of the terminal molecule at one end would have north polarity, and at the other south polarity. Let N represent the north pole of a magnetic needle placed near the magnet AB ; then the south fluid, j, in the terminal mole- cule would tend to attract N, and the north fluid n would tend to repel it ; but as the molecule of south fluid s is nearer N than the molecule of north fluid «, the attraction between j and N would be greater than the repulsion between n and N. Similarly the attraction between s' and N would be greater than the repulsion between n' and N,and so on with the following s" and n'\ etc. And all these forces would give a resultant tending to attract N, whose point of application would have a certain fixed position, which would be the south pole of AB. In like manner it might be shown that the resultant of the forces acting at the other end of the bar would form a north pole, and would hence repel the north pole of the needle, but would attract its south pole. That such a series of polarised particles really acts like an ordinary magnet may be shown by partly filling a glass tube with steel filings, and passing the pole of a strong magnet several times along the outside in one constant direction, taking care not to shake the tube. The individual filings will thus be magnetised, and the whole column of them presented to a magnetic needle will attract and repel its poles just like an ordinary bar magnet, exhibiting a north pole at one end, a south pole at the other, and no polarity in the middle ; but on shaking the tube, or turning out the filings, and putting them in again so as to destroy the regularity, every trace of polarity will disappear. It appears hence that the polarity at each end of a magnet is caused by the fact that the resultant action on a mag- netic body is strongest near the ends, and does not arise from any accu- mulation of magnetic fluids at the ends. The same point may be illustrated by the following experiment, which is due to Grove. In a glass tube with flat glass ends is placed water in which is difl"used magnetic oxide of iron. Round the outside of the tube is coiled some insulated wire. On looking at a light through the tube the liquid appears dark and muddy, but on passing a current of electricity through the wire it becomes clearer (829), This is due to the fact that by the magnetising action of the current, the particles becoming mag- netised, set with their longest dimension parallel to the axis of the tube, in which position they obstruct the passage of light to a less extent. 570 On Magnetism. [647- 647. Experiments with broken niag:nets. — That the two magnetis- ing fluids are present in all parts of the bar, and are not simply accumulated at the ends, is also evident from the following experiment. A steel knitting-needle is magnetised by friction with one of the poles of a magnet, and then, the existence of the two poles and of the neutral line having been ascertained by means of iron filings, it is broken in the middle. But now, on presenting successively the two halves to a magnet, each will be found to possess two opposite poles and a neutral line, and in fact is. a perfect magnet. If these new magnets are broken in turn in two halves, each will be a complete magnet with its two poles and neutral hne, and so on, as far as the division can be continued. It is, therefore, concluded by analogy that the smallest parts of a magnet, the ultimate molecules, contain the two magnetisms. 648. Magrnetic induction. — When a magnetic substance is placed in contact with a magnet, the two fluids of the former become separated ; and so long as the contact remains, it is a' complete magnet, having its two poles and its neutral line. For instance, if a small cylinder of soft iron ab (fig 511), be placed in contact with one of the poles of a magnet, the cyhnder can in turn support a second cyhnder ; this in turn a third J^-> Fi-. 5". and so on, to as many as seven or eight, according to the power of the magnet. Each of these little cylinders is a magnet ; if it be the north pole of the magnet to which the cylinders are attached, the part a will have south, and b north magnetism ; b will in like manner develope in the nearest end of the next cylinder south magnetism, and so on. But these cyhnders are only magnets so long as the influence of a magnetised bar continues. For, if the first cyhnder be removed from the magnet, the other cyhnders immediately drop, and retain no trace of magnetism. The separation of the two magnetisms is only momentary, which proves that the magnet yields nothing to the iron. Hence we may have tejuporary magnets as well as permanent magnets : the former of iron and nickel, the latter of steel and cobalt (643). This action, in virtue of which a magnet can develope magnetism in iron, is called magnetic mdnction or influence, and it can take place without actual contact between the magnet and the iron, as is seen in the following experiment. A bar of soft iron is held with one end near a magnetic needle. If now the north pole of a magnet be approached to the iron without touching it, the needle will be attracted or repelled, accord- ing as its south or north pole is near the bar. For the north pole of the -650] Difference between Magnets and Magnetic Substances. 571 magnet will develope south magnetism in the end of the bar nearest it, and therefore north magnetism at the other end, which would thus attract the south, but repel the north^end of the needle. Obviously, if the other end of the magnet were brought near the iron, the opposite effects would be produced on the needle ; or if the opposite pole of a second magnet of equal strength simultaneously be brought near the iron, the needle would be unaffected, as one magnet would outdo the work of the other. Among other things, magnetic induction explains the formation of the tufts of iron filings which become attached to the poles of magnets. The parts in contact with the magnet are converted into magnets ; these act inductively on the adjacent parts, these again on the following ones, and so on producing a filamentary arrangement of the filings. 649. Coercive force. — We have seen from the above experiments that soft iron becomes instantaneously magnetised under the influence of a magnet, but that this magnetism is not permanent, and ceases when the magnet is removed. Steel likewise becomes magnetised by contact with a magnet, but the operation is effected with difficulty, and the more so as the steel is more highly tempered. Placed in contact with a magnet, a steel bar acquires magnetic properties very slowly, and to make the magnetism complete, the steel must be rubbed with one of the poles. But this magnetism, once evoked in steel, is permanent,, and does not disappear when the inducing force is removed. These different effects in soft iron and steel are ascribed to a coercive force, which, in a magnetic substance, offers a resistance to the separation of the two magnetisms, but which also prevents their recom.bination when once separated. In steel this coercive force is very great, in soft iron it js very small or almost absent. By oxidation, pressure, or torsion, a certain amount of coercive force may be imparted to soft iron : and by heat, hammering, etc., the coercive force may be lessened, as will be afterwards seen. 650. Difference between magrnets and magnetic substances. — Mag7ietic substances are substances which, like iron, steel, nickel, are attracted by the magnet. They contain the two fluids, but in a state of neutralisation. Compounds containing iron are usually magnetic, and the more so in proportion as they contain a larger quantity of iron. Some, however, like iron pyrites, are not attracted by the magnet. A magnetic substance is readily distinguished from a magnet. The former has no poles ; if successively presented to the two ends of a mag- netic needle, ab (fig. 508), it will attract both ends equally, while a mag- net would attract the one, but repel the other. Magnetic substances also have no action on each other, while magnets attract or repel each other, according as unhke or like poles are presented. Iron is not the only substance which possesses magnetic properties ; nickel has considerable magnetic power, but far less than that of iron ; cobalt is less magnetic than nickel; while to even a slighter extent chromium and manganese are magnetic. Further, we shall see that powerful magnets exert a peculiar influence on all substances. 572 On Magnetism. [651- w- A' ^^^ i^'^r On Magnetism. v>' CHAPTER II. TERRESTRIAL MAGNETISM. COMPASSES 1 651. Directive action of the eartb on magrnets. — When a mag- netised needle is suspended by a thread, as represented in fig. 508, or ■^ when placed on a pivot on which it can move freely (fig. 512), it ultimately sets in a position which is more or less north and south. If removed from this position it always re- .' ' turns to it after a certain number of oscil- lations. Analogous observations have been made in different parts of the globe, from which the earth has been compared to an S,.-' ) . immense magnet, whose poles are very near the terrestrial poles, and whose neutral line virtually coincides with the equator. The polarity in the northern hemis- phere is called the northern or boreal polarity and that in the southern hemis- phere the southern or austral polarity. In French works the end of the needle pointing north is called the austral or southern pole, and that pointing to the south, the boreal or northern pole ; a designation based on this hypothesis of a terrestrial magnet, and on the law that unlike magnetisms attract each other. In practice it will be found more convenient to use the English names, and call that end of the magnet which points to the north the north pole, and that which points to the south the south pole. To avoid ambiguity that end of the needle pointing north is in England sometimes spoken of as the marked end of the needle. 652. Terrestrial magnetic couple. — From what has been stated, it is clear that the magnetic action of the earth on a magnetised needle may be compared to a couple., that is, to a system of two equal forces, parallel, but acting in contrary directions. For let ab (fig. 513) be a movable magnetic needle making an angle with the magnetic meridian MM' (653). The earth's north pole acts attractively on the marked pole, a, and repulsively on the other pole, b, and two contrary forces are produced, an, and bn' , which are equal and parallel : for the terrestrial pole is so distant, and the needle so small, as to justify the assumption that the two directions an, and bn', are parallel, and that the two poles are equidistant from the earth's north pole. But the earth's south pole acts similarly on the poles of the needle, and pro- duces two other forces, as and bs', which are also equal and parallel, but the two forces an and as may be reduced to a single resultant rtN (33) and the forces bn' and bs' to a resultant b^ ; these two forces ^zN and /^S are equal, parallel, and act in opposite directions, and they constitute the -653] Magnetic Elements. Declination. 573 terrestrial inagtietic couple ; it is this couple which makes the needle set ultimately in the magnetic meridian, a position in which the two forces N and S are in equilibrium. M Fig. 513- The force which determines the direction of the needle thus is neither attractive nor repulsive, but simply directive. If a small magnet be placed on a cork floating in water, it will at first oscillate, and then gradually set in a line which is virtually north and south. But if the surface of the water be quite smooth, the needle will not move either towards the north or towards the south. If, however, a magnet be approached to a floating needle, attraction or repulsion ensues, according as one or the other of the poles is presented. The reason of the different actions exerted by the earth and by a magnet on a floating needle is as follows : — When the north pole, for instance, of the magnet is presented to the south pole of the needle, the latter is attracted ; it is, however, repelled by the south pole of the magnet. Now the force of magnetic attraction or repulsion decreases with the distance, and as the distance between the south pole of the needle and the north pole of the magnet is less than the distance between the south pole of the needle and the south pole of the magnet, the attraction predominates over the repulsion, and the needle moves towards the magnet. But the earth's magnetic north pole is so distant from the floating needle that its length may be considered infinitely small in comparison, and one pole of the needle is just as strongly repelled as the other is attracted. 653. Mag-netic elements. Declination. — In order to obtain a full knowledge of the earth's magnetism at any place three essentials are requisite, these are : i. Declination; ii. Inclination; iii. Intensity. These three are termed the magnetic elements of the place. We shall explain them in the order in which they stand. The geographical meridian of a place is the imaginary plane passing through this place and through the two terrestrial poles, and the meridian is the outline of this plane upon the surface of the globe. Similarly the magnetic meridian of a place is the vertical plane passing at this place through the two poles of a- movable magnetic needle in equilibrium about its vertical axis. In general the magnetic meridian does not coincide with the geogra- phical meridian, and the angle which the magnetic makes with the geo- graphical meridian, or, what is the same thing, the angle which the direction of the needle makes with the meridian, is called the declination or varia- tio7i of the magnetic needle. The declination is said to be east or wesfy 574 On Magnetism. [653 Year Declination Year 1580 . I r° 30' E. 1825 1663 1830 1700 . 8° 10' W. 1835 1780 . . 19° 55' W. 1850 1785 . 22° W. 1855 1805 . 22° 5'W. i860 1814 . 22° 34' W. 1865 1874 according as the north pole of the needle is to the east or west of the geographical meridian. 654. Variations in declination. — The declination of the magnetic needle, which varies in dififerent places, is at present west in Europe and in Africa, but east in Asia and in the greater part of North and South America. It shows further considerable variations even in the same place ; these variations are of two kinds ; some are regular, and are either secular, annual, or diurnal ; others, which are irregular, are called perturbations or magnetic storms. Secular variatiotis. — ln the same place, the declination varies in the course of time, and the needle appears to make oscillations to the east and west of the meridian, the duration of which extends over centuries. The declination has been known at Paris since 1580, and the following table represents the variations which it has undergone : — Declination . 22° 22' W. . 22° 12' W. . 22° 4'W. . 20° 30' \^^ . i9°57'W. . 19° 32' w. . i8°44'W. . 17° 25 W. This table shows that since 1580 the declination has varied at Paris as much as 34°, and that the greatest westerly declination was attained in 1 8 14, since which time the needle has gradually tended towards the east. At London, the needle showed in 1580 an east declination of 11° 36'; in 1663 it was at zero ; from that time it gradually tended towards the west, and reached its maximum declination of 24° 41' in 1818 ; since then it has steadily diminished; it was 22° 30' in 1850, 19° 32' in 1873, and is now (1875) 19° 16' W. At Yarmouth and Dover the variation is about 40' less than at London; at Hull and Southampton about 20' greater ; at Newcastle and Swansea about 1° 45', and at Liverpool 2° o', at Edinburgh 3° o', and at Glasgow and Dublin about 3° 50', greater than at London. The following are the observations of the magnetic elements at Kew for the last ten years : — Year 1865 . 1866 . 1867 . 1868 . 1869 . 1870 . 1871 . 1872 . 1873 • 1874 . Declination Inclination Horizontal Intensity • . 20° 59' 68° 7' 3-829 . 20° 51' 68° 6' 3-837 . 20° 40' 68° 3' 3-844 . . 20° 33' 68° 2' 3-848 . 20° 25' 68° V 3-852 . 20° 19' 67° 58' 3-857 . 20° 10' 67° 57' 3-863 . 20° 0' 67° 54' 3-869 . . 19° 57' 67° 52' 3-877 . . 19° 52' 67' 50' 3-881 00 w -656] Accidental Magnetic Variations, 575 In certain parts of the earth the magnet coincides with the geographical meridian. These points are connected by an irregularly curved imaginary line, called a line of 110 variation, or agojiic line. Such a line cuts the east of South America, and, passing east of the West Indies, enters North America near Philadelphia, and traverses Hudson's Bay ; thence it passes through the North Pole, entering the Old World east of the White Sea, traverses the Caspian, cuts the east of Arabia, turns then towards Australia, and passes through the South Pole, to join itself again. Isogonic lines are lines connecting those places on the earth's surface in which the declination is the same. The first of the kind was constructed in 1700 by Halley ; as the elements of the earth's magnetism are continu- ally changing, the course of such a line can only be determined for a certain time. One of the newest set of isogonic hnes has been constructed by Captain Evans for the year 1857, and is given in the British Asso- ciation Report for i86r. Maps on which such isogonic lines are depicted are called declination maps ; and a comparison of these in various years is well fitted to show the variations which this magnetic element undergoes. Plate III. represents a map in Mercator's projection giving these lines for the year i860. It extends from 80° N. to 60° S. latitude, and from the nature of the case cannot include both poles, for which a map in polar projection is needed. The figures attached to the red lines represent the observed angles of declination ; the dotted red lines are the result of calculation. 655. Annual variations. — Cassini first discovered in 1780 that the declination is subject to small annual variations. At Paris and London it is greatest about the vernal equinox, diminishes from that time to the summer solstice, and increases again during the nine following months. It does not exceed from 15^ to 18', and it varies somewhat at different epochs. The diurnal variations \i^x^ first discovered by Graham in 1722 ; they can only be observed by means of long needles or delicate indicators such as the reflection of a ray of light and very sensitive instruments (664). In this country the north pole moves every day from east to west from sunrise until one or two o'clock ; it then tends towards the east, and at about ten o'clock regains its original position. During the night the needle is almost stationary. Thus the westerly declination is greatest during the warmest part of the day. At Paris the mean amplitude of the diurnal variation from April to September is from 13' to 15', and for the other months from 8' to 10'. On some days it amounts to 25', and on others does not exceed 5'. The greatest variation is not always at the same time. The amplitude of the daily variations decreases from the poles towards the equator, where it is very feeble. Thus in the island of Rewak it never exceeds 3' to 4'. 656. Accidental variations and perturbations. — The declination is accidentally disturbed in its daily variations by many causes, such as earthquakes, the aurora borealis, and volcanic eruptions. The effect ot the aurora is felt at great distances. Auroras which are only visible in the north of Europe act on the needle even in these latitudes, where 5/6 On Magnetism. [656- accidental variations of i° or 2° have been observed. In polar regions the needle frequently oscillates several degrees ; its irregularity on the day before the aurora borealis is a presage of the occurrence of this pheno- menon. Another remarkable phenomenon is the simultaneous occurrence of magnetic perturbations in very distant countries. Thus Sabine mentions a magnetic disturbance which was felt simultaneously at Toronto, the Cape, Prague, and Van Diemen's land. Such simultaneous perturbations have received the name of magnetic storms. 657. Declination compass. — The declination compass is an instrument by which the magnetic declination of any place may be measured when its astronomical meridian is known. It consists of a brass box, AB (fig. 514), in the bottom of which is a graduated circle, M. In the centre is a pivot, on which oscillates a very light lozenge-shaped magnetic wheel, ab. Fig. 514- To the box are attached two uprights supporting a horizontal axis, X, on which is fixed an astronomical telescope, L, movable in a vertical plane. The box rests on a foot, P, about which it can turn in a horizontal plane, taking with it the telescope. A fixed circle, OR, which is called the azitmithal circle^ serves to measure the number of degrees through which the telescope has been turned, by means of a vernier, V, fixed to the box. The inclination of the telescope, in reference to the horizon, -659] Mariner's Compass. S77 > may be measured by another vernier, K, which moves with the axis of the telescope, and is read off on a fixed graduated arc, x. The first thing in determining the decHnation is to adjust the compass horizontally by means of the screws, SS, and the level, Ji. The astro- nomical meridian is then found either by an observation of the sun at noon exactly, or by any of the ready methods known to astronomers. The box, AB, is then turned until the telescope is in the plane of the astro- nomical meridian. The angle made by the magnetic needle with the diameter, N, which corresponds with the zero of the scale, and is exactly in the plane of the telescope, is then read off on the graduated limb, and this is east or west, according as the pole, a, of the needle stops at the east or west of the diameter, N. <^ 658. Correction of errors. — These indications of the compass are only correct when the magnetic axis of the needle, that is, the right line passing through the two poles, coincides with its axis of figure, or the hne connecting its two ends. This is not usually the case, and a correction must therefore be made, which is done by the method of 7-eversion. For this purpose the needle is not fixed in the cap, but merely rests on it, so that it can be removed and its positions reversed ; thus what was before the lower is now the upper face. The mean between the observations made in the two cases gives the true declination. For, let NS be the astronomical meridian, ab the axis of figure of the needle, and inn its magnetic axis (fig. 515). The true dechnation is not the arc N^; but the arc N;;z, which is greater. If now the needle be turned, the line mn makes the same angle with the meridian NS ; but the north end of the needle which was on the right of nui is now on the left (fig. 516), so that the declination which was previously too small by a certain amount; is now too large by the same amount. Hence the true declination is given by the mean of these two observations. 659. Mariner's compass. — The magnetic action of the earth has received a most important application in the fnariner's compass. This is a declination compass used in guiding the course of a ship. Figure 517 represents a view of the whole, and figure 518 a vertical section. It con- C C 578 On Magnetism. [659- sists of a cylindrical case, which to keep the compass in a horizontal position in spite of the rolling of the vessel, is supported on gimbals. These are two concentric rings, one of which, attached to the case itself. moves about the axis cd, which plays in the outer ring AB, and this moves in the supports PQ, about the axis mil at right angles to the first. In the bottom of the box is a pivot, on which is placed by means of an agate cap, a magnetic bar ab^ which is the needle of the compass. On this is fixed a disc of mica, a little larger than the length of the needle, Fig. 51S. on which is traced a star or rose with thirty-two branches, making the eight points or rhumbs of the wind, the demi-rhumbs and the quarters. The branch ending in a small star and called N, corresponds to the bar abj which is underneath the disc. The compass is placed near the stern of the vessel in the bifuiade. Knowing the direction of the compass in which the ship is to be steered, the pilot has the rudder turned till the direction coincides with the sight vane passing through a line d marked on the inside of the box, and parallel with the keel of the vessel. Neither the inventor of the compass, nor the exact time of its invention, is known. Guyot de Provins, a French poet of the twelfth century, first mentions the use of the magnet in navigation, though it is probable that the Chinese long before this had used it. The ancient navigators, who -660] Magnetic Inclinatioji. 579 were unacquainted with the compass, had only the sun or pole star as a guide, and were accordingly compelled to keep constantly in sight of land for fear of steering in a wrong direction when the sky was clouded. 660. Inclination. XVKagrnetic equator. — It might be supposed from the northerly direction which the magnetic needle takes, that the force acting upon it is situated in a point of the horizon ; this is not the case,, for if the needle be so arranged that it can move freely in a vertical plane about a horizontal axis, it will be seen that, although the centre of gravity of the needle coincides with the centre of suspension, the north pole ir our hemisphere dips downwards. In the other hemisphere the south pole is inclined downwards. The angle which the magnetic needle makes with the horizon, when the vertical plane, in which it moves, coincides with the magnetic meridian, is called the inclijiation or dip of the needle. In any other Fig. 519. plane than the magnetic meridian, the inclination increases^ and is 90° in a plane at right angles to the magnetic meridian. For the magnetic inclination is the resultant of two forces, one acting in a horizontal and the other in a vertical plane. When the needle is moved so that it is at right angles to the magnetic meridian, the horizontal component can only act in the direction of the axis of suspension, and, therefore, cannot affect the needle, which is then solely influenced by the vertical component, and stands vertically. The following considerations will make this clearer : — Let NS (fig. 519) represent a magnetic needle capable of moving in a vertical plane. Let NT represent in direction and intensity the entire force of the earth's magnetism acting on the pole N. Then NT can be resolved into the forces N/^ and NV ; TN/^ being the angle of inclination or dip. 1\^T is termed the total force, and its components are N/^, or the horizontal force, and NV, or the vertical force. Now, it is clear that the greater the angle of dip, TN/^, the less becomes N//, or the horizontal force, and the greater NV, or the vertical force. Hence, in high latitudes the directive force of a compass, which depends on the horizontal force, is less than in low latitudes. At the magnetic poles the horizontal force will be nil, and the vertical force a maximum ; here, therefore, the needle will be vertical. At the magnetic equator the reverse is the case, and the needle will be horizontal. Hence, the oscillations of a compass needle, by which, as will presently be explained, c c 2 58o On Magnetism. [660- the strength of the earth's magnetism is measured, become fewer and fewer in a given time as the magnetic poles are approached, although there is really an increase in the total force of the earth. Again, the reason why a dipping-needle stands vertical when placed E. and W. is clearly because in those positions the horizontal force now acting at right angles to the plane of motion of the needle is ineffectual to move it, and therefore merely produces a pressure on the pivot which supports the needle. But the vertical component of the total force remains unaffected by the new position of the needle. Acting, therefore, entirely alone when the dipping-needle is exactly E. and W., this vertical component drags the needle into a line with itself, that is 90° from the horizontal plane. The value of the dip, like that of the declination, differs in different localities. It is greatest in the polar regions, and decreases with the latitude to the equator, where it is approximately zero. In London at the present time, 1875, the dip is 67° 42', reckoning from the horizontal line. In the southern hemisphere the inclination is again seen, but in a contrary direction, that is, the south pole of the needle dips below the horizontal line. The inag7ietic poles are those places in which the dipping-needle stands vertical, that is, where the inclination is 90°. In 1830 the first of these, the terrestrial north pole, was found by Sir James Ross in 96° 43' west longitude and 70° north latitude. The same observer found in the South Sea, in 76° south latitude and 168° east longitude, that the inclination was 88° 37^ From this and other observations, it has been calculated that the position of the magnetic south pole was at that time in about 1 54° east longitude and 75^° south latitude. The line of no declination passes through these poles, and the lines of equal declination converge towards them. The magnetic equator or aclinic line is the line which joins all those places on the earth where there is no dip, that is, all those in which the dipping-needle is quite horizontal. It is a somewhat sinuous hne, not differing much from a great circle inclined to the equator at an angle of 12°, and cutting it in two points almost exactly opposite each other, one in the Atlantic and one in the Pacific. These points appear to be gradually moving their position and travelling from east to west. Lines connecting places in which the dipping-needle makes equal angles are called isocli7iic lines. Plate IV. is an inclination map for the year i860, the construction of which is quite analogous to that of the map of declination. The incHnation is subject to secular variations, like the dechnation , as is readily seen from a comparison of maps of inclination for different epochs. At Paris, in 167 1, the inclination was 75°; since then it has been continually decreasing, in 1835 it was 67° 14' ; in 1849 67° ; in 1859 66° 14' ; and in 1874 65° 23^ The following table gives the alterations in the inclination at London, from which it will be seen that since 1723, in which it was at its maximum, it has continually diminished by about 2° 6' in a year. -661] Inclination Compass. 581 Year Inclination Year Inclination 1576 . 7i°5o' . 1800 • . 70° 35' 1600 . 72° 182I 70° 31' 1676 . . 73° 30' . 1828 . . 69° 47' 1723 . . 74° 42' . 1838 . 69° 17' 1773 . • 72° 19' . • 1854 68° 31' 1780 72° 8' . . 1859 68° 21' 1790 . . 71° 33' . . 1874 67° 43' 661. Inclination compass. — An inclination compass is an instrument for measuring the magnetic inclination or dip. It consists of a graduated horizontal brass circle, in (fig. 520), supported on three legs, provided with Fig. 520. levelling screws. Above this circle there is a plate, A, movable about a vertical axis, and supporting, by means of two columns, a second graduated circle, M, which measures the inclination. The needle rests on a frame, r, and the diameter passing through the two zeros of the circle, M, can be ascertained to be perfectly horizontal by means of the spirit level, n. To observe the inclination, the magnetic meridian must first be deter- mined, which is effected by turning the plate A on the circle ?;z, until the needle is vertical, which is the case when it is in a plane at right angles to the magnetic meridian (660). The plate A is then turned 90° on the circle ;-^, by which the vertical circle, M, is brought into the magnetic meridian. The angle, dca, which the magnetic needle makes with the horizontal diameter is the angle of inclination. There are here several sources of error, which must be allowed for. 582 On Magnetism. • [661- The most important are three : — i. The magnetic axis of the needle may not coincide with its axis of figure : hence an error, which is corrected by a method of reversion analogous to that already described (658). ii. The centre of gravity of the needle may not coincide with the axis of suspen- sion, and then the angle, dca^ is too great or too small, according as the centre of gravity is below or above the centre of suspension ; for in the first case the action of gravity is in the same direction as that of mag- netism, and in the second is in the opposite direction. To correct this error, the poles of the needle must be reversed by first demagnetising it, and then imparting a contrary magnetism to what it had at first. The inchnation is now redetermined, and the mean taken of the results ob- tained in the two groups of operations, iii. The plane of the ring m.ay not coincide with the true magnetic meridian. It should be in that plane when the needle has its minimum deviation; an observation of this kind should therefore be taken along with that previously described, by which the needle is moved 90° from its maximum deviation. 662. Astatic needle and astatic system. — An astatic needle is one which is uninfluenced by the earth's magnetism. A needle movable about an axis in the plane of the magnetic meridian and parallel to the inchnation would be one of this kind; for the terrestrial magnetic couple acting then in the direction of the axis cannot impart to the needle any determinate direction. An astatic system is a combination of two needles of the same force joined parallel to each other with the poles in contrary direc- tions, as shown in fig. 521. If the two needles have exactly the same magnetic force, the opposite action of the earth's magnetism on the poles a' and b and on Fig. 521. the poles a and b' counterbalance each other ; the system is then completely astatic, and sets at right angles to the magnetic meridian. A single magnetic needle may also be rendered astatic by placing a magnet near it. By repeated trials a certain position and distance can be found at which the action of the magnet on the needle just neutralises that of the earth's magnetism, and the needle is free to obey any third force. 663. Intensity of the eartb's magrnetism. — If a magnetic needle be moved from its position of equilibrium, it will revert to it after a series of oscillations, which follow laws analogous to those of the pendulum {^']). If the magnet be removed to another place, and caused to oscillate during the same length of time as the first, a difl"erent number of oscillations will be observed. And the intensity of the earth's magnetism in the two places will be respectively proportional to the squares of the number of oscillations. If at M the number of oscillations in a minute had been 25 =;/, and at another place, M^, 24 = ?/', we should have — Intensity of the earth's magnetism at M _ ^^^_625_ . Intensity of the earth's magnetism at M' ~ n^^ 576 ~ -663] Magnetic Intensity, 583 That is, if the intensity of the magnetism at the second place is taken as unity, that of the first is i"o85. If the magnetic condition of the needle had not changed in the interval between the two observations, this method would give the relation between the intensities at the two places. In these determinations of the intensity, it would be necessary to have the oscillations of the dipping-needle, which are produced by the whole force of the earth's magnetism. These, however, are difficult to obtain with accuracy, and, therefore, the oscillations of the declina- tion needle are usually taken. The force which makes the declination needle oscillate is only a portion of the total magnetic force, and is smaller in proportion as the inclina- tion is greater. If the line ac (fig. 522) = M represents the total intensity, the angle i the inclination, then the horizontal component ab is M cos i. Hence to express the intensities in the two places by the oscillations of the declination needle, we must substitute in the preceding equation the values M cos / and M' cos i' for M and M', and we have — Fig. 522. M cos i TV*/ v-'-^J smce — M' cos I n^ M M n^ cos i' n''^ cos i That is to say, having observed in two different places tTie number of oscillations, n and 7i\ that the same needle makes in the same time, the ratio of the magnetic force in the two places will be found by multiplying the ratio of the square of the number of oscillations by the inverse ratio of the cosine of the angle of dip. The magnetic intensity increases with the latitude. Humboldt found a point of minimum intensity on the magnetic equator in Northern Peru. In the following table this has been taken as the standard to which the magnetic intensities of the other places specified is referred: — Locality St. Anthony Carthagena Naples . Paris Berlin . Petersburg Spitzbergen Date Latitude 1802 o-o° 1 801 10*25 N. 1805 40-50 1800 48-52 1829 52-51 1828 59-66 1823 79-40 Magnetic Intensity 1-087 1-294 1-274 1-348 1-366 I -410 1-567 According to Gauss the total magnetic action of the earth is the same as that which would be exerted if in each cubic yard there w^re eight bar magnets each weighing a pound. The lines connecting places of equal intensify are called isodynaniic tines. They are not parallel to the magnetic equator, but appear to have about the same direction as the isothermal hues. According to Kuppfer, the intensity appears to diminish at greater heights ; a needle which made one oscillation in 24" vibrated more slowly by 0-0 1 ^' at a height of 1,000 feet: but, according to Forbes, the intensity is only ^^-^^ less at a height of 3,000 feet. There is however, some doubt 584 ' On Magnetism. [663- as to the accuracy of these observations, owing to the uncertainty of the correction for temperature. The intensity varies in the same place with the time of day; it attains its maximum between 4 and 5 in the afternoon, and is at its minimum between 10 and 1 1 in the morning. It is probable, though it has not yet been ascertained with certainty, that the intensity undergoes secular variations. From measurements made at Kew, it appears that, on the whole, the total force experiences a very slight annual increase. 664. Mag-netic observatories. — During the last few years great attention has been devoted to the observation of the magnetic elements, and observatories for this purpose have been fitted up in different parts of the globe. These observations have led to the discovery that the magnetism of the earth is in a state of constant fluctuation, like the waves of the sea. And in studying the variations of the dechnation, etc., the mean of a great number of observations must be taken, so as to eliminate the irregular disturbances, and bring out the general laws. The principle on which magnetic observations are automatically recorded is as follows. Suppose that in a dark room a bar magnet is suspended horizontally, and at its centre is a small mirror ; suppose further that a lamp sends a ray of light to this mirror, the inclination of which, is such, that the ray is reflected and is received on a horizontal drum placed underneath the lamp. The axis of the drum is at right angles to the axis of the magnet ; it is covered with sensitive photographic paper, and is rotated uniformly by clockwork. If now the magnet is quite stationary, and the drum rotates, the reflected spot of light will trace a straight line on the paper with which the revolving drum is covered. But if, as is always the case, the position of the magnet varies during the twenty-four hours, the effect will be to trace a sinuous line on the paper. These lines can afterwards be fixed by the ordinary photographic methods. Knowing the distance of the mirror from the drum, and the length of the paper band which comes under the influence of the spot of light in a given time, twenty-four hours for instance, the angular deflection at any given moment may be deduced by a simple calculation (491). The observations made in the English magnetic observatories have been reduced by Sabine, and have revealed some curious facts in reference to the magnetic storms. He finds that there is a certain periodicity in their appearance and that they attain their greatest frequency about every ten years. Independently of this, Schwabe, a German astronomer, who had studied the subject many years, has found that the spots on the sun, seen on looking at it through a coloured glass, vary in their number, size, and frequency, but attain their maximum between every ten or eleven years. Now Sabine has established the interesting fact that the period of their greatest frequency coincides with the period of greatest magnetic disturb- ance. Other remarkable connections between the sun and terrestrial magnetism have been observed ; one, especially, of recent occurrence has attracted considerable attention. It was the flight of a large luminous -666] Laws of Magnetic Attraction. 585 mass across a vast sun spot, while a simultaneous perturbation of the magnetic needle was observed in the observatory at Kew ; subsequent examination of magnetic observations in various parts of the world showed that within a few hours one of the most violent magnetic storms ever known had prevailed. Magnetic storms are nearly always accompanied by the exhibition of the aurora borealis in high latitudes ; that this is not universal may be due to the fact that many auroras escape notice. The converse of this is true, that no great display of the aurora takes place without a violent magnetic storm. CHAPTER III. LAWS OF MAGNETIC ATTRACTIONS AND REPULSIONS. 665. Ziaw of decrease with distance.— Coulomb discovered the re- markable law in reference to magnetism, that magnetic attractio7is and repulsions are iiivet'sely as the squares of the distances. He proved this by means of two methods : — (i.) that of the torsion balance, and (ii.) that of oscillation. 666. i. The torsion balance. — This apparatus depends on the prin- ciple that, when a wire is twisted through a certain space, the angle of torsion is proportional to the force of torsion (86). It consists ii/f f d (fig. 523) of a glass case closed by a glass top, with an aperture near the edge, to allow the in- troduction of a magnet, A. In another aperture in the centre of the top a glass tube fits, provided at its upper extremity with a micrometer. This con- sists of two circular pieces : d^ which is fixed, is divided on the edge into 360°, while on one e, which is movable, there is a mark, c, to indicate its rotation. D and E represent the two pieces of the micrometer on a larger scale. On E there are two uprights connected by a horizontal axis, on which is a very fine silver wire supporting a magnetic needle, ab. On the side of the case there is a graduated scale, which indicates the angle of the needle ab, and hence the torsion of the wire. When the mark c of the disc E is at zero of the scale, D, the case is so arranged that the wire supporting the needle and the zero of the scale CC3 ig- 523- 586 On Magnetism. [666- in the case are in the magnetic meridian. The needle is then removed from its stirrup, and replaced by an exactly similar one of copper, or any unmagnetic substance ; the tube, and with it the pieces D and E, are then turned so that the needle stops at zero of tjie graduation. The magnetic needle, ab, being now replaced, is exactly in the magnetic meridian, and the wire exerts no torsion. Before introducing the magnet, A, it is necessary to investigate the action of the earth's magnetism on the needle ab, when the latter is re- moved out of the magnetic meridian. This will vary with the dimensions and force of the needle, with the dimensions and nature of the particular wire used, and with the intensity of the earth's magnetism in the place of observation. Accordingl)^, the piece E is turned until ab makes a certain angle with the magnetic meridian. Coulomb found in his experiments that E had to be turned 35° in order to move the needle through 1°; that is, the earth's magnetism was equal to a torsion of the wire corresponding to 35°. As the force of torsion is proportional to the angle of torsion, when the needle is deflected from the meridian by 2, 3 . . . degrees, the directive ;.ction of the earth's magnetism is equal 2, 3 . . . times 35°. The action of the earth's magnetism having been determined, the magnet A is placed in the case so that similar poles are opposite each other. In one experiment Coulomb found that the pole a was repelled through 24°. Now the force which tended to bring the needle into the magnetic meridian was represented by 24° + 24 x 35 = 864, of which the part 24° was due to the torsion of the wire, and 24 x 35° was the equiva- lent in torsion of the directive force of the earth's magnetism. As the needle was in equilibrium, it is clear that the repulsive force which coun- terbalanced those forces must be equal to 864°. The disc was then turned until ab made an angle of 12°. To effect this, eight complete rotations of the disc were necessary. The total force which now tended to bring the needle into the magnetic meridian was composed of: — ist, the 12° of torsion by which the needle was distant from its starting point; 2nd, of 8 X 360° = 2,b8o, the torsion of the wire ; and, 3rd, the force of the earth's magnetism, represented by a torsion of 12x35°. Hence, the forces of torsion which balance the repulsive forces exerted at a distance of 24° and of 1 2° are— 24° 864 12° 3312 Now, 3;3i2 is very nearly four times 864; hence, for half the distance the repulsive force is four times as great. 667. ii. l«etliod of oscillations. — A magnetic needle oscillating under the influence ' of the earth's magnetism may be considered as a pendulum, and the laws of pendulum motion apply to it. The method of oscillations consists in causing a magnetic needle to oscillate first under the influence of the earth's magnetism alone, and then successively under the combined influence of the earth's magnetism, and of a magnet placed at unequal distances. The following determination by Coulomb will illustrate the use of the -668] Magnetic Curves. 587 method. A magnetic needle was used which made 15 oscillations m a minute under the influence of the earth's magnetism alone. A magnetic bar about 2 feet long was then placed vertically in the plane of the mag- netic meridian, so that its north pole was downwards and its south pole presented to the north pole of the oscillating needle. He found that at a distance of 4 inches the needle made 41 oscillations in a minute, and at a distance of 8 inches 24 oscillations. Now, from the laws of the pen- dulum (51), the intensity of the forces are inversely as the squares of the times of oscillations. Hence, if we call M the force of the earth's mag- netism, tn the attractive force of the magnet at the distance of 4 inches, ni' at the distance of 8 inches, we have M : M + ?« = 15^ : 41-, and M : M + w' = 15- : 24-', eliminating M in : m' = ^\^- 15' : 24- -152= 1456 : 351 = 4:1 nearly, or ni : ;«' = 4 : i. In other words, the force acting at 4 inches is quadruple that which acts at double the distance. The above results do not quite agree with the numbers required by the law of inverse squares. But this could only be expected to apply in the case in which the repulsive or attractive force is exerted between two pomts, and not, as is here the. case, between the resultant of a system of points. And it is to this fact that the discrepancy between the theoretical and observed results is due. In the case of the torsion balance, one pole of the magnet to be tested was at so great a distance that it could not appreciably modify the action of the other. When the distance at which two magnets act is large as compared with their dimensions, the total action on one another is nearly inversely as the third power of the distances ; which, it might be shown, is a necessary consequence of the law that the action of the magnetic elements is inversely as the square of the distance. When a magnet acts upon a mass of soft iron, the law of the variation with the distance is modified. The attraction in this case is inversely proportional to the distance between the magnet and the iron. When the distance between the magnet and iron is small, Tyndall has found that the attraction is directly proportional to the square of the strength of the magnet : but when the iron and the magnet are in con- tact, then the attraction is directly proportional to the strength of the magnet. 668. Ma§rnetic curves. — If a stout sheet of paper stretched on a frame be held over a horse-shoe magnet, and then some very fine iron filings be strewn on the paper, on tapping the frame the filings will be found to arrange themselves in thread-like curved lines, stretching from pole to pole (fig. 524). These lines form what are called 7nag7tetic curves. The direction of the curve at any point represents the direction of the mag- netism at this point. 588 On Magnetism: [668- To render these curves permanent, the paper on which they are formed should be waxed ; if then a hot iron plate be held over them, this melts the wax, which rises by capillary attraction (128) between the particles of filings, and on subsequent cooling connects them together. These curves are a graphic representation of the law of magnetic attraction and repulsion with regard to distance ; for under the influence I^'ig 524 of the two poles of the magnet, each particle itself becomes a minute magnet, the poles of which arrange themselves in a position dependent on the resultant of the forces exerted upon them by the two poles, and this resultant varies with the distance of the two poles respectively. A small magnetic needle placed in any position near the magnet will take a direction which is the tangent to the curve at this place. 669. Magrnetic field. — The space in the immediate neighbourhood of any magnet undergoes some change, in consequence of the presence of this magnet, and such a space is spoken of as a tnagnetic field -, the effect produced by the magnet is often said to be due to the magnetic field. Magnets of different powers produce magnetic fields of different intensity. The direction which represents the resultant of the magnetic forces in a magnetic field is spoken of as the direction of the lines of force of this field. In the above figure the magnetic curves represent the direction of the lines of force in the field due to the two poles. A uniform magnetic field is one in which the lines of force are parallel. This is practically the case with a field at some distance from a long thin magnet of uniform magnetisation. The dipping needle, when free to oscillate in a vertical plane in the magnetic meridian, represents the direction of the lines of force due to the terrestrial magnetic field. This field in any one place is uniform. -673] Magnetisation. 589 CHAPTER IV. PROCESSES OF MAGNETISATION. 670. IVKagrnetisation. — The various sources of magnetism are the m- fluence of natural or artificial magnets, terrestrial magnetism, aAd elec- tricity. The three principal methods of magnetisation by magnets are known by the technical names of single touchy separate touch, and double touch. 671. XWIetliod of sing-le touch. — This consists in moving the pole of a powerful magnet from one end to the other of the bar to be magnetised, and repeating this operation several times always in the same direction. The neutral fluid is thus gradually decomposed throughout all the length of the bar, and that end of the bar which was touched last by the magnet is of opposite polarity to the end of the magnet by which it has been touched. This method only produces a feeble magnetic power, and is, accordingly, only used for small magnets. It has further the disadvan- tage of frequently developing consequent poles. 672. nCethod of separate touch. — This method, which was first used by Dr. Knight in 1745, consists in placing the two opposite poles of two magnets of equal force in the middle of the bar to be magnetised, and in moving each of them simultaneously towards the opposite ends of the bar. Each magnet is then placed in its original position, and this opera- tion repeated. After several frictions on both faces of the bar it is mag- netised. • In Knight's method the magnets are held vertically. Duhamel jper- fected the method by inclining the magnets, as represented in fig. 521 ; and still more, by placing the bar to be magnetised on the opposite poles of two fixed magnets, the action of which strengthens that of the mov- able magnets. The relative position of the poles of the magnets is indicated in the figure. This method produces the most regular magnets. 673. XMEetbod of double touch. — In this method, which was invented by Mitchell, the two magnets are placed with their poles opposite each other in the mitidle of the bar to be magnetised. But, instead of moving them in opposite directions towards the two ends, as in the method of separate touch, they are kept at a fixed distance by means of a piece of wood placed between them (fig. 525), and are simultaneously moved first towards one end, then from this to the other end, repeating this operation several times, and finishing in the middle, taking care that each half of the bar receives the same number of frictions. Epinus, in 1758, improved this method by supporting the bar to be magnetised, as in the method of separate touch, on the opposite poles of two powerful magnets, and by inclining the bars at an angle of 15° to 20° In practice, instead of two bar magnets it is usual to employ a horse- shoe magnet, which has its poles conveniently close together. 590 On Magnetism. [673- By this method of double touch, which is the one generally- adopted, powerful magnets are obtained, but they have frequently consequent Fig. 525. poles. As this would be a serious injury to qompass needles, these are best magnetised by separate touch. 674. IVIagrnetisation toy the action of the earth. — The action of the earth on magnetic substances resembles that of a magnet, and hence the terrestrial magnetism is constantly tending to separate the two magnetisms which are in the neutral state in soft iron and in steel. But as the coercive force is very considerable in the latter substance, the action of the earth is inadequate to produce magnetisation, except when continued for a long time. This is not the case with perfectly soft iron. When a bar of this metal is held in the magnetic meridian parallel to the inclination, the bar becomes at once endowed with feeble magnetic polarity. The lower extremity is a north pole, and if the north pole of a small magnetic needle be approached, it will be repelled. This magnetisation is of course unstable, for if the bar be turned, the poles are inverted, as pure soft iron is desti- tute of coercive force. While the bar is in this position, a certain amount of coercive force may be imparted to it by giving it several smart blows with a hammer, and the bar retains for a short time the magnetism which it has thus ob- tained. But the coercive force thus developed is very small, and after a time the magnetism disappears. If a bar of soft iron be twisted while held vertically, or, better, in the plane of the dip, it acquires a feeble permanent magnetism. It is this magnetising action of the earth which developes the magnet- ism frequently olDserved in steel and iron instruments, such as fire-irons, rifles, lamp posts, railings, gates, lightning conductors, etc», which remain for some time in a more or less inclined position. They become magnet- ised with their north pole downward, just as if placed over the pole of a powerful magnet. The magnetism of native black oxide of iron has doubtless been produced by the same causes ; the very different magnetic power of different specimens being partly attributable to the different positions of the veins of ore with regard to the line of dip. The ordinary irons of commerce are not quite pure, and possess a feeble coercive force ; hence a feeble magnetic polarity is generally found to be possessed by the tools in a smith's shop. Cast-iron, too, has usually a great coercive force, and can be permanently magnetised. The turnings, also, of wrought iron and of steel produced by the powerful lathes of our ironworks are found to be magnetised. -675] Magnetism of Iron Ships. 591 675. Magrnetisxn of iron ships. — The inductive action of terrestrial magnetism upon the masses of iron always found in ships exerts a dis- turbing action upon the compass needle. The local attraction, as it is called, may be so considerable as to render the indications of the needle almost useless if it be not guarded against. A full account of the manner in which local attraction is produced, and in which it is com- pensated, is inconsistent with the limits of this book, but the most important points are the following : — i. A vertical mass of soft iron in the vessel, say in the bows, would become magnetised under the influence of the earth ; in the northern hemisphere, the lower end would be a north pole, and the upper end a south pole ; and as the latter may be assumed to be nearer the north pole of the compass needle, it would act upon it. So long as the vessel was sailing in the magnetic meridian this would have no effect ; but in any other direction the needle would be drawn out of the magnetic meridian, and a little consideration will show that when the ship was at right angles to the magnetic meridian the effect would be greatest. This vertical itiduction would disappear twice in swinging the ship round and would be at its maximum twice ; hence the deviation due to this cause is known as semicircular deviation. ii. Horizontal masses again, such as deck-beams, are also acted upon inductively by the earth's magnetism, and their induced magnetism exerts a disturbing influence upon the magnetic needle. The effect of this horizontal induction will disappear when the ship is in the magnetic meridian, and also when it is at right angles thereto. In positions inter- mediate to the above the disturbing influence will attain its maximum. Hence in swinging a ship round there would be four positions of the ship's head in which the influence would be at a maximum and four in which it would be at a minimum. This eftect of horizontal induction is accordmgly spoken of as guadrantal deviation. The influence of both these causes, vertical and horizontal induction, may be remedied in the process of ' swinging the sl.ip.' This consists in comparing the indications of the ship's compass with those of a standard compass placed on shore. The ship is then swung round in various positions, and by arranging small vertical and horizontal masses of soft iron in proximity to the steering compass, positions are found for them in which the inductive action of the earth upon them quite neutralises the influence of the earth's magnetism upon the ship ; and in all positions of the ship, the compass points in the same direction as the one on shore. iii. The extended use of iron in ship-building, more especially when the frames are entirely of iron, has increased the difficulty. In the process of building a ship, the hammering and other mechanical ope- rations to which it is subject, while under the influence of the earth's magnetism, will cause it to become to a certain extent permanently magnetised. The distribution of the magnetism, the direction of its magnetic axis, will depend on the position in which it has been built ; it may or may not coincide with the direction of the keel. The vessel 592 On Magnetism. [675- becomes in short a huge magnet, and will exert an influence of its own upon the compass quite independently of vertical or horizontal induction. This influence is semicircular, that is, it disappears when the magnetic axis of the ship is in the magnetic meridian and is greatest at right angles to it. It may be compensated by two permanent magnets placed near the compass in suitable positions found by trial during the process of swinging the ship. Supposing the inherent magnetism of the ship to have the power of drawing the compass a point to the east, the com- pensating magnets may be so arranged as to tend to draw it a point to the west, and thus keep it in the magnetic meridian. If, however, the inherent magnetism be destroyed, from whatever cause, it is clear that the magnets will now draw it aside a point too much to the west. This IS the source of a new difficulty. It has been found that a ship which at the time of sailing was properly compensated would on returning from a long voyage have its compasses over-compensated. The buffeting which the ship had experienced had destroyed its inherent magnetism, and numerous instances are known where the loss of a vessel can be directly traced to this cause. Fortunately, it has been found that after some time a ship's magnetic condition is virtually permanent, and is unaltered by any further wear and tear. The magnetism which it then retains is called its permanent magnetism, in opposition to the sub-per- manent which it loses. The difficulty of adequately compensating compasses, which is greatly increased by the armour-plated and turret ships now in use, has induced one school to throw over any attempt at correction ; but by careful observation of the magnetic condition of a ship, and tabulating the errors to construct a table, by comparing which with the indications of the compass at any one time, the true course can be made out. In the Royal Navy, the plan now adopted is to combine both methods: compensate the errors to a considerable extent, and then construct a table of the residual errors. 676. Saturation. — Experiment has shown that to a certain extent the magnetic force which can be imparted to a bar or needle increases with the power of the magnets used. But there is a limit to the mag- netic force which can be imparted to a bar or needle, and when this is attained, the bar is said to be saticrated or magnetised to saturation. A bar may indeed be magnetised beyond this point, but this is not permanent ; it gradually diminishes until it has sunk to the point of saturation. This is readily intelligible, for the magnetisms once separated tend to reunite, and when their attractive force is equal to that which opposes their separation, that is, the coercive force of the metal, equilibrium is attained, and the magnet is saturated. Hence, more magnetism ought to be developed in 'bars than they can retain, in order that they may decline to their permanent state of saturation. To increase the magnet- ism of an unsaturated bar, a less feeble magnet must not be used than that by which it was originally magnetised. 678] Magnetic Battery. 593 677. Magnetic battery. — A magnetic battery or inagazme consists of a number of magnets joined together by their similar poles. Sometimes they have the form of a horse-shoe, and sometimes a rectilinear form. The battery represented in fig. 526 consists of five superposed steel plates. That in fig. 527 consists of twelve plates, arranged in three layers of four each. The horse shoe form is best adapted for supporting a weight, for then both poles are used at once. In both the bars are magnetised separ- ately, and then fixed by screws. The force of a battery is not equal to the- sum of the forces of each bar, owing to the repulsive action exerted by each bar on the adjacent ones. The force is increased by making the lateral plates i or 2 centimetres shorter than the one in the middle (fig. 526). 678. Armatures. — When even a steel bar is at its limit of saturation, it gradually loses its magnetism. To prevent this armatures or keepers are used ; these are pieces of soft iron, A and B (fig. 527), which are placed in contact with the poles. Acted on inductively, they become powerful temporary magnets, possessing oppo- site polarity to that of the inducing pole ; they thus react in turn on the permanent magnetism of the bars, preserving and even increasing it. Fig. 526. Fig. 527. When the magnets are in the form of bars, they are arranged in pairs, as shown in fig. 528, with opposite poles in juxtaposition, and the circuit is completed by two small bars of soft iron, AB. Movable magnetic Fig. 528. needles set spontaneously towards the magnetic poles of the earth, the '* influence of which acts as a keeper. 594 On Magnetism. [678- Fig. 529- A horse-shoe magnet has a keeper attached to it, which is usually- arranged so as to support a weight. The keeper becomes magnetised under the influence of the two poles, and adheres with great force; the weight which it can support being much more than double that which a single pole would hold. In respect to this weight, a singular and hitherto inexplicable phenomenon has been observed. When contact is once made, and the keeper is charged with its maximum weight, any further addition would detach it ; but if left in contact for a day, an additional weight may be added without de- taching it, and by slightly increasing the weight every day, it may ultimately be brought to support a far greater load than it would originally. But if contact be once broken, the weight it can now support does not much exceed its original charge. It is advantageous that the surfaces of the magnet and armatures which are in contact should not be plane, but sHghtly cylindrical, so that they touch along a line. In providing a natural magnet with a keeper, the line joining the two poles is first approximately determined by means of iron filings. Two plates of soft iron (tig. 529), each terminating in a massive shoe, are then applied to the faces corresponding to the poles. Under the influence of the natural magnet, these plates become magnetised, and if the letters A and B represent the position of the poles of the natural magnet, the poles of the armature are a and b. 679. Portative Force. Power of magrnets. — The portative force is the greatest weight which a magnet can support. Hacker found that the portative force of a saturated horse-shoe magnet, which, by repeatedly de- taching the keeper, has become constant, maybe represented by the formula p = ^^7^ in which P is the portative force of the magnet, p its own weight, and a a coefficient, which varies with the nature of the steel and the mode of magnetising. Hence a magnet which weighs 1,000 ounces only supports 25 times as much as one weighing 8 ounces or j^.- as heavy. It appears immaterial whether the section of the bar is quadratic or circular, and the distance of the legs is of inconsiderable moment ; it is important, however, that the magnet be suspended vertically, and that the load be exactly in the middle. In Hackers magnets the value of a was 10-33, while in Logemann's it was 23. The strength of two bar magnets may be compared by the following simple method, which is known as Kiilp's co?npe?isation method : — A small magnetic compass needle is placed in the magnetic meridian. One pole of one of the magnets to be tested is then placed at right angles to the magnetic meridian in the same plane as the needle, and so that its axis prolonged would bisect the needle. The compass needle is thereby -680] Cirannstanccs ivhich influence the Power of Magnets. 595 deflected through a certain angle. The similar pole of the other magnet is then placed similarly on the other side of the needle, and a position found for it in which it exactly neutralises the action of the first magnet, that is, when the needle is again in the magnetic meridian. If the mag- nets are not too long, their strengths are approximately as the cubes of the distance of the acting poles from the magnetic needle. 680. Circumstances wbich Influence tlie power of magnets. — All bars do not attain the same state of saturation, for their coercive force varies. Twisting or hammering imparts to iron or steel a considerable co- ercive force. But the most powerful of these influences is the operation of tempering (91). Coulomb found that a steel bar tempered at dull redness, and magnetised to saturation, made ten oscillations in 93 seconds. The same bar tempered at a cherry-red heat, and similarly magnetised to saturation, only took 63 seconds to make ten oscillations. Hence it would seem, the harder the steel the greater is its coercive force ; it receives magnetism with much greater difficulty, but retains it more effectually. Very hard steel bars have, however, the disadvantage of being very brittle, and in the case of long thin bars, a hard tempering is apt to produce consequent poles. Compass needles are usually tempered at the blue heat, that is, about 300° C, by which a high coercive force is obtained without great fragility. Temperature. — Increase of temperature always produces a diminution of magnetic force. If the changes of temperature are small, those of the atmosphere for instance, the magnet is not permanently altered. Kuppfer allowed a magnet to oscillate at different temperatures, and found a definite decrease in its power with increased temperature, as indicated by its slower oscillations. In the case of a magnet 2^ inches in length, he observed that with an increase of each degree of temperature the duration of 800 oscillations was 0-4'^ longer. If 71 be the number of oscil- lations at zero, and Ji the number at /, then n^ = ti (i —ct), where <: is a constant depending in each case on the magnet used. This formula has an important application in the correction of the observations of magnetic intensity which are made at different places and at different temperatures, and which, in order to be comparable, must first be reduced to a uniform temperature. When a magnet has been more strongly heated, it does not regain its original force on cooling to its original temperature, and when it has been heated to redness, it is demagnetized. This was first shown by Coulomb, who took a saturated magnet, and progressively heated it to higher tem- peratures, and observed the number of oscillations after each heating. The higher the temperature to which it had been heated the slower its oscillations. A magnet heated to bright redness loses its magnetism so completely that it is quite indifferent, not only towards iron, but also towards another magnet. Incandescent iron also does not possess the property of being attracted by the magnet. Hence there is in the case of iron a 7nagnetic 59^ On Mag7ietism. [680- litnit, beyond which it is unaffected by magnetism. Such a magnetic limit exists in the case of other magnetic metals. With cobalt^ for instance, it is far beyond a white heat, for at the highest temperatures hitherto examined it is still magnetic ; the magnetic limit of chromium is somewhat below red heat ; that of nickel at about 350° C, and of manga- nese at about 1 5° to 20° C. Torsion. — Torsion exerts a great influence on the magnetisation of a bar, and the interesting phenomenon has been observed that tor- sion influences magnetism in the same manner as magnetism does torsion. Thus the permanent magnetism of a steel bar is diminished by torsion, but not proportionally to the increase of torsion. In like manner the torsion of twisted iron wires is diminished by their being magnetised, though less so than in proportion to their magnetisation. Repeated torsions in the same direction scarcely diminish magnetisation, but a torsion in the opposite direction produces a new diminution of the magnetism. In a perfectly analogous manner, repeated magnetisations in the same sense scarcely diminish torsion, but a renewed magnetisation in the opposite direction does so. 681. Bistribution of free mag'netism. — To investigate the distribution of magnetic force in different parts of a magnet. Coulomb placed a large magnet in a vertical position in the magnetic meridian ; he then took a small magnetic needle suspended by a thread without torsion, and, having ascertained the number of its oscillations under the influence of the earth's magnetism alone, he presented it to different parts of the magnet. The oscillations were fewer as the needle was nearer the middle of the bar, and when they had reached that position, their number was the same as under the influence of the earth's magnetism alone. He found that with saturated bars of more than 7 inches in length the distribution could always be expressed by a curve whose abscissae were the distances from the ends of the magnet, and whose ordinates were the force of magnetism at these points. With magnets of the above dimensions the poles are at the same distance from the end ; Coulomb found the distance to be I -6 inches in a bar 8 inches long. The same physicist found that, with shorter bars, the distance of the poles from the end is \ of the length ; thus with a bar of three inches it would be half an inch. These results presume that the other dimensions of the bar are very small as compared with its length, that it has a regular shape, and is uniformly magnetised. When these conditions are not fulfilled, the positions of the poles can only be determined by direct trials with a magnetic needle. With lozenge-shaped magnets the poles are nearer the middle. Coulomb found that these lozenge-shaped bars have a greater directive force than rectangular bars of the same weight, thickness, and hardness. -683] Frictional Electricity. 597 BOOK IX. FRICTIONAL ELECTRICITY. CHAPTER I. FUNDAMENTAL PRINCIPLES. 682. Electricity. Its nature. — Electricity is a powerful physical agent which manifests itself mainly by attractions and repulsions, but also by luminous and heating effects, by violent commotions, by chemical decompositions, and many other phenomena. Unlike gravity, it is not inherent in bodies, but is evoked in them by a variety of causes, among which are friction, pressure, chemical action, heat, and magnetism. Thales, six centuries before Christ, knew that when amber was rubbed with silk, it acquired the property of attracting light bodies : and from the Greek form of this word {i)XficT.);^ \ maximum charge, Carre's machine \ C ^' is not very much affected by mois- L lure, and it yields a larger supply of electricity. With plates whose dimensions are respectively 38 and 49 centimetres, it gives sparks of 15 to 18 centimetres, and more when a condenser is added, as in Holtz's and Bertsch's machines. 7 K 6. "Work required for the F'» 555 production of electricity. — In all electrical machines electricity is only produced by the expenditure of a definite amount of force, as will at once be seen by a perusal of the preceding descriptions. The action of those machines however, which work continuously, is somewhat complex. Not only is electricity produced, but heat also ; and it has been hitherto impossible to estimate separately the work required for the heat from that required for the electricity. This is easily done in theory, but not in practice ; how difficult, for instance, it would be to determine the tempera- ture of the cushion or of the plate of a Ramsden's machine. In lifting the plate off" a charged electrophorus, a definite expenditure of force is needed, though it be too slight to be directly estimated (706). With a Holtz's machine it may be readily shown that there is a definite expenditure of force in working it. If such a machine be turned without having been charged, the work required is only that necessary to over- come the passive res'stances. If, however, one of the sectors be charged and the electric action comes into play, it will be observed that there must be a distinct increase in the force necessary to work the machine. EXPERIMENTS WITH THE ELECTRICAL MACHINE. 7 1 7. Spark. — One of the most curious phenomena observed with the electrical machine is the spark drawn from the conductor when a finger is presented to it. The positive electricity of the conductor, acting in- ductively on the neutral electricity of the body, decomposes it, repelling the positive and attracting the negative. When the attraction of the op- posed electricities is sufficiently great to overcome the resistance of the air, they recombine with a smart crack and a spark. The spark is instantaneous, and is accompanied by a sharp prickly sensation, more especially with a powerful machine. Its shape varies. When it strikes EE3 634 Frictional Electricity. [717- at a short distance, it is rectilinear, as seen in fig. 556. Beyond two or three inches in length, the spark becomes irregular, and has the form of a sinuous curve with branches (fig. 557). If the discharge is very powerful, the spark takes a zig-zag shape (fig. 558). These two latter appearances are seen in the lightning discharge. A spark may be taken from the human body by the aid of the insulat- ing stool, which is simply a low stool with stout glass legs. The person standing on this stool touches the prime conductor, and as the human Fig. 556. Fig. 557. Fig. 558. body is a conductor, the electrical fluid is distributed over its surface as over an ordinary insulated metallic conductor. The hair diverges in consequence of repulsion, a peculiar sensation is felt on the face, and if another person, standing on the ground, presents his hand to any part of the body, a smart crack with a pricking sensation is produced. A person standing on an insulated stool may be positively electrified by being struck with a catskin. If the person holding the catskin stands on an insulated stool, the striker becomes positively, and the person struck negatively, electrified. 718. Electrical chimes. — The electrical chimes is a piece of apparatus consisting of three bells suspended to a horizontal metal rod (fig. 559). Two of them, A and B, are in metallic connection with the conductor ; the middle bell hangs by a silk thread, and is thus insulated from the conductor, but is connected with the ground by means of a chain. 719] Experiments ivith the Electrical Machine. 63 s Between the bells are small copper balls suspended by silk threads. When the machine is worked, the bells A and B, being positively electrified, attract the copper balls, and after contact repel them. Being now positively electrified, they are in turn attracted by the middle bell, C, which is charged with nega- tive electricity by induction from A to B. After contact they are again repelled, and this process is repeated as long as the machine is in action. Fig. 560 represents an apparatus originally devised by Volta for the purpose of illustrating what he sup- posed to be the motion of hail between two clouds oppositely electrified. It consists of a tubulated glass shade, with a metal base, on which are Fi^. 559- Fig. 560. Fig. 561 some pith balls. The tubulure has a metal cap, through which passes a brass rod, provided with a metallic disc or sphere at the lower end, and at the upper with a knob, which touches the prime conductor. When the machine is worked, the sphere becoming positively electri- fied, attracts the light pith balls, which are then immediately repelled, and, having lost their charge of positive electricity, are again attracted, again repelled, and so on, as long as the machine continues to be worked. An amusing modification of this experiment is frequently made by placing between the two plates small pith figures, somewhat loaded at the base. When the machine is worked, the figures execute a regular dance. 719. Electrical whirl or vane. — The electrical whirl or vane consists of 5 or 6 wires, terminating in points, all bent in the same direction, and 6s6 Frictional Electricity. [719 fixed in a central cap, which rotates on a pivot (fig. 561). When the apparatus is placed on the conductor, and the machine worked, the whirl begins to revolve in a direction opposite that of the points. This motion is not analogous to that of the hydraulic tourniquet (205). It is not caused by a flow of material fluid, but is owing to a repulsion between the electricity of the points and that which they impart to the adjacent air by conduction. The electricity being accumulated on the points in a high state of density, passes into the air, and imparting thus a charge of electricity, repels this electricity, while it is itself repelled. That this is the case is evident from the fact that, on approaching the hand to the whirl while in motion, a slight draught is felt, due to the movement of the electrified air, while in vacuo the apparatus does not act at all. This draught or wind is known as the electrical aura. When the electricity thus escapes by a pomt, the electrified air is repelled so strongly as not only to be perceptible to the hand, but also to engender a current strong enough to blow out a candle. Fig. 562 shows Fig. 562. Fig. 563- this experiment. The same effect is produced by placing a taper on the conductor, and bringing near it a pointed wire held in the hand (fig. 563). The current arises in this case from the contrary fluid, which escapes by the point under the influence of the machine. The electrical orrery and the electrical inclined plane are analogous to these pieces of apparatus. CHAPTER IV. CONDENSATION OF ELECTRICITY. 720. Condensers. Theory of condensers. — A r^^/z^tv/j-^r is an appa- ratus for condensing a large quantity of electricity on a comparatively small surface. The form may vary considerably, but in all cases consists essentially of two insulated conductors, separated by a non-conductor, and the working depends on the action of induction. Epinus's condenser consists of two circular brass plates, A and B 720] Condensation of Electricity. 637 (fig. 564), with a sheet of glass, C, between them. The plates, each provided with a pith ball pendulum, are mounted on insulated glass legs, and can be moved along a support, and fixed in any position. When electricity is F'g- 564- to be accumulated, the plates are placed in contact with the glass, and then one of them, B for instance, is connected with the electrical machine, and the other placed in connection with the ground, as shown in fig. 565. In explaining the action of the condenser, it will be convenient in each Fip. 565. case to call that side ot the metal plate nearest the glass the anterior, and the other the posterior side. And first let A be at such distance 638 Frictional Electricity [720 Fig. 566. from B as to be out of the sphere of its action. The plate B, which is then connected with the conductor of the electrical machine, takes its maximum charge, which is distributed equally on its two faces, and the pendulum diverges widely. If the connection with the machine be interrupted, nothing would be changed ; but if the plate A be slowly approached, its neutral fluid being decomposed by the influence of B, the negative is accumulated on its anterior face, 71 (fig. 566), and the positive passes into the ground. But as the negative electricity of the plate A reacts in its turn on the positive of the plate B, the latter fluid ceases to be equally distributed on both faces, and is accumulated on its anterior face, m. The posterior face, p, having thus lost a portion of its electricity, its density has diminished, and is no longer equal to that of the machine, and the pen- dulum, b^ diverges less widely. Hence B can receive a fresh quantity from the machine, which, acting as just described, decomposes by induction a second quantity of neutral fluid on the plate A. There is then a new accumulation of negative fluid on the face n, and consequently of positive fluid on 7n. But each time that the machine gives off electricity to the plate, only a part of this passes to the face ;«, the other remaining on the face/; the tension here, therefore, continues to increase until it equals that of the machine. From this moment equilibrium is established, and a limit to the charge attained which cannot be exceeded. The quantity of electricity accumulated now • on the two faces m and 71 is very considerable, and yet the pendulum di- verges just as much as it did when A was absent, and no more ; in fact, the density at/ is just what it was then— namely, that of the machine. When the condenser is charged — that is, when the opposite electricities are accumulated on the anterior faces — connection with the ground is broken by raising the wires. The plate A is charged with negative electricity, but simply on its anterior face (fig. 566), the other side being neutral. The plate B, on the contrary, is electrified on both sides, but unequally ; the accumulation is only on its anterior face, while on the posterior, /, the density is simply equal to that of the machine at the moment the connections are interrupted. In fact, the pendulum b di- verges and a remains vertical. But if the two plates are removed, the two pendulums diverge (fig. 564), which is owing to the circumstance that, as the plates no longer act on each other, the positive fluid is equally distri- buted on the two faces of the plate B, and the negative on those of the plate A. 721. Slow discbargre and instantaneous discliargre. — While the plates A and B are in contact with the glass (fig. 565), and the connec- tions interrupted, the condenser may be discharged— that is, restored to the neutral state, in two ways; either by a slow or by an instantaneous discharge. To discharge it slowly, the plate B — that is, the one containing -721] Sloiv Discharge and Instantaneous Discharge . 639 an excess of electricity — is touched witli the finger ; a spark passes, all the electricity on p passes into the ground, the pendulum b falls, but a diverges. For B, having lost part of its electricity, only retains on the face m that held by the inductive influence of the negative on A. But the quantity thus retained at B is less than that on A; this has free electricity, which makes the pendulum a diverge, and if it now be touched, a spark passes, the pendulum a sinks while b rises, and so on by continuing to touch alternately the two plates. The discharge only takes place slowly ; in very dry air it may require several hours. If the plate A were touched first, no electricity would be removed, for all it has is retained by that of the plate B. To remove the total quantity of electricity by the method of alternate contacts, an infinite number of such contacts would theoretically be required, as will be seen from the following calcula- tion : Let the total quantity of positive electricity on B be taken = i ; by induction it retains on A a quantity less than its own of negative elec- tricity ; let this quantity be called m ; in being a fraction in all cases less than unity, but which varies with the distance of the plates and the nature of the dielectric. Now the m of negative electricity on A, reacting in turn on the positive on B, retains there my.m = in- of positive electricity, and therefore the free electricity on B, that which makes the pendulum b diverge is i — w^, and if B be touched this quantity is removed. The in of negative on A now retains, on B, in"^ of positive ; this binds in turn m times its own quantity — that is, in^ of negative on A — and the free negative electricity which now makes the pendulum a diverge is represented by in — m^ = w(i — m^). If A be now touched, this quantity is removed, the pen- dulum a sinks and b rises ; for B has now an excess of free electricity, which it is readily seen is presented by ni^ii—rn^). By pursuing this reasoning, it will be seen that the following expresses the quantities removed and left after each successive contact : — Positive. Negative. I m \—in^\ m^ m^ \ in{\—m^) {\—m^)m'^\ w* nv' \ in^{\~in^) (i— ;;z-)w*; m^ in''; m^\\—in^) (i — in^)in^ ^ ; m^ 111^ + ^ ; in"~\i — m^) An instantaneous discharge maybe effected by means oi tht discharg- ing rod (fig. 567). This consists of two bent brass wires, terminating in knobs, and joined by a hinge. When provided with glass handles as in fig. 567, it forms a glass discharging rod. In using this apparatus one of the knobs is pressed against one plate of the condenser, and the other knob brought near the other. At a certain distance a spark strikes from the plate to the knob, caused by the sudden recomposition of the two opposite electricities. When the condenser is charged by the discharger no sensation is experienced, even though the latter be held in the hand ; of the two con- ductors, the electric fluid always chooses the better, and hence the dis- 640 Frlctional Electricity. [721 - charge is effected through the metal, and not through the body. But if, while one hand is in contact with one plate, the other touches the second, the discharge takes place through the breast and arms, and a considerable shock is felt ; and the larger the surface of the con- denser, and the greater the electric density, the more violent is the shock. 722. Calculation of the condensingr force. — The condensing force is the relation between the whole charge, which the collecting plate can take while under the influence of the second plate, to that which it would take if alone ; in other words, it is the relation of the total quantity of eLectricity on the collecting plate to that which P- g remains free ; for it is assumed that the quantity of free electricity on the collecting plate is the same as that which it would take if it were alone. To calculate the condensing force, let us, as before, express the total quantity of positive electricity which the collecting plate B can take, while under the influence of the condensing plate, by I, then in is the whole quantity of negative electricity on the second plate. But, as we have just seen, the quantity of free electricity on B is \ — m^. Hence is the fraction which expresses the condensing force. The value of in is determined experimentally by means of the proof plane and the torsion balance. Thus, if in were 0-99, the quantity of electricity which could be accumulated on the collecting plate B, under the influence of A, would be 50 times as much as the quantity it could receive if alone; while, if m were 075, the quantity would be 2-28 times as great. 723. Limit of the chargre of condensers. — The quantity of electricity which can be accumulated on each plate is, cceteris paribus, proportional to the density of the electricity on the conductor, and to the surface of the plates : it decreases as the insulating plate is thicker, and it differs with the specific inductive capacity of the substance. Two causes limit the quantity of electricity which can be accumulated. First, that the electric density of the collecting plates gradually increases, and ultimately equals that of the machine, which cannot, therefore, impart any free electricity. The second cause is the imperfect resistance which the insulating plate offers to the recombination of the two opposite electricities ; .for when the force which impels the two fluids to recombine exceeds the resistance offered by the insulating plate, it is perforated, and the contrary fluids unite. 724, Fulminating- pane. Franklin's plate. — This is a simple form of the condenser, and is more suitable for giving strong shocks and sparks. It consists of a glass plate fixed in a wooden frame (fig. 568); on each side of the glass pieces of tin foil are fastened opposite each other, leaving a space free between the edge and the frame. It is well to cover this part of the glass with an insulating layer of shellac varnish. One of the sheets -725] Fulminating Pane. 641 of tin foil is connected with a ring on the frame by a strip of tin foil, so that it can be put in communication with the ground by means of a chain. To charge the pane the insulated side is connected with the machine. As the other side communicates with the ground, the two coatings play exactly the part of the condenser. On both plates there are accumulated large quantities of contrary electricities. The pane may be discharged by simply pressing the knob of the dis- Flg. 568. charger against the lower surface, while the other knob is brought near the upper coating. A spark ensues, due to the recomposition of the two electricities ; but the operator experiences no sensation, for the discharge takes place through the wire. But if the connection between the two coatings be made by touching them with the hands, a violent shock is felt in the hands and breast, for the combination then takes place through the body. 725. Xieydenjar. — The Leydenjar, so named from the town of Leyden, where it was invented, is nothing more than a modified condenser or ful- minating pane rolled up. Fig. 569 represents a Leyden jar of the usual French shape in the process of being charged. It consists of a glass bottle of any convenient size, the interior of which is either coated with tin foil or filled with thin leaves of copper, or with gold leaf. Up to a certain distance from the neck the outside is coated with tin foil. The neck is provided with a cork, through which passes a brass rod, which terminates at one end in a knob, and communicates with the metal in the interior. The metallic coatings are called respectively the iiitenial and external coatings. Like the condenser, the jar is charged by connecting one of the coatings with the ground, and the other with the source of electricity. When it is held in the hand by the external coating, and the knob pre- sented to the positive conductor of the machine, positive electricity is 642 Frictional Electricity. [725- accumulated on the inner, and negative electricity on the outer coating. The reverse is the case if the jar is held by the knob, and the external Fig. 569. coating presented to the machine. The positive charge acting induc- tively across the dielectric, glass, decomposes the electricity of the outer coating, attracting the negative, and repelling the positive, which escapes by the hand to the ground. Thus it will be seen that the theory of the jar is identical with that of the condenser, and all that has been said of this applies to the jar, substituting the two coatings for the two plates, A and B, of fig. 565. Fig. 570- Fig. 571. Like any other condenser, the Leyden jar may be discharged either slowly or instantaneously. For the latter purpose it is held in the hand by the outside coating (fig. 570), and the two coatings are then connected by means of the simple discharger. Care must be taken to touch first the external coating with the discharger, otherwise a smart shock will be felt. To discharge it slowly the jar is placed on an insulated plate, and first the internal and then the external coating touched, either with the hand or with a metallic conductor. A slight spark is seen at each discharge. Fig. 571 represents a very pretty experiment for illustrating the slow dis- -727] Ley den Jar. 643 charge. The rod terminates in a small bell, d, and the outside coating is connected with an upright metallic support, on which is a similar bell, e. ]5etween the two bells a light copper ball is suspended by a silk thread. The jar is then charged in the usual manner and placed on the support in. The internal coating contains a quantity of free electricity ; the pendulum is attracted and immediately repelled, striking against the second bell, to which it imparts its free electricity. Being now neutralised, it is again at- tracted by the first bell, and so on for some time, especially if the air be dry, and the jar pretty large. 726. Iieyden jar with movable coatingrs. — This apparatus (fig. 572) is used to demonstrate that in the Leyden jar, the opposite electricities are Fig. 572. not distributed on the coatings merely, but reside principally on the oppo- site sides of the glass. It consists of a somewhat conical glass vessel, B, with movable coatings of zinc or tin, C and D. These separate pieces placed one in the other, as shown in figure A, form a complete Leyden jar. After having charged the jar, it is placed on a cake of resin ; the internal coating is first removed by the hand, or better a glass rod, and then the glass vessel. The coatings are found to contain very little electricity, and if they are placed on the table they are restored to the neutral state. Nevertheless, when the jar is put together again, as represented in the figure at A, a shock may be taken from it almost as strong as if the coatings had not been removed. It is therefore concluded that the coatings merely play the part of conductors, distributing the electricity over the surface of the glass, which thus becomes polarised, and retains this state even when placed on the table, owing to its imperfect con- ductivity. The experiment may be conveniently made by forming a Leyden jar, of which the inside and outside coatings are of mercury, charging it ; then, having mixed the two coatings, the apparatus is put together again, upon which a discharge may be once more taken. 727. Iiiclitenbergr's fig^ures. — This experiment well illustrates the oppo- site electrical conditions of the two coatings of a Leyden jar. Holding a jar charged with positive electricity by the hand, a series of lines are drawn with the knob on a cake of resin or vulcanite ; then having placed the jar on an insulator, it is held by the knob, and another series traced by means 644 Frictional Electricity, [727- of the outer coating. If now an intimate mixture of red lead and flour of sulphur be projected on the cake, the sulphur will attach itself to the posi- tive lines, and the red lead to the negative lines ; the reason being that in mixing the powders the sulphur has become negatively electrified, and the red lead positively. The sulphur will arrange itself in tufts with numerous diverging branches, while the red lead will take the form of small circular spots, indicating a difference in the two electricities on the surface of the resin. 728. Penetration of tbe cbargre. Residual cliargre. — Not only do the electricities adhere to the two surfaces of the insulating medium which separates them, but they penetrate to a certain extent into the interior, as is shown by the following experiment. A condenser is formed of a plate of shellac, and movable metal plates. It is then charged, retained in that state for some time, and afterwards discharged. On removing the metal coatings and examining both surfaces of the insulator, they show no signs of electricity. After some time, however, each face exhibits the presence of some electricity of the same kind as that of the plate with which it was in contact while the apparatus was charged. This can be explained by assuming that the electricity had slowly penetrated from the exterior to the interior during the first phase of the experiment, and had returned to the surface during the second. A phenomenon frequently observed in Leyden jars is of the same nature. When a jar has been discharged and allowed to stand a short time, it ex- hibits a second charge, which is called the electric residu:. The jar may be again discharged, and a second residue will be left, feebler than the first, and so on, for three or four times. Indeed with a delicate electroscope a long succession of such residues may be demonstrated. Time is required for the penetration of the electricities into the mass ; and hence the residue is greater the longer the jar has remained charged. The magnitude of the residue further depends on the intensity of the charge, and also on the degree in which the metal plates are in contact with the insulator. It varies with the nature of the substance, but there is no residue with either liquids or gaseous insulators. Faraday found that with paraffin the residue was greatest, then with shellac, while with glass and sulphur it was least of all. Kohlrausch has found that the residue is nearly pro- portional to the thickness of the insulator. 729. Electric batteries. — The charge which a Leyden jar can take depends on the extent of the coated surface, and for small thicknesses is inversely proportional to the thickness of the insulator. Hence, the larger and thinner the jar the more powerful the charge. But very large jars are expensive, and liable to break; and when too thin, the accumulated electricities are apt to discharge themselves through the glass, especially if it is not quite homogeneous. Leyden jars have usually from ^ to 3 square feet of coated surface. For more powerful charges electric batteries are used. An electric battery consists of a series of Leyden jars, whose internal and external coatings are respectively connected with each other (fig. 573). They are usually placed in a wooden box lined on the bottom with tin foil. 731] Electric Batteries. 645 This lining is connected with two metal handles in the sides of the box. The internal coatings are connected with each other by metallic rods, and the battery is charged by placing the internal coatings in connection with the prime conductor, while the outer coatings are connected with the ground by means of a chain fixed to the handles. A quadrant electrometer fixed to the jar serves to indicate the charge of the battery. Although Fig. 573- there is a large quantity of electricity accumulated in the apparatus the divergence is not great, for it is simply due to the free electricity on the internal coating. The number of jars is usually four, six, or nine. The larger and more numerous they are, the longer is the time required to charge the battery, but the effects are so much the more powerful. When a battery is to be discharged, the coatings are connected by means of the discharging rod, the outside coating being touched first. Great care is required, for with large batteries serious accidents may occur, resulting even in death. 730. The universal discharg-er. — This is an almost indispensable apparatus in experiments with the electric battery. On a wooden stand (fig. 574) are two glass legs, each provided with universal joints, in which movable brass rods are fitted. Between tliese legs is a small ivory table, on which is placed the object under experiment. The two metal knobs being directed towards the objects, one of them is connected with the external coating of the battery, and the moment communication is made between the other and the internal coating by means of the glass dis- charging rod, a violent shock passes through the object on the table. 731. Chargringr by cascade. — A series of Leyden jars are placed each separately on insulating supports. The knob of the first is in connection with the prime conductor of the machine, and its outer coating joined to the knob of the second, the outer coating of the second to the knob of the 646 Frictional Electricity. [731- third, and so on ; the outer coating of the last communicating with the ground. The inner coating of the first receives a charge of positive elec- tricity from the machine, and the corresponding positive electricity set free by induction on its outer coating, instead of passing to the ground, gives a positive charge to the inner coating of the second, which, acting in like manner, developes a charge in the third jar, and so on, to the last, where the positive electricity developed by induction on the outer coating passes to the ground. The jars may be discharged either singly, by con- necting the inner and outer coatings of each jar, or simultaneously by connecting the inner coating of the first with the outer of the last. In Fig. 574- this way the quantity of electricity necessary to charge one jar is avail- able for charging a series of jars. For from the preceding explanation it is clear, that with a series of similar Leyden jars charged by cascade, if we call the charge of positive electricity which the inside of the first jar receives i, it will develope by induction on the outside a quantity in{in< i) of negative electricity and the same quantity 771 of positive electricity which will pass into the inside of the second jar ; this in turn will develope m x 771 =-771^ of negative electricity on the outside of that jar, and the same quantity 711^ of positive electricity will pass into the inside of the third jar, and so forth. Thus it 732J Lanes Electrometer. 647 ni + 7n'' + ;;/-* + nr + will be seen that the quantities of positive electricity developed in a series of n similar jars by the unit charge of positive electricity will be J fji'^ I +m + 7n'^ + ?n^ + . . . . ;;?" — ^= ^, I —m and of negative electricity on the corresponding outsides of . . . m" = -A /, 1 —m Thus, if there be six jars and m = o'<^, the quantity of positive electricity developed by the unit charge is 4-69. If the external coatings of a charged and uncharged jar are placed in connection, and if the inner coatings are now connected, after separating them they are both found to be charged in the same manner. In this process a current has been produced between the outside coatings and one between the inner ones, to which Dove has given the name charge current, and which has all the properties of the ordinary discharge current. 732. XkXeasurement of tbe cbarg^e of a battery. Ziane's electro- meter. — When the outer and inner coatings of a charged Leyden jar are gradually brought nearer each other, at a certain distance a spontaneous discharge ensues. This distance is called the striking distance. It is inversely proportional to the pressure of the air and directly proportional to the electric density of that point of the inner coating at which the dis- charge takes place. As the density of any point of the inner coating, other things remaining the same, is proportional to the entire charge, the striking distance is proportional to the quantity of electricity in a jar. The measurement of the charge of a battery, however, by means of the striking distance, can only take place when the charge disappears. Fig. 575- By means of Lane's electrometer, which depends on an application of this principle, the charge of a jar or battery may be measured. This apparatus, c (fig. 575), consists of an ordinary Leyden jar, near which there is a vertical metallic support. At the upper end is a brass rod, with a knob at one end, which can be placed in metallic connection with the outside of the jar : the rod being movable, the knob can be kept at a measured distance from the knob of the inner coating. Fig. 575 repre- sents the operation of measuring the charge of a jar by means of this ap- paratus. The jar b, whose charge is to be measured, is placed on an in- 648 Prictional Electricity. [732- Fig. 576. sulated stool with its outer coating in metallic connection with the inner coating of Lane's jar c, the outer coating of which is in connection with the ground, or still better with a system of gas or water pipes ; a is the conductor of the machine. When the machine is worked, positive elec- tricity passes into the jar b ; a proportionate quantity of positive electri- city is repelled from its outer coating, passes into the inner coating of the electrometer, and there produces a charge. When this has reached a certain limit, it discharges itself between the two knobs, and as often as such a discharge takes place, the same quantity of positive electricity will have passed from the machine into the battery ; hence its charge is pro- portional to the number of discharges of the electrometer. Harris's unit jar (fig. 576) is an application of the same principle, and is very convenient for measuring quantities of electricity. It consists of a small Leyden phial 4 inches in length, and f of an inch in diameter coated to about an inch from the end, so as to expose about 6 inches of coated surface. It is fixed hori- zontally on a long insulator, and the charging rod connected at P with the conductor of the machine while the outer coating is connected with the jar or battery by the rod tp. When the accumulation of electricity in the interior has reached a certain height depending on the distance of the two balls ;;/ and n, a discharge ensues, and marks a certain quantity of electricity received as a charge by the battery, in terms of the small jar. 733. ]Laws of electric cbargre. — Harris, by means of experiments with the unit jar suitably modified, and Riess, by analogous arrangements, have found, by independent researches, that for small distances the striking distaYice is directly proportional to ihe quantity of electricity, and inversely proportional to the extent of coated surface ; in other words it is propor- tional to the electric density. Thus, taking the surface of one jar as unity, if a battery of six Leyden jars charged by ico turns of the machine has a striking distance of 9 millimetres, a battery of four similar jars charged by 120 turns will have the striking distance of 16*2 millimetres. For 100 I£0 x= i6-2. The charge also depends on the nature of the glass, or other dielectric, of which the jar is made ; and further, is stated by Wheatstone to be inversely proportional to the square of the thickness of the dielectric. Riess has also found that when a battery or jar is discharged in the striking distance, a charge still remains, for when the coatings are brought nearer a similar discharge may be taken, and so on. The amount of this residual charge when the discharge takes place at the greatest striking distance is always in the safjie prop07'tion to the entire charge. In Riess's -734] Voltds Condensing Electroscope. - 649 experiments, 0-846 or j| of the total charge disappear, and only j\ remain. 734. Volta's condensing- electroscope. — The condensing electroscope invented by Volta is a modification of the ordinary gold leaf electroscope (705). The rod to which the gold leaves are affixed terminates in a disc instead of in a knob, and there is another disc of the same size pro- vided with an insulating glass handle. The discs are covfered with a layer of insulating shellac varnish (fig. 577). Fig. 577- Fig. 578. To render very small quantities of electricity perceptible by this appa- ratus, one of the plates, which thus becomes the collecting plate, is touched with the body under examination. The other '^\2A.^^\\\q condensing plate, is connected with the ground by touching it with the finger. The elec- tricity of the body, being diffused over the collecting plate, acts induc- tively through the varnish on the neutral fluid of the other plate, attracting the opposite electricity, but repelling that of fike kind. The two elec- tricities thus become accumulated on the two plates just as in a condenser, but there is no divergence of the leaves, for the opposite electricities counteract each other. The finger is now removed, and then the source of electricity, and still there is no divergence ; but if the upper plate be raised (fig. 578) the neutralisation ceases, and the electricity being free to move diffuses itself over the rod and the leaves, which then diverge widely. The delicacy of the apparatus is increased by adapting to the foot of the apparatus two metal rods, terminating in knobs, for y F 650 Frictional Electricity, [734- tliese knobs, being excited by induction from the gold leaves, react upon them. A still further degree of delicacy is attained by replacing the rods by two Bohnenberger's dry piles, one of which presents its positive and the other its negative pole. Instead of two gold leaves there is only one ; the least trace of electricity causes it to oscillate either to one side or to the other, and at th'e same time shows the kind of electricity. 735. Thomson's electrometer. — Sir William Thomson has devised a new and delicate form of electrometer, by which quantitative measure- ments of the amount of electrical charge may be made. The principle of this instrument may be understood from the following description of a model of it constructed for lecture purposes by Mr. Becker. A hght flat broad aluminium needle hangs by a very thin wire from the inner coating of a charged Leyden jar, the outer coating being in con- ducting communication with the earth. The whole apparatus is enclosed within a glass shade and the air kept dry by means of a dish of sulphuric acid ; there is, therefore, very little loss of electricity and the needle remains at a virtually constant charge. The needle is suspended over four quadrantal metal plates insulated from each other and from the ground by resting on glass stands. The alternate quadrants are in conducting communication with each other by means of wires. If now all the quadrants are in the same electrical condition, the needle will be at rest when it is directly over one of the diametrical slits. But if the two pairs of quadrants ^'^' ^^^" are charged with opposite kinds of electricity, as when, for instance, they are connected with the two poles of an insulated voltaic cell by means of the knobs, then each end of the needle will be repelled by the pair of quadrants which are electrified like itself, and will be attracted by the other pair. It will thus be subject to the action of a couple tending to set it obliquely to the slit. In order to render the slightest motion of the needle visible, a small silver concave mirror with a radius of about a metre is fixed above it. The light of a petroleum lamp, not represented in the figure, strikes against this and is reflected as a spot of light on a horizontal scale. Any deflection of the needle either on one side or the other, is indicated by the motion of the spot of light on the scale (491). ^% ^7317/ Effects of the Electric Discharge. 651 i THE ELECTRIC DISCHARGE. \ ^ 736. Effects of the electric discbargre. — The recombination of the two electricities which constitutes the electrical discharge may be either continuous or sudden ; continuous, or of the nature of a current, as when the two conductors of a cylinder machine are joined by a chain or a wire ; and sudden, as when the opposite electricities accumulate on the surface of two adjacent conductors, till their mutual attraction is strong enough to overcome the intervening resistances, whatever they may be. But the difference between a sudden and a continuous discharge is one of degree, and not of kind, for there is no such thing as an absolute non-conductor, r\ ^ and the very best conductors, the metals, offer an appreciable resistance to the passage of electricity. Still, the difference at the two extremes of the scale is sufficiently great to give rise to a wide range of phenomena. ^ xp Riess has shown that the discharge of a battery does not consist in a^^^ simple union of the positive and negative electricities, but that it consists of a series of successive partial discharges. The direction of the discharge depends mainly on the length and nature of the circuit. By observations of the image of the spark in a rotating mirror, and of the luminous phenomena at the positive and negative poles when the discharge takes place in highly rarefied gases, as well as by the manner in which a magnet affects the phenomena of discharge, Feddersen and Paalzow have shown that the discharge consists of a series of oscillating currents alternately in opposite directions. As the resistance of the circuit increases, the number of these alternating discharges decreases, but at the same time their duration is greater. With very great resistance, as for instance when a wet thread is interposed, the alternating discharge becomes a single one. The phenomena of the discharge are usually divided into Xki^ physio- logical, luminous, mechanical, magnetical, and chemical effects, 'j'i^']. Physiolog^ical effects. — The physiological effects are tliose pro- duced on living beings, or on those recently deprived of life. In the first case they consist of a violent excitement which the electricity exerts on the sensibility and contractibihty of the organic tissues through which it passes ; and in the latter, of violent muscular convulsions which re- semble a return to life. The shock from the electrical machine has been already noticed ('717). The shock taken from a charged Leyden jar by grasping the outer coating with one hand and touching the inner with the other, is much more violent, and has a peculiar character. With a small jar the shock is felt in the elbow ; with a jar of about a quart capacity it is felt across the chest ; and w4th jars of still larger dimensions in the stomach. A shock may be given to a large number of persons simultaneously by means of the Leyden jar. For this purpose they must form a chain by joining hands. If then the first touches the outside coating of a charged jar, while the last at the same time touches the knob, all receive a simul- taneous shock, the intensity of which depends on the charge, and on the 652 Frictional Electricity. [737- number of persons receiving- it. Those in the centre of the chain are found to receive a less violent shock than those near the extremities. The Abbe Nollet discharged a Leyden jar through an entire regiment of 1,500 men, who all received a violent shock in the arms and shoulders. With large Leyden jars and batteries the shock is sometimes very dangerous. Priestley killed rats with batteries of 7 square feet coated surface, and cats with a battery of about 4|- square yards coating. 738. ]Luxninous effects. — The recombination of two electricities of high potential (752) is always accompanied by a disengagement of light, as is seen when sparks are taken from a machine, or when a Leyden jar is discharged. The better the conductors on which the electricities are accumulated, the more brilliant is the spark ; its colour varies not only with the nature of the bodies, but also with the nature of the surrounding medium and with the pressure. The spark between two charcoal points is yellow, between two balls of silvered copper it is green, between knobs of wood or ivory it is crimson. In atmospheric air at the ordinary pres- sure the electric spark is white and brilliant ; in rarefied air it is reddish ; and in vacuo it is violet. In oxygen, as in air, the spark is white; in hydrogen it is reddish ; and green in the vapour of mercury, in carbonic acid it is also green, while in nitrogen it is blue or purple, and accom- panied by a peculiar sound. Generally speaking, the higher the potential the greater is the lustre of the spark. It is asserted by Fusinieri that in the electric spark there is always a transfer of material particles in a state of extreme tenuity, in which case the modifications in colour must be due to the transport of ponderable matter. When the spark is viewed through a prism, the spectrum obtained is full of dark lines (539), the number and arrangement of which depend on the nature of the poles. 739. Spark and brush discharg:e. — The shapes which luminous electric phenomena assume may be classed under two heads — the spark and the brush. The brush forms when the electricity leaves the con- ductor ifi a continuous flow; the spark, when the discharge is discon- tinuous. The fonnation of one or the jother of these depends on the nature of the conductor and on the nature of the conductor in its vicinity ; and small alterations in the position of the surrounding conductors trans- form the one into the other. The spark which at short distances appears straight, at longer distances has a zigzag-shape with diverging branches. Its length depends on the density at the part of the conductor from which it is taken ; and to obtain the longest sparks the electricity must be of as high density as possible, but not so high as to discharge spontaneously. With long sparks the luminosity is different in different parts of the spark. The brush derives its name from the radiating divergent arrangement of the light, and presents the appearance of a luminous cone, whose apex touches the conductor. Its size and colour differ with the nature and form of the conductor; it is accompanied by a peculiar hissing noise, very different from the sharp crack of the spark. Its luminosity is far less than that of the spark, for while the latter can easily be seen by -741] The Electric Egg. 653 daylight, the former is only visible in a darkened room. The brush discharge may be obtained by placing on the conductor a wire filed round at the end, or, with a powerful machine, by placing a small bullet on the conductor. The brush fiom a negative conductor is less than from a positive conductor; the cause of this difference has not been satis- factorily made out, but may originate in the fact, which Faraday has observed, that negative electricity discharges into the air at a some- what lower density than positive electricity ; so that a negatively charged knob sooner attains that density at which spontaneous discharge takes place than does a positively charged one, and therefore discharges the electricity at smaller intervals and in less quantities. When electricity, in virtue of its high density, issues from a conductor, no other conductor being near, the discharge takes place without noise, and at the places at which it appears there is a pale blue luminosity, called the electrical glow, or on points, a star-like centre of light. It is seen in the dark by placing a point on the conductor of the machine. 740. Electric eggr. — The influence of the pressure of the air on the electric Hght may be studied by means of the electric egg. This consists of an ellipsoidal glass vessel (fig. 580), with metal caps at each end. The lower cap is provided with a stopcock, so that it can be screwed into an air pump, and also into a heavy metal foot. The upper metal rod moves up and down in a leather stuffing box; the lower one is fixed to the cap. A vacuum having been made, the stopcock is turned, and the vessel screwed into its foot; the upper part is then connected with a powerful electrical machine, and the lower one with the ground. On work- ing the machine, the globe becomes filled with a feeble violet light continuous from one end to the other, and resulting from the recomposi- tion of the positive fluid of the upper cap with the negative of the lower. If the air be gradu- ally allowed to enter by opening the stopcock, the light now appears white and brilliant, and is only seen as an ordinary intermittent spark. Fig. 580. Some beautiful effects of the electric light are obtained by means of Geissler's tubes, which will be noticed under Dynamical Electricity. 741. ]Luminous tube, square, and bottle. — The luminous tube (fig. 581) is a glass tube about a yard long, round which are arranged in a spiral form a series of lozenge-shaped pieces of tin foil, between which are very short intervals. There is a brass cap with hooks at each end, in which the spiral terminates. If one end be presented to a machine in action, while the other is held in the hand, sparks appear simultaneously 654 Frictional Electricity. [741 at each interval, and produce a brilliant luminous appearance, especially in the dark. # Fig. 581. The luminous pane (fig. 582) is constructed on the same principle, and consists of a square of ordinary glass, on which is fastened a narrow strip of tin foil folded parallel to itself for a great number of times. Spaces are cut out of this strip so as to represent any figure, a portico for example- Fig. 582. The pane being fixed between two insulating supports, the upper extremity of the strip is connected with the electrical machine, and the lower part with the ground. When the machine is in operation, a spark appears at each interval, and reproduces in luminous flashes the object represented on the glass. The luminous jar (fig. 583) is a Leyden jar, whose outer coating consists of a layer of varnish strewed over with metallic powder. A strip of tin fitted on the bottom is connected with the ground by means of a chain; a second band at the upper part of the coating has a projecting part, and the rod of the bottle is curved so that the knob is -742] Calorific Effects of the Electric Discharge. 655 about f of an inch distant from the projection. This bottle is suspended from the machine, and as rapidly as this is worked, large and brilliant sparks pass between the knob and the outer coating, illuminating the- outside of the apparatus. 742. Calorific effects. — Besides being luminous, the electric spark is a source of intense heat. When it passes through inflammable liquids, as ether or alcohol, it inflames them. An arrangement for effecting this is represented in figure 584. It is a small glass cup through the bottom of which passes a metal rod, terminating in a knob and fixed to a metal foot. A quantity of liquid sufficient to cover the knob is placed in the vessel. The outer coating of the jar having been connected with the foot by means of a chain, the spark which passes when the two knobs are brought near each other inflames the liquid. With ether the experiment succeeds very well, but alcohol requires to be first warmed. Coal gas may also be ignited by means of the electric spark. A person Fig. 583. Fig. 584. Standing on an insulating stool places one hand on the conductor of a machine which is then worked, while he presents the other to the jet of gas issuing from a metallic burner. The spark which passes ignites the gas. When a battery is discharged through an iron or steel wire it becomes heated, and even made incandescent or melted, if the discharge is very powerful. 656 Frictioiial Electidcity. [742- The laws of this heating effect have been investigated independently by Harris and by Riess by means of the electric thermometer. This is essentially an air thermometer, across the bulb of which is a fine platinum wire. When a discharge is passed through the wire it becomes heated, expands the air in the bulb, and this expansion is indicated by the motion of the liquid along the graduated stem of the thermometer. In this way it has been found that the increase in temperature in the wire is proportional to the electric density multiplied by , the quantity of electricity ; and since the electric density is equal to the quantity of electricity — usually measured by the number of discharges of the unit jar (732), divided by the surface, the heating effect is proportional to the square of the number of discharges divided by the surface ; that is, h = ?-. s Rie?s has also found that with the same charge, but with wires of different dimensions, the rise of temperature is inversely as the fourth power of the diameter. Thus, compared with a given wire as unity, the rise of temperature in a wire of double or treble the diameter would be ^^ or g\ as small ; but as the masses of these wires are four and nine times as great, the heat produced v^onldi be respectively \ and | as great as in a wire of unit thickness. When an electric discharge is sent through gunpowder placed on the table of a Henley's discharger, it is not ignited, but is projected in all directions. But if a wet string be interposed in the circuit a spark passes which ignites the powder. This arises from the retardation which electricity experiences in traversing a semi-conductor, such as a wet string : for the heating effect is proportional to the duration of the discharge. When a charge is passed through sugar, heavy spar, fluorspar, and other subtances, they afterwards become phosphorescent in the dark. Eggs, fruit, etc., may be made luminous in the dark in this way. When a battery is discharged through a gold leaf, pressed between two glass plates or between two silk ribbons, the gold is volatilised in a violet powder which is finely divided gold. In this way what are called electric portraits are obtained. Siemens has shown that when a jar is charged and discharged several times in succession the glass becomes heated. Hence there must be movements of the molecules of the glass as Faraday supposed. 743. nxagrnetic effects. — By the discharge of a large Leyden jar or battery, a steel wire may be magnetised if it is laid at right angles to a conducting wire through which the discharge is effected, either in contact with the wire or at some distance. And even with less powerful discharges, a steel bar or needle may be magnetised by placing it inside a tube on which is coiled a fine insulated copper wire. On passing the discharge through this wire the steel becomes magnetised. To effect a deflection of the magnetic needle by the electric current produced by frictional electricity is more difficult. It may be accom- plished by making use of a galvanometer consisting of 400 or 500 turns of fine silk-covered wire, which is further insulated by being -744] Mechanical Effects of the Electric Discharge. 657 coated with shellac varnish, and by separating the layers by means of oiled silk. When the prime conductor of a machine in action is con- nected with one end of the galvanometer wire, and the other with the_ ground, a deflection of the needle is produced. 744. lUEecbanical effects. — The mechanical effects are the violent lacerations, fractures, and sudden expansions which ensue when a power- ful discharge is passed through a badly-conducting substance. Glass is Fig- 585- perforated, wood and stones are fractured, and gases and liquids are vio- lently disturbed. The mechanical effects of the electric spark may be demonstrated by a variety of experiments. Figure 585 represents an arrangement for perforating a piece of glass or card. It consists of two glass columns, with a horizontal cross-piece, in which is a pointed conductor, B. The piece of glass, A, is placed on an insulating glass support, in which is placed a second conductor, terminating also in a point, which is connected with the outside of the battery, while the knob of the inner coating is brought near the knob of B. When the discharge passes between the two conductors the glass is perforated. The experiment only succeeds with a single jar when the glass is very thin ; otherwise a battery must be used. The perturbation and sudden expansion which the discharge produces may be illustrated by means of Kinnersley's thermometer. This consists of two glass tubes (fig. 586), which fit into metallic caps, and communicate with each other. At the top of the large tube is a rod terminating in a knob, and moving in a stuffing-box, and at the bottom there is a similar rod with a knob. The apparatus contains water up to the level of the lower knob. When the electric shock passes between the two knobs F F 3 658 Frictionai Electricity. [744 the water is driven out of the larger tube and rises to a shght extent in the small one. The level is immediately re-established, and therefore the phenomenon is not due to an increase of temperature. Fig. 586 For the production of mechanical effects the universal discharger, fig. 574, is of great service. A piece of wood, for instance, placed on the table between the two conductors, is split when the discharge passes. 745. Chemical effects. — The chemical effects are the decompositions and recombinations effected by the passage of the electric discharge. When two gases which act on each other are mixed in the proportions in which they combine, a single spark is often sufficient to determine their combination ; but when either of them is in great excess, a succession of sparks is necessary. Priestley found that when a series of electric sparks was passed through moist air, its volume diminished, and blue litmus introduced into the vessel was reddened. This, Cavendish found, was due to the formation of nitric acid. Several compound gases are decomposed by the continued action of the electric spark. With olefiant g'as, sulphuretted hydrogen, and am- monia, the decomposition is complete ; while carbonic acid is partially decomposed into oxygen and carbonic oxide. The electric discharge also by suitable means can feebly decompose water, oxides, and salts ; but though the same in kind, the chemical effects of statical electricity are by no means so powerful and varied as those of dynamical electricity. The chemical action of the spark is easily demonstrated by means of a solution of iodide of potassium. A small lozenge-shaped piece of filter- ing paper, impregnated with iodide of potassium, is placed on a glass plate, and one corner connected with the ground. When a few sparks from a -746] Chemical Effects of the Electric Discharge. 659 conductor charged with positive electricity are taken at the other corner, brown spots are produced, due to the separation of iodine. Among the chemical effects must be enumerated the formatioh"~of~ ozone, which is recognised by its peculiar odour and by certain chemical properties. The odour is perceived when electricity issues through a series of points from a conductor into the air. Its true nature is not accurately known ; some regard it, and with great probability, as an alJotropic modification of oxygen, and others as a teroxide of hydrogen. T\vQ electric pistol \'=, 2. svtxdXS. apparatus which serves to demonstrate the chemical effects of the spark. It consists of a brass vessel (fig. 587), in which is introduced a detonating mixture of two volumes of hydrogen and one of oxygen, and which is then closed with a cork. In a tubulure in the side there is a glass tube, in which fits a metallic rod, terminated by the knobs A and B. The knob is held as represented in fig. 588, and brought near the machine. The knob A becomes negatively, and B positively electrified by induction from the machine, and a spark passes between the conductor and A. Another spark passes at the same time between the knob B and the side : this determines the combination of Fig. 587- Fig. 5^ the gases, which is accompanied by a great disengagement of heat, and the vapour of water formed acquires such an expansive force, that the cork is projected with a report like that of a pistol. 746. Application of tbe electrical dischargre to firing: mines. — By the labours of Prof. Abel in this country, and of Baron von Ebner in Austria, the electrical discharge has been applied to firing mines for military purposes, and the methods have acquired a high degree of per- fection. The principle on which the method is based may be understood from the following statement : One end of an insulated wire in which is a small break is placed in contact with the outside of a charged Leyden jar, the other end being placed near the inner coating. If now this end be brought in contact with the inner coating the jar is discharged and a spark strikes across the break ; and if there be here some explosive compound it is ignited, and this ignition may of course be communicated to any gunpowder in which it is placed. If on one side of the break, instead of having an insulated wire direct back to the outer coating of the Leyden jar, an uncovered wire be led into the ground, the outside of the jar being also connected 66o Frictional Electricity. [746 with the ground, the result is unchanged, the earth acting as a return wire. Moreover, if there be several breaks, the explosion will still ensue at each of them, provided the change be sufficiently powerful. In the actual application it is of course necessary to have an arrange- ment for generating frictional electricity which shall be simple, portable, powerful, and capable of working in any weather. In these respects the electrical machine devised by Von Ebner is admirable. Fig. 589 repre- Fig. 589. sents a view of this instrument as constructed by Messrs. Elliott, part of the case being removed to show the internal construction. It consists of two circular plates of ebonite, a, mounted on an axis so that they are turned by a handle, b^ between rubbers, which are so arranged as to be easily removed for the purposes of amalgamation, etc. Fastened to a knob on the base of the apparatus and projecting between the plates is a pointed brass rod, which acts as a collector of the electricity. The condenser or Leyden jar arrangement is inside the case, part of which has been removed to show the arrangement. It consists of India-rubber cloth, coated on each side with tinfoil, and formed into a roll for the purpose of greater compactness. By means of a metal button the knob is in contact with one tmfoil coating, which thus receives the electricity of the machine, and corresponds to the inner coating of the Leyden jar. Another button, connected with the other tinfoil coating, -746] Firing Mines by Electricity. 66 r rests on a brass band at the base of the apparatus which is in metallic contact with the cushions, the knob d, and the perforated knob in which slides a rod at the front of the apparatus. These are all in connectioiT with the earth. The knob e is in metallic connection with a disc g pro- vided with a light arm. By means of a flexible chain this is so connected with a trigger on the side of the apparatus, not represented in the figure, that when the trigger is depressed, the arm, and therewith the knob ^, is brought into contact with the inner coating of the condenser. On depressing the trigger, after a certain number of turns, a spark passes between the knob e and the sliding rod, and the striking distance is a measure of the working condition of the instrument. The fuse used is known as AbeVs electrical fuse, and has the following construction. The ends of two fine copper wires, fig. 591, are imbedded in a thin solid gutta percha rod, parallel to each other, but at a distance of about I -5 mm. At the lower end of the gutta percha a small cap of paper or tinfoil cc is fastened, in which is placed a small quantity of the priming composition, which consists of an intimate mixture of subsulphide of copper, subphosphide of copper, and chlorate of potassium. The paper is fastened down so that the exposed ends of the wires are pre- served in close contact with the powder. This is the actual fuse ; for service the capped end of the fuse is Fig. 590. Fig- 591 placed in a perforation in the rounded head of a wooden cylinder, so as to project slightly into the cavity^ of the cyhnder. This cavity is filled with meal powder which is well rammed down, so that the fuse is firmly 662 Frictional Electricity. [746- imbedded. It is afterwards closed by a plug of gutta percha, and the whole is finally coated with black varnish. The free ends of the wires a a are pressed into small grooves in the head of the cyhnder (fig. 591), and each end is bent into one of the small channels with which the cylinder is provided, and which are at right angles to the central perforation. They are wedged in here by driving in small copper tubes, the ends of which are then filed flush with the surface of the cylinder. The bared ends of two insulated conducting wires are ^hen pressed into one of the small copper tubes or eyes, and fixed there by bending the wire round on to the wood, as shown at c. The conducting wire used in firing may be thin, but it must be well insulated. One end, which is bared, having been pressed into the hole d of the fuse, the other is placed in proximity to the exploder. Into the other hole d' of the fuse a wire is placed which serves as earth wire, care being ta:ken that there is connection between the two wires. The fuse having been introduced into the charge the earth wire is placed in good connection with the ground. The knob f of the exploder is also con- nected with the earth by leading uncovered wire into water or moist earth, and the condition of the machine tested. The end of the insulated wire is then connected with the knob e and the rod drawn down ; at the proper signal the handle is turned the requisite number of times, and when the signal is given the trigger is depressed, and the explosion ensues. When a number of charges are to be fired they are best placed in a single circuit, care being taken that the insulation is good. 747. Duration of the electric spark. — Wheatstone measured the duration of the electric spark, by means of the rotating mirror which he invented for this purpose. At some distance from this instrument, which can be made to rotate with a measured velocity, a Leyden jar is so arranged that the spark of its discharge is reflected from the mirror. Now, from the laws of reflection (489) the image of the luminous point describes an arc of double the number of degrees which the mirror describes, in the time in which the mirror passes from the position in which the image is visible to that in which it ceases to be so. If the duration of the image were absolutely instantaneous the arc would be reduced to a mere point. Knowing the number of turns which the mirror makes in a second, and measuring, by means of a divided circle, the number of degrees occupied by the image, the duration of the spark would be determined. In one experiment Wheatstone found that this arc was 24°; Now, in the time in which the mirror traverses 360° the image traverses 720° ; but in the experiment the mirror made 800 turns in a second, ancj therefore the image traversed 576,000° in this time; and as the arc was 24°, the image must have lasted the time expressed by i?!^ or 24^00 of a second. Thus the discharge is not instantaneous, but has a certain duration, which, however, is excessively short. Feddersen found that when greater resistances were interposed in the circuit through which the discharge was effected, that the duration of the spark was increased. With a tube of water 9 mm. in length, the spark lasted 0-0014 second; and with one of 180 mm. its duration was 0-0183 -747] Duration of the Electric Spark. 66^ second. The duration increased also with the striking distance, and with the dimensions of the battery. _ To determine the duration of the electric spark MM. Lucas and Cazin have used a most accurate method, by which it may be measured in millionths of a second. The method is an application of the vernier. A disc of mica 15 centimetres in dia- meter is blackened on one face, and at the edge are traced 180 equal divisions in very fine transparent lines. The disc Fig. 592. is mounted on a horizontal axis, and by means of a gas engine a velocity of 100 to 300 turns in a second may be imparted to it. A second disc of silvered glass of the same radius is mounted; on the same axis as the other and very close to it at its upper edge six equidistant transparent lines are traced forming a vernier with the lines on the mica. For this, the distance between two consecutive lines on the two discs is such that five divisions of the mica disc DC, correspond to six divisions of the glass disc AB as seen in the figure 592. Thus the vernier gives the sixths of a division of the mica disc (10). In the apparatus the hnes AB are not above the lines CD, but are at the same distance from the axis, so that the latter coincide successively with the former. The mica disc is contained in a brass box D (fig. 593) on the hinder face of which is fixed the vernier. In the front face is a glass window O, through which the coincidence of the two sets of lines can be observed by means of a magnifying lens L. The source of electricity is a battery of 2 to 8 jars, each having a coated surface of 1243 square centimetres and charged continu- ously by a Holtz's machine. The sparks strike between two metal bulbs a and b^ 1 1 millimetres in diameter. Their distance can be varied, and at the same time measured, by means of a micrometric screw r. The two opposite electricities arrive by wires in and ;/, and the sparks strike at the principal focus of a condensing lens placed in the collimator C, so that the rays which fall on the vernier are parallel. The motion is transmitted to the toothed wheels and to the mica disc by means of an endless band, which can be placed on any one of three pullies P. so that the velocity may be varied. At the end of the axis of the pullies is a bent wire which moves a counter, V, that marks on three dials, the number of turns of the disc. These details being premised, suppose the velocity of the disc is 400 turns in a second. In each second 400 x 180 or 72,000 lines pass before the observer's eye in each second ; hence an interval of -^^^ of a second elapses between two consecutive lines. But as the spark is only seen when one of the lines of the disc coincides with one of the six lines of the vernier ; and as this gives sixths of a division of the movable disc, when the latter has turned through a sixth of a division, a second coincidence is produced; so that the interval between two successive coincidences is \ = 0-0000023 of a second. 72000 X 6 664 Frictioital Electricity. [747- That being the case, let the duration of a spark be something between 23 and 46 ten millionths of a second ; if it strikes exactly at the moment of a coincidence, it will last until the next coincidence ; and owing to the persistence of impressions on the retina (588) the observer will see two Fig. 593. luminous lines. But if the spark strikes between two coincidences and has ceased when the third is produced only one brilliant line is seen. Thus, if with the above velocity sometimes i and sometimes 2 bright lines are seen, the duration of the spark is comprised between 23 and 46 ten millionths of a second. By experiments of this kind, with a sl:riking distance of 5 millimetres between the bulbs a and b, and varying the number of the jars, MM, Lucas and Cazin obtained the following results : Number of jars. 2 4 6 Duration in millionths of a second. 26 47 55 .-748] Velocity of Electricity. 66 S It will thus be seen that the duration of the spark increases with the number of jars It also increases with the striking distance; but it is independent of the diameter of the bulbs between which the spark strikes. The spark of electrical machines has so short a duration that it could not be measured with the chronoscope. 748. Velocity of electricity. — To determine the velocity of electri- city, Wheatstone constructed an apparatus the principle of which will be understood from fig. 594 : six insulating metal knobs were arranged in a horizontal line on a piece of wood called a spar^ board; of these the knob I was connected with the outer, while 6 could be connected with the inner coating of a charged Leyden jar ; the knob 1 was a tenth of an inch distant from the knob 2 ; while between 2 and 3 a quarter of a mile of insulated wire was interposed: 3 was hkewise a tenth of an inch from 4, and there was a quarter of a mile of wire between 4 and 5 ; lastly, 5 was a tenth of an inch from 6, from which a wire led directly to the inner coating of the Leyden jar. Hence, when the jar was discharged by con- necting the wire from 6 with the inner coating _<>__ of the jar, sparks would pass between i and 2, between 3 and 4, and between 5 and 6. Thus ^'^" ^^'^' the discharge, supposing it to proceed from the inner coating, has to pass in its course through a quarter of a mile of wire between the first and second spark, and through the same distance between the second and third. The spark board was arranged at a distance of 10 feet from the rota- ting mirror, and at the same height, both being horizontal; and the observer looked down on the mirfor. Thus the sparks were visible when the mirror made an angle of 45° with the horizon. Now, if the mirror were at rest or had only a small velocity, the images of the three sparks would be seen as three dots • , but when the mirror had a certain velocity these dots appeared as lines, which were longer as the rotation was more rapid. The greatest length observed was 24°, which, with 800 revolutions in a second, can be shown to correspond to a duration of 24^00 of a second. With a slow rotation the lines present the appearance ^^^~ ; they are quite parallel, and the ends in the same line. But with greater velocity, and when the rotation took place from left to right they presented the appearance ^~' . and when it turned from right to left the appearance — -- , because the image of the centre spark was formed after the lateral ones. Wheatstone found that this displacement amounted to half a degree before or behind the others. This arc corresponds to a duration of ^ or -^^Act^kt, of a second : 2x720x800 11^2000 the space traversed in this time being a quarter of a mile, gives for the velocity of electricity, 288,000 miles in a second, which is greater than that of light. The velocity of dynamical electricity is far less ; and owing 666 Frictional Electricity. [748- to induction, the transmission of a current through submarine wires is comparatively slow. In the above experiment the images of the two outer sparks appear simultaneously in the mirror, from which it follows that the' electric current issues simultaneously from the two coatings of the Leyden jar. From certain theoretical considerations based upon measurements of constant electrical currents, Kirchhoff has concluded that the motion of electricity in a wire in which it meets with no resistance is like that of a wave on a stretched string, and has the velocity 192,924 miles in a second, which is about that of light in vacuo (477). According to Walker, the velocity of electricity is 18,400 miles, and according to Fizeau and Gounelle, it is 62,100 miles in iron, and 111,780 in copper wire. These measurements, however, were made with telegraph wires, which induce opposite electricities in the surrounding media : there is thus produced a resistance which diminishes the velocity. The velocity is less therefore in water than in air. The nature of the con- ductor appears to have some influence on the velocity; but not the thickness of the wire, nor the potential of the electricity. For atmospheric electricity, reference must be made to the chapter on Meteorology. -749] Galvani's Experiment. 667 BOOK X. DYNAMICAL ELECTRICITV. CHAPTER I. VOLTAIC PILE. ITS MODIFICATIONS. 749. Galvani's experiment and tbeory. — The fundamental experi- ment which led to the discovery of dynamical electricity is due to Galvani, professor of anatomy in Bologna. Occupied with investigations on the in- fluence of electricity on the nervous excitability of animals, and especially « Fig. 595. of the frog, he observed that when the lumbar nerves of a dead frog were connected with the crural muscles by a metallic circuit, the latter became briskly contracted. To repeat this celebrated experiment, the legs of a recently killed frog are prepared, and the lumbar nerves on each side of the vertebral column 66S Dynamical Electricity. [749- are exposed in the form of white threads. A metal conductor, composed of zinc and copper, is then taken (fig. 595), and one end introduced be- tween the nerves and the vertebral column, while the other touches one of the muscles of the thighs or legs ; at each contact a smart contraction of the muscles ensues. Galvani had some time before observed that the electricity of machines produced in dead frogs analogous contractions, and he attributed the phenomena first described to an electricity inherent in the animal. He assumed that this electricity, which he called vital Jiidd, passed from the nerves to the muscles by the metallic arc, and v/as thus the cause of con- traction. This theory met with great support, especially among physiolo- gists, but it was not without opponents. The most considerable of these was Alexander Volta, professor of physics in Pavia. 750. Volta's fundamental experiment. — Galvani's attention had been exclusively devoted to the nerves and muscles of the frog ; Volta's was directed upon the connecting metal. Resting on the observation, which Galvani had also made, that the contraction is more energetic when the connecting arc is composed of two metals than when there is only one, Volta attributed to the metals the active part in the phenomenon of con- traction. He assumed that the disengagement of electricity was due to their contact, and that the animal parts only officiated as conductors, and at the same time as a very sensitive electroscope. By means of the condensing electroscope, which he had then recently invented, Volta devised several modes of showing the disengagement of electricity on the contact of metals, of- which the following is the easiest to perform : The moistened finger being placed on the upper plate of a condensing electroscope (fig. 577), the lower plate is touched with a plate of copper, r, soldered to a plate of zinc, z^ whicli is held in the other hand. On breaking the connection and lifting the upper plate (fig. 578), the gold leaves diverge, and, as may be proved, with negative electricity. Hence, when soldered together, the copper is charged with negative electricity, and the zinc with positive electricity. The electricity could not be due either to friction or pressure ; for if the condensing plate, which is of copper, is touched with the zinc plate 2^ the copper plate to which it is soldered being held in the hand, no trace of electricity is observed. A memorable controversy arose between Galvani and Volta. The latter was led to give greater extension to his contact theory, and pro- pounded the principle that when two heterogeneous substances are placed in cofztact, one of them always assumes the positive and the other the negative electrical condition. In this form Volta's theory obtained the assent of the principal philosophers of his time. Galvani, however, made a number of highly interesting experiments with animal tissues. In some of these he obtained indications of contraction, even though the sub- stances in contact were quite homogeneous. 751. Disengragrement of electricity in chemical actions. — The contact theory which Volta had propounded, and by which he explained -751] Disengagement of Electricity in Chemical Actions. 669 the action of the pile, soon encountered objectors. Fabroni, a country- man of Volta, having observed that in the pile the discs of zinc became oxidised in contact with the acidulated water, thought that this oxidation" was the principal cause of the disengagement of electricity. In England , Wollaston soon advanced the same opinion, and Davy supported it by many ingenious experiments. It is true that in the fundamental experiment of the contact theory (750) Volta obtained signs of electricity. But De la Rive has shown that if the zinc be held in a wooden clamp, all signs of electricity disappear, and that the same is the case if the zinc be placed in gases, such as hydrogen or nitrogen, which exert upon it no chemical action. De la Rive has ac- cordingly concluded that in Volta's original experiment the disengage- ment of electricity is due to the chemical actions which result from the perspiration and from the oxygen of the atmosphere. The development of electricity in chemical actions may be demon- strated in the following manner by means of the condensing electroscope (734). A disc of moistened paper is placed on the upper plate of the condenser, and on this a zinc capsule, in which some dilute sulphuric acid is poured. A platinum wire, communicating with the ground, but insu- lated from the sides of the vessel, is immersed in the liquid, and at the same time the lower plate of the condenser is also connected with the 'ground by touching it with the moistened finger. On breaking contact and removing the upper plate, the gold leaves are found to be positively electrified, proving that the upper plate has received a charge of negative electricity. By a variety of analogous experiments it may be shown that various chemical actions are accompanied by a disturbance of the electrical equi- librium ; though of all chemical actions those between metals and liquids are the most productive of electricity. All the various resultant effects are in accordance with the general rule, that when a liquid acts chemi- cally on a metal the liquid assumes the positive, and the metal the nega- tive condition. In the above experiment the sulphuric acid, by its action on zinc becomes positively electrified, and its electricity passes off through the platinum wire into the ground, while the negative electricity excited in the zinc acts on the condenser just as an excited rod of sealing-wax would do. In many cases the electrical indications accompanying chemical actions are but feeble, and require the use of a very delicate electroscope to render them apparent. Thus, one of the most energetic chemical actions, that of sulphuric acid upon zinc, gives no more free electricity than water alone does with zinc. Opinion, which in this country at least, had mainly by the influence of Faraday's experiments tended in favour of the purely chemical origin of the electricity produced in voltaic action, has of late inclined more towards the contact theory. The following experiments due to Sir W. Thomson {Papers on Electrostatics, Macmillan & Co., p. 317), afford per- haps the most conclusive arguments hitherto adduced in favour of the latter view. 6/0 Dynamical Electricity. [751- A very light metal bar was suspended by a fine wire so as to be movable about an axis, perpendicular to the plane of a ring made up of two halves, one of copper and the other of zinc. When the two halves of the ring were in contact, or were soldered together, the light bar turned from the copper to the zinc when it was negatively electrified, and from the zinc to the copper when it was positively electrified, thus showing that the contact of the two metals causes them to assume different electrical conditions, the zinc taking the positive, and the copper the negative electricity. When however, the two halves instead of being in metallic contact were connected by a drop of water, no change was produced in the position of the bar by altering its electrification, provided it hung quite symmetrically relative to the two halves of the ring. This result shows that under the circumstances mentioned, no difference is produced in the electrical condition of the two metals. Hence the conclusion has been drawn by Sir W. Thomson and others, that the movement of electricity in the galvanic circuit is entirely due to the electrical difference produced at the surfaces of contact of the dissimilar metals. There are, however, other facts which are not easily harmonised with this view ; and indeed the last mentioned experiment can hardly be regarded as proving that in all cases two different metals connected by an electrolytic (772) liquid, assume the same electrical condition. It may' therefore still be regarded as possible, or even probable, that the contact between the metals and the liquids of a cell contribute at least in some cases to the production of the current. An instructive discussion of this question with some additional experi- mental evidence in favour of the chemical theory, will be found in a paper by Mr. J, A. Fleming published in the proceedings of the Physical Society (Taylor and Francis). 752. Potential. — It may be convenient to explain here what is meant by the term potential, which has of late come into extended use in speak- ing of electrical phenomena, to express the conditon of an electrified body and of the space in its neighbourhood. It may be taken to represent what has been frequently called tension, though that word has been often used to express two different things. Introduced originally into electrical science by Green, out of con- siderations arising from the mathematical treatment of the subject, the use of the terrn potential is justified and recommended by the clearness with which it brings out the relations of electricity to work. We have already seen, that in order to lift a certain mass against the attraction of gravitation (56-59) there must be a definite expenditure of work, and the equivalent of this work is met with in the energy which the lifted mass retains, or what is called the potential energy of posi- tion. Let us now suppose that we have a large insulated metal sphere charged with positive electricity, and at a distance which is very great in comparison with the size of the sphere, a small insulated sphere charged -752] Potential. 671 with the same kind of electricity. If now we move the small sphere to any given point nearer the larger one, we must do a certain amount ot work upon it to overcome the repulsion of the two electricities. The work required to be done against electrical forces, in order to move the unit of positive electricity from an infinite distance to a given point in the neighbourhood of an electrified conductor is called the potential at this point. If, in the above case, the larger sphere were charged with negative electricity, then instead of its being needful to do work in order to bring a unit of positive electricity towards it, work would be done by electrical attraction, and the potential of the point near the charged sphere would thus be negative. The potential at any point may also be said to be the work done against electrical force, in moving unit charge of negative electricity from that point. The amount of work required to move the unit of positive electricity against electrical force, from any one position to any other is equal to the excess of the electrical potential of the second position over the electrical potential of the first. This is, in effect, the same as what has been said above, for at an infinite distance the potential is zero. We cannot speak of potential in the abstract, any more than we can speak of any particular height, without at least some tacit reference to a standard of level. Thus, if we say that such and such a place is 300 feet high, we usually imply that this height is measured in reference to the level of the sea. So too we cannot speak of the potential of a mass of electricity without, at least, an impHed reference to a standard of potential. This standard is usually the earth, which is taken at zero potential. If we speak of the potential at a given point, the difference between the potential of this point and the earth is referred to. If in the imaginary experiment described above, we move the small sphere round the large electrified one always at the same distance, we shall do no work upon it for the purpose of overcoming or of yield- ing to electrical attractions or repulsions, just as if we move a body at a certain constant level above the earth's surface, we do no work upon it as respects gravitation. An imaginary surface drawn in the neighbourhood of an electrified body, such, that a given charge of electricity can be moved from any one point of it to any other, without any work being done either by or against electrical force is said to be an equipotetitial surface. Such a surface may be described as having everywhere the same electrical level ; and the notion of bodies at different electrical levels in reference to a particular standard is the same as that of bodies at different potentials. As water only flows from places at a higher to places at a lower level, so also electricity only passes from places at a higher to places at a lower potential. If an electrified body is placed in conducting communication with the earth, electricity will flow from the body to the earth if the body is at a higher potential than the earth ; and from the earth to the body, if the body is at a lower potential. If the potential of a body is higher 6^2 ■ Dynamical Electricity. [752- than that of the earth, it is said to have a positive potential ; and if at a lower potential, a negative potential. A body charged v^'ith free negative electricity is one at a lower potential than the earth ; one charged \i\t\i free positive electricity is at a higher potential. The sense in which electrical potential is to be understood may be further illustrated by reference to heat. In the interchange of heat between bodies of different temperatures, the final result is that heat only passes from bodies at a higher to bodies at a lower temperature. Potential is, as regards electricity, what temperature is, as regards heat. We may have a small quantity of heat at a very high temperature. Thus a short thin platinum wire heated to incandescence has a far higher heat potential or temperature, than a cup full of warm water ; but the latter will have a far larger quantity. A flash of lightning represents electricity at a very high potential, but the quantity is small. On an insulated sphere charged with electricity, the potential as well as the electrical density (694), are everywhere the same. On an ellipsoid, on the other hand, the density is different in different parts, while the potential is everywhere the same. That is to say, that if a small in- sulated test sphere were applied to various parts of the ellipsoid, and each time brought in contact with the fixed ball of the torsion balance, a different degree of repulsion would be shown each time. If however, the small sphere were placed at a sufficient distance from the ellipsoid and were connected by it with a thin wire, then Avherever the wire touched the ellipsoid, the proof sphere when afterwards applied to the torsion balance would in all cases produce the same repulsion. The relation between electrical potential and density may be further illustrated by reference to the head of water in a reservoir. The pressure is proportional to the depth ; the potential is everywhere the same. For suppose we want to introduce an additional pound of water into the reservoir, the same amount of work is required whether the water be forced in at the bottom or be poured in at the top. If a hole be made very near the top of the reservoir, a quantity of water in falling to the ground would generate an amount of heat propor- tional to the fall. If the same quantity escaped through a hole near the bottom, it would not produce so much heat by direct fall ; but it will possess a certain horizontal velocity, the destruction of which will produce a quantity of heat, which, added to that produced by the fall, will give exactly as much as the other. 753. Current electricity,-- When a plate of zinc and a plate of copper are partially immersed in dilute sulphuric acid, no electrical or chemical change is apparent beyond perhaps a slight disengagement of hydrogen from the surface of the zinc plate. If now the plates are placed in direct contact, or, more conveniently, are connected by a metal wire, the chemical action sets in, a large quantity of hydrogen is disengaged, but this hydrogen is no longer disengaged at the surface of the zinc, but at the surface of the copper plate. Here then we have to deal with some- thing more than mere chemical action, for chemical action would be un- able to explain either the increase in the quantity of hydrogen disengaged 753] Current Electricity. ^71> Fig. 596. when the metals touch, or the fact that this hydrogen is now given off at the surface of the copper plate. At the same time, if the wire is examined, it will be found to possess many remarkable thermal magnetic and other properties which will be afterwards described. In order to understand what here takes place, let us suppose that we have two insu- lated metal spheres, and that one is charged with positive and the other with negative electricity, and that they are momentarily connected by means of a wire. Electricity will pass from a place of higher to a place of lower potential, that is, from the positive along the wire to the negative, and the po- tentials become equal. This is, indeed nothing more than an electrical discharge taking place through the wire ; and during the infinitely short time in which this is accomplished, it can be shown that the wire exhibits certain heating and magnetising effects, of which the increase of temperature is perhaps the easiest to observe. If now we can imagine some agency by which the different electrical conditions of the two spheres are renewed as fast as they are discharged, which is what very nearly takes place when the two spheres are respec- tively connected with the two conductors r and r^, of a Holtz's machine (figs. 55 1, 552), this equaUsation of potentials, thus taking place, is virtually continuous, and the phenomena above mentioned are also continuous. Now this is what takes place when the two metals are in contact in a liquid which acts upon them unequally. This is independent of hypo- thesis as to the cause of the phenomena; whether the electrical difference is only produced at the moment of contact of the metals, or whether it is due to the chemical action, or tendency to chemical action between the metal and the liquid. The rapidly, succeeding series of equalisations of potential which takes place in the wire being continuous, so long as the chemical action continues, is what is ordinarily spoken of as the electrical ciin-eiit. If we represent by -^ e the potential of the copper plate, and by -^ the potential of the zinc, then the electrical difference, that is the differ- ence of potentials, is ^- e-{ — e) = '2e. And this is general — the essential point of any such combination as the above is that it maintains, or tends to maintain, a difference of potentials, which difference is constant. If, for instance, the zinc plate be connected with the earth which is at zero potential, its potential also becomes zero ; and since the electrical difference remains constant we have for the potential of the copper plate + 2e. Similarly, if the copper be connected with the earth the potential of the zinc plate is negative and is — 7.e. The conditions under which a current of electricity is formed in the above experiment may be further illustrated by reference to the condi- tions-which determine the flow of water between two reservoirs contain- ing water at different levels. If they are connected by a pipe, water will G G 6/4 • Dynamical Electricity. [753- flow from the one at a higher level to the one at a lower level until the water in the two is at the same level in both, when of course the flow ceases. If we imagine the lower reservoir so large that any water added to it would not affect its level — if it were the sea for example— that would represent zero level, and if the higher reservoir could be kept at a constant level there would be a constant flow in the pipe. We must here be careful not to dwell too much on this analogy. It is not to be supposed that in speaking of current of electricity we mean that any thing actually flows, that there is any actual transfer of matter. We say electricity flows, or a current is produced, in much the same sense as that in which we say sound or light travels. 754- Voltaic couple. Electromotive series. — The arrangement just described, consisting of two metals in metalHc contact, and a conducting liquid in which they are placed, constitutes a simple voltaic element or couple. So long as the metals are not in contact, the couple is said to be open, and when connected it is closed. According to the chemical view to which we shall for the present provisionally adhere, it is not necessary that, for the production of a current, one of the metals be unaffected by the liquid, but merely that the chejnical action upon the one. be greater than upon the other. For then we may assume that the current produced would be due to the difference between the differences of potential which each of the metals separately produces by its contact with the liquid. If the differences of potentials were absolutely equal — a condition, however, impossible of realisation with two distinct metals — we must assume that when the metals are joined no current would be produced. The metal which is most attacked is called the positive or generating plate, and that which is least attacked the negative or collecting plate. The positive metal determines the direction of the current, which proceeds in the liquid from the positive to the negative plate, and out of the liquid through the connecting wire from the negative to the positive plate. In the fundamental experiment, not only the connecting wire but also the liquid and the plates are traversed by the electrical currents — are the scene of electrical actions. In speaking of the directio7i of the current iho. direction of the positive electricity is always understood. The mere immersion of two different metals in a liquid is not alone sufficient to produce a current, there must be chemical action. When a platinum and a gold plate are connected with a delicate galvanometer and immersed in pure nitric acid no current is produced ; but on adding a drop of hydrochloric acid a strong current is excited, which proceeds in the liquid from the gold to the platinum, because the gold is attacked by the nitro-hydrochloric acid, while the platinum is less so, if at all. As a voltaic current is produced whenever two metals are placed in metallic contact in a liquid which acts more powerfully upon one than upon the other, there is a great choice in the mode of producing such currents. In reference to their electrical deportment, the metals 'have been arranged in what is called an electromotive series, in which the most -755] . Electromotive Force. 675 elt'ctropositive are at one end, and the most elcctronegath'e at the other. Hence when any two of these are placed in contact in dilute acid, the current in the connecting wire proceeds from the one lower in the list4^- the one higher. The principal metals are as follows : — I. Zinc 6. Nickel 11. Gold 2. Cadmium 7. Bismuth 12. Platinum 3. Tin 8. Antimony 13. Graphite 4- Lead 9. Copper 5. Iron 10. Silver It will be seen that the electrical deportment of any metal depends on the metal with which it is associated. Iron, for example, in dilute sul- phuric acid is electronegative towards zinc, but is electropositive towards copper; copper in turn is electronegative towards iron and zinc, but is electropositive towards silver, platinum, or graphite. 755. Electromotive force. — The force in virtue of which continuous electrical effects are produced throughout a circuit consisting of two ; metals in metallic contact in a liquid which acts unequally upon them, is 'A usually called the elect7'oi7iotive force. Electromotive force and difference-y. of potentials are commonly used in the same sense. It is however more, correct to regard difference of potentials as a particular case of electro- motive force ; for as we shall afterwards see, there are cases in which electrical currents are produced without the occurrence of that particular condition which we have called difference of potentials. The electro- motive force is greater in proportion to the distance of the two metals from one another in the series. That is to say, it is greater the greater the difference between the chemical action upon the two metals immersed. Thus the electromotive force between zinc and platinum is greater than that between zinc and iron, or between zinc and copper. The law esta- blished by experiment is, that the electromotive force betweefi any two metals is equal to the sum of the electromotive forces betweeji all the interve7iing metals. Thus the electromotive force between zinc and platinum is equal to the sum of the electromotive forces between zinc and iron, iron and copper, and copper and platinum. The electromotive force is influenced by the condition of the metal ; rolled zinc, for instance, is negative towards cast zinc. It also depends on the degree of concentration of the liquid ; in dilute nitric acid zinc is positive towards tin, and mercury positive towards lead ; while in con- centrated nitric acid the reverse is the case, mercury and zinc being respectively electronegative towards lead and tin. The nature of the liquid also influences the direction of the current. If two plates, one of copper and one of iron, are immersed in dilute sul- phuric acid, a current is set up proceeding through the liquid from the iron to the copper : but if the plates, after being washed, are placed in solution of sulphide of potassium, a current is produced in the opposite direction, the copper is now the positive metal. Other examples may be drawn from the following table, which shows the electric deportment of the principal metals with three different liquids. It is arranged like the e-jG Dynamical Electricity . [755 preceding one ; each metal being electropositive towards any one low in the list, and electronegative towards any one higher : — Caustic potass Hydrochloric acid Sulphide of potassium Zinc Zinc Zinc Tin Cadmium Copper Cadmium Tin Cadmium Antimony Lead Tin Lead Iron Silver Bismuth Copper Antimony Iron Bismuth Lead Copper Nickel Bismuth Nickel • Silver Nickel Silver Antimony Iron A voltaic current may also be produced by means of two liquids and one metal. This may be shown by the following experiment: In a beaker containing strong nitric acid is placed a small porous cylinder closed at one end, and containing strong solution of caustic potass. If now two platinum wires connected with the two ends of a galvanometer (773) 3-re immersed respectively in the alkali and in the acid, a voltaic current is produced, proceeding in the wire from the nitric acid to the potass, which thus correspond respectively to the negative and positive plates in ordinary couples. A metal which is acted upon by a liquid can be protected from solution by placing in contact with it a more electropositive metal, and thus form- ing a simple voltaic circuit. This principle is the basis of Davy's pro- posal to protect the copper sheathing of ships, which are rapidly acted upon by sea water. If zinc or iron be connected with the copper, these metals are dissolved and the copper protected. Davy found that a piece of zinc the size of a nail was sufficient to protect a surface of forty or fifty square inches ; unfortunately the proposal has not been of practical value, for the copper must be attacked to a certain extent to prevent the adherence of marine plants and shellfish. 756. Poles and electrodes. — If the wire connecting the two terminal plates of a voltaic couple be cut, it is clear, from what has been said about the origin and direction of the current, that positive electricity will tend to accumulate at the end of the wire attached to the copper or negative plate, and negative electricity on the wire attached to the zinc or positive plate. These terminals have been called the poles of the battery. For experimental purposes, more especially in the decomposition of salts, plates of platinum are attached to the ends of the wires. Instead of the term poles the, word electrode {t'lXtKrpov and oroc a way) is now commonly used; for these are the ways through which the respective electricities emerge. It is important not to confound the positive plate with the positive pole or electrode. The positive electrode is that connected with the negative plate, while the negative electrode is connected with the positive plate. -757] Voltaic Pile. Voltaic Battery. 677 757. Voltaic pile. Voltaic battery.— When a series of voltaic ele- ments or pairs are arranged so that the zinc of one element is connected with the copper of another; the zinc of this with the cop)per of another^ and so on, the arrangement is called a voltaic battery; and by its means the effects produced by a single element are capable of being very greatly increased. The earliest of these arrangements was de- vised by Volta himself. It consists (fig. 597) of a series of discs piled one over the other in the following order : at the bottom, on a frame of wood, is a disc of copper, then a disc of cloth moistened by acidulated water, or by brine, then a disc of zinc; on this a disc of copper, and another disc of moistened cloth, to which again follow as many sets of zinc-cloth-copper, always in the same order, as may be convenient, the highest disc being of zinc. The discs are kept in vertical positions by glass rods. It will be readily seen that we have here a series of simple voltaic couples, the moisture in the cloth acting as the liquid in the cases already mentioned, and that the terminal zinc is the negative and the terminal copper the positive pole. From the mode of its arrangement, and from its discoverer, the apparatus is known as the voltaic pile, a term applied to all apparatus of this kind for accumulating the effects of dyna- mical electricity. The distribution of electricity in the pile varies according as it is in connection with the ground by one of its extremities, or as it is insulated by being placed on a nonconducting cake of resin or glass. In the former case, the end in contact with the ground is neutral, and the rest of the apparatus contains only one kind of electricity ; this is negative if the copper disc, and positive if the zinc disc is in contact with the ground. In the insulated pile the electricity is not uniformly distributed. By means of the proof-plane and the electroscope it may be demonstrated that the middle part is in a neutral state, and that one half is charged with positive and the other with negative electricity, the potential increas- ing from the middle to the ends. The half terminated by a zinc is charged with negative electricity, and that by a copper with positive electricity. The pile is thus similar to a charged Leyden jar ; with this difference, however, that when the jar has been discharged by connecting its two coatings, the electrical effects cease; while in the case of the pile, the cause which originally brought about the distribution of electricity restores this state of charge after the discharge; and the continuous fig- 597- ej'i Dynamical Electricity. [757 succession of charges and discharges form the current. The effects of the pile will be discussed in other places. 758. 'WoUePston's battery. — The original form of the voltaic pile has a great many inconveniences, and possesses now only an historical interest. It has received a great many improvements, the principal object of which has been to facili«:ate manipulation, and to produce greater electromotive force. One of the earliest of these modifications was the crown of cups, or coiiroufie des tasses, invented by Volta himself; an improved form of this is known as IVollaston's battery (fig. 598) ; it is arranged so that when the current is not wanted, the action of the battery can be stopped. Fig. 598. The plates Z are of thick rolled zinc, and usually about eight inches in length by six in breadth. The copper plates C are of thin sheet, and bent so as to surround the zincs without touching them : contact being prevented by small pieces of cork. To each copper plate a narrow strip of copper, (?, is soldered, which is bent twice at right angles and is soldered to the zinc plate ; and the first zinc Z is surrounded by the first copper C ; these two constitute a couple, and each couple is immersed in a glass vessel, containing acidulated water. The copper C is soldered to the second zinc by the strip o, and this zinc is in turn surrounded by a second copper, and so on. Figure 598 represents a pile of sixteen couples united in two parallel series of eight each. All these couples are fixed to a cross frame pf wood, by which they can be raised or lowered at pleasure. When the battery is not wanted, the couples are lifted out of the liquid. The water in these vessels is usually acidulated with ^,\ sulphuric and ^^ of nitric acid. Hare's deflagrator. This is a simple voltaic arrangement, consisting -759] Secondary Ciir rents. 679 of two large sheets of copper and zinc rolled together in a spiral, but preserved from direct contact by bands of leather or horsehair. The whole is immersed in a vessel containing acidulated water, and the two plates are connected outside the liquid by a conducting wire. 759. Enfeeblement of the current in batteries. Secondary cur> rents. Polarity. — The various batteries already described, Volta's, Wollaston's, and Hare's which consist essentially of two metals and one liquid, labour under the objection that the currents produced rapidly diminish in strength. This is principally due to three causes ; the first is the decrease in the chemical action owing to the neutralisation of the sulphuric acid by its combination with the zinc. This is a necessary action, for upon it depends the current ; it therefore occurs in all batteries, and is without remedy except by replacement of acid and zinc. The second is due to what is called local action ; that is, the production of small closed circuits in the active metal, owing to the impurities it contains. These local currents rapidly wear away the active plate, without contributing anything to the continuance of the general current. They are remedied by amalga- mating the zinc with mercury, by which chemical action is prevented until the circuit is closed, as will be more fully explained (768). The third arises from the production of an inverse electromotive force, which tends to produce a current in a contrary direction to the principal current, and therefore to destroy it either totally or partially. In the fundamental experiment (fig. 596), when the circuit is closed, sulphate of zinc is formed, which dissolves in the liquid, and at the same time a layer of hydrogen gas is gradually formed on the surface of the copper plate. This dimi- nishes the activity of the combination in more than one way. In the first place it interferes with the contact between the ijietal and the liquid ; in the second place in proportion as the copper becomes coated with hydrogen, we h'ave virtually a plate of hydrogen instead of a plate of copper opposed to the zinc, and in addition, the hydrogen, by reacting on the sulphate of zinc which accumulates in the liquid, gradually causes a deposition of zinc on the surface of the copper; hence, instead of having two different metals unequally attacked, the two metals become gradually less different, and, consecjuently, the total effect, and the current, become weaker and weaker. ThQ polarisation of the plate (as this phenomenon is termed) may be destroyed by breaking the circuit and exposing the copper plate to the air; the deposited hydrogen is thus more or less , completely got rid of, and on again closing the circuit the current has nearly its original strength. The same result is obtained when the current of another battery is transmitted through the battery in a direction opposite to that of the first. De la Rive found that when the platinum electrodes which had been used in decomposing a liquid were removed from this Hquid and placed in distilled water, they produced a current when connected in a direction opposite to that which they had at first transmitted. He calls this the polarisation of the electrodes. Becquerel and Faraday have shown that 68o Dynamical Electricity. [759- this polarity of the metals results from the deposits caused by the passage of the current. Even when platinum electrodes are used to decompose pure water, polarisation takes place in consequence. This phenomenon, as Mat- teucci has shown, arises from a deposit of hydrogen on the one, and of oxygen on the, other electrode. CONSTANT CURRENTS. 760. Constant currents. — With few exceptions, batteries composed of elements with a single liquid have almost gone out of use, in con- sequence of the rapid enfeeblement of the current produced. They have been replaced by batteries with two liquids, which are called co?istant considerable period of time. The essential point to be attended to in securing a constant current is to prevent the polarisation of the inactive metal ; in other words, to hinder any permanent deposition of hydrogen on its surface. This is effected by placing the inactive metal in a liquid upon which the deposited hydrogen can act chemically. 761. Daniell's battery. — This was the first form of the constant battery, and was invented by Daniell in the year 1836. As regards the constancy of its action, it is perhaps still the best of all con- stant batteries. Fig. 599 represents a single element. A glass or porcelain vessel, V, con- tains a saturated solution of sulphate of copper, in which is immersed a copper cylinder, G, open at both ends, and per- forated by holes. At the upper part of this cylinder there is an arlnular shelf, C, also perforated by small holes, and below the level of- the solution; this is intended to support crystals of sulphate of copper to replace that decomposed as the electrical action proceeds. Inside the cylinder is a ^'s- 599- thin porous vessel, P, of unglazed earth- enware. This contains either water or solution of common salt or dilute sulphuric acid, in which is placed the cylinder of amalgamated zinc, Z. Two thin strips of copper, p and n, fixed by binding screws to the copper and to the zinc, serve for connecting the elements in series. When a Daniell's element is closed', the hydrogen resulting from the action of the dilute acid on the zinc is liberated on the surface of the copper plate, but meets there the sulphate of copper, which is reduced, forming sulphuric acid and metallic copper, which is deposited on the surface of the copper plate. In this way sulphate of copper in solution is taken up, and if it were all consumed, hydrogen would be deposited on the copper, and the current would lose its constancy. This is prevented by the crystals of sulphate of copper which keep the solution saturated. 763] Biinseiis Battery. 6Z The sulphuric acid produced by the decomposition of the sulphate per- meates the porous cylinder, and tends to replace the acid used up by its action on the zinc ; and as the quantity of sulphuric acid formed in the- solution of sulphate of copper is regular, and proportional to the acid used in dissolving the zinc, the action of this acid on the zinc is regular also, and thus a constant current is produced. In order to join together several of these elements to form a battery, the zinc of one is connected either by a copper wire or strip with the copper of the next, and so on, from one element to another, as shown in fig. 603, for another kind of battery. Instead of a porous earthenware vessel a bag of sailcloth may be used for the diaphragm separating the two liquids. The effect is at first more powerful, but the two solutions mix more rapidly, which weakens the current. The object of the diaphragm is to allow the current to pass, but to prevent as much as possible the mixture of the two liquids. The current produced by a Daniell's battery is constant for some hours; its action is stronger when it is placed in hot water. 762. G-rove's battery. — In this battery the sulphate of copper solution is replaced by nitric acid, and the copper by platinum, by which greater electromotive force is obtained. Fig. 609 represents one of the forms of a couple of this battery. It consists of a glass vessel. A, partially filled with dilute sulphuric acid (i : 8) ; of a cylinder of zinc, Z, open at both ends ; of a vessel, V, made of porous pipeclay, and containing ordi- nary nitric acid ; of a plate of platinum, P (fig. 601), bent in the form of an S, and fixed to a cover, r, which rests on the porous vessel. The platinum is connected with a binding screw, b^ and there is a similar binding screw on the zinc. In this battery the hydrogen, which would be disengaged on the platinum, meeting the nitric acid, decomposes it, forming hyponitrous acid, which dis- solves or is disengaged as nitrous fumes. Grove's battery is the most convenient and one of the most powerful of the two-fluid batteries. It is, however, the most expen- sive, owing to the high price of platinum ; besides which the platinum is liable, after some time, to become brittle and break very easily. But as the platinum is not consumed, it retains most of its value ; and when the plates which have been used in a battery are heated to redness, they retain their elasticity. 763. Bunsen's battery. — Bunsen's battery^ also known as the zinc ^s>j^. 4. a cylinder of carbon, C, prepared in the abox-e manner. In the vessel F the nnc is first placed, and in it the carbon C in the porous vessel V as seen in P. To the carbon is fixed a binding screw, wl, to which a copper wire is attached, forming the positive pole. The linc is provided with a similar binding screw, «, and wire, which is thus a n^;ative pole. The elements are arranged to form a battery by connecting each carbon to the tine of the following one by means of the clamps wm and a strip of copper € represented in the top of the figure. The copper is pressed at one «ad between the carbon and the clamp, and at the other it is soldered to the damp « which is fitted on the rinc of the following element, and so forth. The clamp of the first carbon and that of the last xinc are alone provided with binding screws to which are attached the wires. The chemical action of Bunsen's battery is the same as that of Grovels, and bang equally powerful, while less costly, is almost uni\^ersally used on the Continent. But though its first cost is less than that of Gro\-e'^s battery, it is more expensive to work, and is not so convenient to mani> polate^ OUlmis itUitry is a modified form of Grovels. Instead of xinc and plakinum, zinc and platinised lead are used, and instead of pure nitric add CaUan used a mixture of sulphuric add, nitric add, and saturated solution of nitre. The battery is said to be equal in its action to Grove's, and is much dieaper. CaUan has also constructed a battery in which zinc in dilute sulphuric add fonns the positive plate, and cast iron in strong nitric add the nega- tive. Under these circumstances the iron becomes passive; it isstrongly etectroncgative, and does not dissolve. If, however, the nitric add becomes 764] Snucs Battery, 6Sl too weak, the iron is dissolved with simuhaneous disengagement of nitrous fumes. After being in use some time, all the batteries in which the polarisatmn- is prevented by nitric acid disengage nitrous fumes in large quantities, and this is a serious objection to their use, especially in closed rooms. Tq prevent this, nitric acid is frequently replaced by chromic acid, or better, by a mixture of 4 parts bichromate of potassium, 4 parts sulphuric acid, Fig. 603. and 18 water. The liberated hydrogen reduces the chromic acid to the state of oxide of chromium, which remains dissolved in sulphuric acid. With the same view, sesquichloride of iron is sometimes substituted for nitric acid ; it becomes reduced to protochloride. But the action of the elements thus modified is considerably less than when nitric acid is used, owing to the increased resistance. 764. Smee's battery. — In this battery the polarisation of the negative plate is prevented by mechanical means. Each element consists of-a sheet of platinum placed between two vertical plates of zinc, as in Grove's battery ; but as there is only a single liquid, dilute sulphuric acid, the ele- ments have much the form of those in Wollaston s battery. The adherence of hydrogen to the negative plate is prevented by covering the platinum with a deposit of finely divided platinum. In this manner the surface is roughened, which facilitates the disengagement of hydrogen to a remark- able extent, and, consequently, diminishes the resistance of the couple. Instead of platinum, silver covered with a deposit of finely divided pla- tinum is frequently substituted, as being cheaper. Walters battery. — This resembles Smee's battery, but the electro- negative plate is either gas graphite or platinised graphite ; it is excited by dilute sulphuric acid. This battery is used in all the stations of the South Eastern Railway, and promises to come into more extensive use, for it has considerable electromotive force ; it is convenient and econo- mical in manipulation, and large- sized elements can be constructed at a cheap rate. 684 Dynamical Electricity. [765- 765. Recent batteries. — The sulphate 0/ pierctiry hzXiery (fig, 604) de- vised by M. Marie Davy, is essentially a zinc-carbon element, but of smaller dimensions than those elements usually are. In the outer vessel V ordinary M^ater or brine is placed, and in the porous vessel sulphate of mercury. This salt is agitated with about three times its volume of water, in which it is difficultly soluble, and the liquid poured off from the pasty mass. The A r \ r L \ \^_ — ^ ~ ^^ R Fig. 604. Fig. 605. Fitr. 606. carbon being placed in the porous vessel the spaces are filled with the residue and then the decanted hquid poured into it. Chemical action takes place only when the pile is closed. The zinc then decomposes the water, liberating hydrogen, which traversing the porous vessel reduces the sulphate of mercury, forming metallic mercury, which collects at the bottom of the vessel, while the sulphuric acid formed at the same time traverses the diaphragm to act on the zinc and thus in- creases the action. The mercury which is deposited may be used to pre- pare a quantity of sulphate equal to that which has been consumed. A small quantity of the solution of sulphate of mercury may also pass through the diaphragm ; but this is rather advantageous, as its effect is to amalga- mate the zinc. The electromotive force of this element is about a quarter greater than that of Daniell's element, but it has greater resistance ; it is rapidly ex- hausted when continuously worked, though it appears well suited for dis- continuous work, as with the telegraph, and with alarums. Gravity batteries. The use of porous vessels is liable to many objec- tions, more especially in the case of Daniell's battery, in which they gradually become encrusted with copper, which destroys them. A kind of battery has been devised in which the porous vessel is entirely dispensed with, and the separation of the liquids is effected by the difference of density. Such batteries are called gravity batteries ; the one in use at the telegraphic establishment of the Royal Engineers at Chatham is based on this principle. Figure 605 represents a form devised by M. Callaud of Nantes. V is a glass or earthenware vessel in which is a copper plate soldered to a wire insulated by gutta percha. On the plate is a layer of crystals of sulphate —767] Electromotive Force of different Elements. 685 of copper C ; the whole is then tilled with water, and the zinc cylinder Z is immersed in it. The lower part of the liquid becomes saturated with sul- phate of copper ; the action of the battery is that of a Daniell, and the sul-_ phate of zinc which gradually forms floats on the solution of sulphate of copper owing to its lower density. This battery is easily manipulated, the consumption of sulphate of copper is economical, and when not agitated it works constantly for some months, provided care be taken to replace the water lost by evaporation. Minottd's battery. — This may be described as a Daniell's element, in which the porous vessel is replaced by a layer of sawdust or of sand. At the bottom of an earthenware vessel (fig. 606) is placed a layer of coarsely- powdered sulphate of copper a^ and on this a copper plate provided w4th an insulated copper wire /. On this there is a layer of sand or of sawdust be, and then the whole is filled with water in which rests a zinc cylinder Z. The action is just that of a Daniell ; the sawdust prevents the mixture of the liquids but it also offers great resistance, which increases with its thickness. From its simplicity and economy, and* the facility with which it is constructed, this battery merits increased attention. Leclanches elements consist of a rod of carbon placed in a porous pot, which is then tightly packed with a mixture of pyrolusite (peroxide of manganese) and coke. The porous pot is contained in an outer vessel in which is the electropositive element the zinc. The exciting liquid is a solution of sal ammoniac ; it is advantageous not to fill the v^essel more than one-third with the liquid. The battery is coming into very extended use ; its electromotive force is about {^ that of a Daniell, "and its resist- ance about 1 1 of a British Association unit. 766. Electromotive force of different elements. — The following numbers represent the electromotive force of some of the elements most frequently used, compared with that of an ordinary Daniell's cell charged as above described ; they are the means of many careful determina- tions. Daniell's clement set up with water . . . . i -co „ „ pure zinc and pure water, with pure copper and pure saturated solution of sulphate of copper . i-02 Leclanche's ., zinc in saturated solution of chloride of ammonium . .1-32 Marie Davy's „ 1*41 Bunsen's ,, carbon in nitric acid . . .177 „ „ carbon in chromic acid . .1-87 Grove's „ platinum in nitric acid . . .1-82 767. Comparison of the voltaic battery with a frictional electrical machine. — Except in the case of batteries consisting of a very large number of couples, the difference of potentials between the terminals is far weaker than in electrical machines, and is insufficient to give any 686 Dynamical Electricity. [767- visible spark. Gassiott's great battery, however, which consisted of 3,-52o zinc and copper elements with poles ^-^ of an inch apart, gave a series of sparks across this interval which lasted for weeks. In the case of a small battery or of a single cell, very delicate tests are required to detect any signs of electrification. But by means of a delicate condensing electroscope, and by extremely careful insulation it can be shown that one pole possesses a positive and the other a negative charge. For this purpose one of the plates of the electroscope is connected with one end of the pile, and the other with the other end or with the ground. The electroscope thus becomes charged, and on breaking the communications electroscopic indications are observed. A Leyden jar may even be charged when the interior coating is connected with one end of the pile, and the external coating with the other; but this charge is far smaller than that furnished by an electrical machine. On the other hand the strength of a current which a voltaic element can produce in a good conductor, is much greater than that which can be produced by a machine. Faraday immersed two wires, one of. zinc, and the other of platinum, each ^^ of an inch in diameter, in acidulated water for ~ of a second. The effect thus produced on a magnetic needle in this short time was greater than that produced by 23 turns of the large elec- trical machine of the Royal Institution. Rossetti concludes from some experiments that the electromotive force of the current of a Holtz's machine is upwards of 50,000 times that of a Daniell's cell. 768. Amalg^amated zinc. Iiocal currents. — De la Rive observed that perfectly pure distilled zinc was not attacked by dilute sulphuric acid, but became so when immersed in that liquid in contact with a plate of copper or of platinum. Ordinary commercial zinc, on the contrary, is rapidly dissolved by dilute acid. This, doubtless, arises from the impurity of the zinc, which always contains traces either of iron or lead. Being electro-negative towards zinc they tend to produce local electrical currents., which accelerate the chemical action without increasing the quantity of electricity in the connecting wire. Zinc, when amalgamated, acquires the properties of perfectly pure zinc and is unaltered by dilute acid, so long as it is not in contact with a copper or platinum plate immersed in the same liquid. To amalgamate a zinc plate, it is first immersed in dilute sulphuric or hydrochloric acid so as to obtain a clean surface, and then a drop of mercury is placed on the plate and spread over it with a brush. The amalgamation takes place immediately, and the plate has the brilliant aspect of mercury. Zinc as well as other metals are readily amalgamated by dipping them in an amalgam of one part sodium and 200 parts of mercury. Zinc plates may also be amalgamated by dipping them in a solution of mercury prepared by dissolving at a gentle heat one pound of mercury in five pounds of aqua regia (one part of nitric to three of hydrochloric acid), and then adding five parts more of hydrochloric acid. -770] Bohnenbergcr s Electroscope. 68^'^ The amalgamation of the zinc removes from its surface all the im- purities, especially the iron. The mercury effects a solution of pure zinc, which covers the surface of the plate, as with a liquid layer. _: The amalgamation of zinc was first applied to electrical batteries by Kemp. Amalgamated zinc is not attacked so long as the circuit is not closed, that is, when there is no current. With amalgamated zinc the current is more regular, and at the same time more intense, for the same quantity of metal dissolved. 769. Bry piles. — In dry piles the liquid is replaced by a solid hygro- metric substance, such as paper or leather. They are of various kinds ; in Zamboni's, which is most extensively used, the electromotors are tin or silver, and binoxide of manganese. To construct one of these a piece of paper silvered or tinned on one side is taken ; the other side of the paper is coated with finely-powdered binoxide of manganese by slightly moisten- ing it, and rubbing the powder on with a cork. Having placed together seven or eight of these sheets, they are cut by means of a punch into discs an inch in diameter. These discs are then arranged in the same order, so that the tin or silver of each disc is in contact with the manganese of the next. Having piled up, 1,200 to 1,800 couples, they are placed in a glass tube, which is provided with a brass cap at each end. In each cap there is a rod and knob, by which the leaves can be pressed together, so as to produce better contact. The knob in contact with the manganese corresponds to the positive pole, while that at the other end, which is in contact with the silver or tin, is the negative pole. The dry piles are remarkable for the permanence of their action, which may continue for several years. Their action depends greatly on the temperature and on the hygrometric state of the air. It is stronger in summer than in winter, and the action of a strong heat revives it when it appears extinct. A Zamboni's pile of 2,000 couples gives neither shock nor spark, but can charge a Leyden jar and other condensers. A certain time is however necessary, for electricity only moves slowly in the interior. 770. Bolinenbergrer's electroscope. — Bohnenbergcr has constructed ^ ' a dry-pile electroscope of gieat delicacy. It is a condensing electroscope (fig. 577), from the rod of which is suspended a single gold leaf. This is at an equal distance from the opposite poles of two dry piles placed vertically, inside the bell jar, on the plate of the apparatus. As soon as the gold leaf possesses any free electricity it is attracted by one of the poles and repelled by the other, and its electricity is obviously contrary to that of the pole towards which it moves. 6SS Dynamical Electricity. [771- CHAPTER II. DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS. 771. Detection and measurement of voltaic currents. — The remark- able phenomena of the voltaic battery may be classed under the heads physiological, chemical, mechanical, and physical effects; and these latter may be again subdivided into the thermal, luminous, and magnetic effects. For ascertaining the existence and measuring the intensity of voltaic currents, the magnetic effects are more suitable than any of the others, and, accordingly, the fundamental magnetic phenomena will be described here, and the description of the rest postponed to a special chapter on electro-magnetism. 772. Oersted's experiment. — Oersted published in 18 19 a discovery which connected magnetism and electricity in a most intimate man- ner, and became, in the hands of Ampere and of Faraday, the source of a new branch of physics. The fact discovered by Oersted is the directive action which a fixed current exerts at a distance on a magnetic needle. To make this experiment a copper wire is suspended horizontally in the direction of the magnetic meridian over a movable mag- netic needle, as represented in fig. 607. So long as the wire is not traversed by a current the needle remains parallel to it, but as soon as the ends of the wire are respectively connected with the poles of a battery or of a single element, the needle is de- flected, and tends to take a posi- tion which is the more nearly at right angles to the magnetic metidian in proportion as the cicrretit is stronger. In reference to the direction in which the poles are deflected, there are several cases which may, however, be referred to a single principle. Re- membering our assumption as to the direction of the current in the connecting wire (754) the preceding experiment presents the following four cases :— i. If the current passes above the needle, and goes from south to north, the north pole of the magnet is deflected towards the west ; this arrange- ment is represented in the above figure. ii. If the current passes below the needle, also from south to north, the north pole is deflected towards the east. iii. When the current passes above the needle, but from north to south, the north pole is deflected towards the east. Fig. 607. -773] Galvanometer. 689 iv. Lastly, the deflection is towards the west when the current goes from north to south below the needle. Ampere has given the following meinoria technica by which all the_ various directions of the needle under the influence of a current may be remembered. If we imagine an observer placed in the connecting wire in such a manner that the current entering by his feet issues by his head, and that his face is always turned towards the needle, we shall see that ^n the above four positions the north pole is always deflected towards the left of the observer. By thus personifying the current, the different cases may be comprised in this general principle : In the directii'e actioji of currents on magnets, the north pole is always deflected towards the left of the current. yjT,. Galvanometer or multiplier.— The name galvanometer, or sometimes multiplier or rheometer, is given to a very delicate apparatus by which the existence, direction, and intensity of currents may be determined. It was invented by Schweigger in Germany a short time after Oersted's discovery. h [ ^^..-'^^ 71 ^^.-'-^ !- If ^^^ u. 1 ^^- 111) - ^ Fig. 609. In order to understand its principle, let us suppose a magnetic needle suspended by a filament of silk (fig. 608), and surrounded in the plane of the magnetic meridian by a copper wire ninopg, forming a complete circuit round the needle in the direction of its length. When this wire is tra- versed by a current, it follows, from what has been said in the previous paragraph, that in every part of the circuit an observer lying in the wire in the direction of the arrows, and looking at the needle ab, would have his left always turned towards the same point of the horizon, and con- sequently, that the action of the current in every part would tend to turn the north pole in the same direction : that is to say, that the actions of the four branches of the circuit concur to give the north pole the same direction. By coiling the copper wire in the direction of the needle, as represented in the figure, the action of the current has been multiplied. If instead of a single one, there are several circuits, provided they are insulated, the action becomes still more multiplied, and the deflection of the needle increases. Nevertheless, the action of the current cannot be multiplied indefinitely by increasing the number of windings, for, as we shall presently see, the intensity of a current diminishes as the length of the circuit is increased. 690 Dynamical Electricity. [773 A5 the directive action of the earth continually tends to keep the needle in the magnetic meridian, and thus opposes the action of the current, the effect of the latter is increased by using an astatic system of two needles, as shown in fig. 609. The action of the earth on the needle is then very feeble, and, further, the actions of the current on the two needles become accumulated. In fact, the action of the circuit, from the direction of the current indicated by the arrows, tends to deflect the north pole of the lower needle towards the west. The upper needle a'b', is subjected to the action of two contrary currents no and qp, but as the first is nearer, its action preponderates. Now this current passing, below the needle, evi- dently tends to turn the pole a' towards the ea?t, and, consequently, the pole b' towards the west : that is to say, in the same direction as the pole a of the other needle. From these principles it will be easy to understand the theory of the multiplier. The apparatus represented in fig. 610 consists of a thick brass plate, D, resting on levelling screws ; on this is a rotatory plate, P, of the same metal, to which is fixed a copper frame, the breadth of wh'ch Fig. 61 is almost equal to the length of the needles. On this Is coiled a great number of turns of wire covered with silk. The two ends terminate in binding screws, i and ; and in like manner the angle bnf is equal to and ;{/"= bn cos ^ ; and therefore since ;//= nsr, bn cos

that is, C = T tan <■. If any other currenc be passed through the galvanometer we shall have similarly C = T tan ; and since the earth's magnetism does not alter in one and the same place C : C = tan fp : tan '. In this reasoning it has been assumed that the action of the current on the needle is the same whatever be the angle by which it is deflected. This is only the case when the dimensions of the needle are' small corn- Fig. 613. -776] Si7ie Compass. 695 pared with the diameter of the ring ; it should not be more than \ or ^^^ the diameter. In order to measure with accuracy the deflections a hght index is placed at right angles to the needle. ~^ ~ 776. Sine compass. — This is another form of galvanometer for measuring powerful currents. Round the circular frame, M, fig. 614, several turns of stout insulated copper wire are coiled, the two ends of which, /, terminate in the binding screws at E. On a table in the centre of the ring there is a magnetic needle, in ; a second light needle, ?/, fixed Fig. 614. to the first, serves as pointer along the graduated circle, N. Two copper wires, ab, from the sources of electricity to be measured, are connected with E. The circles M and N are supported on a foot O which can move about a vertical axis passing through the centre of a fixed horizontal circle H. The circle M being then placed in the magnetic meridian, and there- fore in the same plane as the needle, the current is allowed to pass. The needles being deflected, the circuit M is turned until it coincides with the vertical plane passing through the magnetic needle m. The directive action of the current is now e.xerted perpendicularly to the direction of the magnetic needle, and it may be shown that the intensity of the current is proportional to the sine of the angle of deflection ; this angle is. measured on the circle H by means of a vernier on the piece C. 696 Dynamical Electricity. [776- This piece, C, fixed to the foot O, turns it by means of a knob, A. The angle of deflection, and hence its sine, being known, the intensity of the current may be thus deduced : let imn^ be the direction of the magnetic meridian, d the angle of deflection, C the strength of the current, and T the directive action of the earth. If the direction and intensity of this latter force be represented by ak, it may be replaced by two components, ah and ac, fig. 609. Now, as the first has no directive action on the needle, the component ac must alone counterpoise the force C, that is, C = ac. But in the triangle, ack, ac = ak cos cak^ from which ac = T sin. d, for the angle cak is the complement of the angle d, and ak is '^" ^^' equal to T ; hence, lastly, C = T sin d, which was to be proved. In like manner for any other current C which produces a deflection d, we shall have C = T sin d\ whence C : C -= sin ^ : sin d\ JJJ. Olim's law.^ — For a knowledge of the conditions which regulate the action of the voltaic current, science is indebted to the late Professor Ohm. His results were at first deduced from theoretical considerations; but by his own researches, as well as by those of Fechner, Pouillet, Daniell, De la Rive, Wheatstone, and others, they have received the fullest confirmation, and their great theoretical and practical importance has been fully established. i. The force or cause by which electricity is set in motion in the voltaic circuit is called the electromotive force. The quantity of electricity which in any unit of time flows through a section of the circuit is called the in- tejtsity or perhaps better the strength of the current. Ohm found that this strength is the same in all parts of one and the same circuit, however heterogeneous they were ; and also that it is proportional to the electro- motive force. It has further been found that when the same current is passed respec- tively through a short and through a long wire of the same material, its action on the magnetic needle is less in the latter case than in the former. Ohm accordingly supposed that in the latter case there was a greater re- sistance to the passage of the current than in the former ; and he proved that Uhe resistance is inversely proportional to the stretigth of the cicrrent.' On these principles Ohm founded the celebrated law which bears his name, that — The strength of the current is equal to the electromotive force divided by the resistance. Which is expressed by the simple formula ^ R' where C is the strength of the current, E the electromotive force, and R the resistance. -777] Ohm's Law. 697 ii. The resistance of a conductor depends on three elements : its con- ductivity, which is a constant, determined for each conductor; its section-^ and its length. The resistance is obviously inversely proportional to the conductivity, that is, the less the conducting power the greater the resist- ance. This has been experimentally shown, and it has also been proved that the resistance is inversely as the sectiofz, and directly as the length of a conductor. If then k is the conductivity, w the section, and \ the length of a conductor, we have = — and C = - ; that is, the strength of a current is inve?'sely proportional to the length of the conductor and directly proportional to its section and conductivity. iii. In a voltaic battery composed of different elements, the strength of the current is equal to the sum of the electromotive forces of all the elements divided by the sum of the resistances. Usually, however, a battery is composed of elements of the same kind, each having the same electromotive force and the same resistance. In an ordinary element there are essentially two resistances to be con- sidered : I. That offered by the liquid conductor between the two plates, which is frequently called the internal or essential resistance ; and, 2. That offered by the interpolar conductor which connects the two plates outside the liquid ; this conductor may consist either wholly of metal, or may be partly of metal and partly of liquids to be decomposed : it is the external or non-essential resistance. Calling the former R and the latter r, Ohm's formula becomes C = -^. iv. If an)' number, ;/, of similar elements are joined together, there is ;/ times the electromotive force, but at the same time n times the internal resistance, and the formula becomes -^ If the resistance in the «R + r interpolar, r, is very small, which is the case, for instance, when it is a short thick copper wire, it may be neglected in comparison with the in- ternal resistance, and then we have ^ _ «E ^ E . ~n^ R' that is, a battery consisting of several elements produces in this case no greater effect than a single element. ^v. If, however, the external resistance is very great, as when the current has to produce the electric light, or to work a long telegraphic circuit, advantage is gained by using a larger number of elements ; for then we have the formula «E C = «R + r ' H H 6gS Dynavtical Electricity. [777 - if r is very great as compared with ;zR, the latter may be neglected, and the expression becomes r that is, that the strength within certain limits is proportional to the number of elements. In a thermo-electric pile, which consists of very short metallic con- ductors, the internal resistance R is so small that it may be neglected, and the strength is inversely as the length of the connecting wire. vi. If the plates of an element be made m times as large, there is no increase in the electromotive force, for this depends on the nature of the metals and of the hquid (755), but the resistance is m times as small, for the section is m. times larger ; the expression becomes then Hence, an increase in the size of the plate, or, what is the same thing, a decrease in the internal resistance, does not increase the strength to an indefinite extent; for ultimately the resistance of the element R vanishes in comparison with the resistance r, and the strength always approximates to the value C = - . 7- vii. Ohm's law enables us to arrange a battery so as to obtain the greatest effect in any given case. For instance, with a battery of six elements there are the following four ways of arranging them : i. In a single series (fig. 616), in which the zinc Z of one element is united with the copper C of the second, the zinc of this with the copper of the third, and so on ; 2. Arranged in a system of three double elements, each element being formed by joining two of the former (fig. 617) ; 3. In a system of two elements, each of which consists of three of the original elements joined, so as to form one of triple the surface (fig. 618) ; 4. Lastly, of one large element, all the zincs and all the coppers being joined, so as to form a pair of six times the surface (fig. 619). With a series of twelve elements there may be six different combina- tions, and so on for a larger number. Now let us suppose that in the particular case of a battery of six elements the internal resistance R of each element is 3, and the external resistance r=i2. Then, in the first case, where there are six elements, we have the value, C= ^?^ -_= _^ =-^ 6R + r 6x3+12 30' If they were united so as to form three elements, each of double the sur- face, as in the second case (fig. 617), the electromotive force would then be the electromotive force in each element ; there would also be a resistance -777] O J Lin's Lazv. 699 R in each element, but this would only be half as great, for the section of the plate is now double ; hence the strength in this case would be C'= 3E _ 3E _6E. 3^ + r + 12 33 accordingly this change would lessen the strength. Fig. 616. If, with the same elements, the resistance in the connecting wire were only r = 2, we should have the values in the two cases respectively — 6xE ^6E 6x3 + 2 20' C = and C' = /_ 3E 3R 2 6E 9 + 4 6E 13* The result in the latter case is, therefore more favourable. If the resist- ance r were 9, the strength would be the same in both cases. Hence, by altering the size of the plates or their arrangement, favourable or unfavour- able results are obtained according to the relation between R and r. 700 Dynamical Electricity. [777- It can be shown that i7i any git' en covibi7iation the maximuin effect is obtained when the total resistance in the elements is equal to the resistance of the interpolar. Suppose that in a given case n elements are arranged so as to form a battery of s couples, each consisting of / cells, then n = st. Denoting the resistance of a single element by r, the total resistance of the battery thus arranged is — ^. Now, according to the above law, the /, where / is the resistance of the interpolar. But / = -, hence -"^ = /, or s = / in 7' If in a given case we have 8 elements, each offering a resistance 1 5, and an interpolar with the resistance 40, we get s = 4-3, But this is an impossible arrangement, for it is not a whole number, and the nearest whole number must be taken. This is 4, and it will be found on making a calculation analogous to that above, that when arranged so as to form 4 elements, each of double surface, the greatest effect is obtained. CHAPTER III. EFFECTS OF THE CURRENT. 778. Physiologrical actions. — Under this name are included the effects produced by the battery-current on living organisms or tissues. When the electrodes of a strong battery are held in the two hands a violent shock is felt, especially if the hands are moistened with acidulated water, which increases the conductivity^ The violence of the shock increases with the number of elements used, and with a large number — as 200 Bunsen's cells — is even dangerous. The power of contracting upon the application of a voltaic current seems to be a very general property of protoplas77i — the physical basis of both animal and vegetable life ; if, for example, a current of moderate strength be passed through such a simple form of protoplasm as an Amceba, it immediately withdraws its processes, ceases its changes of form, and contracts into a rounded ball — soon, however, resuming its activity upon the cessation of the current. Essentially similar effects of the current have been observed in the protoplasm of young vegetable cells. If a frog's fresh muscle (which will retain its vitality for a considerable time after removal from the body of the animal) be introduced into a galvanic circuit, no apparent effect will be observed during the steady passage of the current, but every opening or closure of the circuit will cause a muscular contraction, as will also any sudden and considerable alteration in its intensity. By very rapidly interrupting the current, the muscle can be thrown into a state of uninterrupted contraction, or physio- logical tetanus^ each new contraction occurring before the previous one 779] Elcctrotojius, 701 has passed off. Other things being equal, the amount of shortening exhibited by the muscle increases, up to a certain limit, with the intensity of the current. These phenomena entirely disappear with the life of the- muscle ; hence the experiments are somewhat more difficult with warm- blooded animals, the vitality of whose muscles, after exposure or removal from the body, is maintained with more difficulty ; but the results of careful experiment are exactly the same here as in the case of the frog. The influence of an electric current upon living nerves is very remark- able ; as a general rule, it may be stated that its effect is to throw the nerve into a state of activity, whatever its special function may be ; thus, if the nerve be one going to a muscle, the latter will be caused to contract ; if it be one of common sensation, pain will be produced ; if one of special sense, the sensation of a flash of hght, or of a taste, etc., will be produced, according to the nerve irritated. These effects do not manifest them- selves during the even passage of the current, but only when the circuit is either opened or closed, or both. Of course, the continuity of the nerve with the organ where its activity manifests itself must be maintained intact. The changes set up by the current in the different nerve trunks are probably similar, the various sensations, etc. produced depending on the different terminal organs with which the nerves are connected. 779. Slectrotonus. — In a living nerve, as will be stated more fully in Chapter X., certain parts of the surface are electropositive to certain other parts, so that if a pair of electrodes connected with a galvanometer be ap- plied to these two points, a current will be indicated ; if now another part of the nerve be interposed in a galvanic circuit, it will be found that, if this extraneous current be passing in the same direction as the proper nerve current, the latter is increased, and vice versa ; and this, although it has previously been demonstrated experimentally that none of the battery current escapes down the nerve, so as to exert any influence of its own on the galvanometer. This alteration of its natural electromotive condition, produced through the whole of a nerve by the passage of a constant current through part of it, is known as the electrototiic state ; it is most intense near the extraneous, or, as it is called, the exciting current. It continues as long as the latter is passing, and is attended with important changes in the excitability of the nerve, or, in other words, the readiness with which the nerve is thrown into a state of functional activity by any stimulus applied to it. Pfliiger, who has investigated these changes, has named the part of the nerve through which the exciting current is passing the intrapolar region ; the condition of the nerve close to the positive pole is called anelectrotonus \ that near the negative pole, kathelectro- tonus. The excitabihty of the nerve is diminished in the anelectrotonic region, so that with a motor nerve, for example, a stronger stimulus than before would need to be applied at this part, in order to obtain a muscular contraction; in the kathelectrotonic region, on the contrary, the ex- citability of the nerve is heightened. Moreover, with an exciting current of moderate strength the power of the nerve to conduct a stimulus is lowered in the anelectrotonic region, and increased in the kathelectro- tonic ; with strong currents it is said to be diminished in both. 702 Dynamical Electricity. [779- These facts have to be taken into account in the scientific application of galvanism to medical purposes ; if, for instance, it is wished to diminish the excitability of the sensory nerves of any part of the body, the current should be passed in such a direction as to throw the nerves of that part into a state of anelectrotonus — and similarly in other cases. If a powerful electric current be passed through the body of a recently killed animal, violent movements are produced, as the muscles ordinarily retain their vitality for a considerable time after general systematic death; by this means, also, life has been re-established in animals which were apparently dead — a properly applied current stimulating the respiratory muscles to contract. 780. Tnermal effects. — When a voltaic current is passed through a metal wire the same effects are produced as by the discharge of an electric battery (742) ; the wire becomes heated, and even incandescent if Fig. 620. it is very short and thin. With a powerful battery all metals are melted, even iridium and platinum, the leasit fusible of metals. Carbon is the only element which has not hitherto been fused by it. M. Despretz, how- ever, with a battery composed of 600 Bunsen's elements joined in six series {^JTJ), has raised rods of very pure carbon to such a temperature that they were softened and could be welded together, indicating an incipient fusion. A battery ot 30 to 40 Bunsen's elements is sufficient to melt and vola- tilise fine wires of lead, tin, zinc, copper, gold, silver, iron, and even pla- tinum, with differently coloured sparks. Iron and platinum burn with 2, brilliant white light ; lead with a purple light ; the light of tin and of gold is bluish white ; the light of zinc is a mixture of white and gold ; finally, copper and silver give a green light. The thermal effects of the voltaic current are used for firing mines for military purposes and for blasting operations. The following arrangement devised by Colonel Schaw, is adopted in the English service. Fig. 620 -780] Thermal Effects of the Current. 703 represents a small wooden box provided with a lid. Two moderately stout copper wires, /?'^', insulated by being covered with gutta-percha, are deprived of this coating at the ends, which are then passed through and through the box in the manner represented in the figure. The distance between them is I of an inch, and a very fine platinum, wire (one weighing 1-92 grains to the yard is the regulation size) is soldered across. The object of arranging the wires in this manner is that they shall not be in contact, and that the strain which they exert may be spent on the box, and not on the platinum wire joining them, which, being extremely thin, would be broken by even a very slight pull. The box is then filled with fine-grained powder, and the lid tied down. The wires of the fuse are then carefully joined to the long conducting wires, which lead to the battery ; these should be of copper, and as thick as is convenient, so as to offer very little resistance : No. 16 gauge copper wire is a suitable size. The fuse is then introduced into the charge to be fired : if it is for a submarine explosion, the powder is contained in a canister, the neck of which, after the introduction of the fuse, is carefully fastened by means of cement, When contact is made with the battery, which is .effected through the intervention of mercury cups, the current traversing the platinum wire renders it incandescent, which fires the fuse ; and thus the ignition is communicated to the charge in which it is placed. The thermal effect depends more on the size than on the number of the plates of a battery, for the resistance in the connecting wires is small. An iron wire may be melted by a single Wollaston's element, the zinc of which is 8 inches by 6. Hare's battery (758) has received its name defiagrator on account of its greater heating effect produced by the great surface of its plates. When any circuit is closed, a definite amount of heat is produced throughout the entire circuit ; and the amount of heat produced in any particular part of the circuit is greater, the greater the proportion which the resistance of this part bears to the entire circuit. Hence in firing mines the wire to be heated should be of as small section and of as small conductivity as practicable. These conditions are well satisfied by platinum, which has over iron the advantage of being less brittle and of not being liable to rust. Platinum too has a low specific heat, and is thus raised to a higher temperature by the same amount of heat than a wire of greater specific heat. On the other hand, the conducting wires should present as small a resistance as possible, a condition satisfied by a stout copper wire ; and again, as the heating effect of any circuit is proportional to the square of the strength, and as this is directly as the electromotive force, and inversely as the resistance, a battery with a high electromotive force, and small resistance, such as Grove's or Bunsen's, should be selected. By means of a heated platinum wire, parts of the body may be safely cauterised which could not be got at by a red-hot iron ; the removal of tumours may be effected by drawing a loop of platinum round their base, which is then gradually pulled together. It has been observed that when the temperature of the wire is about 600° C, the combustion of the tissues 704 Dynamical Electricity. [780- is so complete that there is no haemorrhage ; while at 1 500° the action of the wire is Hke that of a sharp knife. 781. £a-ws of beating: effects. Galvano-tbermometer. — Although the thermal effects are most obvious in the case of thin wires, they are not limited to them ; with thicker wires they may be perceived by means of delicate thermometric arrangements, by which also the laws of, the heating effect may be investigated. Such an arrangement is called a galvano-therinometer. It consists essentially of a glass vessel containing alcohol, in which is a delicate thermometer ; the wire to be investigated is fitted to two platinum wires fused in the well-ground stopper of the vessel. The current is passed through the platinum wires, and its strength measured by means of a tangent compass interposed in the circuit. By observing the increase of temperature in the thermometer in a given time, and knowing the weight of the alcohol, the mass of the wire, the specific heat, and the calorimetric values (424) of the vessel, and of the thermometer, compared with al- cohol, the thermal effect .which is produced by the current in a given time can be calculated. By apparatus of this kind the laws of the thermal effects have been investigated by Lenz, Joule, and Becquerel. They are as follows : I. The heat disengaged in a give ft time is directly proportional to the square of the strength of the current, and to the resistance. II. Whatever be the length of a wire, provided its diameter remains the same, and that the same quantity of electricity passes, the increase of temperature is the same in all parts of the wire. III. For the same quatitity of electricity, the increase of tefnperature in different parts of a wire is inversely as the fourth power of the dia- meter. If the current passes through a chain of platinum and silver Avire of equal sizes, the platinum becomes more heated than the silver from its greater resistance ; and with a suitable current the platinum may become incandescent while the silver remains dark. This experiment was de- vised by Children. If a long thin platinum wire be raised to dull redness by passing a voltaic current through it, and if part of it be cooled down by ice, the resistance of the cooled part is diminished, the intensity of the current increases, and the rest of the wire becomes brighter than before. If, on the contrary, a part of the feebly incandescent wire be heated by a spirit-lamp, the resistance of the heated part increases, for the effect is the same as that of introducing fresh resistance, the intensity of the current diminishes, and the wire ceases to be incandescent in the non- heated part. The cooling by the surrounding medium exercises an important in- fluence on the phenomenon of ignition. A round wire is more heated by the same current than the same wire which has been beaten out flat; for the latter with the same section offers a greater surface to the cooling medium than the others. For the same reason, when a wire is stretched in a glass tube on which two brass caps are fitted air-tight, and the wire is raised to dull incandescence by the passage of a current, the incan- -782] Representation of the heating Effects in a Cirenit, 705 descence is more vivid when the air has been pumped out of the tube, because it now simply loses heat by radiation, and not by communication to the surrounding medium. Similarly, a current which will melt a wire in air will only raise it to dull redness in ether, and in oil or in water will not heat it to redness at all, for the liquids conduct heat away more readily than air does. From the above laws it follows that the heating effect is the same in a wire whatever be its length, provided the current is constant ; but it must be remembered that by increasing the length of the wire we increase the resistance, and consequently diminish the intensity of the current ; further, in a long wire there is a greater surface, and hence more heat is lost by radiation and by conduction. 782. Graphical representation of the heating: effects in a circuit. — The law representing the production of heat in a circuit in the unit of time is very well seen by the following geometrical construction, due to Professor Foster, who has devised several similar methods of graphically representing electrical laws. The heat H produced in a circuit in the unit of time is proportional to the square of the strength of the current C, and to the resistance R ; that is, H = C'^R ; but since C E E- - , we shall have H = _p. R R Draw a straight line DAB, and from any point A in it draw a line AC, at right angles to DAB, and of a length proportional to the electro- motive force of the cell. Lay off a length AB proportional to the resist- ance of the circuit. Join CB, and at C draw a line at right angles to EC and let D be the point where the line cuts the line DAB. Then the length AD is proportional to the heat produced in the whole circuit in unit time. For the triangles ADC and ACB are similar and therefore AD : AC -= AC : AB, that is AD = ^— , that is H = — ' AB ' R • Fig. 621. By drawing figures similar to the above it will be found that for a given electromotive force the heat is inversely proportional to the resistance, and for a given resistance directly proportional to the square of the electromotive force. That is, if the resistance is doubled, the heat is re- duced to one half; if the electromotive force is doubled the heat is quadrupled. H H 3 7o6 Dynamical Electricity. [783- 783. Relation of beating- effect to work of a battery. — In every closed circuit chemical action is continuously going on ; in ordinary circuits, the most common action is the solution of zinc in sulphuric acid, which may be regarded as an oxidation of the zinc to form oxide of zinc, and a combination of this oxide of zinc with sulphuric acid to form water and zinc sulphate. It is a true combustion of zinc, and this com- bustion serves to maintain all the actions which the circuit can produce, just as all the work which a steam-engine can effect has its origin in the combustion of fuel (445). By independent experiments it has been found that, when a given weight of zinc is dissolved in sulphuric acid, a certain definite measurable quantity of heat is produced, which, as in all cases of chemical action, is the same, whatever be the rapidity with which the solution is effected. If this solution takes place while the zinc is associated with another metal so as to form a voltaic couple, the rapidity of the solution will be altered, and the whole circuit will become heated — the liquid, the plates, the containing vessel as well as the connecting wire. But although the distribution of the heat is thus altered, its quantity is not. If the values of all the several heating effects in the various parts of the circuit be determined, it will still be found that this sum is exactly equivalent to that produced by the solution of a certain weight of zinc. If the couple be made to do external mechanical work the case is different. Joule made the following remarkable experiment. A small zinc and copper couple were arranged in a calorimeter and the amount of heat determined while the couple was closed for a certain length of time by a short thick wire. The couple still contained in the calorimeter was next connected with a small electromagnetic engine (796), by which a weight was raised. It was thus found that the heat produced in the calorimeter in a given time — while therefore a certain amount of zinc was dissolved — was less while the couple was doing work than when it was not ; and the amount of this diminution was the exact thermal equivalent x>f the work performed in raising the weight (467). . 784. Ibuminous effects.— In closing a voltaic battery a spark is ob- tained at the point of contact, which is frequently of great brilliance. A similar spark is also perceived on breaking contact. These luminous effects are obtained when the battery is sufficiently powerful, by bringing the two electrodes very nearly in contact ; a succession of bright sparks springs sometimes across the interval, which follow each other with such rapidity as to produce a continuous light. With eight or ten of Grove's elements brilliant luminous sparks are obtained by connecting one terminal of the battery with a file, and moving its point along the teeth of another file connected with the other terminal. The most beautiful effect of the electric light is obtained when, with the terminals of the battery, two pencils of charcoal are connected in the manner represented in fig. 622. The charcoal b is fixed, while the char- coal a can be raised and lowered by means of a rack and pinion motion, c. The two charcoals being placed in contact, the current passes, and their ends soon become incandescent. If they are then removed to a -784] Luminous Effects of tJie Current, 707 distance of about the tenth of an inch, according to the strength of the current, a luminous arc extends between the two points, which has ai> exceedingly brilliant lustre, and is called the voltaic arc. — The length of this arc varies with the fo»-ce of the current. In air it may exceed 2 inches with a battery of 600 elements, arranged in six series of 100 each, provided the positive pole is uppermost, as repre- sented in the figure ; if it is undermost, the arc is about one-third shorter. In vacuo the distance of the charcoal may be greater than in air; in fact, as the electricity meets with no resistance, it springs between the two charcoals, even before they are in contact. The voltaic arc can also be Fig. 622. produced in liquids, but it is then much shorter, and its brilliancy is greatly diminished. The voltaic arc has the property that it is attracted when a magnet is presented to it ; a consequence of the action of magnets on currents (818). Some physicists have considered the voltaic arc as formed 0/ a very rapid succession of bright sparks. Its colour and shape depend on the nature of the conductors between which it is formed, and hence it is probable that it is due to the incandescent particles of the conductor, which are volatilised and transported in the direction of the current — that is, from the positive to the negative pole. The more easily the electrodes are disintegrated by the current, the greater is the distance at which the electrodes can be placed. Charcoal, which is a very friable substance, is one of the bodies which gives the largest luminous arc. Recent researches by Edlund have shown that this disintegration of the terminals by the voltaic arc gives rise to an electromotive force opposed in direction to that of the main current. 7o8 Dynamical Electricity. [784- Davy first made the experiment of the electric hght, in 1 80 1, by means of a battery of 2,000 plates, each 4 inches square. He used charcoal points made of light wood charcoal which had been heated to redness, and immersed in a mercury bath ; the mercury, penetrating into the pores of the charcoal, increased its conductivity. When any substance was introduced into the voltaic arc produced by this battery, it became incandescent ; platinum melted like wax in the flame of a candle ; sapphire, magnesia, lime, and most refractory substances were fused. Fragments of diamond, of charcoal, and of graphite rapidly disappeared without undergoing any previous fusion. As charcoal rapidly burns in air, it was necessary to operate in vacuo, and hence the experiment was for a long time made by fitting the two points in an electric ^%%^ like that represented in fig. 580. At present the electrodes are made of gas graphite, a modification of charcoal deposited in gas retorts ; this is hard and compact, and only burns slowly in air : hence it is unnecessary to operate in vacuo. When the experiment is made in vacuo, there is no combustion, but the charcoal wears away at the positive pole, while it is somewhat increased on the negative pole, indicating that there is a transport of solid matter from the positive to the negative pole. 785. Foucault's experiment. — This consists in projecting on a screen the image of the charcoal points produced in the camera obscura at the moment at which the electric light is formed (fig. 623). By means of this experiment, which is made by the photo-electric microscope already described (fig. 459), the two charcoals can be readily distinguished, and the positive charcoal is seen to becom.e somewhat hollow and diminish, while the other increases. The globules represented on the two charcoals arise from the fusion of a small quantity of silica contained in the charcoal. When the current begins to pass, the negative charcoal first 786] Regidator of the Electric L ight. 709 becomes luminous, but the light of the positive charcoal is the brightest ; as it also wears away the most rapidly, it ought to be rather the larger. 786. Reg:ulator of the electric Ugrbt. — When the electric light is to be used for illumination, it must be as continuous as other modes of lighting. For this purpose, not only must the current be constant, but the distance of the charcoals must not alter, which necessitates the use Fig. 624. of some arrangement for bringing them nearer together in proportion as they wear away. One of the best modes of effecting this is by an ap- paratus invented by M. Duboscq. In this regulator the two charcoals are movable, but with unequal velocities, which are virtually proportional to their waste. The motion is transmitted by a drum placed on the axis, xy (fig. 624). This turns in 7 1 Dynajnical Electricity. [786- the direction of the arrows two wheels, a and b, the diameters of which are as i : 2, and which respectively transmit their motion to two rack- works, Of and C. C lowers the positive charcoal, p^ by means of a rod sliding in the tube, H, while the other Q' raises the negative charcoal, «, half as rapidly. By means of the milled head y the drum can be wound up, and at the same time the positive charcoal moved by the hand ; the milled head x moves the negative charcoal also by the hand, and independently of the first. For this purpose the axis, xy consists of two parts pressing against each other with some force, so that, holding the milled head x between the fingers, the other, jj/, may be moved, and by holding the latter the former can be moved. But the friction is sufficient when the drum works to move the two wheels a and b and the two rack- works. The two charcoals being placed in contact, the current of a powerful battery of 40 to 50 elements reaches the apparatus by means of the wires, E and E^ The current rising in H descends by the positive charcoal, then by the negative charcoal, and reaches the apparatus, but without passing into the rackwork, C, or into the part on the right of the plate, N ; these pieces being insulated by ivory discs placed at their lower part. The current ultimately reaches the bobbin B, which forms the foot of the regulator, and passes into the wire, E^ Inside the bobbin is a bar of soft iron, which is magnetised as long as the current passes in the bobbin, and demagnetised when it does not pass, and this temporary magnet is the regulator. For this purpose it acts attractively on an armature of soft iron, A, open in the centre so as to allow the rackwork C to pass, and fixed at the end of a lever, which works on two points, imn^ and transmits a slight oscillation to a rod, d, which, by means of a catch, /, seizes the wheel 2", as is seen on a larger scale in figure 625. By an endless screw, and a series of toothed wheels, the stop is transmitted to the drum, and the rackwork being fixed, the same is the case with the carbons. This is what takes place so long as the magnetisation in the bobbin is strong enough to keep down the armature, A ; but in proportion as the carbons wear away, the current becomes feebler, though the voltaic arc continues, so that ultimately the attraction of the magnet no longer counterbalances a spring, r, which continually tends to raise the armature. It then ascends, the piece d disengages the stop i, the drum works, and the carbons come nearer; they do not, however, touch, because the strength of the current gains the upper hand, the armature A is attracted, and the carbons remain fixed. As their distance only varies within very narrow limits, a regular and continuous light is obtained with this appa- ratus until the carbons are quite used. By means of a regulator, M. Duboscq illuminates the photogenic apparatus represented in fig. 459, by which all the optical experiments may be performed for which solar light was formerly necessary. 787. Brownfngr's regulator. — A much simpler apparatus, repre- sented in fig. 626, has been devised by Mr. John Browning. It has the great advantage of being less costly than the other lamps, and also of requiring a smaller number of elements to work it. The current enters — ^ V 788] Properties of the Electric L ight. 711 the lamp by a wire attached to a binding screw on the base of the instrument, passing up the pillar by the small electromagnet to the centre pillar along the top of the horizontal bar, down the left-hand bar through the two carbons, and away by a wire attached to a binding screw on the left hand. A tube holding the upper carbon slides freely up and down a tube at the end of the cross-piece, and would by its own weight rest on the lower carbon, but the electromagnet is provided with a keeper, to which is attached a rest that encircles the carbon tube and grasps it. When the elec- tromagnet works and attracts the keeper, the rest tightens and there- by prevents the descent of the carbon. When the keeper is not attracted the rest loosens, and the carbon holder descends. When the two carbons are at rest, on making contact with 'a bat- tery the current traverses both car- bons and no light is produced. But if the upper carbon be raised ever so little, a brilliant light is emitted. When the lamp is thus once set to work, the rod attached to the upper carbon may be let go, and the magnet will afterwards keep the lamp at work. For when some of the carbon is consumed, and the interval be- tween the two is too great for the current to pass, the magnet loses some of its power, the keeper loosens its hold on the -carbon, and this descends by its own weight. When they are sufficiently near, but before they are in contact, the current is re-established ; the magnet again draws on the keeper, and the keeper again checks the descent of the carbon, and so forth. Thus the points are retained at the right distances apart, and the light is continuous and brilliant. 788. Properties and intensity of the electric lisbt. — The electric light has similar chemical properties to solar light ; it effects the combi- nation of chlorine and hydrogen, acts chemically on chloride of silver, and applied to photography gives fine impressions remarkable for the warmth of its tones ; it is, however, inapplicable for taking portraits, as it fatigues the sight too greatly. Passed through a prism, the electric light, like the sun, is decomposed and gives a spectrum. WoUaston, and more especially Fraunhofer, have found that the spectrum of the electric light differs from that of other hghts and of the sun-light by the presence of several very bright lines, Fig. 626. 712 Dynamical Electricity, [788- as has been already stated. Wheatstone was the first to observe that by using electrodes of different metals, the spectrum and the lines are modified. Masson has recently studied the electric light in great detail, and has experimented upon the light of the electric machine, that of the voltaic arc, and that of RuhmkorfPs coil. He has found the same colours in the electric spectrum as in the solar spectrum, but traversed by very brilliant luminous bands of the same shade as that of the colour in which they occur. The number and position of these bands do not depend on the intensity of the light, but, as we have seen, upon the substances between which the voltaic arc is formed. With carbon the lines are remarkable for their number and brilliancy ; with zinc the spectrum is characterised by a very marked apple-green tint ; silver produces a very intense green ; with lead a violet tint pre- dominates, and so on with other metals. Bunsen, in experimenting with 48 couples, and removing the charcoals to a distance of a quarter of an inch, has found that the intensity of the electric light is equal to that of 572 candles. Fizeau and Foucault have compared the chemical effects of the solar and the electric lights, by investigating their action on iodized silver plates. Representing the intensity of the sun-light at midday at 1000, these physicists found that that of 46 Bunsen's elements was 235, while that of 80 elements was only 238. It follows that the intensity does not increase to any material extent with the number of the couples ; but experiment shows that it increases considerably with their surface. For with a battery of 46 elements, each consisting of 3 elements, with their zinc and copper respectively united so as to form one element of triple surface (777), the intensity was 385, the battery, working for an hour; that is to say, more than a third of the intensity of the solar light. Despretz observes that too great precautions cannot be taken against the effects of the electric light when they attain a certain intensity. The. light of 100 couples, he says, may produce very painful affections of the eyes. With 600, a single moment's exposure to the light is sufficient to produce very violent headaches and pains in the eye, and the whole frame is affected as by a powerful sunstroke. Mr. Way has obtained a very bright light by passing the electric current along a stream of mercury. The light is produced by the incan- descence of the mercury vapour ; it has a somewhat flickering character, and a greenish tinge. Attempts have been made to apply the electric light to the illumination of rooms, and even of streets ; but partly the cost, and partly the difficulty of producing with it a uniform illumination, inasmuch as the shadows are thrown into too sharp relief, have hitherto been great obstacles to its use. Yet it is advantageously applied in special cases, such as the photo-electric microscope, illuminations in theatres, etc. 789. nxeclianical effects ef tne battery. — Under this head may be included the motion of solids and hquids effected by the current. An ex- ample of the former is found in the voltaic arc, in which there is a passage of the molecules of carbon from the positive to the negative pole (784). -790] Chemical 'Effects of the Current. 7 1 3 If, in a slightly inclined glass tube, a thread of liquid be contained between two platinum wires fused in the glass, and if a current of elec- tricity be passed through the liquid by means of these electrodes, then, if the positive electricity moves upwards, the liquid will be carried along with it — it will become somewhat raised. The ascent is proportional to the intensity of the current and to the section of the tube. The pheno- menon is met with in alcohol and in turpentine, but in a contrary direction ; the liquid rising in the direction of the negative electricity. A similar phenomenon, known as electrical endosjuose, is observed in the following experiment, due to Porret. Having divided a glass vessel into two compartments by a porous diaphragm consisting of bladder, he poured water into the two compartments to the same height, and im- mersed two electrodes of platinum in connection with a battery of 80 elements. As the water became decomposed, part of the liquid was carried in the direction of the current, through the diaphragm, from the positive to the negative compartment, where the level rose above that in the other compartment. A solution of blue vitriol is best for these experiments, because then the disturbing influence of the disengagement of gas at the negative electrode is avoided. The converse of these phenomena is observed when a liquid is forced through a diaphragm by mechanical means ; electrical currents are produced, if on both sides the diaphragm, metal electrodes of the same material are immersed in the liquid in conducting communication with each other. Such currents, which were discovered by Quincke, are called diaphragm ciirrents. According to Wertheim, the elasticity of metallic wires is diminished by the current, and not by the heat alone, but by the electricity ; he has also found that the cohesion is diminished by the passage of a current. To the mechanical effects of the current may be assigned the sounds produced in soft iron when submitted to the magnetising action of a dis- continuous current— a phenomenon which will be subsequently described. 790. Cbemlcal effects. — These are among the most important of all the actions, either of the simple or compound circuit. The first decomposition effected by the battery was that of water, obtained in 1800 by CarUsle and Nicholson by means of a voltaic pile. Water is rapidly decomposed by 4 or 5 Bunsen's cells ; the apparatus (fig. 627) is very convenient for the purpose. It consists of a glass vessel fixed on a wooden base. In the bottom of the vessel two platinum electrodes, j) and w, are fitted, Fig. 627. communicating by means of copper wires with the binding screws. The vessel is filled with water to 714 Dynamical Electricity. [790- which some sulphuric acid has been added to increase its conductivity, for pure water is a very imperfect conductor ; two glass tubes filled with water are inverted over the electrodes, and on interposing the apparatus in the circuit of a battery decomposition is rapidly set up, and gas bubbles rise from the surface of each pole. The volume of gas liberated at the negative pole is about double that at the positive, and on exa- mination the former gas is found to be hydrogen and the latter gas oxygen. This experiment accordingly gives at once the qualitative and quantitative analysis of water. The oxygen thus obtained has the peculiar and penetrating odour observed when an electrical machine is worked (745), and which is due to ozone. The water contained at the same time some peroxide of hydrogen, in producing which some oxygen is consumed. Moreover oxygen is somewhat more soluble in water than hydrogen. Owing to these causes the volume of oxygen is less than that required by the composition of water, which is two volumes of hydrogen to one of oxygen. Hence voltametric measurements are most exact when the hydrogen alone is considered, and when this is liberated at the surface of a small electrode. 791. Electrolysis. — To those substances which, like water, are re- solved into their elements by the voltaic current, the term electrolyte has been applied by Faraday, to whom the principal discoveries in this subject and the nomenclature are due. Electrolysis is the decomposition by the voltaic battery ; the positive electrode was by Faraday called the a?iode, and the negative electrode the kathode. The products of decom- position are tones ; katione, that which appears of the kathode ; and anione, that which appears at the anode. By means of the battery, the compound nature of several substances which had previously been considered as elements has been determined. By means of a battery of 250 couples, Davy, shortly after the discovery of the decomposition of water, succeeded in decomposing the alkalies potass and soda, and proved that they were the oxides of the hitherto Fig. 628. Fig. 629. unknown metals potassium and sodium. The decomposition of potass may be demonstrated with the aid of the battery of 4 to 6 elements in the following manner ; a small cavity is made in a piece of solid caustic -792] Decomposition of Salts. 715 potass, which is moistened, and a drop of mercury placed in it (fig. 628). The potass is placed on a piece of platinum connected with the positive pole of the battery. The mercury is then touched with the negative pole. When the current passes, the potass is decomposed, oxygen is liberated at the positive pole, while the potassium liberated at the negativ^e pole amalgamates with the mercury. On distilling this amalgam out of contact with air, the mercury passes off, leaving the potassium. The decomposition of binary compounds — that is, bodies containing two elements — is quite analogous to that of water and of potass ; one of the elements goes to the positive, and the other to the negative pole. The bodies separated at the positive pole are called electronegative ele- ments, because at the moment of separation they are considered to be charged with negative electricity, while those separated at the negative pole are called cledropositive elements. One and the same body may be electronegative or electropositive, according to the body with which it is associated. For instance, sulphur is electronegative towards hydrogen, but is electropositive towards oxygen. The various elements may be arranged in such a series that any one in combination is electronegative to any following, but electropositive towards all preceding ones. This is called the electrochemical series, and begins with oxygen as the most electronegative element, terminating with potassium as the most electro- positive. The decomposition of hydrochloric acid into its constituents, chlorine and hydrogen, may be shown by means of the apparatus represented in fig. 629. Carbon electrodes must, however, be substituted for those of platinum, which is attacked by the liberated chlorine ; a quantity of salt also must be added to the hydrochloric acid, in order to diminish the solubility of the liberated chlorine. The decomposition of iodide of po- tassium may be demonstrated by means of a single element. For this purpose a piece of bibulous paper is soaked with a solution of starch, to which iodide of potassium is added. On touching this paper with the electrodes, a blue spot is produced at the positive pole, due to the action of the liberated iodine on the starch. 792. Decomposition of salts. — Ternary salts in solution are decom- posed by the battery, and then present effects varying with the chemical affinities, and the intensity of the current. In all cases the acid, or the body which is chemically equivalent to it, is electronegative in its action towards the other constituent. The decomposition of salts may be readily shown by means of the bent tube represented in fig. 629. This is nearly filled with a saturated solution of a salt, say sulphate of sodium, coloured with tincture of violets. The platinum electrodes of a battery of four Bunsen's elements are then placed in the two legs of the tube. After a few minutes the liquid in the positive leg, A, becomes of a red, and that in the negative leg, B, of a green colour, showing that the salt has been resolved into acid which has passed to the positive, and into a base which has gone to the negative pole, for these are the effects which a free acid and a free base respectively produce on tincture of violets. 7 1 6 Dynamical Electricity. [792- In a solution of sulphate of copper, free acid and oxygen gas appear at the positive electrode, and metallic copper is deposited at the negative electrode. In like manner, with nitrate of silver, metallic silver is de- posited on the negative, while free acid and oxygen appear at the positive electrode. This decomposition of salts was formerly explained by saying that the acid was liberated at the positive electrode and the base at the negative. Thus sulphate of potassium, K^OSOg, was considered to be resolved into sulphuric acid, SO3, and potash, KoO. This view regarded salts com- posed of three elements as different in their constitution from binary or haloid salts. Their electrolytic deportment has led to a mode of regard- ing the constitution of salts which brings all classes of them under one category. In sulphate of potassium, for instance, the electropositive element is potassium,' while the electronegative element is a complex of sulphur and oxygen, which is regarded as a single group, SO^, and to which the name oxy-sidphion may be assigned. The formula of sulphate of potassium would thus be K^SO^, and its decomposition would be quite analogous to that of chloride of potassium, KCl, chloride of lead, PbCl.,, iodide of potassium, KI. The electronegative group SO^ corresponds to a molecule of chlorine or iodine. In the decomposition of sulphate of potassium the potassium liberated at the negative pole decomposes water, forming potash and liberating hydrogen. In like manner the electro- negative constituent SO^, which cannot exist in the free state, decomposes into oxygen gas, which is liberated, and into anhydrous sulphuric acid, SO3, which immediately combines with water to form ordinary sulphuric acid, H2SO4. In fact, where the action of the battery is strong these gases are liberated at the corresponding poles ; in other cases they com- bine in the liquid itself, reproducing water. The constitution of sulphate of copper, CuSO^, and of nitrate of silver, AgNOg, and their decomposi- tion, will be readily understood from these examples. 793. Transmissions effected by the current. — In chemical decom- positions effected by the battery there is not merely a separation of the elements, but a passage of the one to the positive and of the other to the negative electrode. This phenomenon has been demonstrated by Davy by means of several experiments, of which the two following are ex- amples : — i. He placed solution of sulphate of sodium in two capsules connected by a thread of asbestos moistened with the same solution, and immersed the positive electrode in one of the capsules, and the negative electrode in the other. The salt was decomposed, and at the expiration of some time all the sulphuric acid was found in the first capsule, and the soda in the second. ii. Having taken three glasses, A, B, and C (fig. 630), he poured into the first, solution of sulphate of sodium, into the second dilute syrup of violets, and into the third pure water, and connected them by moistened threads of asbestos. The current was then passed in the direction from C to A. The sulphate in the vessel A was decomposed, and in the course of time there was nothing but soda in this glass, which formed the nega- tive end, while all the acid had been transported to the glass C, which 795] Laws of Electrolysis, 717 was positive. If, on the contrary, the currents passed from A to C, the soda was found in C, while all the acid remained in A; but in both cases the remarkable phenomenon was seen that the syrup of violets in B neither became red nor green by the passage of the acid or base through its mass, a phenomenon the /j explanation of which is based on the hypothesis enun- "^K: ciated in the following para- -=-—-.-=^-^- =-.„==..-.-=— - - graph. Fis- 630. 794. Grotbiiss's bypothesis. — Grothiiss has given the following ex- planation of the chemical decompositions effected by the battery. Adopting the hypothesis that in every binary compound, or body which acts as such, one of the elements is electropositive, and the other electro- negative, he assumes that, under the influence of the contrary electricities of the electrodes, there is effected, in the liquid in which they are im- mersed, a series of successive decompositions and recompositions from one pole to the other. Hence it is only the elements of the terminal molecules which do not recombine, and remain- ing free appear at the elec- trodes. Water, for instance. Fig. 631. is formed of one atom of oxygen and two atoms of hydrogen, the first gas being electronegative, and the second electropositive. Hence when the liquid is traversed by a sufficiently powerful current, the molecule a in contact with the positive pole arranges itself as shown in fig. 631, that is, the oxygen is attracted and the hydrogen repelled. The oxygen of this molecule is then given off at the positive electrode, the liberated hydrogen immediately unites with the oxygen of the molecule b, the hydrogen of this with the oxygen of the molecule c, and so on, to the negative electrode, where the last atoms of hydrogen become free and appear on the poles. The same theory applies to the metallic oxides, to the acids and salts, and explains why in the experiment mentioned in the preceding paragraph the syrup of violets in the vessel B becomes neither red nor green. The reason why, in the fundamental experiment, the hydrogen is given off at the negative pole when the circuit is closed will be readily understood from a consideration of this hypothesis. 795. Iiaws of electrolysis. — The laws of electrolysis were discovered, by Faraday ; the most important of them are as follows : — I. Electrolysis cannot take place unless the electi'olyte is a conductor. Hence ice is not decomposed by the battery, because it is a bad conductor Other bodies, such as oxide of lead, chloride of silver, etc., are only electrolysed in a fused state — that is, when they can conduct the current. n. The energy 0/ the electrolytic action of the current is the same in all its parts. III. The same quantity of electricity — that is, the same electric current yi8 Dynamical ElecU'icity. [795- — decomposes chemically eqinvalent quantities of all the bodies which it t7'averses ; from which it follows, that the weights of elerneiits separated in these electrolytes are to each other as their chemical equivalents. If an apparatus for decomposing water (fig. 628) and various U-shaped tubes containing respectively fused oxide of lead and chloride of tin are interposed in the same voltaic current, which must be sufficiently power- ful, these substances will be decomposed ; the electronegative elements will be separated at the positive and the electropositive at the negative poles. The quantities of substances liberated are in a certain definite relation. Thus for every 18 parts of water decomposed in the voltameter there will be liberated 2 parts of hydrogen, 207 parts of lead, and 117 of tin at the respective negative electrodes, and 16 parts of oxygen, and 71 (or 2 X 35*5) parts of chlorine at the corresponding positive electrode. Now these numbers are exactly as the equivalents (not as the atomic weights) of the bodies. It will further be found that in each of the cells of the battery 65 parts by weight of zinc have been dissolved, for every two parts by weight of hydrogen liberated ; that is, that for every equivalent of a substance decomposed in the circuit one equivalent of zinc is dissolved. This is the case whatever be the number of cells. An increase in the number only has the effect of overcoming the great resistance which many eleC' trolytes offer, and of accelerating the decomposition. It does not increase the quantity of the eletrolyte decomposed. If in any of the cells more than 65 parts of zinc are dissolved for every two parts of hydrogen liberated, this arises from a disadvantageous succeeding local action ; and the more perfect the battery, the more nearly does it approach this ratio. IV. It follows from the above law, that the quantity of a body decom- posed in a givefi time is proportional to the strength of the current. On this is founded the use of Faraday's voltajneter, in which the intensity of a current is ascertained from the quantity of water which it decomposes in a given time. It consists of a glass vessel, in which two platinum electrodes are fixed. In the neck of a vessel a bent delivery tube is fitted, and the mixed gases are collected in a graduated cylinder, so that their volume can be determined, which, reduced to a constant tempera- ture and pressure, is a measure of their quantity. The use of this voltameter appears simple and convenient ; and hence some physicists have proposed as unit of the strength of the current, that strength which in o?ie minute yields a cubic centimetre of mixed gas reduced to the temperature 0° and the pressure 760 ^nin. Yet, for reasons mentioned before (790), the measurements should be based on the volume of hydrogen liberated. The silver voltameter is an instrument for measuring the intensity of the current. A solution of nitrate of silver of known strength is placed in a platinum dish which is connected with the negative pole ; in this solution is placed the positive pole, which consists of a rod of silver wrapped round with muslin. The silver which separates at the negative pole is washed, dried, and weighed ; and the weight thus produced in a -796] Tangent Compass compared witJi the Voltameter. 'ji<^ given time is a measure for the intensity of the current. The silver par- ticles which become detached from the positive pole are retained in the mushn. The current from the electrical machine, which is of very high in- tensity, is capable of traversing any electrolyte, but the quantity which it can decompose is extremely small as compared even with the smallest voltaic apparatus, and it must be concluded that the quantity developed by the frictional machine is very small as compared with that developed by chemical action. It has been calculated by Weber, that if the quantity of positive elec- tricity required to decompose a grain of water were accumulated on a cloud at a distance of 3,000 feet from the earth's surface, it would exert an attractive force upon the earth of upwards of 1,500 tons. 796. Comparison between tbe tangrent compass and the volta- meter. — There are several objections to the use of the voltameter. In the first place, it does not indicate the strength at any given moment, for in order to obtain measurable quantities of gas the current must be continued for some time. Again, the voltameter gives no indications of the changes which take place, in this time, but only the mean strength. It offers also great resistance, and can thus only be used in the case of strong currents ; for such currents either do not decompose water, or only yield quantities too small for accurate measurement. In addition to this, the indications of the voltameter depend not only on the intensity of the current, but on the acidity of the water, and on the distance and size of the electrodes. The magnetic measurements are preferable to the chemical ones. Not only are they more delicate and offer less resistance, but they give the intensity at any moment. On the other hand, indications furnished by the tangent compass hold only for one special instriynent. They vary with the diameter of the ring and the number of turns ; moreover, one and the same instrument will give different indications on different places, seeing that the force of the earth's magnetism varies from one place to another. The indications of the two instruments may, however, be readily com- pared with one another. For this purpose the voltameter and the tangent compass are simultaneoiisly inserted in the circuit of a battery, and the deflection of the needle and the amount of gas liberated in a given time are noted. In one special set of experiments the following results were obtained : — Number of Elements. Deflection. Gas liberated in three minutes. 12 8 6 3 2 28-5° 24-8 22-0 1375 6-9 I25CC. 106 93 56 24 720 Dynamical Electricity. [796- If we divide the tangents of the angle into the corresponding volume of gas liberated in one minute, we should obtain a constant magnitude which represents how much gas is developed in a minute by a current which could produce on the tangent compass the deflection 45°, for tang. 45° = i. Making this calculation with the above observations, we obtain a set of closely agreeing numbers, the mean of which is 76-5. The gas was measured under a pressure of 737 mm. and at a temperature of 315°, and therefore under normal conditions (309) its volume would be 70 cubic centimetres. That is to say, this is the volume of gas which corresponds to a deflection of 45°. Hence in chemical measure the strength C of a current which produces in this particular tangent compass a deflection of 6° is C = 70 tang. ^. For instance, supposing a current produced in this tangent compass a deflection of 54°, this current, if it passed through a voltameter, would liberate in a minute 70 x tang. 54 = 70 x 1-376 = 96*32 cubic centimetres of gas. If once the reduction factor for a tangent compass has been deter- mined, the strength of any current may be readily calculated in chemical measure by a simple reading of the angle of deflection. This reduction factor of course only holds for one special instrument, and for experi- ments on the same place, seeing that the force of the earth's magnetism varies in different places". The indications of the sine-compass may be compared with those of the galvanometer in a similar manner. 797. Polarisation. — When the platinum electrodes, which have been used in decomposing water, are disconnected from the battery, and con- nected with a galvanometer, the existence of a current is indicated which has the opposite direction to that which had previously passed. This phenomenon is explained by the fact that oxygen has been condensed on the surface of the positive plate, and hydrogen on the surface of the negative plate, analogous to what has been already seen in the case of the non-constant batteries (759). The effect of this is to produce two different electromotors, which produce a current opposed in direction to the original one, and which, therefore, must weaken it. As the two electrodes thus become the poles of a new current, they are said to be polarised^ and the current is called a polarisatioti-current. On this principle batteries may be constructed of pieces of metal of the same kind — for instance, platinum — which otherwise gives no current. A piece of moistened cloth is interposed between each pair, and each end of this system is connected with the poles of a battery. After some time the apparatus has received a charge, and if separated from the battery can itself produce all the effects of a voltaic battery. Such batteries are called secondary batteries. Their action depends on an alteration of the surface of the metal produced by the electric current ; the constituents of the Hquid with which the cloth is moistened having become accumulated on the opposite plates of the circuit. -800] NobilVs Rings. 721 A dry pile which has become inactive may be used as a secondary battery. When a current is passed through it, in a direction contrary to that which the active battery yields, it then regains its activity. To this class belongs Planters secondary battery, which consists of two concentric cylinders of sheet lead, which do not touch, and are immersed in dilute acid. They are charged by being placed in contact with a battery of two or three cells, and there is an arrangement by which they can be detached from the battery and their current utilised. They serve in a certain sense to store up and transform the power of the primary battery, and produce effects of great intensity. 798. Grove's gras battery. — On the property, which metals have, of condensing gases on their surfaces. Grove has constructed h.\s gas battery. In its simplest form it consists of two glass tubes, in each of which is fused a platinum electrode, provided on the outside with binding screws. These electrodes are made more efficient by being covered with finely divided platinum. One of the tubes is partially filled with hydrogen, and the other partially with oxygen, and they are inverted over dilute sulphuric acid, so that half the platinum is in the hquid and half in gas. On connecting the electrodes with a galvanometer, the existence of a current is indicated, whose direction in the connecting wire is from the platinum in oxygen to that in hydrogen ; so that the latter is negative towards the former. As the current passes through water this is decom- posed ; oxygen is separated at the positive plate, and hydrogen at the other. These gases unite with the gases condensed on their surface, so that the volume of gas in the tubes gradually diminishes, but in the ratio of one volume of oxygen to two volumes of hydrogen. These elements can be formed into a battery by joining the dissimilar plates with one another just as they are joined in an ordinary battery. One element of such a battery is sufficient to decompose iodide of potassium, and four will decompose water. 799. Passive state of iron. — With polarisation is probably connected a vei7 remarkable chemical phenomenon, which many metals exhibit, but more especially iron. When this is immersed in concentrated nitric acid it is unattacked. This condition of iron is called the passive state, and upon it depends the possibility of the zinc-iron battery (763). It is probable that in the above experiment a thin superficial layer of sesquioxide of iron is formed, which is then negative towards platinum. 800. XffoMli's rings. — When a drop of acetate of copper is placed on a silver plate, and the silver is touched in the middle of the drop with a piece of zinc, there are formed around the point of contact a series of copper rings alternately dark and light. These are Nobili's coloured rings. They may be obtained in beautiful iridescent colours by the following process : A solution of oxide of lead in potash is obtained by boiling finely powdered litharge in a solution of potash. In this solution is im- mersed a polished plate of silver or of German silver, which is connected with the positive electrode of a battery of eight Bunsen's elements. With the negative pole is connected a fine platinum wire fused in glass, so that only its point projects ; and this is placed in the liquid at a small distance I I 722 Dynamical Electricity. [800- from the plate. Around this point binoxide of lead is separated on the plate in very thin concentric layers, the thickness of which decreases from the middle. They show the same series of colours as Newton's coloured rings in transmitted light. The binoxide of lead owes its origin to a secondary decomposition ; by the passage of the current some oxide of lead is decomposed into metallic lead, which is deposited at the negative pole, and oxygen which is liberated at the positive ; and this oxygen com- bines with some oxide of lead to form binoxide, which is deposited on the positive pole as the decomposition proceeds. The effects are also well seen if a solution of sulphate of copper is placed on a silver plate, which is touched with a zinc rod, the point of which is in the solution; for then a current is formed by these metals and the liquid. 8oi. Arbor Saturni, or lead tree. Arbor Dianae. — When, in a solution of a salt, is immersed a metal which is more oxidisable than the metal of the salt, the latter is precipitated by the former, while the im- mersed metal is substituted equivalent for equivalent for the metal of the salt. This precipitation of one metal by another is partly attributable to the difference in their affinities, and partly to the action of a current which is set up as soon as a portion of the less oxidisable metal has been deposited. The action is promoted by the presence of a slight excess of acid in the solution. A remarkable instance of the precipitation of one metal by another is the arbor Saturni. This name is given to a series of brilliant ramified crystalhsations obtained by zinc in solutions of acetate of lead. A glass flask is filled with a clear solution of this salt, and the vessel closed with a cork, to which is fixed a piece of zinc in contact with some copper wire. The flask, being closed, is left to itself. The copper wire at once begins to be covered with a moss-like growth of metallic lead, out of which brilliant crystallised laminae of the same metal continue to form ; the whole phenomenon has great resemblance to the growth of vegetation, from which indeed the old alchemical name is derived. For the same reason the name arbor DiaiicE has been given to the metallic deposit produced in a similar manner by mercury in a solution of nitrate of silver. ELECTROMETALLURGY. 802. Electrometallurg-y-. — The decomposition of salts by the battery has received a most important application in electro7netatturgy, or galvanoplastics^ by which is meant the art of precipitating certain metals from their solutions by the slow action of a galvanic current, by which means the salts of certain metals are decomposed, the metal being deposited on the negative pole, while the acid is liberated at the positive. The art was discovered independently by Spencer in England, and by Jacobi in Petersburg. In order to obtain a galvanoplastic reproduction of a medal or any other object, a mould must first be made, on which the layer of metal is deposited by the electric current. Electrometallurgy, 723 For this purpose several substances are in use, and one or the other is preferred according to circumstances. For medals and similar objects Avhich can be submitted to pressure, gutta percha may be used witE~ advantage. The gutta percha is softened in hot water, pressed against the object to be copied, and allowed to cool, when it can be detached without difficulty. For the reproduction of engraved woodblocks or type, wax moulds are now commonly used. They are prepared by pouring into a narrow flat pan a suitable mixture of wax, tallow, and Venice turpentine, which is allowed to set, and is then carefully brushed over with very finely powdered graphite. While this composition is still somewhat soft, the woodblock or type is pressed upon it either by a screw press, or, still better, by hydraulic pressure. If plaster of Paris moulds are to be made use of, it is essential that they be first thoroughly saturated with wax or tallow so as to become impervious to water. In all cases, whether the moulds be of gutta percha, of wax, or any non-conducting substance, it is of the highest importance that their surface be brushed over very carefully with graphite and so made a good con- ductor. The conducting surface thus prepared must also be in metallic contact with a wire or a strip of copper by which it is connected with the negative electrode. Sometimes the moulds are made of a fusible alloy (317), which may consist of 5 parts of lead, 8 of bismuth, and 3 of tin. Some of the melted alloy is poured into a shallow box, and just as it begins to solidify the medal is placed horizontally on it in a fixed position. When the alloy has become cool, a slight shock is sufficient to detach the medal. A copper wire is then bound round the edge of the mould, by which it can be connected with the negative electrode of the battery, and then the edge and the back are covered with a thin non-conducting layer of wax, so that the deposit is only formed on the mould itself. The most suitable arrangement for producing an electro-deposit of copper consists of a trough of glass, slate, or of wood, lined with india- rubber or coated with marine glue (fig. 632). This contains an acid solution of sulphate of copper, and across it are stretched copper rods B and D connected respectively with the negative and positive poles of a battery. By their copper conductors the moulds m are suspended in the liquid from the negative rod B, whilst a sheet of copper C, presenting a surface about equal to that of the moulds to be covered, is suspended from the positive rod D, at a distance of about 2 inches, directly opposite to them. The battery employed for the electric deposition of metals ought to be one of great constancy, and Daniell's and Smee's are mostly in use. The currents of electricity furnished by magneto-electrical machines of a special construction are also used in large establishments. The copper plate suspended from the positive pole serves a double purpose ; it not only closes the current, but it keeps the solution in a state of concentration, for the acid liberated at the positive pole dissolves the 724 Dynamical Electricity. [802- copper, and reproduces a quantity of sulphate of copper equal to that de- composed by the current. Another, and very simple process for producing the electric deposit of copper consists in making use of what is in effect a Daniell's cell. A porous pot, or a glass cylinder covered at the bottom with bladder, or with vegetable parchment, is immersed in a vessel of larger capacity containing a concentrated solution of sulphate of copper. The porous vessel contains acidulated water, and in it is suspended a piece of amal- gamated zinc of suitable form; and having a surface about equal to that Fig. 632. of the mould. The latter is attached to an insulated wire connected with the zinc and is immersed in the solution of sulphate of copper in such a position that it is directly opposite to the diaphragm. The action com- mences by the mould becoming covered with a film of copper commencing at the point of contact with the conductor and gradually increasing in thickness in proportion to the action of the Daniell's element thus formed. It is of course essential in the process to keep the solution of copper at a uniform strength which is done by suspending muslin bags filled with crystals of sulphate of copper. How great is the delicacy with which such electric deposits can attain appears from the fact that galvanoplastic copies can be made of daguerre- otypes, which are of the greatest accuracy. • 803. Electrog-ilding-. — The old method of gilding was by means of mercury. It was effected by an amalgam of gold and mercury, which was applied on the metal to be gilt. The objects thus covered were heated in a furnace, the mercury volatilised, and the gold remained in a very thin layer on the objects. The same process was used for silver- ing ; but they were expensive and unhealthy methods, and have now been entirely replaced by electrogilding and electrosilvering. Electro- gilding only differs from the process described in the previous paragraph, in that the layer is thinner and adheres more firmly. Brugnatelli, a pupil .of Volta, appears to have been the first, in 1803, to observe that a body could be gilded by means of the battery and an alkaline solution of gold ; but De la Rive was the first who really used the battery in gilding. The methods both of gilding and silvering owe their present -805] Deposition of Ii'on and Nickel. 725 high state of perfection principally to the improvements of Elkington, Ruolz, and others. The pieces to be gilt have to undergo three processes before gilding. The first consists in heating them so as to remove the fatty matter which has adhered to them in previous processes. As the objects to be gilt are usually of what is called gilding metal or red brass, and which is a special kind of brass rich in copper, and their surface during the operation of heating becomes covered with a layer of suboxide or of protoxide of copper, this is removed by the second operation. For this purpose the objects^ while still hot, are immersed in very dilute nitric acid, where they remain until the oxide is removed. They are then rubbed with a hard brush, washed in distilled water, and dried in gently heated sawdust. To remove all spots they must undergo the third process, which con- sists in rapidly immersing them in ordinary nitric acid, and then in a mixture of nitric acid, bay salt , and soot. When thus prepared the objects are attached to the negative pole of a battery, consisting of three or four Bunsen's or Daniell's elements. They are then immersed in a bath of gold, as previously described. They remain in the bath for a time which depends on the thickness of the desired de- posit. There is great difference in the composition of the baths. That most in use consists of i part of chloride of gold. 10 parts of cyanide of potassium, dissolved in 200 parts of water. In order to keep the bath in a state of concentration, a piece of gold is suspended from the positive electrode, which dissolves in proportion as the gold dissolved in the bath is deposited on the objects attached to the negative pole. The method which has just been described can also be used for silver, bronze, German silver, etc. But other metals^ such as iron, steel, zinc, tin, and lead, are very difficult to gild well. To obtain a good coating, they must first be covered with a layer of copper, by means of the battery and a bath of sulphate of copper ; the copper with which they are coated is then gilded, as in the previous case. 804. Electrosllvering-. — What has been said about gilding applies exactly to the process of electrosilvering. The difference is in the com- position of the bath, which consists of two parts of cyanide of silver, and two parts of cyanide of potassium dissolved in 250 parts of water. To the positive electrode is suspended a plate of silver, which prevents the bath from becoming poorer: the pieces to be silvered, which must be well cleaned, are attached to the negative pole. It may here be observed that these processes succeed best with hot solutions. 805. Electric deposition of iron and nickel. — One of the most valuable applications of the electric deposition of metals is to what is called the steeling (acierage) of engraved copper plates. The bath re- quired for this purpose is obtained by suspending a large sheet of iron, connected with the positive pole of a battery, in a trough filled with a saturated solution of sal-ammoniac ; whilst a thin strip of iron, also im- mersed, is connected with the negative pole. By this means iron from 726 Dyjianiical Electricity, [805- the large plate is dissolved in the sal-ammoniac while hydrogen is given off on the surface of the small one. When the bath has thus taken up a sufficient quantity of iron, an engraved copper plate is substituted for the small negative strip. A bright deposit of iron begins to form on it at once, and the plate assumes the colour of a polished steel plate. The deposit thus obtained in the course of half an hour is exceedingly thin, and an impression of the plate thus covered does not seem different from an uncovered plate; it possesses however an extraordinary degree of hardness, so that a very large number of impressions can be taken from such a plate before the thin coating of iron is worn off. When, however, this is the case, the film of iron is dissolved off by dilute nitric acid and the plate is again covered with the deposit of iron. An indefinite number of perfect impressions may, by this means, be obtained from one copper plate, without altering the original sharp con- dition of the engraving. The covering of metals by a deposit of nickel has of late come into use. The process is essentially the same as that just described. The bath used for the purpose can however be made more directly by mixing, in suitable proportions, salts of nickel with those of ammonia. The positive pole consists of a plate of pure nickel. A special difficulty is met with in the electric deposition of nickel owing to the tendency of this metal to deposit in an uneven manner; and then to become detached. This is got over by frequently removing the articles from the bath, and submitting them to a polishing process. Objects coated with nickel show a highly polished surface of the characteristic bright colour of this metal. The coating is moreover very hard and durable, and is unaffected either by the atmosphere or even by sulphuretted hydrogen. ' CHAPTER IV. ELECTRODYNAMICS. ATTRACTION AND REPULSION OF CURRENTS BY CURRENTS. 806. Electrodynamics. — Under electrodyttamics is understood the laws of electricity in a state of motion, or the action of electric currents upon each other and upon magnets, while electrostatics deals with the laws of electricity in a state of rest. The action of one electrical current upon another was first investigated by Ampere, shortly after the discovery of Oersted's celebrated funda- mental experiment (772). All the phenomena, even the most compli- cated^ follow from two simple laws, which are — I. Two cicrrents which are parallel^ and in the same direction, attract 07ie another. I I. Two currents par at let, but in contrary directions, repel one another. In order to demonstrate these laws, the circuit which the current traverses must consist of two parts, one fixed and the other movable. -806] Elmtrodyna in ics. 727 This is effected by the apparatus (fig. 633), which is a modified and im- proved form of one originally devised by Ampere. It consists of two brass columns, A and D, between which is a shorter one. The column D is provided with a multiplier (773) of 20 turns, MN (fig. 633), which greatly increases the sensitiveness of the instrument. This Fig. 633. can be adjusted at any height and in any position by means of a universal screw clamp (see figs. 633, 635-638). The short column is hollow, and in its interior slides a brass tube ter- minating in a mercury cup, ^, which can be raised or lowered. On the column A is another mercury cup represented in section at fig. 634 in its natural size. In the bottom is a capillary aperture through which passes the point of a sewing needle fixed to a small copper ball. This point ex- tends as far as the mercury, and turns freely in the hole. The movable part of the circuit consists of a copper wire proceeding from a small ball, and turning in the direction of the arrows from the cup a to the cup c. The two lower branches are fixed to a thin strip of wood, and the whole system is balanced by two copper balls sus- pended to the ends. The details being known, the current of a Bunsen's battery of 4 or 5 cells ascending by the column A (fig. 633) to the cup a^ traverses the circuit BC, reaches the cup c, descends the central column, and thence passes by a wire, P, to the multiplier AIN, from whence Fig. 634. it returns to the battery by the wire Q. Now if, before the current passes, 728 Dynamical Electricity. [806 the movable circuit has been arranged in the plane of the multiplier, with the sides B and M opposite each other, when the current passes the side B is repelled, which demonstrates the second law ; for in the branches B and M the currents, as indicated by the arrows, are proceeding in opposite directions. To demonstrate the first law the experiment is arranged as in figure 635 — that is, the multiplier is reversed ; the current is then in the same direc- tion both in the multiplier and in the movable part ; and when the latter is removed out of the plane of the multiplier, so long as the current passes it tends to return to it, proving that there is attraction between the two parts. 807. Ro§ret's vibratingr spiral. — The attraction of parallel currents may also be shown by an experiment known as that of Rogefs vibrating spiral. A copper wire about 07 mm. in diameter is coiled in a spiral of about 30 coils of 25 mm. diameter. At one end it is hung vertically from a binding screw, while the other just dips in a mercury cup. On passing the current of a battery of 3 to 5 Grove's cells through the spiral by means of the mercury cup and the binding screw, its coils are traversed by parallel currents ; they therefore attract one another, and rise, and thus the con- tact with the mercury is broken. The current having thus ceased, the coils no longer attract each other, they fall by their own weight, contact with the mercury is re-established, and the series of phenomena are indefi- nitely reproduced. The experiment is still more striking if a magnetised rod the thickness of a pencil is introduced into the interior. This will be intelligible if we consider the action between the parallel Amperian currents of the magnet and of the helix. 808. Iiaws of angrular currents. — I. Two rectilinear currents, the directions of which form an ajtgle with each other, attract one another when both approach, or recede from, the apex of the angle. . Fig. 635. 1 1. They repel one another if one approaches and the other recedes from the apex of the angle. 808] Laws of Angular Currents. 729 These two laws may be demonstrated by means of the apparatus above described, replacing the movable circuit by the circuit BC (fig. 636). Jii then the multiplier is placed horizontally, so that its current is in the same direction as in the movable current, if the latter is removed and the cur- Fig. 636. rent passes so that the direction is the same as in the movable part, on removing the latter it quickly approaches the multiplier, which verifies the first law. To prove the second law, the multiplier is turned so that the currents are in opposite directions, and then repulsion ensues (fig. 637). Fig. 637. In a rectilinear current each elenient of the current repels the succeeding one, and is itself repelled. This is an important consequence of Ampere's law, and may be experi- mentally demonstrated by the following arrangement, which was devised by Faraday. A U-shaped piece of copper wire, whose ends dip in two separate deep mercury cups, is suspended from one end of a delicate 1 13 730 Dynamical Electricity. [808- balance and suitably equipoised. When the mercury cups are connected with the two poles of a battery, the wire rises very appreciably, and sinks again to its original. position when the current ceases to pass. The current passes into the mercury and into the wire ; but from the construction of the apparatus the former is fixed, while the latter is movable, and is ac- cordingly repelled. 809. Kaws of sinuous currents.^ 77z^ action of a simtoiis current is equal to that of a rectilifuar current of the same length in projection. This principle is demonstrated by arranging the multiplier vertically and M Fig. 638. placing near it a movable circuit of insulated wire half sinuous and half rectihnear (fig. 638). It will be seen that there is neither attraction nor repulsion, showing that the action of the sinuous portion inn is equalled by that of the rectilinear portion. An application of this principle will presently be met with in the appa- ratus called solenoids (822), which are formed of the combination of a sinuous with a rectilinear current. DIRECTION OF CURRENTS BY CURRENTS. 810. Action of an infinite current on a current perpendicular to its direction. — From the action exerted between two angular currents (808) the action of a fixed and infinite rectilinear current, PO (fig. 639), on a movable current, KH, perpendicular to its direction, can be determined. Let OK be the perpendicular common to KH and ?(), which is null if the two lines PQ and KH meet. The current PQ flowing from O to P in the direction of the arrows, let us first consider the case in which the current KH approaches the current QP. From the first law of angular currents (808) the portion QO of the current PQ attracts the current KH, because they both flow towards the summit of the angle formed by their directions. The portion PO, on the contrary, will repel the current KH, for here the two currents are in opposite directions at the summit of the angle. If then 810] Direction of Currents by Querents. 731 mq and mp stand for the two forces, one attractive and the other repulsive, which act on the current KH, and which are necessarily of the same in- tensity, since they are symmetrically arranged in reference to the two sides of the point O, these two forces may be resolved into a single force, w;/, r ~/^ .'■ y Fig. 639. Fig. 640. which tends to move the current KH parallel to the current QP, but in a contrary direction. A little consideration will show that when the current KH is below the current PQ, its action will be the opposite of what it is when above. On considering the case in which the current KH moves away from PO (fig. 640), it will be readily seen from similar considerations that it moves parallel to this current, but in the same direction. Hence follows this general principle : A Jinite movable current which approaches a fixed infinite current is acted on so as to move in a direction parallel and opposite to that of the fixed current; if the movable currerU tends from the fixed current^ it is acted on so as to move parallel to the cnrretit and in the same direction. It follows from this, that if a vertical current is movable about an axis, XY, parallel to its direction (figs. 641 and 642). any horizontal current, PO, will have the effect of turning the movable current about Fig. 641. Fig. 642. its axis, tmtil the plane of the axis and of the current have become parallel to PQ ; the vertical current stopping, in reference to its axis, on the side from which the current PQ cotJtes (fig. 64.1), or on the side towards which it is directed (fig. 642), according as the vertical current descends or ascends — that is, according as it approaches or moves from the horizontal axis. It also follows from this principle that a system of two vertical cur- rents rotating about a vertical axis (fig. 643 and 644) is directed by a horizontal current, PQ, in a plane parallel to this current, when one of the 732 Dynamical Electricity. [810- vertical currents is ascending and the other descending (fig. 643), but that if they are both ascending or both descending (fig. 644), they are not directed. ; Xi Fig. 643. Fig. 644. 811. Action Of an infinite rectilinear current on a rectangular or circular current. — It is easy to see that a horizontal infinite current exercises the same directive action on a rectangular current movable about a vertical axis (fig. 645), as what has been above stated. For, from the direction of the currents indicated by the arrows, the part OY acts by attraction not only on the horizontal portion YD {law of angular currents), but also on the vertical portion AD (laiv of perpetidicular currents). The same action evidently takes place between the part PY and the parts CY and BC. Hence, the fixed current PQ teitds to direct the movable rectangular current ABCD into a position parallel to PQ, and such that in the wires CD and PQ the direction of the two currejits is the sa7ne. This principle is readily demonstrated by placing the circuit ABCD on the apparatus with two supports (fig. 652), so that at first it makes an angle Fig. 645. Fig. 646. with the plane of the supports. On passing below the circuit, a somewhat powerful current in the same plane as the supports, the movable, part passes into that plane. It is best to use the circuit in fig. 652, which is astatic, while that of fig. 645 is not. What has been said about the rectangular current in fig. 645 applies also to the circular current of fig. 646, and is demonstrated by the same experiments. -813] Rotation of Currents by Currents. 733 ROTATION OF CURRENTS BY CURRENTS. 8 1 2. Rotation of a finite horizontal current by an infinite horizontal rectilinear current. — The attractions and repulsions which rectangular currents exert on one another may readily be transformed into a con- tinuous circular motion. Let OA (fig. 647) be a current movable about the point O in a horizontal plane, and let PQ be a fixed infinite current also horizontal. As these two currents flow in the direction of the arrows, *- k/ 1 „-'A" A", P ./' M: N " * Fig. 647. it follows that in the position OA, the movable current is attracted by the current PQ, for they are in the same direction. Having reached the posi- tion OA', the movable current is attracted by the part NQ of the fixed current, and repelled by the part PN. Similarly, in the position OA'^it is attracted by MQ and repelled by PM, and so on ; from which follows a continuous rotatory motion in the direction AA'A'^A'^'. If the movable current, instead of being directed from O towards A, were directed from A towards O, it is easy to see that the rotation would take place in the contrary direction. Hence, by the action of a fixed infinite current, PO, the movable current OA tends to a continuous motion in a direction opposite that of the fixed current. If, both currents being horizontal, the fixed current were circular instead of being rectilinear, its effect would still be to produce a con- tinuous circular motion. For, let ABC (fig. 648) be a fixed circular current, and mn a rectilinear current movable about the axis n, both currents being horizontal. These currents, flowing in the direction of the arrows, would attract one another in the angle nAC, for they both flow towards the summit (808). In the angle «AB, on the contrary, they repel one another, for one goes towards the summit and the other moves from it. Both effects coincide in moving the wire mn in the same direction ACB. 813. Rotation of a vertical current by a horizontal circular current.— A horizontal circular current, acting on a rectilinear vertical current also imparts to it a continuous rotatory motion. In order to show this, the apparatus represented in fig. 649 is used. It consists of a brass vessel, round which are rolled several coils of insulated copper wire, through which a current passes. In the centre of the vessel is a brass support, a, terminated by a small cup containing mercury. In this dips a pivot supporting a copper wire, bb, bent at its 734 Dynamical Electricity. [813- ends in two vertical branches, which are soldered to a very light copper ring immersed in acidulated water contained in the vessel. A current entering through the wire w, reaches the wire A, and having made several circuits, terminates at B, which is connected by a wire underneath with the lower part of the column a. Ascending in this column, it passes by the wires bb into the copper ring, into the acidulated water, and into the sides of the vessel, whence it returns to the battery by the strip D. The current being thus closed, the circuit bb and the ring tend to turn in a direction contrary to that of the fixed current, a motion due to the action of the circular current on the current in the ver- tical branches bb ; for, as follows from the two laws of angular currents, the branch b on the right is attracted by the portion A of the fixed current, Fig. 649. and the branch b on the left is attracted in the contrary direction by the opposite part, and these two motions coincide in giving the ring a con- tinuous rotatory motion in the same direction. The action of the circular current on the horizontal part of the circuit bb would manifestly tend to turn it in the same direction ; but from its distance it may evidently be neglected. 814. Rotation of xnagrnets by currents. — Faraday has proved that currents impart the same rotatory motions to magnets which they do to currents. This may be shown by means of the apparatus represented in fig. 650. It consists of a large glass vessel, almost filled with mercury. In the centre of this is immersed a magnet A about 8 inches in length, which projects a little above the surface of the mercury, and is loaded at the bottom with a platinum cylinder. At the top of the magnet is a small cavity containing mercury ; the current ascending the column 7n passes into this cavity by the rod C. From the magnet it passes by the mercury to a copper ring G, whence it emerges by the column 11. When this takes place the magnet begins to rotate round its own axis with a velocity depending on its magnetic power and on the intensity of the current. Instead of making the magnet rotate on its axis, it may be caused to rotate round a line parallel to its axis by arranging the experiment as shown in fig. 651. This rotatory motion is readily intelligible on Ampere's theory of mag- netism, which will be subsequently explained (827), according to which -815] Action of the Earth a? id of Magnets on Querents. 735 magnets are traversed on their surface by an infinity of circular currents in the same direction, in planes perpendicular to the axis of the magnet. At the moment at which the current passes from the magnet into the mer- cury, it is divided on the surface of the mercury into an infinity of rectilinear currents proceeding from the axis of the magnet to the circumference of the glass. Now each of these currents acts on the currents of the magnet in the same manner as, in fig. 647, the rectilinear current uui acts upon the circular current CAB ; that is to say, that the circle CAB representing one of the currents of the magnet, there is attraction in the angle ;^AC, Fig. 650. Fig. 65] and repulsion in the angle «AB, and, consequently, rotation of the magnet round its axis. The action of the current merely affects the upper part of the magnet, and if the north pole is uppermost, as in the figure, the rota- tion is from west to east. If the north pole is below, or the direction of the current be altered, the rotation of the magnet is in the opposite direction. ACTION OF THE EARTH AND OF MAGNETS ON CURRENTS. 815. Directive action of mag-nets on currents. — Not only do currents act upon magnets, but magnets also act upon currents. In Oersted's fundamental experiment (fig. 607), the magnet being movable while the current is fixed, the former is directed and sets at right angles with the current. If, on the contrary, the magnet is fixed and the current mova- ble, the latter is directed and sets across the direction of the magnet. This may be illustrated by the apparatus represented in fig. 652. This is the original form of Ampere's stand, and is frequently used in experimental demonstration. It needs no explanation. The circuit which the current traverses is movable, and below its lower branch a powerful bar magnet is placed; the circuit immediately begins to turn, and stops after some oscillations in a plane perpendicular to the axis of the magnet. 71^ Dynamical Electricity. [815- For demonstrating the action of magnets upon currents, and indeed for establishing the fundamental laws of electrodynamics, a small apparatus, known as De la 'K\v€s fioating battery, is well adapted. It consists of a small Daniell's element, contained in a glass tube attached to a cork, so that it can float freely on water. The plates are connected with minute Fig. 652. mercury cups on the cork float ; and with these can be connected either circular or rectangular wires, coils, or solenoids ; they are then traversed by a current, and can be subjected to the action either of magnets or of currents. 816. Rotation of currents by magrnets. — Not merely can currents be directed by magnets, but they may also be made to rotate, as is seen from the following experiment, devised by Faraday, fig. 653. On a base with levelling screws, and resting on an ivory support, is a copper rod, BD. It is surmounted in part of its length by a magnetised bundle, AB, and at the top is a rhercury cup. A copper circuit, EF, balanced on a steel point, rests in the cup, and the other ends of the circuit, which terminate in steel points, dip in an annular reservoir full of mercury. The apparatus being thus arranged, the current from 4 or 5 Bunsen's elements enters at the binding screw b ; it thence ascends in the rod D, redescerjds by the two branches, reaches the mercury by the steel points, whence it passes by the framework, which is of copper, to the battery by the binding screw a. If now the magnetised bundle be raised, the circuit EF rotates either in one direction or the other according to the pole by which it is influenced. This rotation is due to currents assumed to cir- culate round magnets, currents which act on the vertical branches EF in the same way as the circular current on the arm in fig. 649. In this experiment the magnetised bundle may be replaced by a solenoid (822) or by an electromagnet, in which case the two binding -817] Electrodynamic Rotation of Liquids. 717 screws in the base of the apparatus on the left give entrance to the current which is to traverse the solenoid or electromagnet. 817. Electrodynamic and electro- mag-netic rotation of liquids. — In the experiments hitherto discussed rotation is produced by causing a fixed current to act upon a movable linear current. The condition of a linear current is not neces- sary. Fig. 654 represents an apparatus devised by M. Bertin to show the electro- dynamic and electromagnetic rotation of liquids. This apparatus consists of an annular earthern vessel, VV ; that is to say, it is open in the centre so as to be traversed by a coil, H. This rests on a board which can be raised along two columns, E and I, and which are fixed by means of the screws KK. Round the vessel VV is a second larger coil, G, fixed on the columns SS. The vessel VV rests on the lower plane. In the centre of the coil there is a bar of soft iron, x, which makes an electromagnet. The vessel . VV contains acidulated water, and in the liquid are plunged two cylindrical copper plates, e and /, soldered to copper wires, e' and /', which convey the current of a battery of four couples through the rods E and I. The whole system is arranged on a larger base, on the left of which is a commutator represented afterwards on a larger scale (fig. 655). With the base of the columns E, I, S, and S', are connected four copper strips, three of which lead to the commutator and the fourth to the binding screw A, which receives the wire from the positive pole. These details being premised, the following three effects may be obtained with this apparatus: — (i), the action of the coil G alone; (2), the action of the electromagnet H alone ; (3), the simultaneous action of the coil and of the electromagnet. I. Fig. 654 represents the apparatus arranged for the first effect. The current coming by the binding screw A attains the column S', which leads it to the coil G, with regard to which it is left — that is, in a contrary direction to the hands of a watch. Then descending by the column S, it reaches the commutator, which leads it by the plate marked centripete to the column E and to the electrode e'. The current here traverses the liquid from the circumference to the centre, attains the electrode /, the column I, and by the intervention of the plate centrifuge the central piece of the commutator. This transmits it finally to the negative binding Fig. 653. 738 Dynamical Electricity. [817- screw, which leads it to the battery. The hquid then commences a direct rotatory motion — that is to say, in the same direction as the coil. If the direction of the current in the liquid is centrifiigal — that is, pro- ceeds from the centre to the circumference^-the rotation is inverse ; that is, is in the opposite direction to that of the coil. In both cases the rotations may be shown to those at a distance by means of small flags, Fig. 654. /",/, fixed on discs of cork which float on the liquid, and which are coated with lampblack to prevent adherence by capillary attraction between the discs and the electrodes e and i. II. To experiment with the electromagnet alone, the positive wire of the battery is joined with the binding screw C, and the binding screws D and B are joined by a copper wire. The current first passes into the electromagnet H, then, reaching the commutator by the binding screw B, passes into the centripetal plate, whence it rises in the column E, tra- verses the liquid in the same direction as at first, reascends by the column I, and from thence to the centre of the commutator and the negative binding screw which leads it to the battery. If the north pole of the electromagnet is at the same height as the glass vessel, as in the figure, the Amperian currents move in the opposite direction to the hands of a watch, and the floats then move* in the same direction as above ; and if the electromagnet is raised until the neutral line is at the same height as the vessel, the floats stop; if it is above them, the floats mote again, but in the opposite direction. III. To cause the coil and the electromagnet to act simultaneously, the positive wire of the battery is attached at C, and the binding screws D and A are connected by a conductor. Hence, after having traversed the coil H, the current arrives from D, and the binding screw A, whence it -819] Bertiiis Commutator. • 739 traverses exactly the same circuit as in the first experiments. The effects are the same, though more intense ; the action of the coil and the electro- magnet being in the same direction. 818. Bertin's commutator. — Commutators are apparatus by which the direction of currents may be changed at pleasure, or by which they may be opened or closed. Bertin's has the advantage of at once showing the direction of the current. It consists of a small base of hard wood on which is an ebonite plate, which, by means of the handle m (fig. 655), is Fig. 655. turned about a central axis, between two stops, c and c'. On the disc are fixed two copper plates, one of which o is always positive, being connected by the axis and by a plate, + , with the binding screw P, which receives the positive electrode of the battery ; the other, z>, bent in the form of a horse- shoe, is connected by friction below the disc witha plate — which passes to the negative electrode N. On the opposite side of the board are two binding screws, b and b\ to which are adapted two elastic metal plates, r and 7''. These details being premised, the disc being turned as shown in the figure, the current coming by the binding screw T passes into the piece 0, the plate r and the binding screw b, which by a second plate, or by a copper wire, leads it to the apparatus of fig. 654, or any other. Then returning to the binding screw ^, the current attains the plate r', the piece / e, and ultimately the binding screw N, which returns it to the battery. If the disc is turned so that the handle is half way between c and c\ the pieces and / e being no longer in contact with the plates r and r, the current does not pass. If ;;/ is turned as far as c, the plate touches r\ the current thus passes first to b' and returns by ^ ; it is therefore reversed. 819. Directive action of tbe earth on vertical currents. — The earth, which exercises a directive action on magnets (65 1), acts also upon currents, giving them, in some cases, a fixed direction, in others a continuous rotatory motion, according as their currents are arranged in a vertical or horizontal direction. The first of these two actions may be thus enunciated : Every vertical current movable about an axis parallel to itself^ places itself under the directive action of the earth in a plane through this axis perpendicular to 740 Dynamical Electricity. [819- the magnetic meridian^ and stops, after some oscillations, otj the east of its axis of rotation when it is descending., and on the west when it is ascending. This may be demonstrated by means of the apparatus represented in fig. 657, which consists of two brass vessels of somewhat different diameters. i-'ig. 656. Fig. 657. The larger, a, about 13 inches in diameter, has an aperture in the centre, through which passes a brass support, b, insulated from the vessel a, but communicating with the vessel K. This column terminates in a small cup, in which a light wooden rod rests on a pivot. At one end of this rod a fine wire is coiled, each end of which dips in acidulated water, with which the two vessels are respectively filled. The current arriving by the wire m passes to a strip of copper, which is connected underneath the base of the apparatus with the bottom of the column b. Ascending in this column, the current reaches the vessel K, and the acidulated water which it contains ; it ascends from thence in the wire c, redescends by the wire e, and traversing the acidulated water, it reaches the sides of the vessel a, and so back to the battery through the wire n. The current being thus closed, the wire e moves round the column b, and stops to the east of it, when it descends, as is the case in the figure ; but if it ascends, which is effected by transmitting the current by the wire n, the wire e stops to the west of the column b, in a position directly opposite to that which it assumes when it is descending. If the rod with a single wire, in fig. 657, be replaced by one with two wires, as in fig. 656, the rod will not move, for as each wire tends to place itself on the east of the column b, two equal and contrary effects are produced, which. counterbalance one another. 820. Action of tbe eartb on horizontal currents movable about a vertical axis. — The action of the earth on horizontal currents, is not directive, h\it gives them a continuous rotatory motion frotn the east to the west when the horizotital current moves away font the axis of rotatioji. and frotn the west to the east when it is directed towards this axis. 821] Action of the Earth on Closed Currents. 741 This may be illustrated by means of the apparatus represented in fig. 658, which only differs from tha^ of fig. 657 in having but one vessel. The- current ascending by the column a, traverses the two wires cc, and descends by the wires bb, from which it regains the pile ; the circuit bccb then begins a continuous rotation, either from the east to the west, or from the west to the east, according as in the wires cc the current goes from the centre, as is the case in the figure ; or according as it goes towards it, which is the case when the current enters by the wire in instead of by 11. But we have seen (819) that the action of the earth on the vertical wires bb is destroyed : hence the rotation is that produced by the action on the horizontal Fig. 658. branches cc. This rotatory action of the terrestrial current on horizontal currents is a consequence of the rotation of a finite horizontal by an infinite horizontal current (812). 821. Directive action of the eartb on closed currents movable about a vertical axis. — If the current on which the earth acts is closed, whether it be rectangular or circular, the result is not a continuous rotation, but a directive action, as in the case of vertical currents (819), in virtue ot which the current places itself in a plane perpe?idiciilar to the magnetic ineridiajt, so that, for an observer looking at the north, it is descendiiig on the east of its axis of rotation, and ascending on the west. This property, which can be shown by means of the apparatus repre- sented in fig. 658, is a consequence of what has been said about horizontal and vertical currents. For in the closed circuit BA, the current in the upper and lower parts tends to turn in opposite directions, from the law of horizontal currents (820); and hence is in equi- librium, while in the lateral parts the current on the one side tends towards the east, and on the other side to the west, from the law of vertical currents (819). From the directive action of the earth on currents, it is necessary, in most ex- periments, to obviate this action. This is effected by arranging the movable circuit symmetrically about its axis of rotation, so that the directive action of the earth tends to turn them in Fig. 65c. 742 Dynamical Electricity. [821- opposite directions, and hence destroys them. This condition is fulfilled in the circuit represented in fig, 652. Such circuits are hence called astatic circuits. SOLENOIDS. 822. structure of a solenoid. — A solenoid is a system of equal and parallel circular currents formed of the same piece of covered copper wire, and coiled in the form of a helix or spiral, as represented in fig. 660. A ^ solenoid, however, is only complete ?Vyr?QVA7Qr?^?9^y?r^ n when part of the wire BC passes in C— VjyjUVJUVUUUVVU the direction of the axis in the interior F^s- 660. of thg helix. With this arrangement, when the circuit is traversed by a current, it follows from what has been said about sinuous currents (780) that the action of a solenoid in a longi- tudinal direction, AB, is counterbalanced by that of the rectilinear current BC. This action is accordingly null in the direction of the length, and the action of a solenoid in a direction perpendicular to its axis is exactly equal to that of a series of equal parallel currents. 823. ilction of currents on solenoids. — What has been said of the action of fixed rectilinear currents on finite rectangular, or circular cur- rents (812), applies evidently to each of the circuits of a solenoid, and hence a rectiUnear current must tend to direct these circuits parallel to itself. To demonstrate this fact experimentally, a solenoid is constructed as shown in fig. 661, so that it can be suspended by two pivots in the cups a and c of the apparatus represented in fig. 633. The solenoid is then Fig. 66 movable about a vertical axis, and if beneath it a rectilinear current QP be passed, which at the same time traverses the wires of the solenoid, the latter is seen to turn and set at right angles to the lower current — that is, in such a position that its circuits are parallel to the fixed current ; and, further, in the lower part of each of the circuits the current is in the same direction as in the rectifinear wire If, instead of passing a rectihnear current below the solenoid, it is passed vertically on the side, an attraction or repulsion will take place, -826] Action of Solenoids. 743 according, as in the vertical wire, and in the nearest part of the solenoid, the two currents are in the same or in contrary directions. 824. Directive action of tlie eartb on solenoids. — If a solenoid be suspended in the two cups (fig. 633), not in the direction of the magnetic meridian, and a current be passed through the solenoid, the latter will begin to move, and will finally set in such a position that its axis is in the direction of the magnetic meridian. If the solenoid be removed, it will, after a few oscillations, return, so that its axis is in the magnetic meridian. Further, it will be found that in the lower half of the coils of which the solenoid consists, the direction of the current is from east to west ; in other words, the current is descending on that side of the coil turned towards the east, and ascending on the west. The directive action of the earth on solenoids is accordingly a consequence of that which it exerts on circular currents. In this experiment the solenoid is directed like a magnetic needle, and the north pole, as in magnets, is that end which points towards the north, and the soiith pole that which points towards the south. This experiment may be well made by means of a solenoid fitted on a De la Rive's floating battery. 825. IVEutual action of magnets and solenoids. — Exactly the same phenomena of attraction and repulsion exist between solenoids and magnets as between magnets themselves. For if to a movable solenoid traversed by a current one of the poles of a magnet be presented, at- traction or repulsion will take place, according as the poles of the magnet and of the solenoid are of contrary or of the sam.e name. The same phenomenon takes place when a solenoid traversed by a current and held in the hand is presented to a movable magnetic needle. Hence the law of attractions and repulsions applies exactly to the case of the mutual action of solenoids and of magnets. 826. Mutual actions of solenoids. -When two solenoids traversed by a powerful current are allowed to act on each other, one of them being ^^>>^^ Fig. 662. held in the hand, and the other being movable about a vertical axis, as shown in fig. 662, attraction and repulsion will take place just as in the case of two magnets. These phenomena are readily explained by refer- 744 Dynamical Electricity. [826 ence to what has been said about the mutual action of the currents, bearing in mind the direction of the currents in the extremities presented to each other. 827. Ampere's theory of magrnetism. — Ampere propounded a theory, based on the analogy which exists between solenoids and magnets, by which all magnetic phenomena may be referred to electro- dynamical principles. Instead of attributing magnetic phenomena to the existence of two fluids, Ampere assumes that each individual molecule of a magnetic substance is traversed by a closed electric current. It is further assumed that these molecular currents are free to move about their centres. The coercive force, however, which is little or nothing in soft iron, but considerable in steel, opposes this motion, and tends to keep them in any position in which they happen to be. When the magnetic substance is not magnetised, these molecular currents, under the influ- ence of their mutual attractions, occupy such positions that their total action on any external substance is null. Magnetisation consists in giving to these molecular currents a parallel direction, and the stronger the magnetising force the more perfect the parallelism. The limit of magnetisation is attained when the currents are completely parallel. The resultant of the actions of all the molecular currents is equivalent to that of a single current which traverses the outside of a magnet. For by inspection of fig. 663, in which the molecular cur- r'^S!^ 0' — -"""^-v rents are represented by a series of small internal circles in the two ends of a cylin- drical bar, it will be seen that the adjacent parts of the currents oppose one another, and cannot exercise any ex- ternal electrodynamic action. i\ 1. W ^>y This is not the case with the surface : there the molecular ^^" ^' currents at ab are not neutra- lised by other currents, and as the points abc are infinitely near, they form a series of elements in the same direction situated in planes perpen- dicular to the axis of the magnet, and which constitute a true solenoid. The direction of these currents in magnets can be ascertained by con- sidering the suspended solenoid (fig. 662). If we suppose it traversed by a current, and in equilibrium in the magnetic meridian, it will set in such a position that in the lower half of each coil the current flows from east to west. We may then establish the following rule. At the north pole {Eftglish) of a magnet the direction of the Amperian currents is opposite that of the hands of a watch, and at the south pole the direction is the same as that of the hands. 828. Terrestrial current. — In order to explain on this supposition terrestrial magnetic effects, the existence of electrical currents is assumed -829] Magnetisation by Currents. 745 which continually circulate round our globe from east to west perpen- dicular to the magnetic meridian. The resultant of their action is a single current traversing the magne- tic equator from east to west. These currents are supposed to be thermo- electric currents due to the variations of temperature caused by the successive influence of the sun on the different parts of the globe from east to west. These currents direct magnetic needles ; for a suspended magnetic needle comes to rest when the molecular currents on its under surface are parallel; and in the same direction as the terrestrial currents. As the mole- cular currents of a magnet are at right angles to the direction of its length, the needle places its greatest length at right angles to east and west, or north and south. Natural magnetisation is probably imparted in the same way to iron minerals. CHAPTER V. MAGNETISATION BY CURRENTS. ELECTROMAGNETS. ELECTRIC TELEGRAPHS. 829, Magrnetisation by currents. — From the influence which cur- rents exert upon magnets, turning the north pole to the left and the south pole to the right, it is natural to think that by acting upon magnetic sub- stances in the natural state the currents would tend to separate the two magnetisms. In fact when a wire traversed by a current is immersed in iron filings, they adhere to it in large quantities, but become detached as soon as the current ceases, while there is no action on any other non- magnetic metal. The action of currents on magnetic substances is well seen in an ex- periment due to Ampere, which consists in coiling an insulated copper wire round a glass tube, in which there is an unmagnetised steel bar. If a current be passed through the wire, even for a short time, the bar becomes strongly magnetised. If, as we have already seen, the discharge of a Leyden jar be trans- mitted through the wire, by connecting one end with the outer coating, and the other with the inner coating, the bar is also magnetised. Hence both voltaic and frictional electricity can be used for magnetising. Fig. 664. If in this experiment the wire be coiled on the tube in such a manner that when it is held vertically the downward direction of the coils is from right to left on the side next the observer, this constitutes a right-handed or dextrorsal spiral or helix (fig. 664), of which the ordinary screw is an K K 746 Dynamical Electricity. [829- example. In a lefl-handed or sinistrorsal helix the coiling is in the opposite direction, that is from left to right (fig. 665). In a right-handed spiral the north pole is at the end at which the Fig. 665. current emerges, and the south pole at the end at which it enters ; the reverse is the case in a left-handed spiral. But whatever the direction of the coiling, the polarity is easily found by the following rule : If a person swimming in the current look at the axis of the spiral the Jiorth pole is always on his left. If the wire be not coiled regularly, but its direction be reversed, at each change of direction a consequent pole (643) is formed in the magnet. The sim- plest method of remembering the polarity produced is as follows : Whatever be the nature of the helix, either right or left-handed, if the end facing the observer has the current flowing in the direction of the hands of a watch, it is a sonth pole and vice versa. The same polarity is produced, whether or not there is an iron core within the helix. The nature of the tube on which the helix is coiled is not without influence. Wood and glass have o effect, but a thick cylinder of copper may greatly affect the action of the current unless the copper be slit longitudinally. This action will be subsequently explained. The same is the case with iron, silver, and tin. In order to magnetise a steel bar by mearts of electricity, it need not be placed in a tube, as shown in figs. 664 and 665. It is sufficient to coil round it a copper wire covered with silk, cotton, or gutta-percha in order to insulate the circuits from one another. The action of the current is thus multiplied, and a feeble current is sufficient to produce a powerful magnetising effect. 830. Slectromagrnets. — Electromagnets are bars of soft iron which, under the influence of a voltaic current, become magnets ; but this magnetism is only temporary, for the coercive force of perfectly soft iron is null, and the two magnetisms neutralise each other as soon as the current ceases to pass through the wire. If, however, the iron is not -830] Electromagnets. 747 quite pure, it retains more or less traces of magnetism. The electro- magnets have the horse-shoe form, as shown in fig. 666, and a copper wire, covered with silk or cotton, is rolled several times round them on the two branches, so as to form two bobbins, A and B. In order that the two ends of the horse-shoe may be of opposite polarity, the winding on the two limbs A and B must be such that if the horse-shoe were straightened out, it would be in the same direction. Electromagnets, instead of being made in one piece, are frequently constructed of two cylinders, firmly screwed to a stout piece of the same metal. Such are the electromagnets in Morse's telegraph (835), the electromagnetic motor (840). The helices on them must be such that the current shall flow in the same direction as the hands of a watch as seen from the south pole, and against the hands of a watch as seen from the north pole. The results at which various experimenters have arrived as regards the force of electromagnets are often greatly divergent, which is partly due to the different senses they have attached to the notion of electromagnetic force. For this may mean (I.) the induction current which the develop- ment and disappearance of the magnetism of an iron core indicate in a spiral which surrounds it ; this is the excited magjietism : or (II.) the free magnetism measured by the action on a magnetic needle, oscillating at a distance ; (III.) the attractive force, or the force required to hold an ar- mature at a distance from the electromagnet; (IV.) the lifting power measured by the force with which an armature is held in direct contact with the pole. The most important results which have been arrived at are the fol- lowing : (i.) Using the term electromagnetic force in the first two senses, it is proportional to the intensity of the currejit. This only applies when the currents are not very powerful, and to stout bars ; for in each bar there is, as Miiller has found, a maximum of magnetisation which cannot be exceeded. (ii.) Taking into account the resistance, the electromagnetic force is independent of the nature and thickness of the wire. Thus the intensity of the current and the number of coils being the same, thick and thin wires produce the same effect. (iii.) With the same current the electromagnetic force is independent oj the width of the coils, provided the iron projects beyond the coils, and the diameter of the coil is small compared with its length. (iv.) The temporary magnetic moment of an iron bar is within certain limits proportional to the number of windings. The product of the in- tensity into the number of turns is usually spoken of as the magnetising poiuer of the spiral. The greatest magnetising power is obtained when the resistance in the magnetising spiral is equal to the sum of the other resistances in the circuit, those of the battery included, and the length and diameter of the wire must be so arranged as to satisfy these con- ditions. (v.) The magnetism in solid and in hollow cylinders of the same 74^ Dynamical Electricity. [830- diameters is the same, provided in the latter case there is sufficient iron for the development of the magnetism. (vi.) The attraction of an armature by an electromagnet is proportional to the square of the intensity of the current so long as the magnetic moment does not attain its maximum. Two unequally strong electro- magnets attract each other with a force proportional to the square of the sum of both currents. (vii.) For powerful currents the length of the branches of an electro- magnet is without influence on the weight which it can support. As regards the quality of the iron used for the electromagnet, it must be pure, and be made as soft as possible by being reheated and cooled a great many times ; it is polished by means of a file so as to avoid twist- ing. If this is not the case the bar retains, even after the passage of the current, a quantity of magnetism which is called the rema?te?it magnetism . A bundle of soft iron wires loses its magnetism more rapidly than a massive bar of the same size. During magnetisation the volume of a magnet does not vary. This has been established by placing the bar to be magnetised with its helix in a sort of water thermometer, consisting of a flask provided with a capillary tube. On magnetising no alteration in the position of the water is observed. But the dimensions vary, the diameter is somewhat lessened, and the length increased ; according to Joule to the extent of about 3^^, if the bar is magnetised to saturation. We shall presently see the numerous applications which have been made of electromagnets in electric telegraphs, in electromagnetic motors, in electric clocks, and in the study of diamagnetic phenomena. 831. Vibratory motion and sounds produced by currents. — When a rod of soft iron is magnetised by a strong electric curren t, it gives a very distinct sound, which, however, is only produced at the moment of closing or opening the current. This phenomenon, which was first observed by Page in America, and by Delezenne in France, has been particularly investigated by De la Rive, who has attributed it to a vibratory motion of the molecules of iron in consequence of a rapid succession of magneti- sations and demagnetisations. When the current is broken and closed at very short intervals, De la Rive has observed, that whatever be the shape or magnitude of the iron bars, two sounds may always be distinguished : one, which is musical, corresponds to that which the rod would give by vibrating transversely ; the other, which consists of a series of harsh sounds, corresponding to the interruptions of the current, is compared by De la Rive to the noise of rain falling on a metal roof The most marked sound, says he, is that obtained by stretching on a sounding board pieces of soft iron wire, well annealed, from i to 2 mm. in diameter, and i to 2 yards long. These wires being placed in the axis of one or more bobbins traversed by power- ful currents, send forth a number of sounds, which produce a surprising effect, and much resemble that of a number of church bells heard at a distance. Wertheim has obtained the same sounds by passing a discontinuous -832] Electric Telegraph. 749 current, not through the bobbins surrounding the iron wires, but through the wires themselves. The musical sound is then stronger and more^ sonorous in general than in the previous experiment. The hypothesis of a molecular movement in the iron wires at the moment of their mag- netisation, and of their demagnetisation, is confirmed by the researches of Wertheim, who has found that their elasticity is then diminished. ELECTRIC TELEGRAPH. 832. Electric telegraplis. — These are apparatus by which signals can be transmitted to considerable distances by means of voltaic currents propagated in metalhc wires. Towards the end of the last century, and at the beginning of the present, many philosophers proposed to corre- spond at a distance by means of the effects produced by electrical machines when propagated in insulated conducting wires. In 181 1, Scemmering invented a telegraph in which he used the decomposition of water for giving signals. In 1820, at a time when the electromagnet was unknown, Ampere proposed to correspond by means of magnetic needles, above which a current was sent, as many wires and needles being used as letters were required. In 1834, Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic current transmitted by a wire acted on a magnetised bar; the oscillations of which under its influence were ob- served by a telescope. They succeeded in thus sending signals from the Observatory to the Physical Cabinet in Gottingen, a distance of a mile and a quarter, and to them belongs the honour of having first demon- strated experimentally the possibility of electrical communication at a considerable distance. In 1837, Steinheil in Munich, and Wheatstone in London, constructed telegraphs in which several wires each acted on a single needle ; the current in the first case being produced by an electro- magnetic machine, and in the second by a constant battery. Every electric telegraph consists essentially of three parts : i, a circiiit consisting of a metallic connection between two places, and an dec- tromotor for producing the current ; 2, a communicator for sending the signals from the one station ; and, 3, an indicator for receiving them at the other station. The manner in which these objects, more especially the last two, are effected can be greatly varied, and we shall limit our- selves to a description of the three principal methods. One form of electromotor still frequently used in England is a modi- fication of Wollaston's battery. It consists of a trough divided into com- partments, in each of which is an amalgamated zinc plate and a copper plate ; these plates are usually about 4^ inches in height by 3^ in breadth. The compartments are filled with sand, which is moistened with diUite sulphuric acid. This battery is inexpensive and easily worked, only requiring from time to time the addition of a little acid ; but it has very low electromotive force and considerable resistance, and when it has been at work for some time, the effects of polarisation begm to be perceived. On the telegraphs of the South Eastern Railway, the platinised graphite 750 Dynamical Electricity. [832- (765) battery invented by Mr. C. V. Walker is used with success. In France, Daniell's battery is used for telegraphic purposes. The connection between two stations is made by means of galvanised iron wire suspended by porcelain supports (fig. 667), which insulate and protect them against the rain, either on posts or against the sides of buildings. In towns, wires co- vered with gutta-percha are placed in tubes laid in the ground. Sub- marine cables, where great strength is required combined with lightness and high conducting power, are formed on the general type of one of the Atlantic cables, a longitudinal view of which is given in fig. 668, while fig. 669 represents a cross section. In the centre is the core which is the conductor ; it consists of seven copper wires, each i mm. irt diameter twisted in a spiral strand and covered with several layers of gutta percha, between each of which is a coating of Chatterton^s compound— 2i mixture of tar, resin, and gutta percha. This forms the msulator proper, and it should have great resistance to the passage of electricity, combined with low specific inductive capacity (702). Round the insulator is a coat- Fig. 667. Fig. 668. Fig. 669. ing of hemp, and on the outside is wound spirally a protecting sheath of steel wire, each of which is spun round with hemp. At the station which sends the despatch, the line is connected with the positive pole of a battery, the current passes by the line to the other station, and if there were a second return line, it would traverse it in the opposite direction to return to the negative pole. In 1837, Steinheil made the very important discovery that the earth might be used for the return conductor, thereby saving the expense of the second line. For this purpose the end of the conductor at the one station, and the negative pole of the battery at the other, are connected with large copper plates, which are sunk to some depth in the ground. The action is then the same as if the earth acted as a return wire. The earth is, indeed, far superior to a return wire ; for the added resistance of such a wire would be considerable, whereas the resistance of the earth beyond a short distance is absolutely nil. The earth really dissipates the electricity, and does not actually return the same current to the battery. -833] Single Needle Telegraph. 751 833. ixnieatstone's and Cooke's singrle needle telegrrapb. — "fhis consists essentially of a vertical multiplier (773) with an astatic needle, the arrangement of which is seen in fig, 671, while fig. 670 gives a front view~ Fig. 670. of the case in which the apparatus is placed. A (fig. 671) is the bobbin consisting of about 400 feet of fine copper wire, wound in a frame in two connected coils. Instead of an astatic needle, Mr. Walker has found it advantageous to use a single needle formed of several pieces of very thin steel strongly magnetised ; it works within the bobbin, and a light index joined to it by a horizontal axis indicates the motion of the needle on the dial. The signs are made by transmitting the current in different directions through the multiplier, by which the needle is deflected either to the right or left, according to the will of the operator. The instrument by which this is effected is a cojiiimctator or key, G ; its construction is shown in fig. 671, while fig. 672 shows on a large scale how two stations are con- nected. It consists of a cylinder of boxwood with a handle, which projects in front of the case (fig. 670). On its circumference parallel to the axis are seven brass strips (fig. 672), the spaces between which are insulated by ivory ; these strips are connected at the end by metallic 752 Dynamical Electricity. [833- wires, also insulated from each other, in the following manner : a with b and <;,y"with d, and e with^. Four springs press against the cylinder ; x and^y are connected with the poles of the battery, m with the earth plate, and 71 with one end of the multiplier, N. When not at work the cylinder and the handle are in a vertical posi- tion, as seen on the left of the diagram. The circuit is thus open, for the pole springs, x and j, are not connected with the metal of the commutator. But if, as in G', the key is turned to the right, the battery is brought into the circuit, and the current passes in the following direction: + pole x'a'b'71'Wq"^, conductor q^pyinbaciriY^p^ earth p'E'm'e'g'y,— -pole. The coils N and N' are so arranged that by the current the motion of the needle corresponds to the motion of the handle. By turning the handle to the left the current would have the following direction : + pole x'd'fvi'Y.'p^ earth pY^jncabttlAq, conductor ^'M';/'<^'rty, — pole, and thus the needle would be deflected in the opposite direction. The signs are given by differently combined deflections of the needle, as represented in the alphabet on the dial (fig. 670). \ denotes a deflec- tion of the upper end of the needle to the left, and / a deflection to the right ; I, for instance, is indicated by two deflections to the left, and M by two to the right. Some of the marks on the alphabet are only half as -834] Dial Telegraphs. 753 long as the others; this indicates that the shortest of the connected marks must first be signalled. Thus, D is expressed by right-left-left, and C by right-left-right-left, etc. These signs are somewhat complicated, and require great practice ; Fig 672. usually not more than 12 to 20 words can be sent in a minute. Hence the single needle telegraph is in many cases replaced by the double needle one, which is constructed on the same principle, but there are two needles and two wires instead of one. 834. Bial telegrraphs. — Of these many kinds exist. Figs. 674 and 675 represent a lecture-model of one form, constructed by M, Froment, and which well serves to illustrate the principle. It consists of two parts : the manipulator for transmitting signals (fig. 674), and the indicator (fig. 675) for receiving them. The first apparatus is connected with a battery, Q, and the two apparatus are in communication by means of metal wires, one of which, AOD (fig. 674), goes from the departure to the arrival station, and the other, HKLI (fig. 675), from the arrival to the departure. In practice, the latter is replaced by the earth circuit. Each apparatus is furnished with a dial with 25 of the letters of the alphabet, on which a needle moves. The needle at the departure station is moved by hand, that of the arrival by electricity. The path of the current and its effects are as follows : From the battery it passes through a copper wire, A (fig. 674), into a brass spring N, which presses against a metal wheel, R, then by a second spring, M, into the K K 3 754 Dynamical Electricity. [834- wire, O, which joins the other station. Thence the current passes into the bobbin of an electromagnet, b^ not fully shown in fig. 675, but of which fig. 673 represents a section, showing the anterior part of the apparatus. This electro- magnet is fixed horizontally at one end, and at the other it attracts an armature of soft iron, a, which forms part of a bent lever, movable about its axis, o, while a spring, r, attracts the lever in the opposite direction. When the current passes, the electromagnet attracts the lever aC, which by a rod, /, acts on a second lever, d, fixed to a horizontal axis, itself connected with a fork, F. When the cur- rent is broken the spring r draws the lever aC^ ms^^^^^^ and therewith all the connected pieces ; a back- ^^s- 673- ward and forward motion is produced, which is communicated to the fork F, which transmits it to a toothed wheel, G, on the axis of which is the needle. From the arrangement of its teeth, the wheel G is always moved in the same direction by the fork. To explain the intermittent action of the magnet, we must refer to fig. 674. The toothed wheel, R, has 26 teeth, of which 25 correspond to letters of the alphabet, and the last to the interval reserved between the letters A and Z. When holding the knob P in the hand the wheel R is turned, the end of the plate N from its curvature is always in contact with the teeth ; the plate M, on the contrary, terminates in a catch cut so that contact is alternately made and broken. Hence the connections with the battery having been made, if the needle P is advanced through four letters, for example, the current passes four times in N and M, and is four times broken. The electromagnet of the arrival station will then have attracted four times, and have ceased to do so four times. Lastly, the wheel G will have turned by four teeth, and as each tooth corresponds to a letter, the needle of the arrival station will have passed through exactly the same number of letters as that of the departure station. The piece S, represented in the two figures, is a copper plate, moveable on a hinge, which serves to make or to break the current at will. From this explanation it will be readily intelligible how communica- tions are made between different places. Suppose, for example, that the first apparatus being at London and the second at Brighton, there being metallic connection between the two towns, it is desired to send the word signal to the latter town : as the needles correspond on each apparatus to the interval retained between A and Z, the person sending the despatch moves the needle P to the letter S, where it stops for a very short time ; as the needle at Brighton accurately reproduces the motion of the London needle, it stops at the same letter, and the person who receives the des- patch notes this letter. The one at London always continuing to turn in the same direction, stops at the letter I, the second needle immediately stops at the same letter; and continuing in the same manner with the 834] Dial Telegraphs. 755 letters G, N, A, L, all the word is soon transmitted to Brighton. The attention of the observer at the arrival station is attracted by means of an electric alarum. Each station further must be provided with the two ap- paratus (figs. 674 and 675), without which it would be impossible to answer. 756 Dynamical Electricity. [836- 835. Morse's telegrrapb. — The telegraphs hitherto described leave no trace of the despatches sent, and if any errors have been made in copying the signals there is no means of remedying them. These inconveniences are not met with in the case of the writing telegraphs, in which the signs themselves are printed on a strip of paper at the time at which they are transmitted. Of the numerous printing and writing telegraphs which have been de- vised, that of Mr. Morse, first brought into use in North America, is best known. It has been almost universally adopted on the Continent. In this instrument there are three distinct parts : the indicator, the commu- nicator, and the relay, figs. 676, 677, and 678 represent these ap- paratus. Indicator. We will first describe the indicator (fig. 676), leaving out Fig. 676. of sight for the moment the accessory pieces, G and T, placed on the right of the figure. The current which enters the indicator by the wire, C, passes into an electromagnet, E, which, when the current is closed, attracts an armature of soft iron. A, fixed at the end of a horizontal lever movable about an axis, x; when the current is open the lever is raised by a spring, r. By means of two screws, m and v, the amplitude of the oscillations is regulated. At the other end of the lever there is a pencil, o, which writes the signals. For this purpose a long band of strong paper, pp, rolled round a drum, R, passes between two copper rollers with a rough surface, m, and turning in contrary directions. Drawn -835] Morse's Telegraph. 7S7 in the direction of the arrows, the band of paper becomes rolled on a second drum, Q, which is turned by hand. A clockwork motion placed in the box, BD, works the rollers, between which the band of paper passes. The paper being thus set in motion, whenever the electromagnet works, the point o strikes the paper, and, without perforating it, produces an indentation, the shape of which depends on the time during which the point is in contact with the paper. If it only strikes it instantaneously, it makes a dot (.) or short stroke ( — ) ; but if the contact has any duration a dash of corresponding length is produced. Hence, by varying the length of contact of the transmitting key at one station, a combination of dots and dashes may be produced at another station, and it is only necessary to give a definite meaning to these combinations. The same telegraphic alphabet is now universally used wherever tele- graphic communication exists ; and the signals for the single needle in- strument (fig, 676), as well as those used for printing have been modified, so that they now correspond to each other. Thus a beat of the top of the needle to the left \ is equivalent to a dot ; and a beat to the right / to a dash. The following figure gives the alphabet : — SINGLE SINGJX PRINTING. XEEDIE. PBINHXG. UEEDIE. A v/ N A B An^ 0^ I/I C^ AA P X Jls D As Q> IIJ E - \ R ^ vA F^ «A S — / G /A T -- H WW TJ vx/ I -- \x V vw/ J^ J// w ^// K IJ X ^ Ax/ L^ sL Y ^,. A// M // /Av Communicator or key. This consists of a small mahogany base, which acts as support for a metallic lever ab (fig. 677), movable in its middle on a horizontal axis. The extremity a of this lever is always pressed up- wards by a spring beneath, so that it is only by pressing with the finger on the key B that the lever sinks and strikes the bottom x. Round the 758 Dynamical Electricity. [835- base there are three binding screws; one connected with the wire P, which comes from the positive pole of the battery ; the second connected with L, the wire of the line; and the third with the wire A, which passes to the indicator, for of course two places in communication are each pro- vided with an indicator and communicator. These details known, there are two cases to be considered: i. The communicator is arranged so as to receive a despatch from a distant station ; the extremity b is then depressed, as represented in the drawing, Fig. 677. so that the current which arrives by the wire of the line L, and ascends in the metallic piece m, redescends in the wire A, which leads it to the indicator of the station at which the apparatus is placed. 2. A despatch is to be transmitted ; in this case the key B is pressed so that the lever comes in contact with the button x. The current of the local battery, which comes by the wire P, ascending then in the lever, redescends by m and joins the wire L, which conducts it to the station to which the despatch is addressed. According to the length of time during which B is pressed, a dot or a line is produced in the receiver to which the current proceeds. Relay. In describing the receiver we have assumed that the current of the hne coming by the wire C (fig. 676) entered directly into the electro- magnet, and worked the armature A, producing a despatch ; but when the current has traversed a distance of a few miles its intensity has diminished so greatly that it cannot act upon the electromagnet with sufficient force to print a despatch. Hence it is necessary to have re- course to a relay — that is, to an auxiliary electromagnet which is still traversed by the current of the line, but which serves to introduce into the communicator the current of a local battery of 4 or 5 elements placed at the station, and which is only used to print the signals trans- mitted by the wire. • For this purpose the current entering the relay by the binding screw, L (fig. 678), passes into an electromagnet, E, whence it passes into the earth by the binding screw T. Now, each time that the current of the line passes into the relay, the electromagnet attracts an armature. A, fixed at the bottom of a vertical lever /, which oscillates about a horizontal axis At each oscillation the top of the lever/ strikes against a button, n, and at this moment the current of the local battery which enters by the -835] Morse s Telegraph. 759 binding screw, c, ascends the column ;«, passes into the lever/, descends by the rod o, which transmits it to the screw Z : thence it enters the-; electromagnet of the indicator, whence it emerges by the wire Z, to return to the local battery from which it started. Then when the current of the line is open, the electromagnet of the relay does not act, and the lever p^ Fig. 678. drawn by a spring r, leaves the button n^ as shown in the drawing, and the local current no longer passes. Thus the relay transmits to the indicator exactly the same phases of passage and intermittence as those effected by the manipulator in the post which sends the despatch. With a general battery of 25 Daniell's elements the current is strong enough at upwards of 90 miles from its starting-point to work a relay. For a longer distance a new current must be taken, as will be seen in the paragraph on the change of current {vide infra). Woi'kitig of the three apparatus. The three principal pieces of Morse's apparatus being thus known, the following is the actual path of the current. The current of the line coming by the wire L (fig. 678) passes at first to the piece T intended to serve as lightning conductor, when, from the influence of atmospheric electricity in time of storm, the conducting wires become charged with so much electricity as to give dangerous sparks. This apparatus consists of two copper discs, d and f provided with teeth on the sides opposite each other, but not touching. The disc d is con- nected with the earth by a metallic plate at the back of the stand which supports this lightning conductor, while the disc /is in the current. The latter coming by the line L enters the lightning conductor by the binding screw fixed at the lower part of the stand on the left ; then rises to a commutator, «, which conducts it to a button, with the binding screw m, with which is Ji||llllil««lil11^Ai| ,,i3„ ,„„„ected one end of the wire of the "''"^ ^ electromagnet ; the other end is connected with a spring c, to which is attached the armature a ; this again is pressed against by a spring C, which in turn is connected with the binding screw n from which the wire leads to. earth. Whenever the current passes, the armature is attracted, carrying with it a hammer P, which strikes against the bell T and makes it sound. The moment this takes place contact is broken between the armature a and the spring C, the current being stopped the electromagnet does not act ; the spring c however in virtue of its elasticity brings the armature in contact with the spring C,the current again passes, and so on as long as the current passes. 841. Electrical' clocks. — Electrical clocks are clockwork machines, in which an electromagnet is both the motor and the regulator, by means of an electric current regularly Fig. 680. Fig. 681 Fig. 682. interrupted, in a manner resembling that described in the preceding paragraph. Fig. 681 represents the face of such a clock, and fig. 682 the mechanism which works the needles. -842] Electromagnetic Machines., 765 An electromagnet, B, attracts an armature of soft iron, P, movable on a pivot, a. The armature P transmits its oscillating motion to a lever, ^, which, by means of a ratchet, n, turns the wheel, A. This, by the pinion, D, turns the wheel C, which by a series of wheels and pinions moves the hands. The small one marks the hours, the large one the minutes ; but as the latter does not move regularly, but by sudden starts Irom second to second, it follows that it may also be used to indicate the seconds. It is obvious that the regularity of the motion of the hands depends on the regularity of the oscillations of the piece P. For this purpose, the oscillations of the current, before passing into the electromagnet B, are regulated by a standard clock, which itself has been previously regulated by a seconds pendulum. At each oscillation of the pendulum, there is nn arrangement by which it opens and closes the current, and thus the armature P beats seconds exactly. To illustrate the use of these electrical clocks, suppose that on the railway from London to Birmingham each station has an electric clock, and that from the London station a conducting wire passes to all the clocks on the line as far as Birmingham. When the current passes in this wire all the clocks will simultaneously indicate the same hour, the same minute, and the same second ; for electricity travels with such enormous velocity, that it takes an inappreciable time to go from London to Birmingham. 842. Electromag-netic maclilnes. — Numerous attempts have been made to apply electromagnetism as a motive force in machines. Fig. 683 represents a machine of this kind constructed by M. Froment . It consists of four powerful electromagnets, ABCD, fixed on an iron frame, X. Between these electromagnets is a system of two iron wheels mov- able on the same horizontal axis, with eight soft iron armatures, M, on their circumference. The current arrives at K, ascends in the wire E, and reaches a metallic arc, O, which serves to pass the current successively into each electro- magnet, so that the attractions exerted on the armatures M shall always be in the same direction. Now this can only be the case provided the current is broken in each electromagnet just when an armature comes in front of the axis of the bobbin. To produce this interruption the arc O has three branches, e, each terminating with a steel spring, to which a small sheave is attached. Two of these establish the communication respectively with an electromagnet, and the third with two. On a central wheel, a, there are cogs, on which the sheaves alternately rest. Whenever one of them rests on a cog, the current passes into the corre- sponding electromagnet, but ceases to pass when there is no longer con- tact. On emerging from the electromagnets the current passes to the negative pole of the battery by the wire H. In this manner, the armatures M being successively attracted by the four electromagnets, the system of wheels which carries them assumes a rapid rotatory motion, which by the wheel P and an endless band is ^66 Dynamical Electricity. [842- transmitted to a sheave, O, which sends it finally to any machine, a grinding mill for example. In his workshops M. Froment has an electromotive engine of one- horse power. But as yet these machines have not been applied in manufactures, for the expense of the acids and the zinc which they use Fig. 683. very far exceeds that of the coal in steam engines of the same force. Until some cheaper source of electricity shall have been discovered there is no expectation that they can be applied at all advantageously. Thus a machine devised by Kravogl produces about 17 per cent, of the useful effect due to the zinc, and therefore in utilising this force they are about equal to the best steam engines. But a pound of coal yields 7,200 thermal units, and a pound of zinc only 1,200; and as zinc is ten times as dear as coal, engines worked by electricity are sixty times as dear as steam engines. \ ^843] Voltaic Induction. 767 CHAPTER VI. VOLTAIC INDUCTION. 843. Induction by currents. — We have already seen (699) that under the name indnctio7i is meant the action which electrified bodies exert at a distance on bodies in the natural state. Hitherto we have only had to deal with electrostatical induction; we shall now see that dynamical electricity produces analogous effects. Faraday discovered this class of phenomena in 1832, and he gave the name of currents of induction or induced currents to instantaneous currents developed in metallic conductors under the influence of metallic conductors traversed by electric currents, or by the influence of powerful magnets, or even by the magnetic action of the earth; and the currents which give rise to them he called inducing currents. The inductive action of a current at the moment of opening or closing may be shown by means of a bobbin with two wires. This consists (fig. 684) of a cylinder of wood or of cardboard, on which a quantity of silk- covered No. 16 copper wire is coiled; on this is coiled a considerably Fig. 684. greater length of fine copper wire about No. 35, also insulated by being covered with silk. This latter coil, which is called the secondary coil, is connected by its ends with two binding screws, a, b, from which wires pass to a galvanometer, while the thicker wire, the primary coil, is con- nected by its extremities with two binding screws,' c and d. One of these, d, being connected with one pole of a battery, when a wire from the other pole is connected with c, the current passes in the primary coil, and in this alone. The following phenomena are then observed : — i. At the moment at which the thick wire is traversed by the current the galvanometer by the deflection of the needle indicates the existence in the secondary coil of a current inverse to that in the primary coil, that is, in the contrary direction ; this is only instantaneous, for the needle 768 Dy7tamical Electricity. [843- immediately reverts to zero, and remains so long as the inducing current passes through cd. ii. At the moment at which the current is opened, that is, when the wire cd ceases to be traversed by a current, there is again produced in the wire ab an induced current instantaneous hke the first, but direct, that is, in the same direction as the inducing current. 844. Production of induced currents by continuous ones. — Induced currents are also produced when a primary coil traversed by a current is approached to or removed from a secondary one : this may be shown by the following apparatus, fig. 685, in which B is a hollow coil consisting of a great length of fine wire, and A a coil consisting of a shorter and thicker wire, and of such dimensions that it can be placed in a secondary coil. Fig. 685. The coil A being traversed by a current, if it is suddenly placed in the coil B, a galvanometer connected with the latter indicates by the direction of its deflection the existence in it of an inverse current ; this is only instantaneous, the needle rapidly returns to zero, and remains so long as the small bobbin is in the large one. If it is rapidly withdrawn, the gal- vanometer shows that the wire is traversed by a direct current. If, instead of rapidly introducing or replacing the primary coil, this is done slowly, the galvanometer only indicates a weak current, and which is the feebler the slower the motion. If, instead of varying the distance of the inducing current, its intensity be varied, that is, either increased by bringing additional battery power into the circuit, or diminished by increasing the resistance, an induced current is produced in the secondary wire, which is inverse if the intensity of the inducing current increases and direct if it diminishes. -846] Inductive Action of the Ley den Discharge. 769 845. Conditions of induction. Kenx's la\(r. — From the experiments which have been described in the previous paragraphs the following prin- ciples may be deduced : — I. The distance remaining the same, a continuous a?id constant current does not induce any curre?it iti an adjacent conductor. II. A current at the ino?nent 0/ being dosed, produces in an adjacent . conductor, an inverse current. III. A current, at the moment it ceases, produces a direct current. IV. A current which is removed, or whose intensity diminishes, gives rise to a direct induced current. V. A current which is approached, or whose intensity increases, gives rise to an inverse induced current. VI. On the induction produced between a closed circuit and a current in activity, when their relative distance varies, Lenz has based the follow- ing law, which is known as Lenzs law: — If the relative position of two conductors A a7id B be changed, of which A is traversed by a ctcrrent, a current is induced in B in such a direction, that by its electrodynamic action on the ctn'rent in A, it would have im- parted to the conductors a motioji of the coittrary kind to that by which the , inducing action was produced. Thus, for instance, in V, when a current is approached to a conductor, an inverse cuiTent is produced ; but two conductors traversed by currents in opposite directions, repel one another according to the received law of electrodynamics. Inversely when a current is moved away from a con- ductor, a current of the same direction is produced ; now two currents in the same direction attract one another. On bringing the inducing wire near the induced as well as in removing it away, work is required ; hence a quantity of heat proportional to the work consumed must result, as Edlund's investigations have shown. On the other- hand, when induction results from the opening and closing of the circuit (II. and III.) no work is lost, but the inducing current loses as much heat as is produced in the induced circuit. 846. Inductive action of the Xieyden discbargre. — Figure 686 repre- sents an apparatus devised by Matteucci, which is very well adapted for showing the development of induced currents produced either by the dis- charge of a Leyden jar or by the passage of a voltaic current. It consists of two glass plates about 12 inches diameter, fixed vertically on the two supports A and B. These supports are on movable feet, and can either be approached or removed at will. On the anterior face of the plate A are coiled about 30 yards of copper wire, C, a millimetre in diameter. The two ends of this wire pass through the plate, one in the centre, the other near the edge, terminating in two binding screws, like those represented in m and n, on the plate B. To these binding screws are attached two copper wires, c and d^ through which the inducing current is passed. On the face of the plate B, which is towards A, is enrolled a spiral of much finer copper wire than the wire C. Its extremities terminate in the binding screws m and n, on which are fixed two wires, h and /, intended LL 770 Dynamical Electricity. [846- to transmit the induced current. The two wires on the plates are not only covered with silk, but each circuit is insulated from the next one by JL>U-JA)fUlnK fir Fig. 686. a thick, layer of shellac varnish, a condition necessary in experimenting with statical electricity, which is always more difficult to insulate than that of the voltaic current. In order to show the production of the induced current by the discharge of a Leyden jar, one end of the wire C is connected with the outer coating, and the other end with the knob of the Leyden jar, as shown in the figure. When the spark passes, the electricity traversing the wire C acts by in- duction on the neutral fluid of the wire on the plate B, and produces an instantaneous current in this wire. A person holding two copper handles connected with the wires i and h, receives a shock, the intensity of which is greater in propertion as the plates A and B are nearer. This experi- ment proves that frictional electricity can give rise to induced currents as well as voltaic electricity. The above apparatus can also be used to show the production of in- duced currents by the influence of voltaic currents. For this purpose the current of a battery is passed through the inducing wire C, while the ends of the other wire, h and /, are connected with a galvanometer. At the moment at which the current commences or finishes, or when the distance of the two conductors is varied, the same phenomena are observed as in the case of the apparatus (843). 847. Induction by magrnets. — It has been seen that the influence of a current magnetises a steel bar ; in like manner a magnet can produce induced currents in metallic circuits. Faraday has shown this by means of a coil with a single wire of 200 to 300 yards in length. The two extremities of the wire being connected with a galvanometer, as shown in fig. 687, a strongly magnetised bar is suddenly inserted in the bobbin, and the following phenomena are observed : — i. At the moment at which the magnet is introduced, the galvanometer indicates in the wire the existence of a current, the direction of which is opposed to that which circulates round the magnet, considering the latter as a solenoid on Ampere's theory (827). -848] Induction. 771 ii. When the bar is withdrawn, the needle of the galvanometer, which has returned to zero, indicates the existence of a direct current. The inductive action of magnets may also be illustrated by the follow- Kig. 687. ing experiment : a bar of soft iron is placed in the above bobbin and a strong magnet suddenly brought in contact with it; the needle of the galvano- meter is deflected, but returns to zero when the magnet is stationary, and is deflected in the opposite direction when it is removed. The induction is here produced by the magnetisation of the soft iron bar in the interior of the bobbin under the influence of the magnet. The same inductive effects are produced in the wires of an electro- magnet, if a strong magnet be made to rotate rapidly in front of the extremities of the wire in such a manner that its poles act successively by influence on the two branches of the electromagnet : or also by forming two coils round a horse-shoe magnet, and passing a plate of soft iron rapidly in front of the poles of the magnet; the soft iron becoming magnetised reacts by influence on the magnet, and induced currents are produced in the wire alternately in different directions. The inductive action of magnets is a striking confirmation of Ampere's theory of magnetism. For as on this theory all magnets are solenoids, ail the experiments which have been mentioned may be explained by the inductive action of currents which traverse the surface of magnets ; the induction of magnets is in short an induction of currents. And it is a useful exercise to see how, on this view, the inductive action of magnets falls under Lenz's law (845). 848. Inductive action of mag^nets on bodies in motion. — Arago was the first to observe, in 1824, that the number of oscillations which a magnetised needle makes in a given time, under the influence of the earth's magnetism, is very much lessened by the proximity of certain metallic masses, and especially of copper, which may reduce the number. 772 Dynamical Electricity. [848- in a given time from 300 to 4. This observation led Arago in 1825 to an equally unexpected fact ; that of the rotative action which a plate of copper in motion exercises on a magnet. This phenomenon may be shown by means of the apparatus represented in fig. 688. It consists of a copper disc, M, movable about a vertical axis. On this axis is a sheave, B, round which is coiled an endless cord Fig. 688 passing also round the sheave A. By turning this with the hand, the disc M may be rotated with great rapidity. Above the disc is a glass plate, on which is a small pivot supporting a magnetic needle, ab. If the disc be now moved with a slow but uniform velocity, the needle is deflected in the direction of the motion, and stops at an angle of from 20° to 30° with the direction of the magnetic meridian, according to the velocity of the rotation of the disc. But if this velocity increases, the needle is ulti- mately deflected more than 90° ; it is then carried along, describes an entire revolution, and follows the motion of the disc until this stops. Babbage and Herschel modified Arago's experiment by causing a horse- shoe magnet placed vertically to rotate below a copper disc suspended on silk threads without torsion ; the disc rotated in the same direction as the magnets. The effect decreases with the distance of the disc, and varies with its nature. The maximum effect is produced with metals ; with wood, glass, water, etc. it disappears. Babbage and Herschel have found that repre- senting this action on copper at 100, the action on other metals is as follows : zinc 95, tin 46, lead 25, antimony 9, bismuth 2. Lastly, the effect is enfeebled if the disc presents breaks in the continuity, especially in the direction of the radii ; but the same physicists have observed that it virtually regains the same intensity if these breaks have been soldered with any metal. Faraday made an experiment the reverse of Arago's first observation ; since the presence of a metal at rest stops the oscillations of a magnetic needle, the neighbourhood of a magnet at rest ought to stop the motion -849] Induction by the Action of the Earth. 773 of a rotating mass of metal. Faraday suspended a cube of copper to a twisted thread, which was placed between the poles of a powerful electro- magnet. When the thread was left to itself, it began to spin round with great velocity, but stopped the moment a powerful current passed through the electromagnet. Faraday was the first to give an explanation ot all these phenomena of magnetism by rotation. They depend on the circumstance that a magnet or a solenoid can induce currents in a solid mass of metal. In the above case the magnet induces currents in the disc, when the latter is rotated ; and conversely when the magnet is rotated while the disc is primarily at rest. Now these induced currents by their electrodynamic action tend to destroy the motion which gave rise to them ; they are simple illustrations of Lenz's law ; they act just in the same way as friction would do. i. For instance, let AB (fig. 689) be a needle oscillating over a copper disc, and suppose that in one of its oscillations it goes in the direction of the arrows from N to M. In approaching the point M, for instance, it developes there a current in the opposite direction, and which therefore repels it ; in moving away from N it pro- duces currents which are of the same kind, and which therefore attract, and both these actions con- cur in bringing it to rest. ii. Suppose the metallic mass turns from N to- '^' ^' wards M, and that the magnet is fixed ; the magnet will repel by induc- tion points such as N which are approaching A, and will attract M which is moving away ; hence the motion of the metal stops, as in Faraday's experiment. iii. If in Arago's experiment the disc is moving from N to M ; N ap- proaches A and repels it, while M moving away attracts it; hence the needle moves in the same direction as the disc. If this explanation is true, all circumstances which favour induction will increase with dynamic reaction; and those which diminish the former will also lessen the latter. We know that induction is greater in good conductors, and that it does not take place in insulating substances ; but we have seen that the needle is moved with a force which is less, the less the conducting powers of the disc, and it is not moved when the disc is of glass. Dove has found that there is no induction on a tube split lengthwise in which a coil is introduced. In order to bring the oscillations of the needle of a galvanometer more quickly to rest, the wire is coiled upon a copper frame. Such an arrange- ment is called a damper^ and in practice it is frequently used. 849. Induction by the action of the earth. — Faraday discovered that terrestrial magnetism can develope induced currents in metallic bodies in motion, acting like a powerful magnet placed in the interior of the earth in the direction of the dipping needle, or, according to the theory of Ampere, like a series of electrical currents directed from east to west parallel to the magnetic equator. He first proved this by placing 774 Dynamical Electricity. [849- a long helix of copper wire covered with silk in the plane of the magnetic meridian parallel to the dipping needle ; by turning this helix i8o° round an axis perpendicular to its length in its middle, he observed that at each turn a galvanometer connected with the two ends of the helix was de- flected. The apparatus depicted in fig. 690, and known as Delezenne's Fig. 6go. circle, serves for showing the existence of terrestrial induced currents. It consists of a wooden ring, RS, about two feet in diameter, fixed to an axis ao, about which it can be turned by means of a handle, M. The axis oa is itself fixed in a frame, PQ, movable about a horizontal axis. By needles fixed to these two axes the inclination towards the horizon of the frame PQ, and therefore of the axis oa, is indicated on a dial, b, while a second dial, c, gives the angular displacement of the ring. This ring has a groove in which is coiled a large quantity of insulated copper wire. The two ends of the wire terminate in a comfnutator analogous to that in Clarke's appa- ratus (855), the object of which is to pass the current always in the same sense, although its direction, SR, changes at each semi-revolution of the ring. Oh each of the rings of the commutator are two brass plates, which successively transmit the current to two wires in contact with the galvanometer. The axis oa being in the magnetic meridian, and the ring RS at right angles to the direction XY of the dipping needle, if it is slowly rotated the needle of the galvanometer is deflected, and by its deflection indicates in the wire coiled on the ring, an induced current whose intensity increases until it has been turned through 90° ; the devia- tion then decreases, and is zero when the ring has made a semi-revolu- tion. If the rotation continues, the current reappears, but in a contrary direction, and attains a second maximum at 270° ; becoming null again after a complete turn. When the axis oa is parallel to the dip there is no current. 850. Induction of a current on itself. Extra current.— If a closed circuit traversed by a voltaic current be opened, a scarcely perceptible 850] Inductio7i of a Qm'efit on itself. 77S spark is obtained, if the wire joining the two poles be short. Further, if the observer himself form part of the circuit by holding a pole in each hand, no shock is perceived unless the current is very strong. If, on the contrary, the wire is long, and especially if it makes a great number of turns, so as to form a bobbin with very close folds, the spark, which is in- appreciable when the current is closed, acquires a great intensity when it is opened, and an observer in the circuit receives a shock which is the stronger the greater number of turns. Faraday has referred this strengthening of the current when it is broken to an inductive action which the current in each coil exerts upon the ad- jacent coils : an action in virtue of which there is produced in the bobbin a direct induced current — that is, one in the same direction as the principal one. This is known as the extra current. To show the existence of this current, at the moment of opening, Fara- day has arranged the experiment as seen in fig. 691. Two wires from the Fig. 691, poles of a battery are connected with two binding screws, D and F, with which are also connected the two ends of a bobbin, B, with a long fine wire which offers therefore a great resistance. On the path of the wires at the points A and C are two other wires, which are connected with a galvanometer, G. Hence the current from the pole E branches at A into two currents, one which traverses the galvanometer, the other the bobbin, and both joining the negative pole E'. The needle of the galvanometer being then deflected by the current which goes from A to C, it is brought back to zero, and kept there by an obstacle which prevents it from turning in the direction Qa, but leaves it free in the opposite direction. On breaking contact at E, it is seen that the moment the circuit is open the needle is deflected in the direction Qa' ; showing a current contrary to that which passed during the exist- ence of the current — that is, showing a current from C to A. But the battery current having ceased, the only remaining one is the current AFBDCA ; and since in the part CA the current goes from C to A, it 'jj6 Dyftamical Electricity. [850- must traverse the entire circuit in the direction AFBDC — that is, the same as the principal current. This current, which thus appears when the circuit is opened, is the extra current. 851. Extra current on opening: and on closing-. — The coils of the spiral act inductively on each other, not merely on opening, but also on closing the current. Hence, in accordance with the general law of induc- tion, each spire acting on each succeeding one induces a current in the opposite direction to its own — that is, an inverse current ; this, which is the extra current on closing, or the inverse extra current, being of con- trary direction to the principal one, diminishes its intensity, and lessens or suppresses the spark on closing. When, however, the current is opened, each spire then acts inductively on each succeeding one, producing a current in the same direction as its own, and which therefore greatly heightens the intensity of the principal current. This is the extra current on opening, or direct extra current. To observe the direct extra current, the conductor on which its effect is to be traced may be introduced into the circuit, by being connected in any suitable manner with the binding screws A and C in the place of the galvanometer. It can thus be shown that the direct extra current gives violent shocks, bright sparks, decomposes water, melts platinum wires, and magnetises steel needles. Abria has found that the intensity of the extra current is about 072 of the principal current. The shock produced by the current may be tried by attaching the ends of the wire to two files, which are held in the hands. On moving the point of one file over the teeth of the other a series of shocks is obtained, due to the alternate opening and closing of the current. The above effects acquire greater intensity when a bar of soft iron is introduced into the bobbin, or, what is the same thing, when the current is passed through the bobbin of an electromagnet ; and still more is this the case if the core, instead of being massive, consists of a bundle of straight wires. Faraday explains this strengthening action of soft iron as follows : If inside the spiral there is an iron bar, when on opening the circuit the principal current disappears, the magnetism which it evokes in the bar disappears too ; but the disappearance of this magnetism acts like the disappearance of the electrical current, and the disappearing magnetism induces a current in the same direction as the disappearing principal current, the effect of which is thus heightened. In the experiments just described the effects of the two extra currents accompany those of the principal current. Edlund has devised an in- genious arrangement of apparatus by which the action of the principal current on the measuring instruments can be completely avoided, so that only that of the extra current remains. In this way he has arrived at the following laws : i. The intensity of the currents used being the same, the extra currents obtained on opening and closing have the same electromotive Jar ce. ii. The electromotive force of the extra current is proportional to the intensity of the primary current. -854] Laws of hidiiced Currents. yjy 852. Induced currents of different orders. — Spite of their instan- taneous character, induced currents can themselves, by their action on closed circuits, give rise to new induced currents, these again to others, and so on, producing induced currents of different orders. These currents, discovered by Henry, may be obtained by causing to act on each other a series of bobbins, each formed of a copper wire covered with silk, and coiled spirally in one plane, like that represented in the plate A, in fig. 673. The currents thus produced are alternately in oppo- site directions, and their intensity decreases in proportion as they are of a higher order. 853. Properties of induced currents. — Notwithstanding their instan- taneous character, it appears from the preceding experiments that in- duced currents have all the properties of ordinary currents. They produce violent physiological, luminous, calorific, and chemical effects, and finally give rise to new induced currents. They also deflect the magnetic needle, and magnetise steel bars when they are passed through a copper wire coiled in a helix round the bars. The strength of the shock produced by induced currents renders their effects comparable to those of electricity of high potential. The direct induced current and the inverse induced current have been compared as to three of their actions : the violence of the shock, the de- flection of the galvanometer, and the magnetising action on steel bars. In these respects they differ greatly : they are about equal in their action on the galvanometer; but while the shock of the direct current is very powerful, that of the inverse current is scarcely perceptible. The same difference prevails with reference to the magnetising force. The direct current magnetises to saturation, while the inverse current does not mag- netise. 854. 3baws of induced currents. — In his special treatise on induction, Matteucci has deduced from his own researches, and from those of Fara- day, Lenz, Dove, Abria, Weber, Marianini, and Felici, the following laws in reference to induced currents : i. The strength of induced currents is proportional to that of the in- ducing currents. ii. This strength is proportional to the product of the length 0/ the inducing and induced currents. iii. The electromotive force developed by a given quantity of electricity is the same whatever be the nature ^ section, or shape of the inducing cir- cuit. iv. The electromotive force developed by the induction of a current on any given conducting circuit is independent of the nature of the con- ductor. V. The development ofitiduction is independent of the nature of the in sulating body ijiterposed between the induced and tJtducing circuit. This latter law is in disaccord with the experiments of Faraday, on the induction of statical electricity (702). L L3 7/8 Dynamical Electricity. [855 APPARATUS FOUNDED ON INDUCTION. 855. Magneto-electrical apparatus. — After the discovery of magneto- electrical induction, several attempts were made to produce an uninter- rupted series of sparks by means of a magnet. Apparatus for this purpose were devised by Pixii and Ritchie, and subsequently by Saxton, Ettings- hausen, and Clarke. Fig. 692 represents that invented by Clarke. It con- sists of a powerful horse-shoe magnetic battery, A, fixed against a vertical Fig. 692. wooden support. In front of this there are two bobbins, BB^, movable round a horizontal axis. These bobbins are coiled on two cylinders of soft iron joined at one end by a plate of soft iron, V, and at the other by a similar plate of brass. These two plates are fixed on a copper axis, terminated at one end by a commutator, qi, and at the other by a pulley, which is moved by an endless band passing round a large wheel, which is turned by a handle. Each bobbin consists of about 1,500 turns of very fine copper wire covered with silk. One end of the wire of the bobbin B is connected on the axis of rotation with one end of the wire of the bobbin B", and the two other ends of these wires terminate in a copper ferrule or washer, q^ which is fixed to the axis, but is insulated by a cylindrical envelope of 855] Apparatus founded on Induction. 779 ivory. In order that in each wire the induced current may be in the same direction, it is coiled on the two bobbins in difterent directions— that is, one is right-handed, the other left-handed. ' ^^ When now the electromagnet turns, its two branches become alter- nately magnetised in contrary directions under the influence of the magnet A, and in each wire an induced current is produced, the direction of which changes at each half turn. Let us follow one of the bobbins — B, for instance — while it makes a complete revolution in front of the poles a and b of the magnet ; calling the poles of the electromagnet successively a' and b'. Let us further consider the latter when it passes in front of the north pole of the magnetic battery (fig. 694). The iron has then a south pole in which, as we know, the Am- Fig. 694. Fig. 695. Fig. 696. Fig. 697. perian currents move like the hands of a watch. The contrary seems to be represented in fig. 694, but it must be remembered that the bobbins are seen here as they are in fig. 692; and hence, when viewed at the end which grazes the magnet, the Amperian currents seem to turn like the hands of a watch. These currents act inductively on the wire of the bobbin, producing a current in the same direction (854, iii.), for the bobbin moves away from the pole a, its soft iron is demagnetised, and the Amperian currents cease (845). The intensity of the induced current in the bobbin decreases, until the right line joining the axes of the 780 Dynamical Electricity. [855- twq bobbins is perpendicular to that which joins the poles a and b of the bar. There is now no magnetism in the bar, but quickly approaching the pole b, its soft iron is then magnetised in the opposite direction — that is, it iDecomes a north pole (fig. 695). The Amp^rian currents are then in the direction of the arrow a' : and as they are commencing, they develope in the wire of the bobbin an inverse current (845), which is in the same direction as that developed in the first quarter of the revolution. More- over, this second current adds itself to the first, for while the bobbin moves away from a, it approaches b. Hence, during the lower half revolution from a to b, the wire was successively traversed by two induced currents in the same direction, and if the rotatory motion is sufficiently rapid, we might admit during this half revolution the existence of a single current of the wire. The same reasoning applied to the figures 696 and 697 will show that during the upper half revolution the wire of the bobbin B is still traversed by a single current, but in the opposite direction to that of the lower half revolution. What has been said about the bobbin B applies obviously to the bobbin B' ; yet as one of these is right-handed and the other left- handed, during each upper or lower half revolution the currents are constantly in the same direction in the two bobbins. At each successive half revolution they both change, but are in the same direction as regards each other ; the term direction having here reference to figs. 694-697. 856. Commutator. — The object of this apparatus (fig. 698), of which fig. 699 is a section, is to bring the two alternating currents always in the Fig. same direction. It consists of an insulating cylinder of ivory or ebony, J, in the axis of which is a copper cylinder, K, of smaller diameter, fixed to -856] Commutator. 781 the armature V, and turning with the bobbins. On the ivory cyHnder is first a brass ferrule, q, and in front of it two half ferrules, o and o\ also of brass and completely insulated from one another. The half ferrule o is connected with the ferrule ^ by a tongue, x. On the sides of a block of wood, M, there are two brass plates, ;«, «, on which are screwed two elastic springs, b and c^ which press successively on the half ferrules and o', when rotation takes place. We have already seen that the two ends of the wire of the bobbin, those in the same direction with respect to the currents passing through them at any time, which will be found to be those farthest away from the armature V, terminate in the metalhc axis k, and therefore on the half ferrule 0' ; while the other two ends, both in the same direction with respect to the current, are joined to the ferrule q, and therefore to the half fer- rule 0. It follows that the pieces o 0' are constantly poles of alternating cur- rents which are developed in the bobbins ; and as these are alternately in contrary directions, the pieces o and o' are al- ternately positive and ne- gative. Now, taking the case in which the half ferrule o' is positive, spring b^ follows the plate ;«, arrives at n by the joining wire /, ascends in Cj and is closed by contact with the piece ; then, when in consequence of rotation o takes the place of o\ the current retains the same direction ; for, as it is then reversed in the bobbins, has become positive and 0' negative, and so forth as long as the bobbin is turned. With the two springs b and c alone, the opposite currents from the two pieces and 0' could not unite when m and « are not joined ; this is effected by means of a third spring, a (fig. 692), and of two appendices, /, only one of which is visible in the figure. These two pieces are insu- lated from one another on an ivory cylinder, but communicate respectively with the pieces and 0'. As often as the spring a touches one of these pieces it is connected with the spring b^ and the current is closed, for it passes from b to ^, and then reaches the spring c by the plate n. On the contrary, as long as the spring a does not touch one of these appendices the current is broken. For physiological effects the use of the spring a greatly increases the intensity of the shocks. For this purpose two long spirals of copper wire with handles, / and ^', are fixed at n and in. Holding the handles in the hands so long as the spring a does not touch the appendices /, the current passes through the body of the experimenter, but without appre- ciable effect ; while each time that the plate a touches one of the appen- dices /, the current, as we have seen above, is closed by the pieces b, a. Fig. 699. the current descends by the 782 Dynamical Electricity. [856- and c and ceasing then to pass through the wires 7ip, inp\ there is pro- duced in this and through the body a direct extra-current which produces a violent shock. This is renewed at each semi-revolution of the electromagnet, and its intensity increases with the velocity of the rotation. The muscles con- tract with such force that they do not obey the will, and the two hands cannot be detached. With a well-constructed apparatus of large dimen- sions a continuance of the shock is unendurable ; the person receiving it is prostrated, rolls on the ground, and is soon completely at the mercy of the operator. All the effects of voltaic currents may be produced by the induced current of Clarke's machine. Fig. 693 shows how the apparatus is to be arranged for the decomposition of water. The spring a is suppressed, the current being closed by the two wires which represent the electrodes. For physiological and chemical effects the wire rolled on the bobbins is fine, and each about 500 to 600 yards in length. For physical effects, on the contrary, the wire is thick, and there are about 25 to 35 yards on each bobbin. Figs. 700 and 701 represent the arrangement of the bobbins and the commutator in each case. The first represents the in- flammation of ether, and the second the incandescence of a metal wire. Fig. 700. Fig. 701. 0. in which the current from the plate a to the plate c always passes in the same direction. Pixii's and Saxton's electromagnetic machine differs from Clarke's in having the electromagnet fixed while the magnet rotates. Wheatstone has recently devised a compendious form of the magneto- electrical machine, for the purpose of using the induced spark in firing mines (746). 857. WCagrneto-electrical machine. — The principle of Clarke's ap- paratus has received in the last few years a remarkable extension in large magneto-electrical machines, by means of which mechanical work is transformed into powerful electric currents by the inductive action of magnets on bobbins in motion. The first machine of this kind was invented by Nollet, in Brussels, in 1850 ; this has been greatly improved by Van Malderen, who has also applied it to electrical illumination. This machine is represented in fig, 702, as it stands in a workshop at the Hotel des Invalides, in Paris, where it was constructed. One of 857] Magneto- Electrical Machine. 783 these machines was exhibited in the International Exhibition of 1862. It consists of a cast-iron frame, 5^ feet in height, on the circumference of which eight series of five powerful horse-shoe-magnetic batteries, A, A, A, are arranged in a parallel order on wooden cross-pieces. These batteries, each of which can support from 120 to 130 pounds, are so arranged that, W W II 1 1 illl Fig 702, if they are considered either parallel to the axis of the frame, or in a plane perpendicular to this axis, opposite poles always face one another. In each series the outside batteries consist of three magnetised plates, while the three middle ones have six plates, because they act by both faces, while the first only acts by one. On a horizontal iron axis going from one end to the other of the frame 784 Dynamical Electricity. [857- four bronze wheels are fixed, each corresponding to the intervals between the magrtetic batteries of two vertical series. There are 16 bobbins on the circumference of each of these — that is, as many as there are magnetic poles in each vertical series of magnets. These bobbins, represented in fig. 704, differ from those of Clarke's apparatus in having, instead of a single wire, 12 wires each, 11^ yards in length, by which the resistance is diminished. The coils of these bobbins are insulated by means of bitumen dissolved in oil of turpentine. These are not rolled upon solid cylinders of iron, but on two iron tubes, slit longitudinally ; this device renders the magnetisation and demagnetisation more rapid when the bobbins pass in front of the poles of the magnet. Further, the discs of copper which terminate the bobbins are divided in the direction of the radius, in order to prevent the formation of induced currents in these discs. The four wheels being respectively provided with 16 bobbins each, there are altogether 64 bobbins arranged in 16 horizontal series of four, as seen at D, on the left of the frame. The length of the wire on each bobbin being 12 times 11^ yards, or 138 yards, the total length in the whole apparatus is 64 times 138 yards, or 8,832 yards. The wires are coiled on all the bobbins in the same direction, and not only on the same wheel, but on all four, all wires are connected with one another. For this purpose the bobbins are joined, as shown in fig. 703 ; on the first wheel the twelve wires of the first bobbin, x, are con- nected on a piece of mahogany fixed on the front face of the wheel with a plate of copper, w, connected by a wire, O, with the centre of the axis Fig. 703. Fig. 704. which supports the wheels. At the other end, on the other face of the wheel, the same wires are soldered to a plate indicated by a dotted line which connects them with the bobbin y ; from this they are connected with the bobbin s' by a plate, /, and so on, for the bobbins /, ?^ . . . up to the last, V. The wires of this bobbin terminate in a plate «, which traverses the first wheel, and is soldered to the wires of the first bobbin of the next wheel, on which the same series of connections is repeated ; these wires pass to the third wheel, thence to the fourth, and so on, to the end of the axis. The bobbins being thus arranged, one after another, like the elements of a battery connected in a series {T]']), the electricity has high potential. But the bobbins may also be arranged by connecting the plates alternately, -857] Magneto-Electrical Machine. 785 not with each other, but with two metal rings in such a manner that all the ends of the same name are connected with the same ring. Each of these rings is then a pole, and this arrangement may be used where a high degree of potential is not required. From these explanations it will be easy to understand the manner in which electricity is produced and propagated in this apparatus. An endless band receiving its motion from a steam engine passes round a pulley fixed at the end of the axis which supports the wheels and the bobbins, and moves the whole system with any desired rapidity. Expe- rience has shown that to obtain the greatest degree of light, the most suitable velocity is 235 revolutions in a minute. During this rotation, if we at first consider a single bobbin, the tube of soft iron on which it is coiled, in passing in front of the poles of the magnet, undergoes at its two ejids an opposite induction, the effects of which are added, but change from one pole to another. As these tubes, during one rotation, pass successively in front of sixteen poles alternately of different names, they are magnetised eight times in one direction, and eight times in the opposite direction. In the same time there are thus produced in the bobbin eight direct induced currents and eight inverse induced currents ; in all, sixteen currents in each revolution. With a velocity of 235 turns in a minute, the numbers of currents in the same tin)e is 235 x 16 = 3,760 alternately in opposite directions. The same phenomenon is produced with each of the 64 bobbins ; but as they are all coiled in the same direc- tion, and are connected with each other, their effects accumulate, and there is the same number of currents, but they are more intense. To utilise these currents in producing an intense electric light, the communications are made as shown in fig. 705. On the posterior side Fig. 705. the last bobbin, x' , of the fourth wheel terminates by a wire, G, on the axis MN, which supports the wheels : the current is thus conducted to the axis, and thence over all the machine, so that it can be taken from any desired point. In the front the first bobbin, x, of the first wheel communicates by the wire 0, not with the axis itself, but with a steel cylinder, c, fitted in the axis, from which, however, it is insulated by an ivory collar. The screw c, to which the wire O is attached, is hkewise y86 Dynamical Electricity. [857- insulated by a piece of ivory. From the cylinder c the current passes to a fixed metaUic piece, K, from which it passes to the wire H, which transmits it to the binding screw a of fig. 702. The binding screw b communicates with the framework, and therefore with the wire of the last bobbin, x' (fig. 705). From the two binding screws a and b the current is conducted by means of two copper wires to two charcoals, the distance of which is regulated by means of an apparatus analogous in principle to that already described (786). In this machine the currents are not rectified so as to be in the same direction ; hence each carbon is alternately positive and negative, and in fact they are consumed with equal rapidity. Experiment has shown that, when these currents are applied to produce the electric light, it is not necessary they should be in the same direction ; but when they are to be used for electrometallurgy, or for magnetising, they must be rectified, which is effected by means of a suitable commutator. The light produced by the magneto-electrical machine is very intense ; with a machine of four wheels the hght obtained is equal to that of 150 Carcel lamps. A machine of six wheels gives a hght equal to 200 Carcel lamps. Serrin has constructed a new regulator for this light, which, like the older ones, brings the charcoals together in proportion as they become used ; and further removes them when they are in contact. It contains no clockwork motion, and is worked by the weight of one of its pieces. This light, which requires no other expenditure than that of a single horse-power to turn the coils when there are not more than four of them, is advantageously used for signalling by night on large vessels, and for lighthouses. One of these, constructed by Holmes, is now in use at the South Foreland lighthouse. 858. Siemens' armature. — Siemens has devised an armature or bobbin for magneto- electrical machines, in which the insulated wire is wound longitudinally on the core, instead of transversely, as is usually the case. It consists of a soft iron cylinder, AB (fig. 706), from one foot to three feet in length, according to circumstances. A deep groove is cut on the outer length of this core and on the ends, //i in which is coiled the insulated wire as in a multiplier. To the two ends of the cylinder brass discs, E and D, are secured. With E is connected a commutator, C, consisting of two pieces of steel insulated from each other and connected respectively with the two ends of the wire. On the other disc is a pulley, round which passes a cord, so that the bobbin moves very rapidly on the two pivots. -859] Wild's Magneto-Electrical Machine. y^y When a voltaic current circulates in the wire, the two cylindrical seg- ments, A and B, are immediately magnetised, one with one polarity and the other with the opposite. On the other hand, if, instead of passing a voltaic current through the wire of the bobbin, the bobbin itself be made to rotate rapidly between the opposite poles of magnetised masses, as the segments A and B become alternately magnetised and demagnet- ised, their induction produces in the wire a series of currents alternately positive and negative, as in Clarke's apparatus (855). When these cuirents are collected in a commutator which adjusts them — that is, sends all the positive currents on one spring and all the negative on another — these springs become electrodes, from one of which positive electricity starts and from the other negative. If these springs are connected by a conductor, the same effects are obtained as when the two poles of a battery are united. Siemens has constructed magneto-electrical machines in which this armature is utilised. It has the great advantage that a large number of small magnets may be used instead of one large one. As, weight for weight, the former possesses greater magnetic force than the latter, they can be made more economically. And as the armature is always very near the magnets, it receives greater momentum, and is more rapidly changed. 859. IVild's magrneto-electrical machine. — Mr. Wild has recently constructed a magneto-electrical machine, in which Siemens' armature is used along with a new principle — that of the multiplication of the current. Instead of utilising directly the current produced by the induction of a magnet, Mr. Wild passes it into a strong electromagnet, and by the in- duction of this latter a more energetic current is obtained. This machine consists first of a battery of 12 to 16 magnets P, each of which weighs about 3 pounds, and can support about 20 pounds. Between the poles of the magnets two soft iron keepers, CC, are arranged, separated by a brass plate, O. These three pieces are joined by bolts, and the whole compound keeper is perforated longitudinally by a cylindrical cavity, in which works a Siemens' armature, 71, about 2 inches in diameter. The wire of this armature terminates in a commutator, which leads the positive and negative currents to two binding screws, a and b. This commutator is represented on a larger scale in ifig. 709. At the other end is a pulley by which the armature can be turned at the rate of 25 turns in a second. The wire on the armature is 20 yards long. Below the support for the magnets and their armatures are two large electromagnets, BB. Each consists of a rectangular soft iron plate, 36 inches in length by 26 in breadth and i\ inch thick, on which are coiled about 1,600 feet of insulated copper wire. The wires of these electro- magnets are joined at one end, so as to form a single circuit of 3,200 feet. One of the other ends is connected with the binding screw a and the other with b. At the top the two plates are joined by a transverse plate of iron so as to form a single electromagnet. At the bottom of the electromagnets BB are two iron armatures sepa- rated by a brass plate, O, and in the entire length is a cylindrical channel 7SS Dynamical Electricity. [859- in which works a Siemens' armature 711 as above : this armature, however, is above a yard in length, nearly 6 inches in diameter, and its wire is 100 feet long. The ends are connected with a commutator, from which the Fig. 707. adjusted currents pass to two wires, r and s. The armature m is rotated at the rate of 1,700 turns in a minute. Fig. 708 shows on a larger scale a cross section of the bobbin m of the armatures CC and of the plates AA, on which is coiled the wire of the electromagnets BB. 860] Ladd's Dynamomagnetic Machine. 789 These details being premised, the following is the working of the machine. When the armatures ;/ and vi are rotated by means of a steam engine with the velocity mentioned, the magnets produce in the first armature induced currents, which, adjusted by the commutator, pass into the electromagnet BB, and magnetise it. But as these impart to the lower armatures CC opposite polarities, the induction of these latter pro- duces in the armature ni a series of positive and negative currents far Fig. 708. Fig. 709 more powerful than those of the upper armature ; so that when these are adjusted by a commutator and directed by the wires r and j, very power- ful effects are obtained. These effects are still further intensified if, as Mr. Wild has done, the adjusted current of the armature m is passed into a second electric magnet, whose armatures surround a third and larger Siemens' armature turning with the two others. A current is thus obtained which melts an iron wire a foot long and more than 2 inches in diameter. 860. Ziadd's dynamoznag-netic machine. — Mr. Ladd, philosophical instrument maker, in Beak Street, Regent Street, has invented a very remarkable dynamomagnetic machine. It consists of two Siemens' arma- tures, rotating with great velocity, and of two iron plates, AA (fig. 710), surrounded by an insulated copper wire. Ladd's machine differs from that of Wild in the following respects : i. There are no permanent magnets : ii. the electromagnets BB are not joined so as to form a single electromagnet, but are two distinct electromagnets, each having at the end two hollow cylinders, CC, m which are fitted two Siemens' armatures, m and n\ the current of the armature n passing round the electromagnets reverts to itself. This reaction of the current upon itself is an essential feature of the machine ; it is an application of a principle announced simultaneously by Mr. Wheatstone and by Mr. Siemens. The wire of the armature in is inde- pendent, and passes into the apparatus which is to utilise the current — for instance, two carbon points, D. The machine being thus arranged, if a voltaic current be passed once for all through the electromagnets BB, it magnetises the plates AA and 790 Dynamical Electricity. [860- their keepers, which by their reciprocal action retain a quantity of rema- nent magnetism sufficient to work the machine. If, then, the armatures in and 7i be rotated by means of two bands passing round a common drum, the magnetism of the hollow cylinders CC acting upon the arma- ture «, excites induction currents, which, adjusted by a commutator, pass round the electromagnets BB, and more strongly magnetise the cylinders or shoes CC. These in their turn reacting more powerfully on the armature «, strengthen the current; we thus see that n and B continu- ally and mutually strengthen each other as the velocity of the rotation increases. Hence as the iron of the armature m becomes more and more strongly magnetised under the influence of the electromagnets BB, a gradually more intense induced current is developed in this armature, Fig. 710. which is directed, commutated or not, according to the use for which it is designed. In a machine which Mr. Ladd exhibited at the Paris exhibition of 1867 the plates AA were only 24 inches in length by 1 2 inches in width. With these small dimensions the current is equal to 25 to 30 Bunsen's cells. It can work the electric light and keep incandescent a platinum wire a metre in length and 0-5 mm. in diameter. The above form of the machine is worked by steam power. Mr. Ladd has devised a more compact form, which may be worked by hand. This is represented in fig, 711. The two armatures are fixed end to end, and the coils are wound on it at right angles to each other, as shown m the figure. The current from this can raise to white heat 18 inches of -861] Gramme's Magnetic-Electrical Machine. 791 platinum wire o-oi in. thickness, and with an inductorium containing 3 miles of secondary wire 2 in. sparks can be obtained. Both Ladd's and Wild's machines are liable to the objection of re- quiring to be rotated at a rapid rate. The armatures become heated by Fig. 7 the repeated development of induction currents. This has been remedied by Mr. Ladd, who has introduced into the shoes or hollow cylinders several apertures through which a stream of cold water is made to flow. Before they can be applied industrially, their velocity must be reduced, either by multiplying the number of Siemens' armatures or modifying their arrangement. These machines furnish a remarkable instance of the transformation of mechanical force into electricity, light, and heat (273, 467). 861. Gramme's magrneto-electrical machine. — The magneto-elec- trical machines which have hitherto been described are all open to the objection that they only give momentary currents, alternately positive and negative. These currents may indeed be used for lighting and for physiological purposes, but for other applications, such as for electro- plating, they must be rectified-, that is, by means of a commutator, they must be sent always in the same direction. This, however, is in all cases accompanied by a certain loss of electricity, and sparks are produced which rapidly wear away the armatures of the commutators. These inconveniences are not met with in an apparatus invented by M. Gramme, of which fig. 712 is a representation in about ^th of the natural size. On a base is a powerful magnetic battery, between the limbs of which an axle is rotated by means of a pulley and an . endless band. On this axle, and in the same plane as the branches of the magnet, is a soft iron ring, on which are wound 35 coils of insulated copper wire, each having nearly 300 turns. In each one the wire is bent inside the ring, and is soldered to an insulated piece of brass. It is then again 792 Dynamical Electricity. [861- folded on the ring so as to form a second coil. From this it passes to a piece of brass similar to the first, and so on, forming a continuous con- ductor divided into 35 identical bobbins. Fig. 712. All the pieces of brass to which the copper wire is soldered are in- sulated from the apparatus, and form a bundle at c around the axis. There, on the same horizontal diameter of the ring, one part of these pieces is in contact with two brass discs, m and ;z, represented in tig. 701, which shows below them the bobbins and their accessories. These two discs sHde on their supports in the direction of the axis, and two springs press them against the pieces c. Suppose now that the ring with its coils turn from right to left in pass- ing under the pole B of the magnet, the upper part of the ring acquires a polarity the reverse of that of the ring, and its magnetisation devejopes a current the inverse of the Amperian currents (845) in the coils which approach the pole, and direct in those which recede from it. Hence, if the current formed on the right near the middle part, R, of the system is positive, that developed in the opposite region is negative. In front of the pole A a similar effect is produced, but here the polarity of A being the opposite of that of B, the inverse current from below towards R is positive, and the current on the left which is negative. Thus there are continually two positive currents proceeding from the upper and lower coils towards the medial region R, and two negative currents directed towards the opposite sides. These Fig- 713- -862] hiductorium. Rtihmkorff's Coil, 793 currents pass thence to the corresponding pieces c, whence they are collected by the discs m and «, which transmit them to the two binding screws a and b. A continuous current is thus produced which is always in the same direction, m being the positive pole and 7t the negative pole. If the rotation is in the opposite direction, the poles are reversed. This apparatus, though small in size— 9 inches in height— is very power- ful ; it can decompose water and heat to redness an iron wire 20 centi- metres in length and a millimetre in diameter. Its power increases with the velocity of its rotation up to a limit of 700 to 800 turns in a minute, and its effects vary according as the wire of the bobbins is thick and short or fine and long. 862. znductoriuxn. RulnukorfTs coil. — These are arrangements for producing induced currents, in which a current is induced by the action of an electric current, whose circuit is alternately opened and closed in rapid succession. These instruments, known as inductoriMms or induction coils, present considerable variety in their construction, but all consist essentially of a hollow cylinder in which is a bar of soft iron, or bundle of iron wires, with two helices coiled round it, one connected with the poles of a battery, the current of which is alternately opened and closed by a self-acting arrangement, and the other serving for the development of the induced current. By means of these apparatus, with a current of three or four Grove's cells, physical, chemical, and physiological effects are produced equal to and superior to those obtainable with electrical machines and even the most powerful Leyden batteries. Of all the forms those constructed by Ruhmkorff are the most powerful. Fig. 714 is a representation of one, the coil of which is about 14 inches Fig. 714. in length. T\i^ primary or inducing wire is of copper, and is about 2 mm. in diameter and 40 or 50 yards in length. It is coiled directly on a cylinder of cardboard, which forms the nucleus of the apparatus, and is enclosed in an insulating cylinder of glass, or of caoutchouc. On these is coiled the secondary or induced wire, which is also of copper, and is about ^mm. in diameter. A great point in these apparatus is the insula- tion. The wires are not merely insulated by being in the first case M M 794 Dynamical Electricity. [862- iFig. 715. covered with silk, but each individual coil is separated from the rest by a layer of melted shellac. The length of the secondary wire varies greatly ; in some of Ruhmkorff's largest sizes it is as much a^ 60 miles. With these great lengths the wire is thinner, about |mm. The thinner and longer the wire the higher the potential of the induced electricity. The following is the working of the apparatus. The current arriving by the wire P at a binding screw, a, passes thence into the commutator C, to be afterwards described (fig. 716), thenpe by the binding screw b it enters the primary wire, where it acts inductively on the secondary wire ; having traversed the primary wire, it emerges by the wire s (fig. 715). Following the direction of the arrows, it will be seen that the current ascends in the binding screw /, reaches an oscillating piece of iron, 0, called the ham- mer, descends by the anvil h^ and passes into a copper plate, K, which takes it to the commu- tator C. It goes from there to the binding screw c, and finally to the negative pole of the bat- tery by the wire N. The current in the primary wire only acts inductively on the secondary wire (843), when it opens or closes and hence must be constantly interru,pted. This is effected by means of the oscillating hammer o (fig. 715). In the centre of the bolDbin is a bundle of soft iron wires, forming together a cylinder a little longer than the bobbin, and thus projecting at the end as seen at A. When the current passes in the primary wire, this hammer o is attracted ; but immediately, there being no contact between o and h, the current is broken, the magnetisation ceases, and the hammer falls ; the current again passing, the same series of phenomena recommences, so that the hammer oscillates with great rapidity. 863. Condenser. — In proportion as the current passes thus intermit- tently in the primary wire of the bobbin, at each interruption an induced current, alternately direct and inverse, is produced in the secondary wire. But as this is perfectly insulated, the induced current acquires such a strength as to produce very powerful effects. Fizeau has increased this strength still more by interposing a condenser in the primary circuit. As constructed by Ruhmkorfffor his largest apparatus, this consists of 150 sheets of tinfoil about 18 inches square, so that the total surface is about 75 square yards. These sheets being joined, are fastened on two sides of a band of oiled silk, which insulates them, forming thus two coatings ; they are then coiled several times round each other, another band of silk being interposed, so that the whole can be placed below the helix in the base of the apparatus. One of these coatings, the positive, is connected with the binding screw 2, which receives the current on emerging from -864] Effects of Kuhinkorff's' Coil, 795 the bobbin ; and the other, the negative, is connected with the binding screw 7n, which communicates by the plate K with the commutator C, and with the battery. To understand the effect of the condenser, it must be observed that at each break of the inducing current an extra current is produced in the same direction, which, continuing in a certain manner, prolongs its dura- tion. It is this extra current which produces the spark that passes at .each break between the hammer and the anvil ; when the current is strong this spark rapidly alters the surface of the hammer and anvil, though they are of platinum. By interposing the condenser in the in- ducing circuit, the extra current, mstead of producing so strong a spark, passes into the condenser ; the positive electricity in the coating connec- ted with /, and the negative in that connected with in. But the opposite electricities combining quickly by the thick wire of the primary coil, by the battery and the circuit CK;;z, give rise to a current con- trary to that of the battery, which instanta- neously demagnetises the bundle of soft iron ; the induced current is thus shorter and more intense. The binding screws in and n on the base of the apparatus are for receiving this extra current. ,„„ , . The commutator or key serves to break ^ l^^^m^WW^ contact or send the current in either direc- Fig. ^^g. tion. The section in fig. 716 is entirely of brass, excepting the core A, which is ebonite ; on the two sides are two brass plates CC. Against these press two elastic brass springs, joined to two binding screws, a and r, with which are also connected the elec- trodes 01 the battery. The current arriving at a ascends in C, thence by a screw y it attains the binding screw b and the bobbin ; then re- turning by the plate K, which is connected with the hammer, the current goes to Q' by the screw x^ descends to ^, and rejoins the battery by the wire N. If by means of the milled head the key is turned 180 degrees, it is easy to see that exactly the opposite takes place ; the current reaches the hammer by the plate K and emerges at b. Finally, if it is only turned through 90 degrees, the elastic plates rest on the ebonite A instead of on the plates CC, and the current is broken. The two wires from the bobbin at and o' (fig. 714) are the two ends of the secondary wire. They are connected with the thicker wires PP^, so that the current can be sent in any desired direction. With large coils the hammer cannot be used, for the surfaces become so much heated as to melt. But M. Foucault has recently invented a mertury interrupter which is free from this inconvenience, and which is an important im- provement. - 864. Sffects produced by RubrnkorfTs coil. — The high degree of tension which the electricity of induction coil machines possesses has Tong been known, and many luminous and calorific effects have been obtained by their means. But it is orJy since the. improvements which" ^* 796 Dynamical Electricity. [864- Ruhmkorff has introduced into his coil, that it has been possible to utilise all the potential of induced currents, and to show that these currents possess the properties of statical as well as dynamical electricity. Induced currents are produced in the coil at each opening and break- ing of contact. But these currents are not equal either in duration or in potential. The direct current, or that on openings is of shorter duration, but higher potential ; that of closing of longer duration but lower potential. Hence if the two ends P and P' of the fine wire (figs. 714 and 715) are connected, as there are two equal and contrary quantities of electricity in the wire the two currents neutralise each other. If a galvanometer is placed in the circuit, only a very feeble deflection is produced in the direction of the direct current. This is not the case if the two extremities P and P' of the wire are separated. As the resistance of the air is then opposed to the passage of the currents, that which has highest potential, that is, the direct one, passes in excess, and the more so the greater the distance of P and P' up to a certain limit at which neither pass. There are then at P and P' nothing but potentials which are alternately con- trary. The effects of the coil, like those of the battery, may be classed under the heads physiological, chemical, calorific, luminous, mechanical ; with this difference, that they are enormously more intense. T\i^ physiological effects of Ruhmkorff's coil are very powerful: in fact, the shocks are so violent that many experimenters have been suddenly prostrated by them. A rabbit may be killed with two of Bunsen's elements, and a somewhat larger number of couples would kill a man. The calorific effects are also easily observed ; it is simply necessary to interpose a very fine iron wire between the two ends P and P' of the induced wire ; this iron wire is immediately melted, and burns with a bright light. A curious phenomenon may here ^ be observed, namely, that when each of the wires P and P' terminates in a very fine iron wire, and these two are brought near each other, the wire corresponding to the negative pole alone melts, indicating that the tension is greater at the negative than at the positive pole. The chemical effects are very varied, inasmuch as the apparatus produces electricity both in quantity and of high potential. Thus, according to the shape and distance of the platinum electrodes im- mersed in water, and to the degree of acidulation of the water, either luminous effects may be produced in water without decomposition, or the water may be decomposed and the mixed gases disengaged at the two poles, or the decomposition may take place, and the mixed gases separate either at a single pole or at both poles. Gases may also be decomposed or combined by the continued action of the spark from the coil. Becquerel and Fr^my have found that if the current of a Ruhmkorff's coil be passed through a hermetically sealed tube containing air, as shown in fig. 717, nitrogen and oxygen combine to form nitrous acid. The himinous effects of Ruhmkorff's coil are also very remarkable, and vary according as they take place in air, in vapour, or in very rarefied >864] Eff£cts of Rhumkorff's Coit. 797. vapours. In air the coil produces a very bright loud spark, which, with the largest-sized coils, has a length of i8 inches. In vacuo the effects are also remarkable. The experiment is made by connecting the two wires of the coil P and P' with the two rods of the electrical ^gg (fig. 580) used for pro- ducing in vacuo the luminous effects of the electrical machine. A vacuum having been produced up to I or 2 millimetres, a beautiful luminous trail is produced from one knob to the other, which is virtually con- stant, and has the same intensity as that obtained with a powerful electrical machine when the plate is rapidly turned. This experiment is shown in figs. 722 and 723. Fig. 721 represents a remarkable deviation which light undergoes when the hand is presented to the tgg. The positive pole of the current shows the greatest brilliancy ; its light is of a fiery red, while that of the negative pole is of a feeble violet colour ; moreover, the latter extends along all the length of the negative rod, which is not the case with the positive pole. The coil also produces mechanical effects so powerful that with the largest apparatus glass plates two inches thick have been perforated. This result, however, is not obtained by a single charge, but by several successive charges. The experiment is arranged as shown in fig. 718. The two poles of Fig. 718. the induced current correspond to the binding screws a and b ; by means of a copper wire, the pole a is connected with the lower part of an apparatus for piercing glass like that already described (fig. 585), the other pole is attached to the other conductor by a wire d. The latter is insulated in a large glass tube r, filled with shellac, which is run in while in a state of fusion. Between the two conductors is the glass to be per- forated, V, When this presents too great a resistance, there is danger ^/ 798". 'Dyjihimcal Electricity, [864 lest the spark pass in the coil itself, perforating the insulating layer which. separates the wire, and then the coil is destroyed. To avoid this, two wires, e and c, connect the poles of the coil with two metallic rods whose distance from each other can be regulated. If then the spark cannot penetrate through the glass, it bursts across, and the coil is not injured. The coil can also be used to charge Leyden jars. With a large coil: giving sparks of 6 to 8 inches, and using 6 Bunsen's elements with a large surface, Ruhmkorff -charged large batteries of 6 jars each, having about 3l square yards of coated surface. : The experiment with a single Leyden jar (fig. 719) is made as follows. The coatings of the latter are in connectibn with the poles of the coil by the wires ^and /, and these same poles are also connected, by means of Fig. 720. the wires e and ^:,'With the two horizontal rods of a universal discharger (%• 574)- :Th^ jar is then b^ing constantly charged by the wires 2 and dy 865] Stratification of the Electric Light. 799 sometimes in one direction and sometimes in another, and as constantly discharged by the wires e and c ; the discharge from m to n taking place as a spark two or three inches in length, very luminous, and producing a deafening sound 5 they can scarcely be compared with the sparks of the electrical machine, but are rather true lightning discharges. To charge a battery the form of the experiment is somewhat varied ; the external coating being connected with one pole of the coil by the wire d, and the internal coating with the other by the rods m, 7i, and the wire c (fig. 720). The rods w and n are not, however, in contact. If they were, as the two currents, the inverse and direct, pass equally, the battery would not be constantly charged and discharged ; while from the distance between ?n and n the direct current, that of opening,~ which has higher potential, passes alone, and it is this which charges the battery. 865. Stratification of the electric ligrht. — M. Quet has observed, in studying the electric light which Ruhmkorff 's coil gives in a vacuum, that if some of the vapour of turpentine, wood spirit, alcohol, or bisulphide of carbon, etc., be introduced into the vessel before exhaustion, the aspect of Fig. 721 Fig. 722. Fig. 723, the ight is totally modified. It appears then like a series of alternately bright and dark zones, forming a pile of electric light between the two poles (fig. 722). 8oo Dynamical Electricity. [865- In this experiment it follows from the discontinuity of the current of induction, that the light is not continuous, but consists of a series of dis- charges which are nearer each other in proportion as the hammer a (fig. 7 1 5) oscillates more rapidly. The zones appear to possess a rapid gyratory and undulatory motion. M. Quet considers this as an optical illusion ; for if the hammer is slowly moved by the hand, the zones appear very distinct and fixed. The light of the positive pole is most frequently red, and that of the negative pole violet. The tint varies, however, with the vapour or gas in the globe. M. Despretz has observed that the phenomena obtained by Ruhmkorff and by Quet, with a discontinuous current, are also reproduced with an ordinary continuous current, with this important difference, that the con- tinuous current requires a considerablenumberof couples, while the discon- tinuous current of the coil only requires a single element. It is remarkable that the luminous effects of this coil are very little increased by an increase in the number of elements. 866. Geissler's tubes. — The brilliancy and beauty of the stratification of the electric light are most remarkable when the discharge of the Ruhm- korff s coil takes place in glass tubes containing a highly rarefied vapour or gas. These phenomena, which have been investigated by Masson, Grove, Gassiot, Pliicker, etc., are produced by means of sealed glass tubes first constructed by Geissler, of Bonn. These tubes are filled with different gases or vapours, and are then exhausted, so that the pressure does not exceed half a millimetre. At the ends of the tubes two platinum wires are soldered into the glass. When the two platinum wires are connected with the ends of a Ruhm- korff 's coil, magnificent lustrous striag, separated by dark bands, are pro- duced all through the tube. These striae vary in shape, colour, and lustre with the degree of the vacuum, the nature of the gas or vapour, and the dimensions of the tube. The phenomenon has occasionally a still more brilliant aspect from the fluorescence which the electric discharge excites in the glass. Fig. 724 represents the striae given by hydrogen under half a milli- tjuum^ Fig. 724. metre of pressure ; in the bulbs the light is white, in the capillary parts it is red. Fig. 725 shows the striae in carbonic acid under a quarter of a millimetre -867]- Rotation of Induced Currents. 80 1 pressure ; the colour is greenish, and the striae have not the same form as hydrogen. In nitrogen the light is orange yellow. Pliicker has found that the light in Geissler's tube does not depend Fig. 725. on the substance of the electrodes, but simply on the nature of the gas or vapour in the tube. He has found that the lights furnished by hydro- gen, nitrogen, carbonic oxide, etc., give different spectra when they are decomposed by a prism. The discharge of the coil which passes through a highly rarefied gas would not pass through a perfect vacuum, from which it follows that the presence of a ponderable substance is absolutely necessary for the passage of electricity. By the aid of a powerful magnet Pliicker tried the action of mag- netism on the electric discharge in a Geissler's tube, as Davy had done with the ordinary voltaic arc, and obtained many curious results, one of which may be mentioned. He found that where the discharge is perpendicular to the line of the poles, it is separated into two distinct parts, which can be referred to the different action exerted by the electromagnet on the two extra currents produced in the discharge. The light of Geissler's tubes has been ap- plied to medical purposes. A long capillary tube is soldered to two bulbs provided with platinum wires ; this tube is bent in the middle, so that the two branches touch, and their ex- tremities are twisted, as shown at a in fig. 726 This tube contains a highly rarefied gas, like those previously described, and, when the discharge passes, a light is pro- duced at rt, bright enough to illuminate any cavity of the body into which the tube is introduced. 867. Rotation of Induced currents Xxj magrnets. — De la Rive has recently devised an experiment which shows in a most ingenious manner that magnets act on the light in Geisslei-'s tubes in accordance with the laws with which they act on any other movable conductor. M M 3 Fie. 726. 802 Dynamical Electricity. [867- This apparatus consists of a glass globe or electrical ^). Causes of tbermo-electrlc currents. — The thenno-electric Currents cannot be attributed to contact, for they can be produced in-' circuits formed of a single metal. Nor do they arise from chemical actions, for Becquerel has found that they are formed in hydrogen, and even in vacuo. The same physicist ascribes them to the unequal pro- pagation of heat in the different parts of the circuit. He found that when all the parts of a circuit are homogeneous, no current is produced on heating, because the heat is equally propagated in all directions. This is the case if the wires of the galvanometer are connected by a second' copper wire. But if the uniformity of this is destroyed by coiling it in a spiral, or by knotting it, the needle indicates by its deflection a current going from the heated part to that in which the homogeneity has been destroyed. If the ends of the galvanometer wires be coiled in spiral, and one end is heated and touched with the other, the current goes from the heated to the cooled end. When two plates of the same metal, but at different temperatures, are placed in a fused salt such as borax, which conducts electricity but exerts no chemical action, a current passes from the hotter metal through the 8l2 Dynamical Electricity, [873 fused salt to the colder one. Hot and cold water in contact produce a current which goes from the warm water to the cold. Svanberg has found that the thermo-electromotive force is influenced by the crystallisation ; for instance, if the cleavage of bismuth is parallel to the face of contact, it is greater than if both are at right angles, and that the reverse is the case with antimony. Thermo-electric elements may be constructed of either two pieces of bismuth or two pieces of antimony, if in the one the principal cleavage is parallel to the place of contact, and in the other is at right angles. Hence the position of metals in the thermo-electric series is influenced by their crystaUine structure. 874. Tberino* electric couples. — From what has been said it will be understood that a thermo-electric couple consists of two metals soldered together, the two ends of which can be joined by a conductor. Fig. 734 represents a bis- muth-copper couple ; fig. 735 represents a series of couples used by M. Pouillet. It consists of a bar of bismuth bent twice at right angles, at the ends of which are soldered two copper strips, c^ d, which terminate in two binding screws fixed on some insulating material. When several of these couples are joined so that the second copper of the first is soldered to the bismuth of the second, then the second copper of this to the bismuth of the third, and so on, this arrangement constitutes a thermo-electric battery, which is worked by keeping the odd solderings, for instance, in ice, and the even ones in water, which is kept at 100°. 875. iroblli'8 thermo-electric pile. — Nobili devised a form of thermo- electric battery, or pile as it is usually termed, in which there are a large Fig. 734- _j|||^ ^ MO^m^m^^ Fig- 735. number of elements in a very small space. For this purpose he joined the couples of bismuth and antimony in such a manner, that after having -876] BecquereVs Thermo-electric Battery, 813 formed a series of five couples, as represented in fig. 737, the bismuth from b was soldered to the antimony of a second series arranged similarly; the last bismuth of this to the antimony of a third, and so on for four vertical series, containing together 20 couples, commencing by antimony, finishing by bismuth. Thus arranged, the couples are insulated from one another by means of small paper bands covered with varnish, and then enclosed in a copper frame, P (fig. 736), so that only the solderings appear at the two ends of the pile. Two small copper binding-screws, 7n and n, insulated in an ivory ring, communicate in the interior, one with the first antimony, representing the positive pole, and the other with the last bismuth, representing the negative pole. These binding screws communicate with the ex- tremities of a galvanometer wire when the thermo-electric current is to be observed. 876. Becquerel's tbermo-electric battery. — Becquerel has found that artificial sulphuret of copper heated from 200° to 300° is powerfully positive, and that a couple of this substance and copper has an electro- motive force nearly ten times as great as that of the bismuth and copper couple in fig. 734. Native sulphuret, on the contrary, is powerfully nega- tive. As the artificial sulphuret only melts at about 1035°, it may be used at very high temperatures. The metal joined with it is German silver (90 of copper and 10 of nickel). Fig. 738 represents the arrangement of Fig. 736, Fig- 737. Fig. 738. a battery of 50 couples arranged in two series of 25. Fig. 740 gives on a larger scale the view of a single couple, and fig. 739 that of 6 couples in two series of 3. The sulphuret is cut in the form of rectangular prisms, 10 centimetres in length, by i8mm. in breadth, and 12mm. thick. In front is a plate of German silver w, intended to protect the sulphure 8i4 DynamicaC Electricity, [876= from roasting when it is placed in a gas flame. Below there is a plate of German silver MM, which is bent several times so as to be joined to the sulphuret of the next, and so on. The couples, thus arranged in two series of 25, are fixed to a wooden frame supported by two brass columns A B, on which it can be more or less raised. Below the couples there is a brass trough, through w^iigh water is constantly flowing; arriving by Fig. 739. Fig. 740. the tube b and emerging by the stopcock r. The plates of German silver are thus kept at a constant temperature. On each side of the trough are two long burners, on the Argand principle, fed by gas from a caoutchouc tube, a. The frame being sufficiently lowered, the ends are kept at a temperature of 200° to 300°. For collecting the current, two binding screws are placed on the left of the frame, one communicating with the first sulphuret, that is, the positive pole, and the other with the last German silver, or the negative pole. At the other end of the frame are two binding screws, which facihtate the arrangement of the couples in different ways. The current of this battery may be used for telegraphing even through a great distance, and passed into an electromagnet can lift a weight of 200 pounds. It can raise a short piece of fine iron wire to redness, and can freely decompose water. The electromotive force of a Daniell's cell is equal to about 8 or 9 of these couples. 877. Melloni's tbermomultipller. — We have already noticed the use which Melloni has made of Nobili's pile, in conjunction with the galva- nometer, for measuring the most feeble alterations of temperature. The arrangement he used for his experiment is represented in fig. 741. On a wooden base, provided with levelling screws, a graduated copper rule, about a yard long, is fixed edgeways. On this rule the various parts composing the apparatus are placed, and their distances can be fixed by means of binding screws. ^ is a support for a Locatelli's lamp, or other source of heat ; F and E are screens ; C is a support for the bodies experimented, and in is a thermo-electrical battery. Near the apparatus is a galvanometer, D ; this has only a comparatively few turns of a tolerably thick (i mm.) copper wire ; for the electromotive force of the thermocurrents is small, and as the internal resistance is small too, for it. -878] Uses^ of'Theymo-electric Currents. tn only consists of metal, it is clear that no great resistance can be intro- duced into the circuit if the current is not to be completely stopped. JSuch galvanometers are called thermomultipliers. The delicacy of this Fig. 741 apparatus is so great that the heat of the hand is enough at a distance of a yard from the pile to deflect the needle of the galvanometer. In using it for measuring temperature, the relation of the deflection of the needle, and therefore of the intensity of the current, to the difference of the temperatures of the two ends, must be determined. That known, the temperatures of the ends not exposed to the source of heat being known, the observed deflection gives the temperature of the other, and therewith the intensity of the source of heat. 878. Properties and uses of thermo-electric currents. — Thermo- electric currents are of extremely low tension, but of great constancy ; for their opposite junctions, by means of melting ice and boiling water, can easily be kept at 0° and 100° C. On this account. Ohm used them in the experimental establishment of his law. They can produce all the actions of the ordinary battery in kind, though in less degree. By means of a thermo-electrical pile consisting of 769 elements of iron and German silver, the ends of which differed in temperature by about 10° to 15", Kohlrausch proved the presence of free positive and negative electricity at the two ends of the open pile respectively. He found that the density of the free electricity was nearly proportional to the number of elements, and also that the electromotive force of a single element under the above circumstances was about -^^^-^ that of a single Daniell's element. On account of their feeble tension, thermo-electric piles produce only feeble chemical actions. Botto, however, with 120 platinum and iron wires, has decomposed water. Besides these, sparks can be obtained on breaking circuit, and mag- netic and physiological effects produced as with other sources of elec- tricity. 8i6 Dynamical Electricity. [879- 879. Becqnerel's electrical thermometer.— This consists of a copper and iron wire of many yards in length soldered at their ends, but other- wise insulated from each other by being covered with gutta-percha. The copper wire is cut twice and connected with the binding screws of a galvanometer (fig. 742). One of the solderings is arranged in the place Fig. 742. whose temperature is to be measured. In the figure it is at B at the top of a pole A, and is underneath a hood, which protects it from rain and the sun, but allows air to circulate round it. The other soldering is immersed in mercury contained in a glass tube, and which in turn is placed in a larger cylinder C containing ether. On one side is a very delicate thermometer /, which indicates the temperature of the ether. By means of a small bellows S, a caoutchouc tube and a glass tube, a current of air can be sent through the ether, which being thus vaporised is cooled. If, on the contrary, the temperature of the ether is to be raised a tinplate vessel containing hot water is brought near the cylinder C. These details being known, when the solderings are at the same temperature no current is produced in the circuit, and the galvanometer remains at zero ; but when there is the least difference in temperature, the deflection of the galvanometer tells which of these solderings is the hottest. If it is the one which is immersed in the mercury, the bellows is worked until the ether being cooled the galvanometer reverts to zero* -880] BecquereVs Elect fie Pyrometer. 817 The two solderings being then at the same temperature, the thermometer / at once indicates the temperature in B. Becquerel has applied this instrument to investigations on the tem- perature of the ground at various depths, that of the air at different heights, and also on the temperature of plants and animals. 880. Becquerel's electric pyrometer. — This apparatus is an improved form of one originally devised by Pouillet. It consists (fig. 743) of two Fig. 743. wires, one of platinum and the other of palladium, both two metres in length and a square millimetre in section. They are not soldered at the ends, but firmly tied for a distance of a centimetre with fine platinum wire. The palladium wire is enclosed in a thin porcelain tube : the platinum wire is on the outside, and the whole is enclosed in a larger porcelain tube P. At the end of this is the junction, which is adjusted in the place the temperature of which is to be investigated. At the other end project the platinum and palladium wires ;« and n, which are soldered to two copper wires that lead the current to a magnetometer G. These wires at the junction are placed in a glass tube immersed N N 8r8 Dynamical Electricity. [880- in ice, so that, being both at the same temperature, they give rise to no current. The magnetometer, which was devised by Weber, is nothing more than a large galvanometer. It consists of a magnetised bar ab placed in the centre of a copper frame which deadens the oscillations (848) and rests on a stirrup H, which in turn is suspended to a long and very fine platinum wire. On the stirrup is fixed a mirror M, which moves with the magnet, and gives by reflection the image of divisions traced on a horizontal scale E at a distance. These divisions are observed by a telescope. With this view, before the current passes, the image of the zero of the scale is made to coincide with the micrometer wire of the telescope ; then the slightest deflection of the mirror gives the image of another division, and therefore the angular deflection of the bar (491). This angle is always small and should not exceed 3 or 4 degrees : this is effected by placing, if necessary, a rheostat or any resistance coil, in the circuit. The angular deflection being known, the intensity of the current and the temperature of the junction are deduced from pyrometric tables. These are constructed by interpolation when the strengths are known, which correspond to two temperatures near those to be observed. The indications of the pyrometer extend to the fusing point of the palladium. 881. Peltier's cross. — Peltier found that an electric current, in passing through a conductor, in some cases produces heat, in others cold. He obtained the greatest increase of temperature when the negative current passed from a good conductor of electricity to a bad one — for example, from copper to zinc; and the least increase when the positive current passed in this direction. But when a bar of bismuth and a bar of antimony were soldered together, the temperature of the air sank at the soldering when the positive current passed from the first to the second metal, and rose in the opposite case. This experiment may be made by hermetically fixing in two tubulures in an air thermometer, a com- pound bar consisting of bismuth and antimony soldered together, in such a manner that the ends project on each side. The projecting parts are provided with binding screws, so as to allow a current to be passed through. When the positive current passes from the antimony to the bismuth, the air in the bulb is heated, it expands, and the liquid in the stem sinks ; but if it passes in the opposite direction the air is cooled, it contracts, and the liquid rises in the stem. For this experiment the current must have a certain definite strength, which is found by experi- ment ; it is best regulated by a rheostat (882). These experiments form an interesting illustration of the principle, that whenever the effects of heat are reversed, heat is produced ; and whenever the effects ordinarily produced by heat are otherwise produced, cold is the result. 883] Determinatio7i of Electrical Conductivity. 819 CHAPTER IX. DETERMINATION OF ELECTRICAL CONDUCTIVITY. 882. Rbeostat. — The rheostat is an instrument by which the resistance of any given circuit can be increased or diminished without opening the circuit. As invented by Mr. Wheatstone, it consists of two parallel cylin- ders, one, A, of brass, the other, B, of wood (fig. 744). In the latter there is a spiral groove, which terminates at ^ in a copper ring, to which is fixed the end of a fine brass wire. This wire, which is about 40 yards long, is partially coiled on the groove ; it passe? to the cylinder A, and, after a great number of turns on this cylinder, is fixed at the extremity e. Two binding screws, n and 0, con- nected with the battery, communi- cate by two steel plates ; one with the cylinder A, the other with the ring a. When a current enters at 0^ it simply traverses that portion of the wire rolled on the cylinder B, where the windings are insulated by the grooves ; passing thence to the cylinder A, which is of metal, and in contact with the wire, the current passes directly to ;//, and thence to n. Hence, if the length of the cur- rent is to be increased, the handle, d, must be turned from right to left. If, on the contrary, it is to be dimin- Fig. 744. ished, the handle is to be fixed on the axis, c, and turning then from left to right, the wire is coiled on the cylinder A. The length of the circuit is indicated in feet and inches, by two needles, at the end of the apparatus not seen in the figure, which are moved by the cylinders A and B. 883. Betermination of the resistance of a conductor. Reduced lengrtli. — If in the circuit of a constant element a tangent compass be interposed, a certain deflection of the needle will be produced. If, then, different lengths of copper wire of the same diameter be successively interposed, corresponding deflections will in each case be produced. Let us suppose, that in a particular case the tangent of the angle of deflection (775) observed with the element and tangent compass alone was i -88, and that when 5,40, 70, and 100 yards of copper wire were successively placed in the circuit, the tangents of the corresponding deflections were 0-849, 0*172, 0*105, and 0*074. Now, in this experiment, the total resistance consists of two components ; the resistance offered by the element and the tangent compass, and the resistance offered by the wire in each case. The former resistance may be supposed to be equal to the resistance of 820 Dynamical Electricity. -. [883- X yards of copper wire of the same diameter as that used, and then we have the following relations : Length of wire. Tangent of angle of deflection. X yards i-88 ^+5 » 0'849 ;r + 40 „ . . 0-172 ;ir + 7o „ 0-105 x-v 100 „ 0-074 If the intensities of the currents are inversely as the resistances — that is, as the lengths of the circuits — the proportion must prevail, X : ;ir+5=o-849 : 1-886 ; from which ;r = 4-i i. Combining, in like manner, the other observations, we get a series of numbers, the mean of which is 4-08. That is, the resistance offered by the element and galvanometer is equal to the resist- ance of 4-08 yards of such copper wire, and this is said to be the reduced length of the element and galvanometer in terms of the copper wire. It is of great scientific and practical importance to have a U7iit or standard of comparison of resistance, and numerous such have been pro- posed. Jacobi proposed the resistance of a metre of a special copper wire a millimetre in diameter. Copper is however ill adapted for the purpose, as it is difficult to obtain pure. Matthiessen has proposed an alloy of gold and silver, containing two parts of gold and one of silver ; its con- ducting power is very little affected by impurities in the metals, by an- nealing, or by moderate changes of temperature. Siemens' unit is a metre of pure mercury, having a section of a square millimetre. It is 0-9536 of an Ohmad or BA unit (884). The Varley U7iit, which is used in telegraphic work, is a standard mile of a special copper wire i of an inch in diameter. Matthiessen has proposed instead of this a mile of pure annealed copper wire j\ in. in diameter. 884. British Association unit of electrical resistance. — The great importance, both theoretically and practically, of having some uniform standard for the comparison of electrical resistance has for years past engaged the attention of a committee of the British Association, which includes the principal electricians in this country. Their labours have resulted in the adoption of a standard which has received the approval of men of science both in this and other countries. The following account of this unit, which it is proposed to call the Ohmad or BA unit, has been kindly furnished by the secretary to the Committee, Mr. Fleeming Jenkin. It represents a convenient multiple of the so-called absolute unit of electrical resistance. The word ' absolute,' as here used, does not imply accuracy of construction, but is intended to express that the measurement of electrical resistance is made by a unit which bears a definite relation to the fundamental units of time, mass, and space only ; instead of being a mere comparison with* the resistance of some particular piece of metal -884] British Association Unit of Electrical Resistance. 821 arbitrarily chosen as the unit. In a similar sense a square foot and a cubic foot may be called absolute units of surface and capacity, an acre and a gallon arbitrary units. It seems strange at first that the unit of electrical resistance can be measured by reference to time, mass, and space only, without reference to the specific qualities of any material ; but our chief knowledge of electric phenomena is derived from an observation of mechanical effects, and we need, therefore, feel no surprise at learning that those phenomena can be measured in purely mechanical units. The voltaic current, electromotive force, and resistance, quantity, and capacity can all be so measured in more than one way. The electromagnetic measurement of current is determined by the following considerations. If /be the force exerted by a current of strength C, and length L, on a pole of a magnet, 7n being the magnetic strength of that pole, and K its distance from the current, it is found by experiment that / varies as .^^, so that C = K •; , where k is some constant. Now if the unit current be that which L,7n in unit length of circuit exerts unit force on a unit pole at unit distance, we get K = I, and the equation for C becomes -4§- ■ -y ■ • ■ ^'^ and C may be measured by the expression J- — Again, for the resistance we get W where W is the work done in the time / by a current C flowing in a circuit of the resistance r. Now, the first equation allows us to measure a current in terms of a force / two lengths K and L, and a magnitude ni, which again depends on measurements of force and length only, so that we here have a current measured in mechanical units in virtue of a ma- thematical relation between the phenomena produced by the current and the mechanical units. It follows from the equation that the unit current will be that of which each unit length exerts a unit force on a unit pole at unit distance. The second equation, like the first, is deduced from obser- vation. The resistance of a circuit is found to be proportional to the work done by a current in that circuit, and inversely proportional to the square of the current and to the time during which it acts ; any two circuits for which — 2> ^s equal have equal resistances ; if this quantity for circuit A is double what it is for circuit B, then the resistance of circuit A is double that of circuit B. Therefore, we have exactly the same ground for saying that — measures the resistance of the circuit that we have for saying c^ measures the contents of a square with sides equal to ^. In equation 2, 822 Dynamical Electricity. [884- W, the work, is essentially a mechanical measurement, for, though gene- rally observed in the form of heat, it is by Joule's equivalent referred to the mechanical unit of energy or work. Moreover from Ohm's law C= - (3) further measures electromotive force in terms of C and r, and Faraday's discovery expressed by equation where Q is the quantity of electricity conveyed by the current C in the time /, shows how quantity is measured in the same mathematical series. Although nothing can be simpler than the mathematical conceptions here involved, the practical measurement of resistance, or any other ot the above magnitudes, by direct reference to force, work, time, etc., in- volves much labour, so that for each kind of measurement it is necessary for practical use to construct a standard which affords the desired mea- sure by direct and simple comparison with the thing measured. Thus, a Frenchman to measure wine does not work out the cubic contents of a bottle, but measures the number of litres by reference to a standard Htre, which is a simple decimal submultiple of the cubic metre. In like manner practical measurements of resistance are made by comparison with the Ohm or BA unit prepared to represent a simple decimal multiple (ten million times) the absolute electromagnetic unit ; the metre, the gramme, and the second of time were taken as fundamental units by the committee, and on which is approximately equal to 10^ metre seconds. Great care has been taken in the determination and construction of the standard, which is represented by several coils of wires of various metals and alloys, and by tubes of mercury which have all been adjusted to represent one and the same standard unit, the variety of materials being intended as a safeguard against possible alteration in resistance of one or more of the coils or tubes. Certified copies of the unit, consisting of coils of platinum-silver wire, are issued by the Committee. It is intended that similar standards for the measurement of currents, electromotive force, quantity, and capacity will also be issued. The Ohmad or Ohm is 1-0486 of a Siemens' unit (883) ; that is, it is equal to the resistance of a prism of pure mercury i square millimetre in section and i -0486 metre in length at the temperature 0°. 885. Equivalent conductors. — The resistance of a conductor depends, as we have seen ijT])^ on its length, section, and conductivity. Two conductors, C and C, whose length, conductivity, and section are re- spectively \ \', K k', w w', would offer the same resistance, and might be substituted for each other in any voltaic circuit, without altering its intensity, provided that — = — - ; and such conductors are said to be equivalent to each other. An example will best illustrate the application of this principle. It is required to know what length of a cylindrical copper wire 4 mm. -886] Wheatstone's Bridge, ' 823 in diameter would be equivalent to 12 yards of copper wire i mm. in diameter. Let A = 1 2 the length of the copper wire i mm. in diameter, and A' the length of the other wire ; then since in this case the material is the same, \ X' the conductivity is the same, and the equation becomes - = — . Now it) to the sections of the wires are directly as the squares of the diameters, and 12 X' hence we have - = — ^ , or X' = 12 x 16 = 192. That is 192 yards of copper wire 4 mm. in thickness would only offer the same resistance as 12 yards of copper wire i mm. in thickness. How thick must an iron wire be which for the same length shall offer the same resistance as a copper wire 2*5 mm. in diameter ? Here the length being the same, the expression becomes »fa; = KV. or since the sections are as the squares of the diameters, K(P' = K'd'. The conductivity of copper is unity, and that of iron 0*138. Hence we have 2-5^ = ^/''^ x 0-138, or ^'^ = 6-25 -^-0-138 = 45-3 mm., or d' = 6'y mm. That is, any length of a copper wire 2*5 mm. in diameter might be replaced by iron wire of the same length, provided its diameter were 67 mm. 886. Wheatstone's bridge. — The various methods of determining the electrical conductivity of a body consist essentially in ascertaining the ratio between the resistance of a certain length of the conductor in question, having a given section, to that of a known length of a known section of some substance taken as standard. The most convenient- method of ascertaining experimentally the ratio between the resistance of two conductors, is by a method known as that of Wheatstone^s bridge^ the general principle of which may be thus stated : — The conductors, which may be denoted by AB and BC, are connected end to end as shown in fig. 745, and one end of each is also connected Fig. 745- with a battery, say the end A of AB with the positive pole, and the end C of BC with the negative pole ; the ends that are in connection with the battery are likewise connected together by another conductor AB'C. A current will thus pass from A to C by each of the two paths ABC and AB'C, and there will be a gradual fall of potential in passing from A to C along either path, so that for every point in the conductor AB and BC, there is a point in the wire AB'C which has the same potential. If one end of a galvanometer wire BGB' be connected with the*point of junction B, the point of AB'C which has the same potential as the point B, can be found by applying the other end of the galvanometer wire to it, and shifting 824 Dynamical Electricity. [886- the point of contact towards A or C until the galvanometer shews no de- flection. Let B be the point so found ; the fact that when it is connected with B by the bridge BGB' no current passes from one to the other, proves that the potential at B' is the same as the potential at B. From this it follows, that if r and r' are the resistances of AB and BC re- spectively, and s and s^ the resistances of AB' and B'C, r \ r' = s \ s\ If the conductor AB'C is a wire of uniform material and diameter, the ratio of the resistances s and s^ will be the ratio of the lengths of the corre- sponding portions of wire, and can therefore be at once readily ascertained. To prove this, let MN, NO, MN' and N'O' (fig. 746) be taken in the Q 1 > X a' s r r' ^~~"^^^ (y JM Fig. 746. same straight Hne, proportional respectively to the several resistances r, r^y Jj s^ ; and let MP be drawn at right angles to O'MO of a length proportional to the difference of potential between the points A and C. Then if the straight lines PO and PO' be drawn, the potential at N (the points of junction of the conductor whose resistances r and r^ are to be compared, the point corresponding to B in the previous figure) will be given by the length of the hne NQ, drawn from N at right angles to NO; and the point N' (corresponding to B' in the previous figure) where the potential is the same as at N will be found by drawing QQ^ parallel to 00', and letting fall from Q' the perpendicular Q'N' upon O'M. The geometry of the figure gives obviously r + r' MP J + J, MP' and therefore since NQ = N^Qp 887. Determination of the internal resistance of an element. — The following is a method of determining the internal resistance of an element. A circuit is formed consisting of one element, a rheostat and a galvanometer, and the strength C is noted on the galvanometer. A second element is then joined with the first, so as to form one of double the size, atid therefore half the resistance, and then by adding a length, /, of the rheostat wire, the strength is brought to what it originally was. Then if E is the electromotive force, and R the resistance of an element, r, the resistance of the galvanometer and the other parts of the circuit j -888] Electrical Conductivity. 825 the strength C in the one case is C and in the other : R + r ^R + r + /' and since the strength in both cases is the same, R = 2/. 888. Slectrical conductivity. — We can regard conductors in two aspects, and consider them as endowed with a greater or less faciUty for allowing electricity to traverse them, a property which is termed conduc- tivity ; or we may consider conductors interposed in a circuit as offering an obstacle to the passage of electricity — that is, a resistance which it must overcome. A good conductor offers a feeble resistance, and a bad con- ductor a great resistance. Conductivity and resistance are the inverse of each other. The conductivity of metals has been investigated by many physicists by methods analogous in general to that described in the preceding para- graph, and very different results have been obtained. This arises mainly from the different degrees of purity of the specimens investigated, but their molecular condition has also great influence. Matthiessen finds the difference in conductivity between hard-drawn and annealed silver wire to amount to 8-5, for copper 2*2, and for gold 1-9 per cent. The following are results of a series of careful experiments by Matthiessen on the electrical conductivity of metals at 0° C. compared with silver as a standard : — Silver . loo-o Iron . . 1 6-8 Copper . 99-9 Tin . . . . 131 Gold 8o-o Lead . • 8-3 Aluminium 56-0 German Silver . 77 Sodium . 37*4 Antimony . 4-6 Zinc 29-0 Mercury 1-6 Cadmium. 237 Bismuth 1-2 Potassium 20-8 Graphite 0-07 Platinum . i8-o The conductivity of metals is diminished\y^ an increase in. temperature The law of this diminution is expressed by the formula K-< = Kr„ (i —at + bt^) ; where r, and k„ are the conductivities at t and 0° respectively, and a and b are constants, which are probably the same for all pure metals. For ten metals investigated by Matthiessen he found that the conductivity is expressed by the formula K, =K„ (i -0-0037647^ + 0-00000834/2). Liquids are infinitely worse conductors than metals. The conductivity of a solution of one part of chloride of sodium in 100 parts of water is 30050000 ^^^^ °f copper. In general acids have the highest and solutions of alkalies and neutral salts the lowest conductivity. Yet, in solutions, the conductivity does not increase in direct proportion to the quantity of salt dissolved. The following is a list of the conductivity of a few liquids as compared with that of pure silver : — N N 3 826 Dynamical Electricity. [888- Pure silver 100,000,000-00 Nitrate of copper, saturated solution 8-99 Sulphate of copper ditto 5*42 Chloride of sodium ditto 31-52 Sulphate of zinc ditto 577 Sulphuric acid, I -lo sp. gr. . 99-07 „ i-24sp. gr. . 132-75 „. „ i-4osp.gr. . 90-75 Nitric acid, commercial 88-68 Distilled water o-oi Liquids and fused conductors increase in conductivity by an increase of temperature. This increase is expressed by the formula ff = fo (l +^0> and the values of a are considerable. Thus, for a saturated solution of sulphate of copper, it is 0-0286. By most physicists the conductivity of liquids has been regarded as a purely electrolytic conductivity, that is, due to chemical decomposition. Yet Faraday, in stating his law of electrolytic decomposition, had an- nounced that it was subject to certain restrictions in cases in which liquids could conduct electricity without being decomposed. Foucault has recently shown by delicate experiments, that liquids have a peculiar conductivity, «^>^jj/Vrt/ conductivity analogous to that of metals. This is, however, much less than the electrolytic conductivity, but may have a distinct influence on the chemical effects of currents and on Faraday's law. An influence of light upon electrical conductivity has been ascertained to exist in the case of selenium. A thin strip of this metalloid, about 38 mm. in length by 13 in breadth, was provided at the ends with con- ducting wires and placed in a box with a draw lid. The selenium, having been carefully balanced in a Wheatstone's bridge, was exposed to diffused light by withdrawing the lid, when the resistance at once fell in the ratio of 1 1 to 9. On exposure to the various spectral colours, after having been in the dark, it was found to be most affected by the red ; but the maximum action was just outside the red, where the resistance fell in the ratio of 3 to 2. Momentary exposure to the light of a gas lamp . or even to that of a candle, causes a diminution of resistance. Exposure to full sunlight diminished the resistance to one half. The effect produced on exposure to light is immediate, while recurrence to the normal state takes place more slowly. A vessel of hot water placed near the strip produced no effect, and hence the phenomenon cannot be due to heat, but there appear to be certain rays which have the power of producing a molecular change in the selenium by which its conductivity is increased. 889. Betermination of electromotive force. IXHieatstone's metbod. — In the circuit of the element whose electromotive force is to be deter- mined, a tangent compass and a rheostat are inserted, the latter being so from which we have -890] Siemens' Electrical Resistance Thermometer. 827 arranged that the strength C of the current is a definite amount ; for example, the galvanometer indicates 45°. By increasing the amount of the rheostat wire by the length /, a diminished strength, c (for instance, 40°) is obtained. A second standard element is then substituted for that under trial, and by arranging the rheostat, the strength of the current is first made equal to C, and then, by the addition of / lengths of the rheostat, is made = c. Then if E and E^ are the two electromotive forces, R and R^, their re- sistances when they have the intensity I, and / and /^ the lengths added, we have Trial element. Standard element. ^"R ^"r; r^^^ C- ^1 ■ R + / Ri + ^x' Hence the electromotive forces of the elements compared are directly as the lengths of the wire interposed. Another method is described by Wiedemann. The two elements are connected in the same circuit with a tangent galvanometer, or other appa- ratus for measuring strength, first in such a manner that their currents go in the same direction, and, secondly, that they are opposed. Then if the electromotive forces are E and E', their resistances R and R'', the other resistances in the circuits r, while C, is the intensity when the elements are in the same direction, and Cj the intensity when they go in opposite directions, then, r _ E + E' '"R + R' + r' E — E' and Cd = T5 — ^7 — ) R + R' + r whence ^,^ E(C.~Ca) ^ • 890. Siemens' electrical resistance tbermometer. — Supposing in a Wheatstone's bridge arrangement, after the ratio r \r^ = s \ s^ has been established, the temperature of one of the coils, r, for instance, be in- creased, the above ratio will no longer prevail, for the resistance of r. will have been altered by the temperature, and the ratio of s and Jj, must be altered so as to produce equivalence. On this idea Siemens has based a mode of observing the temperature of places which are difficult of direct access. He places a coil of known resistance in the particular locality whose temperature is to be observed; it is connected by means of long good conducting wires with the place of observation, where it forms part of a Wheatstone's bridge arrangement. The resistance of 828 Dynamical Electricity. [890- the coil is known in terms of the rheostat, and by preliminary trials it has been ascertained how much additional wire must be introduced to balance a given increase in the temperature of the resistance coil. This being knowft, and the apparatus adjusted at the ordinary temperature, when the temperature .of the resistance coil varies, this variation in either direction is at once known by observing the quantity which must be brought in or out of the rheostat to produce equivalence. This apparatus has been of essential service in watching the tempera- ture of large coils of telegraph wire, which, stowed away in the hold ot vessels, are very liable to become heated. It might also be used for the continuous and convenient observation of underground and submarine temperatures. If a coil of platinum wire were substituted for the copper, the apparatus could be used for watching the temperature of the interior of a furnace. 891. Derived currents. — In fig. 747 the current from a Bunsen's element traverses the wire rqpnm : let us take the case in which any two Fig. 747. points of this circuit, 71 and q, are joined by a second wire, nxq. The current will then divide at the point q into two others, one of which goes in the direction qpnm, while another takes the direction qxjtm. The two points q and n from which the second conductor starts and ends are called the points of derivation, the wire qpn and the wire qxn are derived wir-es. The currents which traverse these wires are called the derived or partial currerits ; the current which traversed the circuit rqpnm before it branches is the primitive current ; and the name principal curre7it is given to the whole of the current which traverses the circuit when the derived wire has been added. The principal current is stronger than the primitive one, because the interposition of the wire qxn lessens the total resistance of the circuit. If the two derived wires are of the same length and the same section, their action would be the same as if they were juxtaposed, and they might be replaced by a single wire of the same length but of twice the section, and therefore with half the resistance. Hence the current would divide into two equal parts along the two conductors. When the two wires are of the same length but of different sections, the current would divide unequally, and the quantity which traversed each wire would be proportional to its section, just as when a river divides into two branches, the quantity of water which passes in each branch is proportional to its dimensions. Hence the resistance of -891] Derived Currents. 829 the two conductors joined would be the same as that of a single wire of the same length, the section of which would be the sum of the two sections. If the two conductors qpn and qxn are different, both in kind, length, and section, they could always be replaced by two wires of the same kind and length, with such sections that their resistances would be equal to the two conductors ; in short, they might be replaced by equivalent conductors. These two wires would produce in the circuit the same effect as a single wire, which had this common length, and whose section would be the sum of the sections thus calculated. The current divides at the junction into two parts proportional to these sections, or inversely as the resistances of the two wires. Suppose, for instance, qp7i is an iron wire 5 metres in length and 3 mm square in section, and qxn a. copper wire. The first might be replaced by a copper wire a metre in length, whose section would be f x i (taking the conductivity of copper at 7 times that of iron) or /g square mm. The second wire might be replaced by a copper wire a metre in length with a section of | square mm. These two wires would present the same resistance as a copper wire a metre in length, and with a section of 3^ + | = 3Y5 square millimetres. The principal current would divide along the wires in two portions, which would be as /g : |. The most important laws of divided circuits are as follows : — i. TAe sum of the strengths in the divided parts of a circuit is equal to the strength of the principal current. ii. The strengths of the currents in the divided parts of a circuit are inversely as their resistances j or, what is the same, the division of a current into partial currents which lie between two points, is directly as the respec- tive conductivities of these branches. And as problems on divided circuits frequently occur in telegraphy^ the following formulce, which include these laws, are given for a simple case. If C be the strength of the current in the undivided part of the circuit rqpnm, and if c is the strength in one branch (say -in the above figure qpn) and c' in qx7i ; if R, r, and r^ are the corresponding resistances, the electro- motive force being E, then C = E(^ + ^i ) Rr + Rr^ + rr^ Rr + Rr^ + rrl Rr + R^i + rr^ The resistance R^ of the whole circuit through which the current cir- culates is R^ = R + J*^^„, and therefore the total resistance of the derived cnrxtnts qpn and qxn is rr. 830 Dynamical Electricity, [892- CHAPTER X. ANIMAL ELECTRICITY. 892. Muscular currents. — The existence of electrical currents in living muscle was first indicated by Galvani, but his researches fell into oblivion after the discovery of the Voltaic pile, which was supposed to explain all the phenomena. Since then, NobiH, Matteucci, and others, especially, in late years, Du Bois Reymond, have shown that electric currents do exist in living muscles and nerves, and have investigated their laws. For investigating these currents it is necessary to have a delicate gal- vanometer, and also electrodes which will not become polarised or give a current of their own, and which will not in any way alter the muscle when placed in contact with it ; the electrodes which satisfy these con- ditions best are those of Du Bois Reymond, as modified by Bonders. Each consists of a glass tube, one end of which is narrowed and stopped by a plug of paste made by moistening china-clay with a half per cent, solution of common salt ; the tube is then partially filled with a saturated solution of sulphate of zinc, and into this dips the end of a piece of thoroughly amalgamated zinc wire, the other end of which is connected by a copper wire with the galvanometer; the moistened china-clay is a conducting medium which is perfectly neutral to the muscle, and amal- gamated zinc in solution of sulphate of zinc does not become polarised. 893. Currents of muscle at rest. — In describing these experiments the surface of the muscle is called the natural longitudinal section ; the tendon, the natural transverse section; and the surfaces obtained by cutting the muscle longitudinally or transversely are respectively the artificial longitudinal and artificial transverse sections. If a living irritable muscle be removed from a recently killed frog, and the clay of one electrode be placed in contact with its surface, and of the other with its tendon, the galvanometer will indicate a current from the former to the latter ; showing, therefore, that the surface of the muscle is positive with respect to the tendon. By varying the position of the electrodes, and making various artificial sections, it is found — I. That any longitudinal section is positive to any transverse. ■ 2. That any point of a longitudinal section nearer the middle of the muscle is positive to any other point of the same section farther from the centre. 3. In any artificial transverse section any point nearer the periphery is positive to one nearer the centre. 4. The current obtained between two points in a longitudinal or in a transverse section is always much more feeble than that obtained between two different sections. 5. No current is obtained if two points of the same section equidistant from its centre be taken. -893] Animal Electricity. 831 6. To obtain these currents it is not necessary to employ a whole muscle, or a considerable part of one, but the smallest fragment that can "be experimented with is sufficient. 7. If a muscle be cut straight across, the most powerful current is that from the centre of the natural longitudinal section to the centre of the artificial transverse ; but if the muscle be cut across obhquely, as in Fig. 748. fig. 748, the most positive point is moved from c towards b, and the most negative from d towards a {' Currents of inclination^). To explain the existence and relations of these muscular currents, it may be supposed that each muscle is made up of regularly disposed electromotor elements, which may be regarded as cylinders whose axis is parallel to that of the muscle, and whose sides are charged with positive and their ends with negative electricity ; and, further, that all are sus- pended and enveloped in a conducting medium. In such a case (fig. 749) it is clear that throughout most of the muscle the positive electricities of the opposed surfaces would neutralise one another, as would also the negative charges of the ends of the cylinders ; so that, so long as the muscle was intact, only the charges at its sides and ends would be left free to manifest themselves by the production of electromotive pheno- mena; the whole muscle being enveloped in a conducting stratum, a current would constantly be passing from the longitudinal to the trans- verse section, and, a part of this being led off by the wire circuit, would manifest itself in the galvanometer. This theory also explains the currents between two different points on the same section ; the positive charge at b, for instance (fig. 749), would ^^H ^^H ^^H ^^H ^^B + + + + + ^+ ^+ ^+ ^+ ^+ ■+ 4- -*- -4- + ^^H ^^H ^^B ^^H ^^H + + + + + ^^H ^^H ^^H ^^M ^^M + + + + -f- ^^^ ^^' ^^^ ^^^ ^^^ + + + + + tt h Fig. 749. have more resistance to overcome in getting to the transverse section than that at d, therefore it has a higher tension ; and if b and d are connected by the electrodes, b will be found positive to d, and a current will pass from the former to the latter. 832 Dynamical Electricity. [893- What are called currents of inclination are also explicable on the above hypothesis, for the obhque section can be represented as a number of elements arranged as in fig. 750, so that both the longitudinal surfaces and the ends of the cylinders are laid bare, and it can thus be regarded as a sort of obhque pile whose positive pole is towards b and its negative Fig. 750. at a, and whose current adds itself algebraically to the ordinary current and displaces its poles as above mentioned. . A perfectly fresh muscle, very carefully removed, with the least possible contact with foreign matters, sometimes gives almost no current loetween its different natural sections, and the current always becomes more marked after the muscle has been exposed a short time ; nevertheless, the phenomena are vital, for the currents disappear completely with the life of the muscle, sometimes becoming first irregular or even reversed in direction. 894. Rheoscoplc frog*. Contraction \irlthout metals. — The exist- ence of the muscular currents can be manifested without a galvanometer, by using another muscle as a galvanoscope. Thus if the nerve of one living muscle be dropped suddenly on another living muscle, so as to come in contact with its longitudinal and transverse sections, a contraction of the first muscle will occur, due to the stimulation of its nerve by the passage through it of the electric current derived from the surface of the second. 895. Currents in active muscle. — When a muscle is- made to con- tract there occurs a sudden diminution of its natural electric current, as in- dicated by the galvanometer. This is so instantaneous that, in the case of a single muscular contraction it does not overcome the inertia of the needle of the galvanometer ; but if the contractions be made to succeed one another very rapidly — that is, if the muscle be tetanised (778) — then the needle swings steadily back towards zero from the position in which the current of the resting muscle had kept it, often gaining such momen- tum in the swing as to pass beyond the zero point, but soon reverting to some point between zero and its original position. The negative variation in the case of a simple muscular contraction can, however, be made manifest by using another muscle as a rheoscope; if the nerve of this second muscle be laid over the first muscle in such a position that the muscular current passes through it, and the first muscle be then made to contract, the sudden alteration in the intensity of its current stimulates the nerve laid on it (jjZ), and so causes a contraction of the muscle to which the latter belongs. -897] Electrical Fish. 833 The same phenomena can be demonstrated in the muscles of warm- blooded animals; but with less ease, on account of the difficulty of keep- ing them alive after they are laid bare or removed from the body. Experiments made by placing electrodes outside the skin, or passing them through it, are inexact and unsatisfactory. 896. Electric currents In nerve. — From nerves the same electro- motor indications can be obtained as from muscles ; at least, as far as their smaller size will permit; the currents are more feeble than the muscular ones, but can be demonstrated by the galvanometer in a similar way. Negative variation has been proved to occur in active nerve as in active muscle. The effect of a constant current passed through one part of a nerve on the amount of the normal nerve current, measured at another part, has already been described (Chap. III., Electrotonus). 897. Slectrical flsli. — Electrical fish are those fish which have the remarkable property of giving, when touched, shocks like those of the. Leyden jar. Of these fish there are several species, the best known of which are the torpedo, the gymnotus, and the silurus. The torpedo, which is very common in the Mediterranean, has been carefully studied by MM. Becquerel and Breschet in F>ance, and by M. Matteucci in Italy. The gymnotus has been investigated by Humboldt and Bonpland in South America, and in England by Faraday, who had the opportunity of examining live specimens. The shock which they give serves both as a means of offence and of defence. It is purely voluntary, and becomes gradually weaker as it is repeated and as these animals lose their vitahty, for the electrical action soon exhausts them materially. The shock is very violent. According to Faraday the shock which the gymnotus gives is equal to that of a battery of 15 jars exposing a coating of 25 square feet, which explains how it is that horses frequently give way under the repeated attacks of the gymnotus. Numerous experiments show that these shocks are due to ordinary electricity. For if, touching with one hand the back of the animal, the belly is touched with the other, or with a metal rod, a violent shock is felt in the wrists and arms : while no shock is felt if the animal is touched with an insulating body. Further, when the back is connected with one end of a galvanometer wire and the belly with the other, at each discharge the needle is deflected, but immediately returns to zero, which shows that there is an instantaneous current ; and, moreover, the direction of the needle shows that the current goes from the back to the belly of the fish. Lastly, if the current of a torpedo be passed through a helix, in the centre of which is a small steel bar, the latter is magnetised by the passage of a discharge. By means of the galvanometer, Matteucci has established the follow- ing facts : I. When a torpedo is lively, it can give a shock in any part of its body ; but as its vitality diminishes, the parts at which it can give a shock are nearer the organ which is the seat of the development of electricity. 834 Dyjiamical Electricity. [897- 2. Any point of the back is always positive as compared with the cor- responding point of the belly. 3. Of any two points at different distances from the electrical organ, the nearest always plays the part of positive pole, and the furthest that of negative pole. With the belly, the reverse is the case. The organ where the electricity is produced in the torpedo is double, and formed of two parts symmetrically situated on the two sides of the head, and attached to the skull bone by the internal face. Each part consists of nearly parallel lamellae of connective tissue inclosing small chambers, in which lie the so-called electrical ptates^ each of which has a final nerve ramification distributed on one of its faces. This face, on which the nerve ends, is turned the same way in all the plates, and when the discharge takes place is always negative to the other. Matteucci investigated the influence of the brain on the discharge. For this purpose he laid bare the brain of a living torpedo, and found that the first three lobes could be irritated without the discharge being produced, and that when they were removed the animal still possessed the faculty of giving a shock. The fourth lobe, on the contrary, could not be irritated without an immediate production of the discharge ; but if it was removed, all disengagement of electricity disappeared, even if the other lobes re- mained untouched. Hence it would appear that the primary source of the electricity elaborated is the fourth lobe, whence it is transmitted by means of the nerves to the two organs described above, which act as multipliers. In the silurus the head appears also to be the seat of the electricity ; but in the gymnotus it is found in the tail. 898. Application of electricity to medicine. — The first applications of electricity to medicine date from the discovery of the Leyden jar. Nollet and Boze appear to have been the first who thought of the applica- tion, and soon the spark and electrical frictions became a universal panacea; but it must be admitted that subsequent trials did not come up to the hopes of the experimentalists. After the discovery of dynamic electricity Galvani proposed its appli- cation to medicine : since which time many physicists and physiologists have been engaged upon this subject, and yet there is still much uncer- tainty as to the real effects of electricity, the cases in which it is to be applied, and the best mode of applying it. Practical men prefer the use of currents to that of statical electricity, and, except in a few cases, dis- continuous to continuous currents. There is, finally, a choice between the currents of the battery and those of induction currents ; further, the effects of the latter differ, according as induction currents of the first or second order are used. In fact, since induction currents, although very intense, have a very feeble chemical action, it follows that when they traverse the organs, they do not produce the chemical effects of the current of the battery, and hence do not tend to produce the same disorganisation. Further, in electrifying the muscles of the face, induction currents are to be pre- ferred, for Dr. Duchenne has found that these currents only act feebly on the retina, while the currents of the battery act energetically on this organ. -898] Applicatio7i of Electricity to Medicine. 835 and may affect it dangerously, as serious accidents have shown. There is a difference in the action of induced currents of different orders : for while the primary induced current causes lively muscular actions, but has little action on the cutaneous sensibility, the secondary induced current, on the contrary, increases the cutaneous sensibility to such a point, that its use ought to be proscribed to persons whose skin is very irritable. Hence electrical currents should not be applied in therapeutics without a thorough knowledge of their various properties. They ought to be used with great prudence, for their continued action may produce serious accidents. Matteucci, in his lectures on the physical phenomena of living bodies, expresses himself as follows : * In commencing, a feeble current must always be used. This precaution now seems to me the more im- portant, as I did not think it so before seeing a paralytic person seized with almost tetanic convulsions under the action of a current formed of a single element. Take care not to continue the application too long, especially if the current is energetic. Rather apply a frequently-inter- rupted current than a continuous one, especially if it be strong ; but after 20 or 30 shocks at most, let the patient take a few moments' rest.' Of late years, however, feeble continuous currents have come more into use. They are frequently of great service when applied skilfully so as to throw the nerves of the diseased part into a state of cathelectro- tonus or analectrotonus, according to the end which is wished for in any given case. 836 Meteorology. [899- ELEMENTARY OUTLINES i OF METEOROLOGY AND CLIMATOLOGY. METEOROLOGY. 899. Meteorologry. — The phenomena which are produced in the at- mosphere are called fneteors ; and meteorology is that part of physics which is concerned with the study of these phenomena. A distinction is made between aerial meteors, such as winds, and hurricanes, and whirlwinds ; aqueous meteors, comprising fogs, clouds, rain, dew, snow, and hail ; and luminous meteors, as lightning, the rain- bow, the aurora borealis. Aerial Meteors. 900. Birection and velocity of winds. — Winds are currents moving in the atmosphere with variable directions and velocities. There are eight principal directions in which they blow — north, north-east, east, south-east, south, south-west, west, and north-west. Mariners further divide each of the distances between these eight directions into four others, making in all 32 directions, which are csW&d. points or rhumbs. A figure of these '32 rhumbs on a circle, in the form of a star, is known as the mariner's card. The direction of the wind is determined by means of vanes, and its velocity by means of the anetnometer. There are several forms of this instrument ; the most usual consists of a small vane with fans, which the wind turns ; the velocity is deduced from the number of turns made in a given time, which is measured by means of an endless screw and wheel- work. In our climate the mean velocity is from 18 to 20 feet in a second. With a velocity of 6 or 7 feet, the wind is moderate ; with 30 or 35 feet, it is fresh ; with 60 or 70 feet, it is strong ; with a velocity of 85 to 90 feet, it is a tempest ; and, from 90 to 120, it is a hurricane. We have but few experimental results as to the laws of the intensity of the force which wind exerts on surfaces exposed to its action. Smeaton gives a table compiled by Rouse from a considerable number of facts and experiments ; he observes that these experiments do not deserve as much confidence for velocities above as for velocities below 50 miles an -902] Meteorology. 837 hour. The numerical values for the pressures given in this table seem to have been calculated on the supposition that the pressure is proportional to the square of the velocity of the wind ; they are approximately given by the formula /= 0-002214 V^ where V being the velocity of the wind in feet per second,/ is the pres- sure in pounds per square foot. 901. Causes of winds. — Winds are produced by a disturbance of the equilibrium in some part of the atmosphere ; a disturbance always resulting from a difference in temperature between adjacent countries. Thus, if the temperature of a certain extent of ground becomes higher, the air in contact with it becomes heated, it expands and rises towards the higher regions of the atmosphere ; whence it flows, producing winds which blow from hot to cold countries. But at the same time the equi- librium is destroyed at the surface of the earth, for the barometric pressure on the colder adjacent parts is greater than on that which has been heated, and hence a current will be produced with a velocity dependent on the difference between these pressures ; thus two distinct winds will be produced, an upper one setting outwards from the heated region, and a lower one setting i7iwards towards it. 902. Regrular, periodical, and variable winds. — According to the more or less constant directions in which winds blow, they may be classed as regular, periodical, and variable winds. i. Regular winds are those which blow all the year through in a virtually constant direction. These winds, which are also known as the trade winds, are uninterruptedly observed far from the land in equatorial regions, blowing from the north-east to the south-west in the northern hemisphere, and from the south-east to the north-west in the southern hemisphere. They prevail on the two sides of the equator as far as 30° of latitude, and they blow in the same direction as the apparent motion of the sun — that is, from east to west. The air above the equator being gradually heated, rises as the sun passes round from east to west, and its place is supplied by the colder air from the north or south. The direction of the wind, however, is modified by this fact, that the velocity which this colder air has derived from the rotation of the earth — namely, the velocity of the surface of the earth at the point from which it started — is less than the velocity of the surface of the earth at the point at which it has now arrived ; hence the currents acquire in reference to the equator, the constant direction which consti- tutes the trade winds. ii. Periodical winds are those which blow regularly in the same direc- tion at the same seasons, and at the same hours of the day : the monsoon, simoom, and the land and sea breeze are examples of this class. The name monsoon is given to winds which blow for six months in one direc- tion and for six months in another. They are principally observed in the Red Sea and in the Arabian Gulf, in the Bay of Bengal and in the Chinese Sea. These winds blow towards the continents in summer, and in a contrary direction in winter. The simoom is a hot wind which blows 8sS Winds, [902- over the deserts of Asia and Africa, and which is characterised by its high temperature and by the sands which it raises in the atmosphere and carries with it. During the prevalence of this wind the air is darkened, the skin feels dry, the respiration is accelerated, and a burning thirst is experienced. This wind is known under the name of sirocco in Italy and Algiers, where it blows from the great desert of Sahara. In Egypt, where it prevails from the end of April to June, it is called kamsin. The natives of Africa, in order to protect themselves from the effects of the too rapid perspiration occasioned by this wind, cover themselves with fatty substances. The /andcind sea breeze is a wind which blows on the sea coast, during the day from the sea towards the land, and during the night from the land to the sea. For during the day the land becomes more heated than the sea, in consequence of its lower specific heat and greater conduc- tivity, and hence as the superincumbent air becomes more heated than that upon the sea, it ascends and is replaced by a current of colder and denser air flowing from the sea towards the land. During the night the land cools more rapidly than the sea, and hence the same phenomenon is produced in a contrary direction. The sea breeze commences after sunrise, increases to three o'clock in the afternoon, decreases towards evening, and is changed into a land breeze after sunset. These winds are only perceived at a slight distance from the shores. They are regular in the tropics, but less so in our climates ; and traces of them are seen as far as the coasts of Greenland. The proximity of mountains also gives rise to periodical daily breezes. iii. Variable winds are those which blow sometimes in one direction and sometimes in another, alternately, without being subject to any law. In mean latitudes the direction of the winds is very variable ; towards the poles this irregularity increases, and under the arctic zone the winds frequently blow from several points of the horizon at once. On the other hand, in approaching the torrid zone, they become more regular. The south-west wind prevails in the north of France, in England, and in Germany ; in the south of France the direction inclines towards the north, and m Spain and Italy the north wind predominates. 903. law of tlie rotation of winds. — Spite of the great irregularity which characterises the direction of the winds in our latitude, it has been ascertained that the wind has a preponderating tendency to veer round according to the sun's motion — that is, to pass from north, through north- east, east, south-east to south, and so on round in the same direction from west to north ; that it often makes a complete circuit in that direc- tion, or more than one in succession, occupying many days in doing so, but that it rarely veers, and very rarely or never makes a complete circuit in the opposite direction. This course of the winds is most regularly observed in winter. According to Leverrier, the displacement of the north-east by the south-west wind arises from the occurrence of a whirl- wind formed upon the Gulf-stream. For a station in south latitude a contrary law of rotation prevails. -905] Fogs and Mists. 839 This law, though more or less suspected for a long time, was first formally enunciated and explained by Dove, and is known as Dove's law of the 7'otation of winds. 904. Fogrs and mists. — When aqueous vapours rising from a vessel of boiling water diffuse in the colder air, they are condensed ; a sort of cloud is formed which consists of a number of small hollow vesicles of water, which remain suspended in the air. These are usually spoken of as vapours, yet they are not so, at any rate not in the physical sense of the word ; for they are partially condensed vapours. When this condensation of aqueous vapours is not occasioned by con- tact with cold solid bodies, but takes place throughout large spaces of the atmosphere, they constitute fogs or mists^ which, in fact, are nothing more than the appearance seen over a vessel of hot water. A chief cause of fogs consists in the moist soil being at a higher tem- perature than the air. The vapours which then ascend condense and become visible. In all cases, however, the air must have reached its point of saturation before condensation takes place. Fogs may also be produced when a current of hot and moist air passes over a river at a lower temperature than its own, for then the air being cooled, as soon as it is saturated, the excess of vapour present is condensed. The distinction between mists and fogs is one of degree rather than of kind. A fog is a very thick mist. 905. Clouds. — Clouds are masses of vapour, condensed into little drops or vesicles of extreme minuteness, like fogs ; from which they only differ Fig- 751. in occupying the higher regions of the atmosphere ; they always result from the condensation of vapours which rise from the earth. According 840 Fogs and Mists. Clouds. [905- to their appearance, they have been divided by Howard into four princi- pal kinds : the nimbjis, the stratus^ the cumulus, and the cirrus. These four kinds are represented in fig. 751, and are designated respectively by one, two, three, and four birds on the wing. The cirrus consist of small whitish clouds, which have a fibrous or wispy appearance, and occupy the highest regions of the atmosphere. The name of mare^ tails, by which they are generally known, well describes their appearance. From the low temperature of the spaces which they occupy, it is more than probable that cirrus clouds consist of frozen particles ; and hence it is that haloes, coronas, and other optical appearances, produced by refraction and reflection from ice crystals, appear almost always in these clouds and their derivatives. Their ap- pearance often precedes a change of weather. The cumulus are rounded spherical forms which look like mountains piled one on the other. They are more frequent in summer than in winter, and after being formed in the morning, they generally disappear towards evening. If, on the contrary, they become more numerous, and especially if surmounted by cirrus clouds, rain or storms may be expected. Stratus clouds consist of very large and continuous horizonal sheets, which chiefly form at sunset, and disappear at sunrise. They are fre- quent in autumn and unusual in spring time, and are lower than the preceding. The nimbus, or rain clouds, which are sometimes classed as one of the fundamental varieties, are properly a combination of the three preceding kinds. They affect no particular form, and are solely distinguished by a uniform grey tint, and by fringed edges. They are indicated on the right of the figure by the presence of one bird. The fundamental forms pass into one another in the most varied manner ; Howard has classed these traditional forms as cirro-cumulus, cirro-stratus, and cumulo-stratus, and it is often very difficult to tell from the appearance of a cloud, which type it most resembles. The cirro- cumulus is most characteristically known as a ' mackerel sky ; ' it consists of small roundish masses, disposed with more or less irregularity and connection. - It is frequent in summer, and attendant on warm and dry weather. Cirro-stratus appears to result from the subsidence of the fibres of cirrus to a horizontal position, at the same time approaching laterally. The form and relative position when seen in the distance frequently give the idea of shoals of fish. The tendency of cmmilo- stratus is to spread, settle down into the nitnbus, and finally fall as rain. The height of clouds varies greatly ; in the mean it is from 1,300 to 1,500 yards in winter, and from 3,300 to 4,400 yards in summer. But they often exist at greater heights ; Gay-Lussac, in his balloon ascent, at a height of 7,650 yards, observed cirrus-clouds above him, which appeared still to be at a considerable height. In Ethiopia, M. d'Ab- badie observed storm clouds whose height was only 230 yards above the ground. In order to explain the suspension of clouds in the atmosphere, Halley -906] Formation of Clouds, 841 first proposed the hypothesis of vesicular vapours. He supposed that clouds are formed of an infinity of extremely minute vesicles, hollow, like soap bubbles filled with air, which is hotter than the surrounding air : so that these vesicles float in the air like so many small balloons. This theory, which was first propounded by Saussure, has been defended by Kratzenstein, subsequently by Bravais and most physicists; it has, however, been combated by Desaguiliers, and afterwards by Monge, and has at present many opponents. These latter assume that clouds and fogs consist of extremely minute droplets of water, which are retained in the atmosphere by the ascensional force of currents of hot air, just as light powders are raised by the wind. Ordinarily, clouds do not appear to descend, but this absence of downward motion is only apparent. In fact, clouds do usually fall slowly, but then the lower part is continually dissipated on coming in contact with the lower and more heated layers ; at the same time the upper part is always increasing from the condensa- tion of new vapours ; so that from these two actions clouds appear to retain the same height. 906. Formation of clouds. — Many causes may concur in the for- mation of clouds, i. The low temperature of the higher regions of the atmosphere. For, owing to solar radiation, vapours are constantly disengaged from the earth . and from the waters, which from their elastic force and lower density rise in the atmosphere; meeting there continually colder and colder layers of air, they sink to the point of saturation, and then condensing in infinitely small droplets, they give rise to clouds. ii. The hot and moist currents of air rising during the day undergo a gradually feebler pressure, and thus is produced an expansion which is a source of intense cold, and produces a condensation of vapour. Hence it is that high mountains, stopping the aerial currents, and Jforcing them to rise, are an abundant source of rain. iii. A hot, moist current of air mixing with a colder current, undergoes a cooling, which brings about a condensation of the vapour. Thus the hot and moist winds of the south and south-west, mixing with the colder air of our latitudes, give rain. The winds of the north and north-east tend also, in mixing with our atmosphere, to condense the vapours ; but as these winds, owing to their low temperature, are very dry, the mixture rarely attains saturation, and generally gives no rain. The formation of clouds is thus explained by Hutton. The tension of aqueous vapour, and therewith the quantity present in a given space when saturated, diminishes according to a geometric progression, while the temperature falls in arithmetical progression, and therefore the elas- ticity of the vapour present at any time is reduced by a fall of tempera- ture more rapidly than in direct proportion to the fall. Hence if a current of warm air, saturated with aqueous vapour, meet a current of cold air also saturated, the air acquires the mean temperature of the two, but can only retain a portion of the vapour in the invisible condition, and a cloud or mist is formed. Thus suppose a cubic metre of air at 10° C. mixes with a cubic metre of air at 2o°C-j and that they are respectively saturated 00 842 Meteorology. [906- with aqueous vapour. By formula (375) it is easily calculated that the weight of water contained in the cubic metre of air at 10° C. is 9-397 grammes, and in that at 20° C. is I7-632 grammes, or 27-029 grammes in all. When mixed they produce two cubic metres of air at 15° C. ; but as the weight of water required to saturate this is only 2 x 12-8 = 25-6 grammes, the excess, 1-429 grammes, will be deposited in the form of mist or clouds. 907. Rain. — When by the constant condensation of aqueous vapour the individual vapour vesicles become larger and heavier, and when finally individual vesicles unite, they form regular drops which fall as rain. The quantity of rain which falls annually in any given place, or the annual rainfall, is measured by means of a rain gauge or pluviometer. Ordinarily it consists of a cylindrical vessel M (figs. 752 and 753), closed Fig. 752. t'ig- 753- at the top by a funnel-shaped lid, in which there is a very small hole, through which the rain falls. At the bottom of the vessel is a glass tube, A, in which the water rises to the same height as inside the rain gauge, and is measured by a scale on the side, as shown in the figures. The apparatus being placed in an exposed situation, if at the end of a month the height of water in the tiihe is two inches for example, it shows that the water has attained this height in the vessel ; and, consequently, that a layer of two inches in depth expresses the quantity of rain which this extent of surface has received. It has been noticed that the quantity of rain indicated by the rain gauge is greater as this instrument is nearer the ground. This has been ascribed to the fact that the rain-drops,, which are generally colder than the layers of air which they traverse, condense the vapour in these layers, and, therefore, constantly increase in volume. Hence more rain falls on the surface of the ground than at a certain height. But it has been objected that the excess of the quantity of rain which falls, over that at a certain height, is six or seven times that which could arise from condensation, even during the whole course of the rain-drops from the clouds to the earth. The difference must, therefore, be ascribed to purely local causes, and it is now assumed that the difference arises from eddies produced in the air about the rain gauge, which are more perceptible as -909] Rain, Waterspouts, 8^3 it is higher above the ground ; as these eddies disperse the drops which would otherwise fall into the instrument, they diminish the quantity of water which it receives. In any case it is clear that if rain-drops traverse moist air, they will, from their temperature, condense vapour and increase in volume. If, on the contrary, they traverse dry air, the drops tend to vaporise, and less rain falls than at a certain height ; it might even happen that the rain did not reach the earth. Many local circumstances may affect the quantity of rain which falls in different countries ; but, other things being equal, most rain falls in hot climates, for there the vaporisation is most abundant. The rain-fall decreases, in fact, from the equator to the poles. At London it is 23-5 inches; at Bordeaux it is 25-8; at Madeira it is 277 ; at Havannah it is 91-2, and at St. Domingo it is 107-6. The quantity varies with the seasons ; in Paris, in winter, it is 4*2 inches ; in spring 6*9 ; in summer 6'3, and in autumn 4-8 inches. The heaviest annual rain-fall at any place on the globe is on the Khasia Hills in Bengal, where it is 600 inches ; of which 500 inches fall in seven months. The driest recorded place in England is Lincoln, where the mean rainfall is 20 inches, and the wettest is Stye, at the head of Borrowdale in Cumberland, where it amounts to 165 inches. An inch of rain on a square yard of surface expresses a fall of 4674 pounds, or 4-67 gallons. On an acre it corresponds to 22,622 gallons, or 100-9935 tons. 100 tons per inch per acre is a ready way of remember- ing this. 908. "Waterspouts. — These are masses of vapour suspended in the lower layers of the atmosphere which they traverse, and endowed with a gyratory motion rapid enough to uproot trees, upset houses, and break and destroy everything with which they come in contact. These meteors, which are generally accompanied by hail and rain, often emit lightning and thunder, producing the sound of carriages rolling over a stony road. Many of them have no gyratory motion, and about a quarter of those observed are produced in a calm atmo- sphere. When they take place on the sea they present a curious phenomenon. The water is disturbed, and rises in the form of a cone, while the clouds are depressed in the form of an inverted cone ; the two cones then unite and form a continuous column from the sea to the clouds (fig. 754), which are called waterspouts. Even, however, on the high seas the water of these waterspouts is never salt, proving that they are formed of con- densed vapours, and not of sea water raised by aspiration. 'the origin of these is not known. Kaemtz assumes that they are due principally to two opposite winds which pass by the side of each other, or to a very high wind which prevails in the higher regions of the atmo- sphere. Peltier and many others ascribe to them an electrical origin. 909. Influence of aqueous vapour on climate.-*-One of the most important elements in meteorology is undoubtedly the property possessed 844 Meteorology. [909 by aqueous vapour of powerfully absorbing and radiating heat. The same physicist who discovered this property (411)? has applied it to the explanation of some obscure points in meteorological science, and there can be no doubt that the knowledge of it will gradually lead to a clearer understanding of many inexplicable and apparently capricious meteorolo- gical phenomena. Fig. 754- Tyndall has established the fact, that in a tube 4 feet long the atmo- spheric vapour on a day of average dryness absorbs 10 per cent, of obscure heat. With the earth warmed by the sun, as a source, there can be no doubt that at the very least 10 per cent, of its heat is intercepted within 10 feet of the surface. If aqueous vapour be compared atom for atom with air, its power of absorption and radiation is more than 16,000 times that possessed by air. Such facts as these are sufficient to show the importance of the small quantity of this vapour that exists in our atmo- sphere. The radiative power of aqueous vapour may be the main cause of the ^ torrential rains that occur in the tropics, and also of the formation of cumuli clouds in our own latitudes. This same property probably causes the descent of a very fine rain, called serei?i, which has more the characteristics of falling dew, as it appears a short time after sunset, when the sky is clear ; its production has therefore been attributed to the cold, resulting from the radiation of the air. It is not the air, however, but the aqueous vapour in the air, which by its own radiation chills itself, so that it condenses into sdreiii. -910] Injiuence of A queoiis Vapour on Climate. 845 The absorbejit power of aqueous vapour is even of greater importance. Whenever the air is dry, terrestrial radiation at night is so rapid as to cause intense cold. Thus, in the central parts of Asia, Africa, and Aus- tralia, the daily range of the thermometer is enormous; in the interior of the last continent a difference in temperature of no less than 40° C. has been recorded within 24 hours. In India, and even in the Sahara, owing to the copious radiation, ice has been formed at night. But the heat which aqueous vapour absorbs most largely is of the kind emitted from sources of low temperature ; it is to a large extent transparent to the heat emitted from the sun, whilst it is almost opaque to the heat radiated from the earth. Consequently, the solar rays penetrate our atmosphere with a loss, as estimated by Pouillet, of only 25 per cent., when directed vertically down- wards, but after warming the earth they cannot retraverse the atmosphere. Through thus preventing the escape of terrestrial heat, the aqueous vapour in the air moderates the extreme chilling which is due to the unchecked radiation from the earth, and raises the temperature of that region over which it is spread. Tyndall has thus described the action of this substance : — * Aqueous vapour is a blanket more necessary to the vegetable life of England than clothing is to man. Remove for a single summer night the aqueous vapour from the air which overspreads this country, and every plant capable of being destroyed by a freezing tempe- rature would perish. The warmth of our fields and gardens would pour itself unrequited into space, and the sun would rise upon an island held fast in the iron grip of frost.' 910. Tyndall's researclies.— Tyndall has recently examined the action of solar and of the electric light on vapours under a great degree of attenua- tion ; and has found that under these circumstances they are decomposed. This new reaction not only puts a most powerful agent of chemical de- composition into the hands of chemists, which remains for them to make use of, but it has led Tyndall to important conclusions regarding the origin of the blue colour of the sky, and the polarisation of daylight For these experiments he used a glass tube with glass ends, such as he had used for his researches on radiant heat. This could be exhausted and then filled with air charged with the vapours of volatile liquids, by allowing the air to pass through small Wolff bottles containing them. By mixing with different proportions of pure air the air charged with vapour, and by varying the degree of exhaustion, it was possible to have a vapour under any degree of attenuation. It was also possible to fill the tube with the vapour of a liquid alone. The tube having been filled with air charged with vapours of nitrite of amyle, a somewhat convergent beam from the electric lamp was passed into the tube. For a moment the tube appeared optically empty, but suddenly a shower of liquid spherules was precipitated on the path of the beam forming a luminous white cloud. The nature of the sub- stance thus precipitated was not specially investigated. This effect was not due to any chemical action between the vapour and the air, for when either dry oxygen or dry hydrogen was used instead of air, or when the vapour was admitted alone, the effect was substantially 846 Meteorology. [910- the same. Nor was it due to any heating effect, for the beam had been previously sifted by passing through a solution of alum, and through the thick glass of the lens. The unsifted beam produced the same effect ; the obscure calorific rays did not seem to interfere with the result. The sun's hght also affects the decomposition of the nitrite of amyle vapour ; and this decomposition was found to be mainly due to the more refrangible rays. When the electric light, before entering the experimental tube, was made to pass through a layer of the liquid nitrite of amyle an eighth of an inch in thickness, the luminous effect was not appreciably diminished, but the chemical action was almost entirely stopped. Thus that special constituent of the luminous radiation which effects the decomposition of the vapour is absorbed by the liquid. The liquid nitrite of amyle is probably decomposed by light; but its decomposition, if it take place at all, is far less rapid and distinct than that of the vapour. The circum- stance that the absorption is the same whether the nitrite is in the liquid or in the vaporous state, is considered by Tyndall as a proof that the absorption is not the act of the molecule as a whole, but that it is atomic, that is, that it is to the atoms that the peculiar rate of vibration is trans- ferred, which brings about the decomposition of the body. Besides nitrite of amyle, the vapour of a number of other substances was examined, such, for example, as benzole, iodide of allyle, bisulphide of carbon. By varying the nature of the vapour, the shape of a cloud could be greatly varied, and in many cases presented the most fantastic and beautiful forms. It was also found that a vapour which when alone resists the action of light, may, by being associated with another gas or vapour, exhibit a vigorous or even violent action. Thus, when the tube was filled with atmospheric air, mixed with nitrite of butyle vapour, the electric hght produced very little effect. But with half an atmosphere of this mixture, and half an atmosphere of air which had passed through hydrochloric acid, the action of the light was almost instantaneous. In another case mixed air and nitrite of butyle vapour were passed into the tube so as to depress the barometer the j^^th of an inch ; that is, the mixed air and vapour were under a pressure of 3^^ of an atmosphere. Air passed through solution of hydrochloric acid was intro- duced until the pressure was 3 inches. The condensed beam passed through for some time without change, but afterwards a superbly blue cloud was formed. In cases where the vapours are under a sufficient degree of attenua- tion, whatever otherwise be their nature, the visible action commences with the formation of a blue cloud. The term cloud, however, must not be understood in its ordinary sense : the blue cloud is invisible in ordinary daylight, and to be seen must be surrounded by darkness, it alone being illuminated by a powerful beam of light. The blue cloud differs in many important particulars from the finest ordinary clouds, and may be con- sidered to occupy an intermediate position between these clouds and true cloudless vapour. r.911] Dew. Hoar Frost. ;847 By graduating the quantity of vapour, the precipitation may be ob- tained of any required degree of fineness : forming either particles dis- tinguishable by the naked eye, or particles beyond the reach of the highest microscopic power. There is no reason to doubt that particles may be thus obtained whose wave-length is but a very small fraction of the length of a wave of violet light. The case is similar to that of carbonic acid gas, which, diffused in the atmosphere, resists the decomposing action of solar light, but when in contiguity with the chlorophyle in the leaves of plants is decomposed. When the blue cloud produced in these experiments was examined by any polarising arrangement, the light emitted laterally from the beam — that is, in a direction at right angles to its axis — was found to be perfectly polarised. This phenomenon was observed in its greatest perfection the more perfect the blue of the sky. It is produced by any particles, pro- vided they are sufficiently fine. This is quite analogous to the light of the blue sky. When this is examined by a Nicol's prism, or any other analyser, it is found that the light, emitted at right angles to the path of the sun's rays, is polarised. These two phenomena, the fundamental blue, and the polarisation of the sky light, which have long been the enigmas of meteorologists, find their definite solution in these experiments. We have only to assume the existence in the higher regions of the atmosphere of excessively fine particles of water ; for particles of any kind produce this effect. It is not difficult to conceive the existence of such particles in the higher regions, even on a hot summer's day. For the vapour must there be in a state of extreme attenuation ; and inasmuch as the oxygen and nitrogen of the atmosphere behave like a vacuum to radiant heat, the extremely attenu- ated particles of aqueous vapour are practically in contact with the absolute cold of space. ' Suppose the atmosphere surrounded by an envelope impervious to light, but with an aperture on the sunward side, through which a parallel beam of solar light could enter and traverse the atmosphere. Surrounded on all sides by air not directly illuminated, the track of such a beam would resemble that of the parallel beam of the electric light through an incipient cloud. The sunbeam would be blue, and it would discharge light laterally in the same condition as that discharged by the incipient cloud. The azure revealed by such a beam would be to all intents and purposes a blue cloud.' 911. Dew. Hoar frost. — Dew is merely aqueous vapour which has condensed on bodies during the night in the form of minute globules. It is occasioned by the chilling which bodies near the surface of the earth experience in consequence of nocturnal radiation. Their temperature having then sunk several degrees below that of the air, it frequently happens, especially in hot seasons, that this temperature is below that at which the atmosphere is saturated. The layer of air which is immediately in contact with the chilled bodies, and which virtually has the same temperature, then deposits a portion of the vapour which it contains ; just as when a bottle of cold water is brought into a warm room, it be- 848 Meteorology, [911- comes covered with moisture, owing to the condensation of aqueous vapour upon it. According to this theory, which was first propounded by Dr. Wells, all causes which promote the cooling of bodies increase the quantity of dew. These causes are the emissive power of bodies, the state of the sky, and the agitation of the air. Bodies which have a great radiating power more readily become cool, and therefore ought to condense more vapour. In fact, there is generally no deposit of dew on metals, whose radiating power is very small, especially when they are polished; while the ground, sand, glass, and plants, which have a great radiating power, become abundantly covered with dew. The state of the sky also exercises a great influence on the formation of dew. If the sky is cloudless, the planetary spaces send to the earth an inappreciable quantity of heat, while the earth radiates very considerably, and therefore becoming very much chilled, there is an abundant deposit of dew. But if there are clouds, as their temperature is far higher than that of the planetary spaces, they radiate in turn towards the earth, and as bodies on the surface of the earth only experience a feeble chilling, no deposit of dew takes place. Wind also influences the quantity of vapour deposited. If it is feeble, it increases it, inasmuch as it renews the air ; if it is strong, it diminishes it, as it heats the bodies by contact, and thus does not allow the air time to become cooled. Finally, the deposit of dew is more abundant accord- ing as the air is moister, for then it is nearer its point of saturation. Hoarfrost and rime are nothing more than dew which has been depo- sited on bodies cooled below zero, and has therefore become frozen. The flocculent form which the small crystals present, of which rime is formed, shows that the vapours solidify directly without passing through the liquid state. Hoar frost, like dew, is formed on bodies which radiate most, such as the stalks and leaves of vegetables, and is chiefly deposited on the parts turned towards the sky. 912. Snow. Sleet. — Snow is water solidified in stellate crystals, variously modified, and floating in the atmosphere. These crystals arise from the congelation of the minute vesicles which constitute the clouds, when the temperature of the latter is below zero. They are more regular when formed in a calm atmosphere. Their form may be investigated by collecting them on a black surface, and viewing them through a strong lens. The regularity, and at the same time variety, of their forms are truly beautiful. Fig. 755 shows some of the forms as seen through a microscope. It snows most in countries near the poles, or which are high above the sea level. Towards the poles, the earth is constantly covered with snow; the same is the case on high mountains, where there are perpetual snows even in equatorial countries. Sleet is also solidified water, and consists of small icy needles pressed together in a confused manner. Its formation is ascribed to the sudden congelation of the minute globules of the clouds in an agitated atmo- sphere. -914] Ice. Regelatioii. 849 913. Bail. — Hail is a mass of compact globules of ice of different sizes, which fall in the atmosphere. In our chmate hail falls principally during spring and summer, and at the hottest times of the day ; it rarely falls at night. The fall of hail is always preceded by a peculiar noise. Hail is generally the precursor of storms, it rarely accompanies them, and follows them more rarely still. Hail falls from the size of small peas Fig. 755- to that of an ^g% or an orange. The formation of hailstones has never been altogether satisfactorily accounted for; nor more especially their great size. 914. Ice. Hegrelation. — Ice is nothing more than an aggregate of snow crystals, such as are shown in fig. 755. The transparency of ice is due to the close contact of these crystals, which causes the individual particles to blend into an unbroken mass, and renders the substance optically, as well as mechanically, continuous. When large masses of ice slowly melt away, a crystalline form is sometimes seeri by the gradual disintegration into rude hexagonal prisms : a similar structure is fre- quently met with, but in greater perfection, in the ice caves or glaciers of cold regions. An experiment of Tyndall has more clearly revealed the beautiful structure of ice. When a piece of ice is cut parallel to its planes of freezing, and the radiation from any source of light, as the sun, a gas or oil flame, is permitted to pass through it, the disintegration of the sub- stance proceeds in a remarkable way. By observing the plate of ice through a lens, numerous small crystals will be seen studding the interior of the block; as the heat continues these crystals expand, and finally assume the shape of six-rayed stars of exquisite beauty. This is a kind of negative crystallisation, the crystals produced being composed of water ; they owe their formation to the molecular disturbance caused by the absorption of heat from the source. Nothing is easier than to reproduce this phenomenon, if care be taken in cutting the ice. The planes of freezing can be found by noting the direction of the bubbles 003 SCO Meteorology. [914- in ice, which are either sparsely arranged in striae at right angles to the suface, or thickly collected in beds parallel to the surface of the water. A warm and smooth metal plate should be used to level and reduce the ice to a slab not exceeding half an inch in thickness. A still more important property of ice remains to be noticed. Faraday discovered that when two pieces of melting ice are pressed together they freeze into one at their points of contact. This curious phenomenon is now known under the name of regeiatioii. The cause of it has been the subject of much controversy, but the simplest explanation seems to be that given by its discoverer. The particles on the exterior of a block of ice are held by cohesion on one side only : when the temperature is at o° C, these exterior particles being partly free are the first to pass into the liquid state, and a film ot water covers the solid. But the particles in the interior of the block are bounded on all sides by the solid ice, the force of cohesion is here a maximum, and hence the interior ice has no tendency to pass into a liquid, even when the whole mass is at o°. If the block be now split in halves, a liquid film instantly covers the fractured surfaces, for the force of cohesion on the broken surfaces has been lessened by the act. By placing the halves together, so that their original position shall be regained, the liquid films on the two fractured surfaces again become bounded by ice on both sides. The film being excessively thin, the force of cohesion is able to act across it; the consequence of this is, the liquid particles pass back into the solid state, and the block is, reunited by regelation. Not only do ice and ice thus freeze together, but regelation also takes place between moist ice and any nonconducting solid body, as flannel or sawdust ; a similar explanation to that just given has been apphed here, substituting another solid for the ice on one side. It must be remarked, however, that many eminent philosophers dissent from the explanation here given. Whatever may be the true cause of regelation, there can be no doubt that this interesting observation of Faraday's explains many natural phenomena. For example, the formation of a snowball depends on the regelation of the snow granules composing it, and as regelation cannot take place at temperatures below o° C, for then both snow and ice are dry, it is only possible to make a coherent snowball when the snow is melting. The snow bridges, also, which span wide chasms in the Alps and else- where, and over which men can walk in safety, owe their existence to the regelation of gradually accumulating particles of snow. 915. Glaciers.— Tyndall has applied this regelating property of ice to the explanation of still grander phenomena — the formation and motion of glaciers, of which the following is a brief description. In elevated regions, what is termed the snow line marks the boundary of eternal snow, for above this the heat of summer is unable to melt the winter's snow. By the heat of the sun and the consequent percolation of water melted from the surface, the lower portions of the snow field are raised to 0° C. ; at the same time this part is closely pressed together by the weight of the snow above, regelation therefore sets in, converting the loose snow into a coherent mass. -916] Atmospheric Electricity. 851 By increasing pressure the intermingled air which renders snow opaque becomes ejected and transparent ; ice then results. Its own gravity, and the pressure from behind, urge downwards the glacier which has thus been formed. In its descent from the mountain the glacier behaves in all respects like a river, passing through narrow gorges with comparative velocity, and then spreading" out and moving slowly as its bed widens. Further, just as the central portions of a river move faster than the sides, so Professor Forbes has ascertained that the centre of a glacier moves quicker than its margin, and from the same reason (the difference in the friction encountered) the surface moves more rapidly than the bottom. To explain these facts Forbes assumed ice to be a viscous body capable of flexion, and flowing hke lava ; but as ice has not the properties of a viscous substance, the now generally accepted explanation of glacier motion is that supplied by the theory of regelation. According to this theory, the brittle ice of the glacier is crushed and broken in its passage through narrow channels, such as that of Trelaporte on Mont Blanc ; and then, as it emerges from the gorge which confined it, becomes reunited by virtue of regelation ; in this instance forming the well-known Mer de Glace. By numerous experiments Tyndall has established that rege- lation is adequate to furnish this explanation, and with complete success has artificially imitated, on a small scale, the moulding of glaciers by the crushing and subsequent regelation of ice. LUMINOUS METEORS., 916. Atmospheric electricity. Franklin's experiment. — The most frequent luminous phenomena, and the most remarkable for their effects, are those produced by the free.electricity in. the atmosphere. The first physicists who observed the electric spajrk compared it to the gleam of lightning, and its crackling to the sound of thunder. But Franklin, by the aid of powerful electrical batteries, first established a complete parallel between lightning and electricity; and he indicated, in a memoir published in 1749, the experiments necessary to attract electricity from the clouds by means of pointed rods. The experiment was tried by Ualibard in France; and Franklin, pending the erection of a pointed rod on a spire in Philadelphia, had the happy idea of flying a kite, provided with a metallic point, which could reach the higher regions of the atmosphere. In June 1752, during stormy weather, he flew the kite in a field near Philadelphia. The kite was flown with ordinary pack-thread, at the end of which Franklin attached a key, and to the key a silk cord, in order to insulate the apparatus ; he then fixed the silk cord to a tree, and having presented his hand to the key, at first he obtained no spark. He was beginning to despair of success, when, rain having fallen, the cord became a good conductor, and a spark passed. Franklin, in his letters, describes his emotion on witnessing the success of the experiment as being so great that he could not refrain from tears. Franklin, who had discovered the power of points (695), but who did not understand its explanation, imagined that the kite withdrew from the 852 Meteorology. [916- cloud its electricity ; it is, in fact, a simple case of induction, and depends on the inductive action which the thunder-cloud exerts upon the kite and the cord. 917. Apparatus to Investigrate tbe electricity of the atmosphere. — The apparatus used to ascertain the presence of electricity in the atmo- sphere are : the electroscope, either with pith balls, straw, or gold leaf : the apparatus first used by Dalibard, and which consisted of an insulated iron rod, 36 yards in height : arrows discharged into the atmosphere, and even kites and captive balloons. To observe the electricity in fine weather, when the amount is generally small, an electrometer is used, as devised by Saussure for this kind of in- vestigation. It is an electroscope similar to that already described, but the rod to which the gold leaves are fixed is surmounted by a conductor 2 feet in length, and terminating either in a knob or a point (fig, 756). To protect the apparatus against rain, it is covered with a metallic shield 4 inches in diameter. The glass case is square, instead of being round, and .a divided scale on its inside face indicates the divergence of the gold leaves or of the straws. This electrometer only gives signs of atmo- spheric electricity as long as it is raised in the atmosphere, so that it is in layers of air of which the electrical condition is superior to its own. To ascertain the electricity of the atmosphere, Saussure also used a copper ball, which he pro- jected vertically with his hand. This ball was fixed to one end of a metallic wire, the other end of which was attached to a ring, which could glide along the conductor of the electrometer. From the divergence of the straws, or of the gold leaves, the electrical condition of the air at the height which the ball attained could be determined. M. Becquerel, in experiments made on the St. Bernard, improved Saussure's apparatus, by substituting for the knob an arrow, which was projected into the atmosphere by means of a bow. A gilt silk thread, 88 yards long, was fixed with one end to the arrow, while the other end was attached to the stem of an electroscope. Peltier used a gold-leaf electroscope, at the top of which was a somewhat large copper globe. Provided with this instrument, the observer stations himself in a commanding position — it is then quite sufficient to raise the electroscope even a foot or so to obtain signs of electricity. To observe the electricity of clouds, where the tension is very con- siderable, use is made of a long bar terminating in a point. This bar, which is insulated with care, is fixed to the summit of a building, and its lower end is connected with an electrometer, or even an electric chimes Fig. 756. -918] Ordinary Electricity of the Atmosphere. 853 (fig. 559), which announces the presence of thunder-clouds. As, however, the bar can then give dangerous shocks, a metalHc ball must be placed near it, which is well connected with the ground, and which is nearer the bar than the observer himself ; so that if a discharge should ensue, it will strike the ball and not the observer. Professor Richmann, of St. Peters- burg, was killed in an experiment of this kind, by a discharge which struck him on the forehead. Sometimes also captive balloons or kites have been used, provided with a point, and connected by means of a gilt cord with an electrometer. A good collector of atmospheric electricity consists of a fishing-rod with an insulated handle which projects from an upper window. At the summit is a bit of lighted amadou held in a metallic forceps, the smoke of which, being an excellent conductor, conveys the electricity of the air down a wire attached to the rod. A sponge moistened with alcohol, and set on fire, is also an excellent conductor. A very convenient instrument for investigating atmospheric electricity has been introduced by Sir W. Thomson ; it consists of an insulated can of water placed on a table or on a window-sill on the ijiside. The water discharges through a zinc nozzle at the end of a narrow pipe which projects through the partially open window to a distance of two or three feet, with a head of water of about 10 inches, and a discharge so slow that there is no trouble in replenishing the can ; the atmospheric electricity is quickly collected and may be examined by connecting the can with any electrometer. 918. Ordinary electricity of the atmosphere. — By means of the dif- ferent apparatus which have been described, it has been found that the presence of electricity in the atmosphere is not confined to stormy weather, but that the atmosphere always contains free electricity, usually positive but sometimes negative. When the sky is cloudless, the electricity is always positive, but it varies in amount with the height of the locality, and with the time of day. The amount is greatest in the highest and most isolated places. No trace of positive electricity is found in houses, streets, and under trees ; in towns positive electricity is most perceptible in large open spaces, on quays, or on bridges. In all cases, positive electricity is only found at a certain height above the ground. On flat land, it only becomes perceptible at a height of 5 feet ; above that point it increases according to a law which is not made out, but which seems to depend on the hygrometric state of the air. At sunrise the free positive electricity is feeble ; it increases up to 1 1 o'clock, according to the season, and then attains its first maximum. It then decreases rapidly until a Httle before sunset, and then increases till it reaches its second maximum, a few hours after sunset ; the re- mainder of the night the electricity decreases until sunrise. Thus the greatest amount of electricity is observed when the barometric pressure is greatest. These increasing and decreasing periods, which are ob- served all the year, are more perceptible when the sky is clearer, and the weather more settled. The positive electricity of fine weather is much stronger in winter than in summer. 854 Meteorology, [918- In foggy weather the electricity of the air is more strongly positive than at other times. When the sky is clouded, the electricity is some- times positive and sometimes negative. It often happens that the electricity changes its sign several times in the course of the day, owing to the passage of an electrified cloud. During storms, and when it rains or snows, the atmosphere may be positively electrified one day, and negatively the next, and the numbers of the two sets of days are virtually equal. The electricity of the ground has been found by Peltier to be always negative, but to different extents, according to the hygrometric state and temperature of the air. 919. Causes of the atmosplierie electricity. — Many hypotheses have been propounded to explain the origin of the atmospheric electricity. Some have ascribed it to the friction of the air against the ground, some to the vegetation of plants, or to the evaporation of water. Some, again, have compared the earth to a vast voltaic pile, and others to a thermo- electrical apparatus. Many of these causes may, in fact, concur in pro- ducing the phenomena. Volta first showed that the evaporation of water produced electricity. Pouillet and others have subsequently shown that no electricity is pro- duced by the evaporation of distilled water ; but if an alkali or a salt is dissolved, even in small quantity, the vapour is positively and the solution is negatively electrified. The reverse is the case if the water contains acid. Hence it has been assumed that as the waters which exist on the surface of the earth and on the sea always contain salt dissolved, the vapours disengaged ought to be positively and the earth negatively elec- trified. The development of electricity by evaporation may be observed by heating strongly a platinum dish, adding to it a small quantity of liquid, and placing it on the upper plate of the condensing electroscope (fig. 567), taking care to connect the lower plate with the ground. When the water of the capsule is evaporated, the connexion with the ground is broken, and the upper plate raised. The gold leaves then diverge if the water contained salts, but remain quiescent if the water was pure. Reasoning from this experiment, Pouillet has ascribed the development of electricity by evaporation to the separation of particles of water from the substances dissolved ; but Reich and Riess have shown that the elec- tricity disengaged during evaporation could be attributed to the friction which the particles of water carried away in the current of vapour exercise against the sides of the vessel, just as in Armstrong's electrical machine. By a recent series of experiments, Gaugain has arrived at the same result : and thinks it no longer allowable to ascribe the atmospheric electricity to any changes that take place during the tranquil evaporation of sea water. In support of the hypothesis which considers the earth as an immense source of voltaic electricity due to chemical actions, Becquerel has re- cently published numerous experiments to show that when earth and water come in contact electricity is always produced : the earth taking a -921] Electricity of Clouds. Lightning. 855 considerable excess of positive or negative electricity, and the water a corresponding excess of the opposite electricity, according to the nature of the salts or other compounds which the water held dissolved. This is a general fact which, according to M. Becquerel, is liable to no ex- ception. Becquerel experimented with an ordinary multiplier, the wire of which was connected with two platinum plates immersed in the pieces of ground, or the water whose electrical condition he wished to investigate. He thus found that when two moist pieces of ground are connected, that which contained the strongest solution took an excess of positive elec- tricity. He found that in the neighbourhood of a river, even at some distance, the land and objects placed on the surface possessed an excess of negative electricity, while the water and the aquatic plants which swam on the surface where charged with positive electricity. But accord- ing to the nature of the substances dissolved in the water, different effects were produced. As from Becquerel's experiments, the waters are some- times positive and sometimes negative, and the earth in a contrary con- dition, it follows that water in evaporating must constantly send into the atmosphere an excess of positive or negative electricity, while the earth, by the vapours disengaged on its surface, allows an excess of the contrary electricity to escape. Now this excess of electricity ought necessarily to influence the distribution of the electricity in the atmosphere, and may serve to explain how it is that the clouds are sometimes positively and sometimes negatively electrified. 920. Electricity of clouds. — In general the clouds are all electrified, sometimes positively and sometimes negatively, and only differ in their greater or less tension. The formation of positive clouds is usually ascribed to the vapours which are disengaged from the ground, and con- dense in the higher regions. Negative clouds are supposed to result from fogs, which, by their contact with the ground, become charged with nega- tive fluid, which they retain on rising into the atmosphere ; or that, separated from the ground by layers of moist air, they have been nega- tively electrified by induction from the positive clouds, which have re- pelled into the ground positive electricity. 921. Iiigrlitningr. — This, as is well known, is the dazzling light emitted by the electric spark when it shoots from clouds charged with electricity. In the lower regions of the atmosphere the light is white, but in the higher regions, where the air is more rarefied, it takes a violet tint ; as does the spark of the electrical machine in a rarefied medium (740). The flashes of lightning are sometimes several leagues in length ; they generally pass through the atmosphere in a zigzag direction : a phenome- non ascribed to the resistance offered by the air condensed by the passage of a strong discharge. The spark then diverges from a right line, and takes the direction of least resistance. In vacuo electricity passes in a straight line. Several kinds of Hghtning flashes may be distinguished — i. the zigzag flashes which move with extreme velocity in the form of a fine of fire with sharp outlines, and which entirely resemble the spark of an clec- 856 Meteorology. [921- trical machine ; 2. the flashes which, instead of being linear, like the preceding, fill the entire horizon without having any distinct shape. This kind, which is most frequent, appears to be produced in the cloud itself, and to illuminate the mass. According to Kundt the number of sheet discharges are to the zigzag discharges as 11:6; and from spectrum observations it would appear that the former are brush discharges between clouds, while the latter are true electrical discharges between the clouds and the earth. Another kind is called heat lightning, because it -illuminates the summer nights without the presence of any clouds above the horizon, and without producing any sound. The most prob- able of the many hypotheses which have been proposed to account for its origin, is that which supposes it to consist of ordinary lightning flashes, which strike across the clouds at such distances that the rolling of thunder cannot reach the ear of the observer. There is further the very unusual phenomenon oi globe light ni?tg, or the flashes which appear in the form of globes of fire. These, which are sometimes visible for as much as ten seconds, descend from the clouds to the earth with such slowness that the eye can follow them. They often rebound on reaching the ground ; at other times they burst and explode with a noise like that of the report of many cannon. The duration of the light of the first three kinds does not amount to a thousandth of a second, as has been determined by Mr. Wheatstone by means of a rotating wheel, which was turned so rapidly that the spokes were invisible : on illuminating it by the Hghtning flash, its duration was so short that, whatever the velocity of rotation of the wheel, it appeared quite stationary; that is, its displacement is not perceptible during the time the lightning exists. 922. Tbunder. — The thunder is the violent report which succeeds lightning in stormy weather. The lightning and the thunder are always simultaneous, but an interval of several seconds is always observed between these two phenomena, which arises from the fact that sound only travels at the rate of about 1,100 feet in a second (216), while the passage of light is almost instantaneous. Hence an observer will only hear the noise of thunder five or six seconds, for instance, after the lightning, according as the distance of the thunder-cloud is five or six times 1,100 feet. The noise of thunder arises from the disturbance which the electric discharge produces in the air, and which may be witnessed in Kinnersley's thermometer. Near the place where the lightning strikes, the sound is dry and of short duration. At a greater distance a series of reports are heard in rapid succession. At a still greater distance the noise, feeble at the commencement, changes into a prolonged rolling sound of varying intensity. If the lightning is at a greater distance than 14 or 1 5 miles, it is no longer heard, for sound is more imperfectly propagated through air than through solid bodies ; hence, there are lightning discharges without thunder; these occur at times when the sky is cloud- less. Some attribute the noise of the rolling of thunder to the reflection of sound from the ground and from the clouds. Others have considered -924] Effects of L ighUting. 857 the lightning not as a single discharge, but as a series of discharges, each of which gives rise to a particular sound. But as these partiaL discharges proceed from points at different distances, and from zones of unequal density, it follows not only that they reach the ear of the observer successively, but that they bring sounds of unequal density, which occasion the duration and inequality of the rolling. The phenomenon has finally been ascribed to the zigzags of lightning themselves, assuming that the air at each salient angle is at its greatest compression, which would produce the unequal intensity of the sound. 923. Effects of lig^btningr. — The lightning discharge is the electric discharge which strikes between a thunder-cloud and the ground. The latter, by the induction from the electricity of the cloud, becomes charged with contrary electricity ; and when the tendency of the two electricities to combine exceeds the resistance of the air, the spark passes, which is often expressed by saying that a thunder-belt has fallen. Lightning in general strikes from above, but ascending lightning is also sometimes observed ; probably this is the case when the clouds being negatively the earth is positively electrified, for all experiments show that at the ordinary pressure the positive fluid passes through the atmosphere more easily than negative electricity. From the first law of electrical attraction, the discharge ought to fall first on the nearest and best-conducting objects, and, in fact, trees, elevated buildings, metals, are more particularly struck by the discharge. Hence it is imprudent to stand under trees during a thunder-storm. The effects of lightning are very varied, and of the same kind as those of batteries (736), but of far greater intensity. The lightning discharge kills men and animals, inflames combustible matters, melts metals, breaks bad conductors in pieces. When it penetrates the ground it melts the siliceous substance in its way, and thus produces in the direction of the discharge those remarkable vitrified tubes c^W^di fulgurites, some of which are as much as 12 yards in length. When it strikes bars of iron, it mag- netises them, and often inverts the poles of compass needles. After the passage of lightning, a highly peculiar odour is generally produced, like that perceived in a room in which an electrical machine is being worked. This "odour was first attributed to the formation of an oxygenised compound, to which the name ozone was given : but S-chonbein, in 1840, has shown that ozone is a peculiar allotrophic modification of oxygen. 924. Return sbock. — This is a violent and sometimes fatal shock which men and animals experience, even when at a great distance from the place where the lightning discharge passes. This is caused by the inductive action which the thunder-cloud exerts on bodies placed within the sphere of its activity. These bodies are then, like the ground, charged with the opposite electricity to that of the cloud ; but when the latter is discharged by the recombination of its electricity with that of the ground the induction ceases, and the bodies reverting rapidly from the electrical state to the neutral state, the concussion in question is produced, the return shock. A gradual decomposition and reunion of the electricity produces 858 Meteorology. [924- invisible effects ; yet it appears that such disturbances of the electrical equilibrium are perceived by nervous persons. The return shock is always less violent than the direct one ; there is no instance of its having produced any inflammation, yet plenty of cases in which it has killed both men and animals ; in such cases no broken limbs, wounds, or burns, are observed. The return shock may be imitated by placing a gold leaf electroscope connected by a wire with the ground near an electrical machine ; when the machine is worked at each spark taken from it the gold leaves diverge. 925. Xlgrhtning conductor. — The ordinary form of this instrument is an iron rod, through which passes the electricity of the ground attracted by the opposite electricity of the thunder-clouds. It was invented by Franklin in 1755. There are two principal parts in lightning conductors ; the rod and the conductor. The rod is a pointed bar of iron, fixed vertically to the roof of the edifice to be protected; it is from 6 to 10 feet in height, and its basal section is about 2 or 3 inches in diameter. The conductor is a bar of iron which descends from the bottom of the rod to the ground, which it penetrates to some distance. As, in consequence of their rigidity, iron bars cannot always be well adapted to the exterior of buildings, they are best formed of wire cords, such as are used for rigging and for suspension bridges. In a report made by the Academy of Sciences on the construction of lightning conductors, the use of copper instead of iron wire in these conductors is recommended, inasmuch as copper is a better conductor than iron. The metallic section of the cords ought to be about ^ a square inch, and the individual wires 0-04 to o-o6 inch in diameter; they ought to be twisted in three strands, like an ordinary cord. The point of the lightning conductor ought to be of copper instead of platinum, for the sake of better conductivity. The conductor is usually led into a well, and to connect it better with the soil it ends in two or three ramifications. If there is no well in the neighbourhood, a hole is dug in the soil to the depth of 6 or 7 yards, and the foot of the conductor having been introduced, the hole is filled with wood ashes, which conduct very well and preserve the metal from oxidation. Powdered coke serves the same purpose. The action of a lightning conductor depends on induction and the power of points (695); when a storm-cloud, positively electrified, for instance, rises in the atmosphere, it acts inductively on the earth, repels the positive and attracts the negative fluid, which accumulates in bodies placed on the surface of the soil, the more abundantly as these bodies are at a greater height. The tension is then greatest on the highest bodies, which are therefore most exposed to the electric discharge ; but if these bodies are provided with metal points, like the rods of conductors, the nega- tive electricity, withdrawn from the soil by the influence of the cloud, flows into the atmosphere, and neutralises the positive electricity of the cloud. Hence, not only does a lightning conductor tend to prevent the acumu- -926] - Rainbow, 859 lation of electricity on the surface of the earth, but it also tends to restore the clouds to their natural state, both which concur in preventing light- ning discharges. The disengagement of electricity is, however, some- times so abundant, that the lightning conductor is inadequate to discharge the ground, and the lightning strikes ; but the conductor receives the discharge, in consequence of its greater conductivity, and the edifice is preserved. Experiment has shown that, approximately, a lightning conductor protects a circular space around it, the radius of which is double its height. Thus, a building, 64 yards in length, would be preserved by two rods 8 yards in height, at a distance of 32 yards. A conductor, to be efficient, ought to satisfy the following conditions : i. the rod ought to be so large as not to be melted if the discharge passes ; ii. it ought to terminate in a point to give readier issue to the electricity disengaged from the ground, hence the rod is usually provided with a point of platinum or of gilt copper ; iii. the conductor must be continuous from the point to the ground, and the connexion between the rod and the ground must be as intimate as possible ; iv. if the building which is provided with a lightning conductor contains metallic surfaces of any extent, such as zinc roofs, metal gutters, or iron work, these ought to be connected with the conductor. If the last two conditions are not ful- filled, there is a great danger of lateral discharges : that is to say, that the discharge takes place between the conductor and the edifice, and then it only increases the danger. 926. Rainbow. — The rainbow is a luminous meteor which appears in the clouds opposite the sun when they are resolved into rain. It consists of seven concentric arcs, presenting successively the colours of the solar spectl-um. Sometimes only a single bow is perceived, but there are usually two \ a lower one, the colours of which are very bright, and an external or secondary one, which is paler, and in which the order of the colours is reversed. In the interior rainbow the red is the highest colour ; in the other rainbow the violet is. It is seldom that three bows are seen ; theoretically a greater number may exist, but their colours are so feeble that they are not perceptible. The phenomenon of the rainbow is produced by the decomposition of the white light of the sun when it passes into the drops and by its reflec- tion from their inside face. In fact, the same phenomenon is witnessed in dewdrops and in jets of water ; in short, wherever solar light passes into drops of water under a certain angle. The appearance and the extent of the rainbow depend on the position of the observer, and on the height of the sun above the horizon ; hence only some of the rays refracted by the rain drops, and reflected in their concavity to the eye of the spectator, are adapted to produce the pheno- menon. Those which do so are called elective rays. To explain this let « (fig. 757) be a drop of water, into which a solar ray S^: penetrates. At the point of incidence, a, part of the light is re- flected from the surface of the liquid ; another, entering it, is decomposed 86o Meteorology. [926- and traverses the drop in the direction ab. Arrived at b part of the light emerges from the rain drop, the other part is reflected from the concave surface, and tends to emerge at^. At this point the light is again par- tially reflected, the remainder emerges in a direction gO, which forms with the incident ray, S^:, an angle, called the angle of deviation. It is such rays as^O, proceeding from the side next the observer, -jvhich pro- 1 — TT" _ _ — ^^^^^^^^^g. i^- "-"-" "" ^^^B ^9^^B '; -±z-— 1 ^m E S'' '^B ^BP^^§ ^pBfo =: ^^B J^E^^^^Bfl ^Ht VV^^B - -^^i ^^B^^'-^H ^ ■'""'^^Kl-- l^v^^^^^^l ^^^K-^'~i^i f fli E^^^^^H SHfl i p ^m % i i Lt^HKi?^it M 1 ^ si ^M H i M ||jr^^~\«S^'^^ ^s Fig- 757. duce on the retina the sensation of colours, provided the light is suffi- ciently intense. It can be shown mathematically that in the case of a series of rays which impinge on the same drop, and only undergo a reflection in the interior, the angle of deviation increases from the ray ^"n, for which it is zero, up to a certain limit, beyond which it decreases, and that near this limit rays passing parallel into a drop of rain, also emerge parallel. From this parallelism a beam of light is produced sufficiently intense to impress the retina ; these are the rays which emerge parallel and are efficient. As the different colours which compose white light are unequally re- frangible, the maximum angle of deviation is not the same for all. For red rays the angle of deviation corresponding to the active rays is 42° 2', and for violet rays it is 40° 17'. Hence, for all drops placed so that rays proceeding from the sun to the drop make, with those proceeding from the drop to the eye, an angle of 42° 2', this organ will receive the sen- sation of red light ; this will be the case with all drops situated on the circumference of the base of a cone, the summit of which is the spectator's eye ; the axis of this cone is parallel to the sun's rays, and the angle formed by the two opposed generating lines is 84° 4'. This explains the formation of the red band in the rainbow : the angle of the cone in the case of the violet band is 80° 34'. The cones corresponding to each band have a common axis called the visual axis. As this right line is parallel to the rays of the sun, it follows that when this axis is on the horizon, the visual axis is itself horizontal, and the rainbow appears as a semicircle. If the sun rises, the visual axis sinks, and with it the rainbow. Lastly, when the sun is at a height of -927] Aurora Borealis. 86 1 42° 2', the arc disappears entirely below the horizon. Hence the phe- nomenon of the rainbow never takes place except in the morning and evening. What has been said refers to the interior arc. The secondary bow is formed by rays which have undergone two reflections, as shown by the ray S^i dfeO, in the drop p. The angle S'lO formed by the emergent and incident ray is called the angle of deviation. This angle is no longer susceptible of a maximum, but of a minimum, which varies for each kind of rays, and to which also efficient rays correspond. It is calculated that the minimum angle for violet rays is 54° 7', and for red rays only 50° 57'; hence it is that the red bow is here on the inside, and the violet arc on the outside. There is a loss of light for every internal reflection in the drop of rain, and, therefore, the colours of the secondary bow are always feebler than those of the internal one. The secondary bow ceases to be visible when the sun is 54° above the horizon. The moon sometimes produces rainbows like the sun, but they are very pale. 927. Aurora borealis. — The aurora bo7'ealis, or northern light, or more properly, pola?' aurora, is a remarkable luminous phenomenon which is frequently seen in the atmosphere at the two terrestrial poles. The following is a description of an aurora borealis observed at Bossekop, in Lapland, lat. 70°, in the winter of 1 838-1839. In the evening, between 4 and 8 o'clock, the upper part of the fog which usually prevails to the north of Bossekop became coloured. This light became more regular, and formed an indistinct arc of a pale yellow, with its concave side turned towards the earth, while its summit was in the magnetic meridian. Blackish rays soon separated the luminous parts of the arc. Luminous rays formed, becoming alternately rapidly and slowly longer and shorter, their lustre suddenly increasing and diminishing. The bottom of these rays always showed the brightest light, and formed a more or less regular arc. The length of the rays was very variable, but they always con- verged towards the same point of the horizon, which was in the prolon- gation of the north end of the dipping needle; sometimes the rays were prolonged as far as their point of meeting, and thus appeared like a frag- ment of an immense cupola. The arc continued to rise in an undulatory motion towards the zenith. Sometimes one of its feet or even both left the horizon ; the folds became more distinct and more numerous ; the arc was now nothing more than a long band of rays convoluted in very graceful shapes, forming what is called the boreal crown. The lustre of the rays varied suddenly in in- tensity, and attained that of stars of the first magnitude ; the rays darted with rapidity, the curves formed and reformed like the folds of a serpent (fig. 758), the base was red, the middle green, while the remainder re- tained its bright yellow colour. Lastly, the lustre diminished, the colours disappeared : everything became feebler or suddenly went out. A French scientific commission to the North observed 150 auroras boreales in 200 days; it appears that at the poles, nights without an aurora 862 Meteorology, [927- borealis are quite exceptional, so that it may be assumed that they take place every night, though with varying intensity. They are visible at a considerable distance from the poles, and over an immense area. Some- Fig. 758. times the same aurora borealis has been seen at the same time at Moscow, Warsaw, Rome, and Cadiz. Numerous hypotheses have been devised to account for the aurorae boreales. The constant direction of their arc as regards the magnetic meridian, and their action on the magnetic needle (663), show that they ought to be attributed to electric currents in the higher regions of the atmosphere. This hypothesis is confirmed by the circumstance observed in France and other countries on August 29 and September i, 1859, that two brilliant auroras boreales acted powerfully on the wires of the electric telegraph ; the alarums were for a long time violently rung, and despatches were frequently interrupted by the spontaneous abnormal working of the apparatus. The spectrum of the aurora borealis has been found by Vogel to consist of five lines in the green, and of an indistinct line in the blue : to which must be added a red line due to the red protuberances ; these lines are the same as those of nitrogen greatly rarefied and at a low temperature. According to M. dela Rive the aurorae boreales are due to electric dis- charges which take place in polar regions between the positive electricity of the atmosphere and the negative electricity of the terrestrial globe ; electricities which themselves are separated by the action of the sun, principally on the equatorial regions. The occurrence of irregular currents of electricity which manifest them- selves by abnormal disturbances of telegraphic communications is not in- frequent ; such currents have received the name of earth currents. Sabine -929] Climatology. 863 has found that these magnetic disturbances are due to a peculiar action of the sun, and probably independently of its radiant heat and light. It has also been ascertained that the aurora borealis as well as earth currents in- variably accompany these magnetic disturbances. According to Balfour Stewart, aurorse and earth currents are to be regarded as secondary cur- rents due to small but rapid changes in the earth's magnetism ; he likens the body of the earth to the magnetic core of a Ruhmkorff' s machine, the lower strata of the atmosphere forming the insulator, while the upper and rarer, and therefore electrically conducting strata, may be considered as the secondary coil. On this analogy the sun may perhaps be likened to the primary cur- rent which performs the part of producing changes in the magnetic state of the core. Now in Ruhmkorff's machine the energy of the secondary current is derived from that of the primary current. Thus if the analogy be correct, the energy of the aurora borealis may in like manner come from the sun ; but until we know more of the connection between the sun and terrestrial magnetism these ideas are to be accepted with some reserve. CLIMATOLOGY. 928. »Kean temperature. — The inean daily tejnper attire, or simply temperature, is that obtained by adding together 24 hourly observations, and dividing by 24. A very close approximation to the mean temperature is obtained by taking the mean of the maxima and minima temperatures of the day and of the night, which are determined by means of the maxi- mum and minimum thermometers. These ought to be protected from the solar rays, raised above the ground, and far from all objects which might influence them by their radiation. The temperatures of a month is the mean of those of 30 days, and the temperature of the year is the mean of those of 12 months. Finally, the temperature of a place is the mean of its annual temperature, for a great series of years. The mean temperature of London is 8*28° C, or 46-9° F. The temperatures in all cases are those of the air and not those of the ground. 929. Causes wbicb modify the temperature of ttae air. — The principal causes which modify the temperature of the air are the latitude of a place, its height, the direction of the winds, and the proximity of seas. Influence of the latitude. The influence of the latitude arises from the greater or less obliquity of the solar rays, for as the quantity of heat absorbed is greater the nearer the rays are to the normal incidence (382), the heat absorbed decreases from the equator to the poles, for the rays are then more oblique. This loss is, however, in summer, in the tem- perate and arctic zones, partially compensated by the length of the days. Under the equator, where the length of the days is constant, the tem- perature is almost invariable ; in the latitude of London, and in more northerly countries, where the days are very unequal, the temperature 864 Meteorology. [929- varies greatly ; but in summer it sometimes rises almost as high as under the equator. The lowering of the temperature produced by the latitude is small ; thus in a latitude of 115 miles north of France, the temperature is only 1° C. lower. hifltience of altitude. The height of a place has a much more consider- able influence on the temperature than its latitude. In the temperate zone a diminution of 1° C. corresponds in the mean to an ascent of 180 yards. The cooling on ascending in the atmosphere has been observed in balloon ascents, and a proof of it is seen in the perpetual snows which cover the highest mountains. ]t is caused by the greater rarefaction of the air, which necessarily diminishes its absorbing power ; besides which the air is at a greater distance from the ground, which heats it by con- tact ; and finally dry air is very diathermanous. The law of the diminution of temperature corresponding to a greater height in the atmosphere has not been made out, in consequence of the numerous perturbing causes which modify it, such as the prevalent winds, the hygrometric state, the time of day, etc. The difference between the temperature of two places at unequal heights is not proportional to the difference of level, but for moderate heights an approximation to the law may be made. As the mean of a series of very careful observations made by Mr. Walsh during balloon ascents, a diminution of 1° C. corresponded to an increase m height of 232 yards. Direction of winds. As winds share the temperature of the countries which they have traversed, their direction exercises great influence on the air in any place. In Paris, the hottest winds are the south, then come the south-east, the south-west, the west, the east, the north-west, north, and, lastly, the north-east, which is the coldest. The character of the wind changes with the seasons ; the east wind, which is cold in winter, is hot in summer. Proximity of the seas. The neighbourhood of the sea tends to raise the temperature of the air, and to render it uniform. The average tem- perature of the sea in equatorial and polar countries is always higher than that of the atmosphere. With reference to the uniformity of the tem- perature, it has been found that in temperate regions — that is, from 25° to 50° of latitude, the difference between the maximum and minimum tem- perature of a day does not exceed, on the sea, 2° to 3°; while upon the continent this amounts to 12° to 15°. In islands the uniformity of tem- perature is very perceptible, even during the greatest heats. In con- tinents, on the contrary, the winters for the same latitudes become colder, and the difference between the temperature of summer and winter be- comes greater. 930. Culf stream. — A similar influence to that of the winds is exerted by currents of warm water. To one of these, the Gulf stream, the mild- ness of the climate in the north-west of Europe is mainly due. This great body of water, taking its origin in equatorial regions, flows through the Gulf of Mexico, from whence it derives its name ; passing by the southern shores of North America, it makes its way in a north-westerly direction across the Atlantic, and finally washes the coast of Ireland and -933] IsotJiermal lines. Cliviate. 865 the north-west of Europe generally. Its temperature in the Gulf is about 28° C. (and generally it is a little more than 5° C.) higher than the rest of the ocean on which it floats, owing to its lower specific gravity. To its in- fluence is due the milder climate of west Europe as compared with that of the opposite coast of America ; thus the river Hudson, in the latitude of Rome, is frozen over three months in the year. It also causes the polar regions to be separated from the coasts of Europe by a girdle of open sea ; and thus the harbour of Hammerfest is open the year round. Besides its influence in thus moderating climate, the Gulf stream is an important help to navigators. 931. Isothermal lines. — When on a map aW the points whose tem- perature is known to be the same are joined, curves are obtained which Humboldt first noticed, and which he called isothermal lities. If the tem- perature of a place only varied with the obliquity of the sun's rays, that is, with the latitude, isothermal lines would all be parallel to the equator ; but as the temperature is influenced by many local causes, especially by the height, the isothermal lines are always more or less curved. On the sea, however, they are almost parallel. A distinction is made between isothcr- ?nal lilies, isotheral lines, and isochimenal lines, where the m.&2in general ,, the mean summer, and the mean winter temperatures are respectively con- stant. An isothermal zone is the space comprised between two isothermal lines. Kupffer also distinguishes isogeothermic lines where the mean tem- perature of the soil is constant. 932. Climate.— By the climate of a place is understood the whole of the meteorological conditions to which a place is subjected ; its mean annual temperature, summer and winter temperatures, and by the extremes within which these are comprised. Some writers distinguish seven classes of climates according to their mean annual temperature : a hot climate from 29° 5' to 25° C. ; a warm cliinate from 25° to 20° C. ; a inild climate horn 20° to 15° ; a temperate climate from 15° to 10° C. ; a cold climate from 10° to 5° ; a very cold climate from 5° to zero ; and an arctic climate where the temperature is below zero. Those climates, again, are classed as constant clzjnates, where the dif- ference between the mean and summer and winter temperature does not exceed 6° to 8° ; variable climates, where the difference amounts to from 16° to 20° ; and extreme climates, where the difference is greater than 30° The climates of Paris and London are variable ; those of Pekin and New York are extreme. Island climates are generally little variable, as the temperature of the sea is constant ; and hence the distinction between land and sea climates. Marine climates are characterised by the fact that the difference between the temperature of summer and winter is always less than in the case of continental climates. But the temperature is by no means the only character which influences climates ; there are in addition, the humidity of the air, the quantity and frequency of the rains the number of storms, the direction and intensity of the winds, and the nature of the soil. 933. Bistribution of temperature on the surface of the globe. The temperature of the air on the surface of the globe decreases from the PP S66 Meteorology. [933 equator to the poles ; but it is subject to perturbing causes so numerous and so purely local, that its decrease cannot be expressed by any law. It has hitherto not been possible to do more than obtain by numerous obser- vations the mean temperature of each place, or the maximum and minimum temperatures. The following table gives a general idea of the distribution of heat in the northern hemisphere :— Mean temperature at different latitudes. Abyssinia . 3i-o°C. Paris io-8° C Calcutta . 28-5 London 8-3 Jamaica . • 26-1 Brussels IO'2 Senegal 24-6 Strasburg . 9-8 Rio de Janeiro . 23-1 Geneva 97 Cairo . 22-4 Boston 9-3 Constantino . 17-2 Stockholm . 5-6 Naples . . 167 Moscow 3-6 Mexico i6-6 St. Petersburg . 3-5 Marseilles . 14-1 St. Gothard -ro Constantinople . 137 Greenland . -77 Pekin . 127 Melville Island . -187 These are mean temperatures. The highest temperature which has been observed on the surface of the globe is 47*4° at Esne, in Egypt, and the lowest is — 567 at Fort Reliance, in North America ; which gives a difference of io4'i° between the extreme temperatures observed on the surface of the globe. The highest temperature observed at Paris was 38*4° on July 8, 1793, and the lowest -23-5 on December 26, 1798. The highest observed at Greenwich was 35° C. in 1808, and the lowest —20° C. in 1838. No arctic voyagers have succeeded in reaching the poles, in conse- quence of these seas being completely frozen, and hence the temperature is not known. In our hemisphere the existence of a single glacial pole, that is, a place where there was the maximum cold, has been long assumed. But the bendings which the isothermal lines present in the northern hemisphere have shown that in this hemisphere there are two cold poles, one in Asia, to the north of Gulf Taymour, and the other in America, north of Barrow's Straits, about 1 5° from the earth's north pole. The mean temperature of the first of these poles has been estimated at — 17°, and that of the second at — 19°. With respect to the austral hemispheres, the observations are not sufficiently numerous to tell whether there are one or two poles of greatest cold, or to determine their position. 934. Temperature of lakes, seas, and springrs. — In the tropics the temperature of the sea is generally the same as that of the air ; in polar regions the sea is always warmer than the atmosphere. The temperature of the sea under the torrid zone is always about 26° to 27° at the surface ; it diminishes as the depth increases, and in tempe- rate as well as in tropical regions the temperature of the sea at great depths is between 2-5° and 3-5°. The temperature of the lower layers is -935] Distribution of Land and Water. S67 caused by submarine currents which carry the cold water of the polar seas towards the equator. The variations in the temperature of lakes are more considerable ; their surface, which becomes frozen in winter, may become heated to 20° or 25° in summer. The temperature of the bottom, on the contrary, is virtually 4°, which is that of the maximum density of water. Springs which arise from rain water which has penetrated into the crust of the globe to a greater or less depth necessarily tend to assume the temperature of the terrestrial layers which they traverse; Hence when they reach the surface their temperature depends on the depth which they have attained. If this depth is that of the layer of invari- able temperature, the springs have a temperature of 10° or 11° in this country, for this is the temperature of this layer, or about the mean annual temperature. If the springs are not very copious, their tempera- ture is raised in summer and cooled in winter, by that of the layers which they traverse in passing from the invariable layer to the surface. But if they come from below the layer of invariable temperature,, their tempera- ture may considerably exceed the mean temperature of the place, and they are then called thermal springs. The following list gives the tem- perature of some of them : C. Wildbad . .... 37-5' Vichy 4P Bath ...... 46 Ems . . . . 56 Baden-Baden ... 67-5 Chaudes-Aigues .... 88 Trincheras 97 Great Geyser, in Iceland, at a depth of 66 ft. 124 From their high temperature they have the property of dissolving many mineral substances which they traverse in their passage, and hence form jnmeral waters. The temperature of mineral waters is not modified m general by the abundance af rain or of dryness ; but it is by earth- quakes, after which they have sometimes been found to rise and at others to sink. 935. Distribution of land and water. — The distribution of water on the surface of the earth exercises great influence on climate. The area covered by water is considerably greater than that of the dry land ; and the distribution is unequal in the two hemispheres. The entire surface of the globe occupies about 200 millions of square miles, nearly | of which is covered by water ; that is, the extent of the water is nearly three times as great as that of the land. The surface of the sea in the southern hemisphere is to that in the northern in about the ratio of 13,10 9. The depth of the open sea is very variable, the lead generally reaches the bottom at about 300 to 450 yards ; in the ocean it is often 1,300 yards and instances are known in which a bottom has not been reached at a depth of 4,500. It has been computed that the total mass of the water does not exceed that of a liquid layer surrounding the earth with a depth of about 1,100 yards. PROBLEMS AND EXAMPLES IN PHYSICS. 1. A body being placed successively in the two pans of a balance, requires i8o grammes to hold it in equilibrium in one pan, and i8i grammes in the other ; required the weight of the body to a milligramme. From the formula deduced (72) we have X = a/i8o X 181 = 180S', 499. 2. What resistance does a nut offer when placed in a pair of nutcrackers at a distance of | of an inch from the joint if a pressure of 5 pounds applied at a distance of 4 inches from the joint is just sufficient to crack it? Ans. 26^ pounds. 3. What force is required to raise a cask weighing 6 cwt. into a cart o"8 metre high along a ladder 275 metres in length ? Ans. 195^ pounds. 4. If a horse can move 30 cwt. along a level road, what can it move along a road the inclination of which is i in 80? Ans. 26§ cwt. 5. The piston of a force-pump has a diameter of 8 centimetres, and the arms of the lever by which it is worked are respectively 12 and 96 centimetres in length, what force must be exerted at the longer arm if a pressure of 12 "36 pounds on a square cen- timetre is to be applied ? Ans. 78 pounds. 6. A stone is thrown from a balloon with a velocity of 50 metres in a second. How soon will the velocity amount to 99 metres in a second, and through what distance will the stone have fallen ? To find the time requisite for the body to have acquired the velocity of 99 metres in a second, we have V = V + gt', in which V is the initial velocity, g the acceleration of gravity which, with sufficient approximation, is equal to 9 '8 metres in a second, and t the time. Substituting these values, we have t = 99-5 = 49 =, 5 seconds. 9-8 9-8 ^ For the space traversed we have s =: Vt + ^gi^ = 50 X 5 + 4'9 X 25 =372*5 metres. 7. A projectile was thrown vertically upwards to a height of 5io™-22, Disregard- ing the resistance of the air, what was the initial velocity of the body ? The velocity is the same as that which the body would have acquired on falling from a height of 5 10 "22 metres. From the formula t^ = v^2^.yweget V = sj'z X 9-8 X 510*22 = \/ioooo = 100 metres. 8. A stone is thrown vertically upwards with an initial velocity of 100 metres. After what time would it return to its original position ? In this cas-a since its velocity at its highest point is null, we have, from the formula V = V - gt, V = 100 — gt, whence t = — = io"2 seconds. The time required for the body to fall is that in which it would have acquired the velocity of 100, that is 100 = ^/ or / = 10-2, and therefore the whole time is 2 X io'2 = 2o"4 seconds. 8/0 Problems and Examples in Physics. 9. A stone is thrown vertically upwards with an initial velocity of loo metres ; after X seconds a second stone is thrown with the same velocity. The second stone is rising 87 seconds before it meets the first. What interval separated the throws? The rising stone will have the velocity v = V — gt, whence v = too — 9-8 x 87. On the other hand, the falling stone, at the moment the stones meet, will have the velocity given by the equation v = gt' in which t' is the time during which the stone falls before it meets the second one. This time is equal to 87 seconds + x — ^^. Hence 9-8 its velocity is ^ v . = 9-8 (8-7 + - - P). Equating the two values of v and reducing, we obtain ^- = 3 seconds. 10. A body moving with a uniformly accelerated motion traverses a space of 1000 metres in 10 seconds. What would be the space traversed during the eighteenth second if the motion continued in the same manner ? The formula J = ^^/'^ gives. for the accelerating force ^.f = 20 metres per second. The space traversed during the eighteenth second will be equal to the difference of the space traversed in 18 seconds and that traversed at the end of the seventeenth. 350 metres. 11. A cannon-ball has been shot vertically upwards with a velocity of 250 metres in a second. After what interval of time would its velocity have been reduced to 54 metres under the retarding influence of gravity, and what space would have been traversed by the ball at the end oi this time ? If / be the time, then at the end of each second the initial velocity would be dimi- nished by 9"' •8. Hence we shall have 54 = 250- t X 9-8, whence t = 20 seconds and for the space traversed t == 250 X 20 - -9:8 X 20'2 _ 3040 metres. 12. Required the time in which a body would fall through a height of 2000 metres, neglecting the resistance of the air. From J = 5 gfi and substituting the values, we have ^000 = 5_ /2^ whence t = 20*2 seconds. 2 13. A body falls in air from a height of 4000 metres. Required the time of its fall and its velocity when it strikes the ground. From the formula s = \i gf^ we have for the time / = / — ; and, on the other V g hand, from the formula for velocity v = gt we have t = ^. Hence '^ = ^—, from which l^ = y/2 sg, and substituting the values for s and g, V = 200 metres. 14. A stone is thrown into a pit 150 metres deep and reaches the bottom in 4 seconds. With what velocity was it thrown, and what velocity had it acquired on reaching the ground ? Ans. The stone was thrown with a velocity of 17-9, and on reaching the ground had acquired the velocity 57-1. 15. A stone is thrown downwards from a height of 150 metres with a velocity of 10 metres per second. How long will it require to fall ? The distance through which the stone falls is equal to the sum of the distances through which it would fall in virtue of its initial impulse and of that which it would traverse under the influence of gravity alone : that is, 150 = 10 ^ + ^'^^^. 2 Taking the positive value only we get ^ = 4-61 seconds. Problems and Examples in Physics. 87 1' 16. Required the time of oscillation of a single pendulum whose length is 0-99384 and in a place where the intensity of gravity is 9-81. From the general formula t = v /-, in which / expresses the time of one oscil- lation, / the length of the pendulum, and'^ the intensity of gravity, we have / = ■5"i4i6 / -°?3 -4 = I second. 17. What is the intensity of gravity in a place in which the length of the seconds pendulum is o™"99i ? _ In this case zf = tt / _ ; and also t = i.- / ■, and therefore ■ = - , from ^, ^ g V g' g' which g' = *— . Substituting in this latter equation the values of g' I and /', we have^' = 9°i7o8. 18. In a place at which the length of the seconds pendulum is "99384, it is required to know the length of a pendulum which makes one oscillation in 5 seconds. In the present case, as g remains the same in the general formula, and t varies, the length / must vary also. We shall have, then. ^-s/'-A from which, reducing and introducing the values, we have /' = 5- X 0*99384 = 24-846. 19. A pendulum, the length of which is 1^-95, makes 61,682 oscillations in a day. Required the length of the seconds pendulum.. Ans. 0-99385 metres. 20. A pendulum clock loses 5 seconds in a day. By how much must it be shortened to keep correct time ? Ans. By 0-0001157 of its original length. 21. What is the normal acceleration of a body which traverses a circle of 4-2 metres diameter with a rectangular velocity of 3 metres ? Ans. 4-286 metres. 22. An iron ball falls from a height of 68 cm. on a horizontal iron plate, and rebounds to a height of 27 cm. Required the co-efficient of elasticity of the iron ? If an imperfectly elastic ball with the velocity v strikes against a plate, it rebounds with the velocity v =^ — k v, from which, disregarding the sign, k = -'. Now we V have the velocity t/^ = '^2. gh^ and v = \J -z gh, from which ^ = '-. Substitut- \/ h ing the corresponding values, we get k = 0-63. 23. Two inelastic bodies, weighing respectively 100 and 200 pounds, strike against each other with velocities of 50 and 20 feet, what is their common velocity after the impact? Ans. 30, or 3 -3, according as they move in the same or in opposite directions before impact. 24. The force with which a hydraulic press is worked is 20 pounds ; the arm of the lever on which this force acts is 5 times as long as that of the resistance ; lastly, the area of the large piston is 70 times that' of the smaller one. Required the pressure transmitted to the large piston. If /'' be the power, and p the pressure transmitted to the smaller piston, we have from the principle of the lever {40) / x i = /■" x 5. Moreover, from the principle of the equality of pressure (93) P X 1 =/X70 = 5X20X70 = 7000 pounds. 25. The force with which a hydraulic press is worked being 30 kilos, and the arm of the lever by which this force is applied being 10 times as long as that of the resist- ance, and the diameter of the small piston being two centimetres ; find the diameter of the large piston, in order that a pressure of 2000 kilos, may be produced. Ans. 16-33 centimetres. 8/2 Problems and Examples in Physics. ; 26. One of the limbs of a U-shaped glass tube contains mercury to a height of ©■"•lys ; the other contains a different hquid to a height of o'»*42 ; the two columns being in equilibrium, required the density of the second hquid with reference to mer- cury and to water. If d is the density of the liquid as compared with mercury and d^ the density com- pared with water, then i* x 0-175 = 0*42 x d\ and 13-6 x 0-175 = 0-42 x d/, whence d = 0-416 and d^ = 5-66. 27. What force would be necessary to support a cubic decimetre of platinum in mercury at zero ? Density of mercury 13-6 and that of platinum 21-5. From the formula P = VD the weight of a cubic decimetre of platinum is I X 21-5 = 21'' -5 and that of a cubic decimetre of mercury is i x 13-6 = 13^-6. From the principle of Archimedes the immersed platinum loses part of its weight -equal to that of the mercury which it displaces. Its weight in the hquid is therefore 21-5 — 13-6 = 7-9, and this represents the force required. 28. Given a body A which weighs 7-55 grammes in air, 5-17 gr. in water, and 6-35 gr. in another liquid, B ; required from these data the density of the body A and that of the liquid B. The weight of the body A loses in water 7 '55 — 5-17 = 2-38 grammes ; this repre- sents the weight of the displaced water. In the liquid B it loses 7-55 — 6-35 = 1-2 gr. ; this is the weight of the same volume of the body B, as that of A and of the displaced water. The specific gravity of A is therefore 755 = 3-172, and that of .g -^ = 0-504. 238 238 29. A cube of lead, the side of which is 4 cm., is to be supported in water by being suspended to a sphere of cork. What must be the diameter of the latter, the specific gravity of cork being 0-24, and that of lead 11-35? The volume of the lead is 64 cubic centimetres ; its weight in air is therefore 64 X 11-35 and its weight in water 64 ^ 11 '35 - 64 = 662-4 gr. If r be the radius of the sphere in centimetres its volume in cubic centimetres will be ^-^~, and its weight in grammes is ^^ ° ^'^ . Now, as the weight of the 3 3 displaced -water is obviously - w r^ in grammes, there will be an upward buoyancy represented by ^^ — — ^-^ ^ ^ \ = ^— ^1^7 ^ which must be equal to the 3 ^ r5 X o- 6 ^ weight of the lead : that is ^^ ^^ = 662-5, from which r = 5'^™-925 and the diameter = 11-85. 30. A cylindrical steel magnet 15 cm. in length and 1-2 mm. in diameter is loaded at one end with a cylinder of platinum of the same diameter and of such a length th»t when the .solid thus formed is in mercury, the free end of the steel projects 10 mm. above the surface. Required the length of this platinum. Specific gravity of steel being 7-8 and of platinum 21-5. The weight of the steel in grammes will be 15 w r'^ x 7-8 and of the platinum X ir r"^ X 21-5. These are together equal to the weight of the displaced mercury, which is w 7-2 (j^^ ^ ^) j^.^ fi-QiYi which X = 9-01 cm. 31. A cylindrical silver wire o'°-ooi5 in diameter weighs 3-2875 grammes ; it is to be covered with a layer of gold o'n-0002 in thickness. Required the weight of the gold ; the specific gravity of silver being 10-47 and that of gold 19-26. If r is the radius of the silver wire and ^ its radius when covered with gold, then r = o'=-075 and J? = o<=-095. The volume of the silver wire will be n r"^ I and its weight TT r^ 1 10-26, from which / = xT'-jeZ. The volume of the layer of gold is n [R-i _ ^2) 17-768, and its weight IT (0-0952 — 0-0752) X 17768 X 19-26 = 3-657 nearly. 32. A kilogramme of copper is to be drawn into wire having a diameter of 0-16 centimetre. What length will it yield ? Specific gravity of copper 8-88. Problems and Examples in Physics. ' 873 The wire produced represents a cylinder /cm. in length, the weight of which is T r^ / 8 88, and this is equal to looo grammes. Hence / = 56">*oo85. 33. Determine the volumes of two liquids, the densities of which are respectively 1-3 and 07, and which produce a mixture of three volumes having the density o'g. If X and y be the volumes, then from P = FD, 1-3 jc + o'jjv = 3 x 0*9 and AT + J)/ = 3, from which x — 1 and / = 2. 34. The specific gravity of zinc being 7 and that of copper 9, what weight of each metal must be taken to form 50 grammes of an alloy having the specific gravity 8-2 ; it being assumed that the volume of the alloy is exactly the sum of the alloyed metals ? Let :*: = the weight of the zinc, and j> that of the copper, then x + y = ^o, and p from the formula P = VD, which gives f^ = 7^. the volumes of the two metals and of the alloy are respectively -+'''= ^° , From these two equations we get x = 17 "07 and J = 32-93. 35. A platinum sphere 3 cm. in diameter is suspended to the beam of a very ac- curate balance, and is completely immersed in mercury. It is exactly counterbalanced by a copper cylinder of the same diameter completely immersed in water. Required the height of the cylinder. Specific gravity of mercury 13-6, of copper 8-8, and of platinum 21 "5. Ans. 2-025 centimetres. 36. To balance an ingot of platinum 27 grammes of brass are placed in the other pan of the balance. What weight would have been necessary if the weighing had been effected in vacuo? The density of platinum is 21-5, that of brass 8-3, and air under a pressure of 760 mm. and at the temperature 0° has the density of water. 770 The weight of brass in air is not 27 grammes, but this -veight minus the weight of a volume of air equal to its own. Since P = VD .• . V = - and the weight of the air is -^-^^^^ = =Z , D D X 770 8-3 X 770 By similar considerations, if x is the weight of platinum in vacuo, its weight in air will be x minus the weight of air displaced, that is :*: — , and this weight 21-5 X 770 is equal to that of the true weight of the brass ; and we have 27 — ^ — ?Z ; from which x = 26-996. 21-5 X 770 8-3 X 770 37. A body loses in carbonic acid 1-15 gr. of its weight. What would be its loss of weight in air and in hydrogen respectively ? Since a litre of air at 0° and 760 mm. weighs 1-293 gramme, the same volume of carbonic acid weighs 1-293 ^ i"524 = 1-97 gramme. We shall, therefore, obtain the volume of carbonic acid corresponding to 1-15 gr. by dividing this number by 1-97, which gives 0-5837 litre. This being then the volume of the body, it displaces that volume of air, and therefore its loss of weight in air is 0-5837 x 1-293 = 0-7547 grammes, and in hydrogen 0*5837 x 1-293 ^ 0*069 = 0*052076. 38. Calculate the ascensional force of a spherical balloon of oiled silk which, when empty, weighs 62-5 kilos, and which is filled with impure hydrogen, the density of which is ? that of air. The oiled silk weighs 0*250 kilo the square metre. 13 The surface of the balloon is ^ = 250 square metres. This surface being that of 0-25 a sphere, is equal to 4 tt R-, whence 4 tt i??2 = 250 and R = 4*459 ; therefore V — ^~— 3 = 371-52 cubic metres. The weight of air displaced is 371*52 x 1-293 ^i^o = 480-375 kilos ; the weight of the hydrogen is 39-88 kilos, and therefore the ascensional force is 480*375 - (36-88 + 62-5) = 38o*995- 39. A balloon 4 metres in diameter is made of the same material and filled with the same hydrogen as above. How much hydrogen is required to fill it, and what weight can it support ? 8/4 * Problems and Examples in Physics. The volume is ^ „ K^ = 33*5 1 cubic metres, and the surface 4 «• i?2 ^ 50-265 square 3 metres. The weight of the air displaced is 33-51 x 1-293 = 43'328 kilos, and that of the hydrogen is from the above data 3*33 kilos, while the weight of the material is 12-566 kilos. Hence the weight which the balloon can support is 43-328 - (12-566 + 3-33) = 27-432 kil. 40. Under the receiver of an air-pump is placed a balance, to which are suspended two cubes; one of these is 3 centimetres in the side, and weighs 26-324 gr., and the other is 5 centimetres in the side, and weighs 26-2597 grammes. When a partial vacuum is made these cubes just balance each other. What is the pressure? Ans. 0^-374. 41. A soap bubble 8 centimetres in diameter was filled with a mixture of one volume of hydrogen gas and 15 volumes air. The bubble just floated in the air ; re- quired the thickness of the film. The weight of the volume of air displaced is ^ t r^ x 0-001293 grammes, and that 3 of the mixture of gases "^ ^ ^^ x 0-001293 x ^■^ o_2_93 . ^nd the difference of 3 10 these will equal the weight of the soap bubble. This weight is that of a spherical shell, which, since its thickness / is very small, is with sufficient accuracy 4 if r^ t s va. grammes, where s is the specific gravity = 1-1. Hence -ttr^ \ -001293 — -001293 X ii^ 93 \ _ ^ ^ ,,0 ^ j,j 3 \ 16 y Dividing each side by '^ w r^, and putting r = 4, we get 3 4 X -001293 {t. - ^1^^) = 3'3 t\ •001293 X -23^ _ 2-3 ^ whence / = -00009116629 cm. 42. In a vessel wliose capacity is 3 litres, there are introduced 2 litres of hydrogen under the pressure 5 atmospheres ; 3 htres of nitrogen under the pressure of half an atmosphere, and 4 htres of carbonic acid under the pressure 4 atmospheres. What is the final pressure of the gas, the temperature being supposed constant during the experiment ? The pressure of the hydrogen, from Dalton's law, will be ?-AJ, that of the nitro- 3 gen will remain imchanged, and that of the carbonic acid will be l^Li. Hence the 3 total pressure will be = 9^ atmospheres. % ^^ + L 2 43, A vessel containing 10 litres of water is first exposed in contact with oxygen under a pressure of 78 cm. until the water is completely saturated. It is then placed in a confined space containing 100 litres of carbonic acid under a pressure of 72 cm Required the volumes of the two gases when equilibrium is established. The coeffi- cient of absorption of oxygen is 0-042, and that of carbonic acid unity. The volume of oxygen dissolved is 0-42. Being placed in carbonic acid it will act as if It alone occupied the space of the carbonic acid, and its pressure will be 78 X -^-^ — = 0-326 cm. 100-42 Similarly the 10 litres of water will dissolve 10 litres of carbonic acid gas the total volume of which will be no, of which 100 are in the gaseous state and 10 are dissolved. Its pressure is therefore 72 x ^ = 65-454 cm. Problems and Exaniples in Physics, 875 Hence the total pressure when equihbrium is established is o'326 + 65"454 = 6578 cm. ; and the volume of the oxygen dissolved reduced to the pressure 6578 is o"'*42"x ° 3^ _ o"'*oo2o8, and that of the carbonic acid 10 x -5^:54 _ q.q- 6578 4578 44. In a barometer which is immersed in a deep bath the mercury stands 743 mm. above the level of the bath. The tube is lowered until the barometric spape, which contains air, is reduced to one-third, and the mercury is then at a height of 701 mm. Required the atmospheric piessure at the time of observation. Ans. — 764. 45. What is the pressure on the piston of a steam boiler of 8 decimetres diameter if the pressure in the boiler is 3 atmospheres ? Ans. 10385 "8. 46. What is the pressure of that height at which an ascent of 21 metres corre- spond to a diminution of t^"^ in the barometric height ? Ans. 380""". 47. What would be the height of the atmosphere if its density were everywhere uniform? Ans. 7987 metres, or nearly 5 miles. 48. How high must we ascend at the sea level to produce a depression of i mm. in the height of the barometer ? Taking mercury as 10500 times as heavy as air, the height will be 10*5 metres. 49. Mercury is poured into a barometer tube so that it contains 15 cc. of air under the ordinary atmospheric pressure. The tube is then inverted in a mercury bath and the air then occupies a space of 25 cc. ; the mercury occupying a height of 302 mm. What is the pressure of the atmosphere ? Let X be the amount of this pressure, the air in the upper part of the tube will have a pressure represented by ^- , and this, together with the height of the mercurial 25 column 302, will be the pressure exerted in the interior of the tube on the level of the mercury in the bath, which is equal to the atmospheric pressure ; that is ^-^- + 302 = X, from which x = 755 mm. 50. What effort is necessary to support a cylindrical bell-jar full of mercury immersed in mercury ; its internal diameter being 6 centimetres, its height oi> above the surface of the mercury (fig. i) 18 centimetres, and the pressure of the atmosphere 077 centimetre? The bell-jar supports on the outside a pressure equal to that of a column of mercury, the section of whose base is cd, and the height that of the barometer. This pressure is equal to y?2 X 077 X 13-6. The pressure on the inside is that of the atmosphere less the weight of a column of mercury whose base is cd andheight^^. This is equal to tt 7?^ x (077 — o'i8) x I3'6; and the effort necessary is the difference of these two pres- sures. Making ^ = 3 cm., this is found to be 6"92i6 kilo- grammes. 51. A barometer is placed within a tube which is after- wards hermetically closed. At the moment of closing, the ^^'^' ^• temperature is 15° and the pressure 750 mm. The external space is then heated to 30°. What will be the height of the barometer ? The effect of the increase of temperature would be to raise the mercury in the tube in the ratiai + -^°- to i + -^-^-, and the height k would therefore be 5550 55SO 5550 and since in the closed space, the elastic force of the air increases in the ratio I + 15 a : I + 30 * we shall have finally A = 30174 mm. 8/6 Problems and Examples in Physics. 52. The heights of two barometers A and B have been observed at — lo'^ and + 15^, respectively, to be yi = 737 and B = 763. Required their corrected heights at oP. Ans. A = 738'33. B — jSog^. 53. A voltaic current gives in an hour 840 cubic centimetres of detonating gas under a pressure of 760 and at the temperature 12° -5 ; a second voltaic current gives in the «ame time 960 cubic centimetres under a pressure of 755 and at the temperature i5°'5- Compare the quantities of gas given by the two currents. Ans. 1 : i'i25. 54. The volume of air in the pressure gauge of an apparatus for compressing gases is equal to 152 parts. By the working of the machine this is reduced to 37 parts, and the mercury is raised through ©•48 metres. What is the pressure of the gas ? Here AB = 152, AC = 37 parts, and BC = ©'"•48. The pressure of air therefore in AC is, from Boyle's law, ^? = 4atm-io8 = 3™ -122. 37 r The pressure in the receiver is therefore 3'i22 + 0*48 = 3»n-6o2, which is equal to 474 atmospheres. Flo. 2. 55. An air-tight bladder holding two litres of air at the standard pressure and temperature is immersed in sea water to a depth of 100 metres where the temperature is 4°. Required the volume of the gas. The specific gravity of sea water being i '026, the' depth of 100 metres will repre- sent a column of pure water 102-6 metres in height. As the pressure of an atmo- sphere is equal to a pressure of io'33 metres of pure water, the pressure of this column 102 -68 = = Q 94 atm. 10-33 Hence, adding the atmospheric pressure, the bladder is now under a pressure of 10 "94 atmospheres, and its volume being inversely as the pressure will be — ^ -^ = 0"'i83 litre, 10-94 if the temperature be unaltered. But the temperature is increased by 4°, and therefore the volume is increased in the ratio 277 to 273, and becomes 0-183 277 _ 273 = 0-1855 litres. 56. To what height will water be raised in the tube of a pump by the first stroke of the piston, which is o-5m. in diameter, the height of the tube 6 metres, and its section iV that of the piston? At starting the air in the tube is under a pressure of 10 metres. If we take the section of the tube as unity, that of the body of the pump is 10 ; and the volumes of the tube and of the body of the pump are in the ratio of 6 to 5. Then if X is the height to which the water is raised in the pipe, the volumes of air in the pump before and after the working of the pump are 6 at the pressure 10, and 5 + 6 - jr at the pressure 10 — x. Forming an equation from these terms, and solving, we have two values, x' = 18™ 26 and x" = 2-74. The first of these must be rejected as being physically impossible ; and the true height is j: = 2*74 metres. 57. A receiver with a capacity of 10 litres contains air under the pres.sure 76 cm. It is closed by a valve, the section of which is 32 square centimetres, and is weighted with 25 kilogrammes. The temperature of the air is 30° ; its density at 0== and 76 cm. pressure is that of water. The coefficient of the expansion of gases is 0-00366. Required the weight of air which must be admitted to raise the valve. The air already present need not be taken into account as it is under the pressure Problems and Examples in Physics. 877 of the atmosphere. Let x be the pressure in centimetres of mercury of that which is admitted, X X i3"6 will represent in kilogrammes its pressure on a square centi- metre ; and therefore the internal pressure on the valve, and which is equal to the ex- X X I3'6 X 32 1000 temal pressure of 25 kilogrammes, is For the weight we shall have 25 k. From which jr = 57*44. P = ^' 0-00I293 ^ 57-44 ^ 8 -8055 grammes. I + o "00366 X 30 76*00 58. A bell-jar contains 3*17 litres of air; a pressure gauge connected with it marks zero when in contact with the air (fig. 3). The jar is closed and the machine worked ; the mercury rises to 65 cm. A second barometer stands at 76 cm. during the experiment. Required the weight of air withdrawn from the bell-jar and the weight of that which re- mains. At 0° and 76 cm. the weight of air in the bell-jar is 1*293 X 3*17 = 4*09881. At 0° and under the pressure 76 — 65 the weight of the residual air is 4*09881 X II 76 = 0*5932, and therefore the weight of that which is withdrawn is 4*0988 - 0*5932 = 3-5056 gr. 1 ^IE13^^^^H H jjjjjJSllllB [M^^^Mj IhhihhI Fig. 3. 59. The capacity of the receiver of an air-pump is 7*53 ; it is full of air under the ordinary atmospheric pressure and at 0°. Required the weight of air when the pressure is reduced to 0*21 ; the weight withdrawn by the piston ; and the weight which would be left at 15°. The weight of 7*53 litres of air under the ordinary conditions is 9*736 grammes. Under a pressure of 0*21 it will be 2 69 grammes, and at the temperature 15° it will 2*69 be I + 0*00366 X 15 = 0*255 gramme. 60. In a theoretically perfect air pump, how great is the rarefaction after 10 strokes, if the volumes of the barrel and the receiver are respectively 2 and 3 ? Ans. 4-59" or about - - of an atmosphere. 166 61. What must be the capacity of the barrel of an air-pump if the air in a re- ceiver of 4 litres is to be reduced to ^ the density in two strokes ? Ans. 2*9. 62. The reservoir of an air-gun, the capacity of which is 40 cubic inches, con- tains air whose density is 8 times that of the mean atmospheric pressure. A shot is fired when the pressure is 741 cm. and the gas which escapes occupies a volume of 80 cubic inches. What is the elastic force of the residual air? Ans. 6*05 atmospheres. 63. If water is continually flowing through an aperture of 3 square inches with a velocity of 10 feet, howmany cubic feet will flow out inanhour ? Ans. 750 cubic feet. 64. With what velocity does water flow from an aperture of 3 square inches, if 37*5 cubic feet flow out every minute? Ans. 30 feet. 65. What is the ratio of the pressure in the above two cases? Ans. i : 9. 66. What is the theoretical velocity of water from an aperture which is 9 feet below the surface of water ? ■ Ans. 24 feet. 67. In a cylinder, water stands 2 feet above the aperture and is loaded by a piston which presses with a force of 6 pounds on the square inch. Required the velocity of the effluent water. Ans. 32 feet. SyS Problems and Examples in Physics. 68. How deep must the aperture of the longer leg of a syphon, which has a sec- tion of 4 square centimetres, be below the surface of the water in order that 25 litres may flow out in a minute? Ans. 104 cm. 69. Through a «>^«/ar aperture having an area of o'oiqS square cm. in the bottom of a reservoir of water which was kept at a constant level, 55 cm. above the bottom, it was found that 98 "5 grammes of water flowed in 22 seconds. Required the coeffi- cient of efflux. Since the velocity of efflux through an aperture in the bottom of a vessel is given by the formula v = J agh, it will readily be seen that the weight .in grammes of water which flows in a given time,/, will be given by the formula w = a at \/ 2gh, where (2 is the area in square centimetres, a the coefficient of efflux, t the time in seconds and h the height in centimetres. Hence in this case a = 0-69609. 70. Similarly through a square aperture, the area of which was almost exactly the same as the above, and at the same depth, 104 '4 grammes flowed out in 21 '6 seconds. In this case a = 073. 71. A stone is dropped into a well, and 4 seconds afterwards the report of its striking the water is heard. Required the depth, knowing that the temperature of the air in the pit was 1074°. From the formula v = 333 s/i + a/ we get for the velocity of sound at the tem- perature in question 343 metres. Let / be the time which the stone occupies in falling ; then \ gfi = x will represent the depth of the well ; on the other hand, the time occupied by the report will be 4 — /, and the distance will be {\ — t)v = x (i) ; thus [^ — t) v = ^ gf- (ii), from which, substituting the values, (4-0 343 = 4*9 f^ t = 3793 seconds, andl substituting this value in either of the equations (i) or (ii), we have the depth = 70*5 metres nearly. 72. A bullet is fired from a rifle with a velocity of 414 metres, and is heard to strike a target 4 seconds afterwards. Required the distance of the target from the marks- man ; the temperature being assumed to be zero. - — + = a; X = 738 "2. 414 333 73. At what distance is an observer from an echo which repeats a sound after 3 seconds ; the temperature of the air being 10° ? In these 3 seconds the sound traverses a distance of 3 x 337 = im metres ; this distance is twice that between the observer and the reflecting surface ; hence the dis- tance is — ^ = 505 metres. 2 74. Between a flash of lightning and the time at which the corresponding thunder is first heard two beats of the pulse are counted. Knowing that the pulse makes 80 beats in a minute, what is the distance of the discharge ? Ans. 222 metres. 75. A stone is thrown into a well with a velocity of 12 metres ; and strikes the water 4 seconds afterwards. Required the depth of the well. Ans. About no metres. 76. What is the velocity of sound in coal gas at 0°, the density being 0-5? Afis, 475 metres. 77. What must be the temperature of air in order that sound may travel in it with the same velocity as in hydrogen at 0° ? Ans. About 3650° C. 78. What must be the temperature of air in order that the velocity of sound may be the same as in carbonic acid at 0° ? Ans. — io5°5'C. 79. The report of a cannon is heard 15 seconds after the flash is seen. Required the distance of the cannon, the temperature of the air being 22°. From the formula for the velocity of sound we have 15 X 333 \/i + 0-003665 X 22 = 5175 metres. Prohlems and Examples in Physics. Sf^ 80. A person stands 150 feet on one side of the line of fire of a rifle range 450 feet in length and at right angles to a point 150 feet in front of the target. What is the velocity of the bullet if the person hears it strike ^ of a second later than the report 9 of the gun? Ans. 2013 feet. 81. An echo repeats five syllables, eagh of which requires a quarter of a second to pronounce, and half a second elapses between the time the last syllable is heard, and the first syllable is repeated. What is the distance of the echo, the temperature of the air being 10° C. ? Afzs. 295 seconds. 82. The note given by a silver wire a millimetre in diameter and a metre in length being the middle C, what is the tension of the wire? Ans. zz'Sj kilogrammes, 83. The density of iron being 7 '8 and that of copper 8*8, what must be the thickness of wires of these materials of the same length and equally stretched so that they may give the same sound ? From the formula for the transverse vibration of strings we have for the number of vibrations n = ^ / — . As in the present case, the tensions, the length of the rl^ ft d strings, and the number of vibrations are the same, we have ^ /^ = -, /Z", from which i A=i /I; r"- d' 8-8 , r /8^ . , whence — = , = — ; hence - = ^ / — = 1 062. r,2 d 7*8 r, V 7-8 84. A wire stretched by a weight of 13 kilos sounds a certain note. What must be the stretching weight to produce the major third ? The major third having ^ the number of vibrations of the fundamental note, and as 4 all other things being the same, the numbers of vibrations are directly as the square roots of the stretching weight, we shall have x = 20'3i2 kilos. 85. The diameters of two wires of the same length and material are 0*0015 and 0-0038 m. ; and their stretching weights 400 and 1600 grammes respectively. Required the ratio of the numbers of their vibrations. Ans. n : n, = 1-266 : i. 86. A brass wire i metre in length stretched by a weight of 2 kilogrammes, and a silver wire of the same diameter, but 3 "165 metres in length, give the same number of vibrations. What is the stretching weight in the latter case ? Since the number of vibrations is equal, we shall have ris/ d rl\/ n d/ from which, replacing the numbers, we get ^ = 25 kilos. 87. A brass and a silver wire of the same diameter are stretched by the weights of 2 and 25 kilogrammes respectively, and produce the same note. What are their lengths, knowing that the density of brass is 8-39, and of silver 10-47. Ans. The length of the silver wire is 3-16 times that of the brass. 88. A copper wire 1-25 mm. in diameter and a platinum one of 0*75 mm. are stretched by equal weights. What is the ratio of their lengths, if, when the copper wire gives the note C the platinum gives F on the diatonic scale ? Ans. The length of the copper is to the length of the platinum = 1-264 : i- 89. An organ pipe gives the note C at a temperature 0° ; at what temperature will it yield the major third of this note? Ans. 153O C. 90. A brass wire a metre in length and stretched by a weight of a kilogramme, yields the same note as a silver wire of the same diameter but 2-5 metres in length and stretched by a weight of 7-5 kilogrammes. Required the specific gravity of the silver. Ans. 10 32, 91. Two mercurial thermometers are constructed of the same glass ; the internal diameter of one of the bulbs is 7™™ '5 and of its tube 2-5 ; the bulb of the other is 88o Problems and Examples in Physics, 6-2 in diameter and its tube 1-5. What is the ratio of the length of a degree of the first thermDmeter to a degree of the second ? Let A and B be the two thermometers, D and D' the diameters of the bulbs, and d and d' the dia- meters of the tubes. Let us imagine a third thermo- meter C with the same bulb as B and the same tube as A, and let /, /', and /" denote the length of a degree in each of the thermometers respectively. Since the stems of A and C have the equal dia- meters, the lengths / and /" are directly as the volumes of the tubes, or what is the same, as the cubes of their diameters ; and as B and C have the same bulk, the lengths /' and /" are inversely pro- portionate to the sections of the stems, or what amounts to the same, to the squares of their dia- meters. We have then Fig. introducing the values and solving, we have J, = 0-638. 92. A capillary tube is divided into 180 parts of equal capacity, 25 of which weigh 1*2 gramme. What must be the radius of a spherical bulb to be blown to it so that 180 divisions correspond to 150 degrees centigrade? Since 25 divisions of the tube contain 12 gramme, 180 divisions contain ' ^ ^ ^ ° = 8?''*64. And since these 180 divisions are to represent 150 degrees, the 25 weight of mercury corresponding to a single degree is 8^64 [50* But as the expansion cor- responding to one degree is only the apparent expansion of mercury in glass, the weight — 4- jg I _ Qf tj^g mercury in the reservoir, which is ^ irR^. From this ^ = I'Sy centi- 150 6480 3 metre. 93. By how much is the circumference of an iron wheel, whose diameter is 6 feet, increased when its temperature is raised 400 degrees ? Co-efficient of expansion of iron = o'ooooi22. Ans. By 0*092 foot. 94. What must be the length of a wire of this metal which for a temperature of 1° expands by one foot ? Ans. = 81967 feet. 95. A pendulum consists of a platinum rod, on a flattening at the end of which rests a spherical zinc bob. The length of the platinum is / at 0°. What must be the diameter of the bob, so that its centre is always at the same distance from the point of suspension wliatever be the temperature ? Coefficient of expansion of platinum o •0000088 and of zinc o •0000294. Ans. The diameter of the bob must be ^ of the length of the platinum. 96. At the temperature zero a solid is immersed 0*975 of its total volume in alcohol. At the temperature 25° the solid is wholly immersed. The coefficient of expansion of the solid being o •000026, required the coefficient of expansion of the alcohol. Ans. o •001052. 97. Into a glass globe, the capacity of which at 0° is 250 cc, are introduced 25 cc. of air measured at 0° and 76 cm. The flask being closed and heated to 100° required the internal pressure. Coefficient of cubical expansion of glass 38700' At 100^ the capacity of the flask is 250 (i + — -22_^ ; again at 100° the volume of V 38700/ X o •00366). the free air under the pressure 76 is 25 (i + 0100 250 y ^— under a pressure x. Hence 387 76 : ;»; = 250 x ■^^^ : 25 x 1-366, from which .But its real volume is 388 387 10-3548 cm. Problems and Examples in Physics. 88 r 98. The specific gravity of mercury at o° being i3'6, required the volume of 3c kilogrammes at 85°. Coefficient of expansion The volume at 0° will be 3° and at 85° -22. x ( i + — ^^- ) = 2-239 litres. 13-6 13-6 V 5550 >' 99. A hollow copper sphere 20 cm. in diameter is filled with air at 0° under a pressure of i^ atmosphere ; what is the total pressure on the interior surface when the enclosed air is heated to a temperature of 600°? Ans. 6226*5 kilogrammes. 100. Between the limits of pressure 700 to 780mm. the boiling point of water varies o°'0375 C. for each mm. of pressure. Between what limits of temperature does the boiling point vary, when the height of the barometer is between 735 and 755 mm. Ans. Between 99*^-0625 and 99° "8125. 101. Liquid phosphorus cooled down to 30°, is made to solidify at this tempera- ture. Required to know if the solidification will be complete, and if not, what weight will remain melted ? The melting point of phosphorus is 44*2 ; its latent heat of fusion 5-4, and its specific heat 0*2. Let X be the weight of phosphorus which solidifies ; in so doing it will give out a quantity of heat = 5'4 •*■ ; this is expended in raising the whole weight of the phos- phorus from 30 to 44-2. Hence we have 5-4 jr = i x (44-2 - 30) 0*2, from which X — "^A = 0*526, so that 0*474 of phosphorus will remain liquid. 5 '4 102. A pound of ice at o*^ is placed in two pounds of water at 0° ; required the weight of steam at 100° which will melt the ice and raise the temperature of the mix- ture to 30°. The latent heat of the liquefaction of ice is 79*2 and that of the vaporisa- tion of water 536. Ans. *279 pounds. 103. 65*5 grammes of ice at — 20° having been placed in x grammes of oil of turpentine at - 3°, the final temperature is found to be — 1°. The specific heat of turpentine is 0*4, and it is contained in a vessel weighing 25 grammes, whose specific heat is o*i. The specific heat of ice is 0*5. Required the value of x. Ans. x = 382*0 grammes. 104. In what proportion must water at a temperature of 30° and linseed oil (sp heat = 0*5) at a temperature of 50° be mixed so that there are 20 kilogrammes of the mixture at 40°? Ans. Water = 6*66 kilos, and linseed oil = 13*34. 105. By how much will mercury at 0° be raised by an equal volume of water at 100° ? Ans. 6%°-SC. 106. The specific heat of gold being 0*03244, what weight of it at 45° will raise a kilogramme of water from i2°*3 to i5°*7? Let X be the weight sought ; then x kilogrammes of gold in sinking from 45° tc 1 5° 7 will give out a quantity of heat represented by x (45° — 15° '7) 0*0324, and this is equal to the heat gained by the water that is to i (15*7 — 12*3) = 3*4, that is :*:• = 3*58. 107. The specific heat of sulphide of copper is 0*1212 and that of sulphide of silver 0*0846. 5 kilos, of a mixture of these two bodies at 40°, when immersed in 16 kilos, of water at 7*66 degrees, raises its temperature to 10°. How much of each sulphuret did the mixture contain ? The weight of the copper sulphuret = 2 and that of the silver sulphuret 3. 108. Into a mass of water at 0°, 100 grammes of ice at — 12° are introduced ; a weight of 7*2 grammes of water at 0° freezes about the lump immersed, while its temperature rises to zero. Required the specific heat of ice. Latent heat of water 79*2. Ans. 0*48114. 109. Four pounds of copper filings at 130° are placed in 20 pounds of water at 20°, the temperature of which is thereby raised 2 degrees. What is the specific heat, c, of copper? Ans. c = 0*0926. 110. Two pieces of metal weighing 300 and 350 grammes, heated to a temperature X, have been immersed, the former in 9408 grammes of water at 10°, and the latter in 546 grammes at the same temperature. The temperature in the first case rises to 20"^ and in the second to 30°. Required the original temperature and the specific heat of the metal. Ans. x the temperature = 1908° ; c the specific heat = •1038. 111. In what proportions must a kilogramme of water at 50° be divided in order that the heat which one portion gives out in cooling to ice at zero may be sufficient to change the other into steam at 100® ? Ans. x = 0*830. 882 Problems and Examples in Physies. 112. In 25-45 kilogrammes of water at i2°-5^ are placed 6-17 kilos of a body at a temperature of 80° ; the mixture acquires the ternperature 14° 'i. Required the specific heat of the body. If c is the specific heat required, then mc [f — 6) represents the heat lost by the body in cooling from 80° to i^P'i ; and that absorbed by the water in rising from 12"^ -5 to i4°'i is m' (B — i). These two values are equal. Substituting the numbers, we have c = O'OII. 113. Equal lengths of the same thin wire traversed by the same electrical current are placed respectively in i kilogramme of water and in 3 kilogrammes of mercury. The water is raised 10° in temperature, by how much will the mercury be raised ? Ans. 100° '04. 114. How many cubic feet of air under constant pressure are heated through 1° C. by one thermal unit ? Ans. 52 cubic feet. 115. Given two pieces of metal, one x weighing 2 kilos heated to 80°, and the other y weighing 3 kilos and at the temperature 50^. To determine their specific heats they are immersed in a kilogramme of water at 10°, which is thereby raised to 26°-3. The experiment is repeated, the two metals being at the temperature 100° and 40° respectively, and, as before, they are placed in a kilogramme of water at 10°, which this time is raised to. 28°*4. Required the specific heats of the two metals. Ans. X = -115 ; y = 0-0555. 116. For high temperatures the specific heat of iron is o"io53 + o •000071 /. What is the temperature of a red-hot iron ball weighing a kilogramme which, plunged in 16 kilogrammes of water, raises its temperature from 12° to 24° ? What was the tempe- rature of the iron ? (0*1053 -^ o"ooooi7/) (/ — 24) = 16 (24 — 12), or •000017 fi + "1048892 t — 2*5272 = 192 ; transposing and dividing by the coefficient of fi, we get ^2 + 6170 / = 1 1442776, /2 + 6170 t + (3085)- = 20960001 ; hence / + 3085 = 4578^3 nearly ; .-. t = 1493.3. 117. A kilogramme of the vapour of alcohol at 80° passes through a copper worm placed in io-8 kilogrammes of water at 12°, the temperature of which is thereby raised to 36°. The copper worm and copper vessel in which the water is contained weigh together 3 kilogrammes. Required the latent heat of alcohol vapour. Ans. 210-4^. 118. Determine the temperature of combustion of charcoal in burning to form car- bonic acid. We know from chemistry that one part by weight of carbon in burning unites with 2§ parts by weight of oxygen to form 3§ parts by weight of carbonic acid. Again the number of thermal units produced by the combustion of a pound of charcoal is 8080 ; the whole of this heat is contained in the 3§ parts of carbonic acid produced, and if its specific heat were the same as that of water, its temperature would be — — = 2204° C. ; but since the specific heat of carbonic acid is 0-2163 that of an equal weight of water, the temperature will be .^?21 = 10189 C. 0^2163 119. Through a U-tube containing pumice saturated with sulphuric acid a cubic metre of air at 15° is passed, and the tube is found to weigh 3^95 grammes more. Required the hygrometric state of the air. The pressure of aqueous vapour at 15° is 12^699 ; hence the weight of a cubic metre of aqueous vapour saturated at 15° is 1293 x i2^699 x 5 ^ ^^.^^ grammes, I + ^^ 760 X 8 273/ and the hygrometric state is -3 '95 _ o-qoo 12-79 120. The quantity of water given out by the lungs and skin may be taken at 30 ounces m 24 hours. How many cubic inches of air already half saturated at 10° will be fully saturated by the moisture exhaled from the above two sources by one man ? Tension of aqueous vapour in inches = 0-532. Pressure of the atmosphere = 30 inches. Ans. 328782-5 c.i. = a cube 5-752 feet in the side. * Problems and Examples in Physics. 883 121. A mass of air extending over an area of 60,000 square metres to a height of 300 metres has the dew point at 15° its temperature being 20°. How much rain will fall if the temperature sinks to 10° ? The weight of vapour condensed from one cubic metre under these circumstances will be 3*1435 grammes and therefore from 18,000,000 cubic metres it will be 56,583 kilogrammes, which is equal to a rainfall 0*0943 mm. in depth. 122. When 3 cubic metres of air at 10° and 5 cubic metres at 18°, each saturated with aqueous vapour at those temperatures, are mixed together is any water precipi- tated ? And if so how much ? The weight of water contained in the two masses under the given conditions are respectively 28"i8 and 76*59 grammes ;the weight required to saturate the mixture at the temperature of 15° is 102*39 grammes, and therefore 2*38 grammes will be precipitated. 123. The temperature of the air at sunset being 10°, what must be the lowest hygro- metric state, in order that dew may be deposited, it being assumed that in conse- quence of nocturnal radiation the temperature of the ground is 7° below that of the air ? Atts. The hygrometric state must be at least 0*62 of total saturation. 124. A raindrop falls to the ground from a height of a mile. By how much would its temperature be raised, assuming that it imparts no heat to the air or to the ground? Ans. 30*8 C. 125. A lead bullet falls through a height of 10 metres ; by what amount will its temperature have been raised when it reaches the ground, if all the heat is expended in raising the temperature of the bullet ? Ans. 0744° Centigrade. 126. From what height must a lead bullet fall in order that its temperature may be raised ;/ degrees ? — and what velocity will it have acquired ? It is assumed that all the heat is expended in raising the temperature of the bullet, the specific heat of lead is taken at 0*0314 and Joule's equivalent in metres at 424. Ans. 13*31 X n metres ; ?7 = 16*2 y/ n. 127. How much heat is disengaged if a bullet weighing 50 grammes and having a velocity of 50 metres strikes a target ? Atis. Sufficient to raise one gramme of water through 15° C. 128. How much heat is produced in the room of a manufactory in which i 2. horse- power of the motor is consumed each hour in overcoming the resistance of friction? Ans. A quantity sufficient to raise 41,024 pounds of water one degree centigrade. 129. What is the ratio between the quantities of heat which are respectively pro- duced, when a bullet weighing 50 grammes and having a velocity of 500 metres, and a cannon ball weighing 40 kilogrammes with a velocity of 400 metres, strike a target? A71S. i : 512. 130. How many candles are required to produce at a distance of 2*5 metres, the same illuminating effect as one candle at a distance of 0*45 m. ? Am. 31. 131. Two sources of light whose intensities are as i : 2 are two metres apart. At what position is a space between them equally illuminated ? Ans. 0*82 metres from the less intense light. 132. A candle sends its rays vertically against a plane surface. When the candle i? removed to thrice the distance and the surface makes an angle of 60° with the original position, what is the ratio of the illuminations in the two cases ? Ans. i : — i8- 133. An observer, whose eye is 6 feet above the ground, stands at a distance of 18 feet from the near edge of a still pond, and sees there the image of the top of a tree, the base of which is at a distance of 100 yards from the place at which the image is formed. Required the height of the tree. Ans. 100 feet. 134. What is the height of a tower which' casts a shadow 56*4 in length when a vertical rod 0*95 m. in height produces a shadow 1*38 in length? Ans. 38 -8. 135. A minute hole is made in the shutter of a dark room ; and at a distance of 2*5 metres a screen is held. What is the size of the image of a tree which is 15-3 metres high and is at a distance of 40 metres? Ans. 0*95625 metres. 136. What is the length of the shadow of a tree 50 feet high when the sun is 30° above the horizon? What when it is 45° and 60°? Ans, 86*6 ; 50 and 28*867 feet. 884 Problems and Examples in Physics, ♦ 137. Under what visual angle does a line of 30 feet appear at a distance of 18 feet ? Atis. 79° '36. 138. The apparent diameter of the moon amounts to 31' 3". What is its real dia- meter if its distance from the earth is taken at 51535 geographical miles? A7ts. 465 geographical miles. 139. For an ordinary eye an object is visible with a moderate illumination and pure air under a visual angle of 40 seconds. At what distance, therefore, can a black circle (6 inches in diameter) be seen on a white ground ? Ans. 2578 feet. 140. At what distance from a circle with a diameter of one foot is the visual angle a second? Ans. 206265 feet. 141. At what distance would a circular disc i inch in diameter, of the same bright- ness as the sun's surface, illuminate a given object to the same extent as a vertical sun in the tropics, the light absorbed by the air being neglected ? Ans. Taking the sun's angular diameter at 30', j; = 38 inches. 142. What is the minimum deviation for a glass prism « = i •53, whose refracting angle is 60°? Ans. 39° 48'. 143. What is the minimum deviation for a prism of the same substance when the refracting angle is 45° ? Ans. 63° 38'. 144. The refracting angle of a prism of silicate of lead has been found by measure- ment to be 21° "1 2, and the minimum deviation to be 24° "46. Required the refractive index of the substance. Atis. 2*122. 145. Construct the path of a ray which falls on an equiangular crown-glass prism at an angle of 30° ; and find its deviation. Ans. 70° "45. 146. What are the angles of refraction upon a ray which passes from air into glass at an angle of 40° ; from air into water at an angle of 65° ; and from air into diamond at an angle of 80°? Ans. 25° '22 ; 43° '49 ; 23° -12. 147. The focal distance of a concave mirror is 8 diameters. What is the distance of the image from the mirror when the object is respectively at 12, 5, and 7 diameters distance? Ans. 24; — 13-3 and — 56. 148. An object at a distance of 10 feet produces a distinct image at a distance of 3 feet. What is the focal distance of the mirror? Ans. 2 '3077 feet. 149. Required the focal distance of a crown glass meniscus, the radius of curvature of the concave face being 45 mm., and that of the convex face 30 mm. Ans. f = 180 mm. 150. What is the principal focal distance of a double-convex lens of diamond, the radius of curvature of each of whose faces is 4 mm., and the refractive index of dia- mond 2*487? Ans. 1*34 mm. 151. A watch-glass with ground edges, the curvature of which was 4*5 cm., was filled with water and a glass plate slid over it. The focus of the plano-convex lens thus formed was found to be 13*5 cm. Required the refractive index of the water. Ans. n = i'33- 152. What is the focal distance of a double-convex lens when the distances of the image and object are respectively 5 and 36 centimetres? Ans. 4*4 centimetres. 153. The radii of curvature of a double-convex lens of crown glass are six and eight inches. What is the focal distance? Ans. 6*85 inches. 154. The focal distance pf a double-convex lens is 4 inches, the radius of cur- vature of one of its faces is 3 inches. What is that of the second? Ans. 6 inches. 155. The radius of curvature of a plano-convex lens is 12 inches. Required its focal distance. Ans. 24 inches. 156. If the focal distance of a double-convex lens is r centimetre, at what distance must a luminous object be placed so that its image is formed at 2 centimetres dis- tance from the lens. Ans. 2 centimetres. 157. A candle at a distance of 120 centimetres from a lens forms an image on the other side of the lens at a distance of 200 feet. Required the nature of the lens and its focal distance. Ans. It is a convex lens, and its focal distance is 75 cm. 158. A plano-convex lens was found to produce at a distance of 62 cm. a sharp image of an infinitely distant object. In front of the same lens, at a distance 84 cm., a millimetre scale was placed, and a sharp image was formed at a distance of 250 cm. It was thus found that 10 millimetres in the object corresponded to 29 in the image. Problems and Examples in Physics. 885 From these three observations determine the focal distance of the lens. Ans. The mean of the three results is 62*4. 159. The image of a distant tree was sharply formed at a distance of 31 cm. from the centre of a concave mirror. In another case the image of an object 18 mm. in length at a distance of 405 mm. from the mirror was formed at 1350 mm. from the mirror and had a length of 61 mm. In another experiment the distances of object and image and the size of the image were respectively 2200, 355 and 3 mm. Deduce from these several data the focal distance of the mirror. A)is. 31 '2; 30*5. 160. A compass needle at the magnetic equator makes 15 oscillations in a minute ; how many will it make in a place where the horizontal force of the earth's magnetism is ? — as great? A?is. 12. 25 161. A compass needle makes q oscillations a minute under the influence of the earth's magnetism alone ; how many will it make when re-magnetised so as to be half as strong again as before? Ans. 11. 162. On a table where the earth's magnetism is counteracted, the north pole of a compass needle makes 20 oscillations in a minute under the attraction of a blue pole 4 inches distant ; how many will it make when the blue pole is 3 inches distant ? Ans. 26 "6. 163. If the oscillating magnet be re-magnoitised so as to be twice as strong as before, how many oscillations in a minute will it make ? Ans. 3771. 163a. At one end of a light glass thread, carefully balanced so as to oscillate in a vertical plane, is a pith ball. Over this and in contact with it is a fixed pith ball of the same dimensions. Both balls being charged with the same electricity it is found that to keep them i "4 inch apart, a weight of '9 mgr. must be placed at the free end of the glass thread. .What weight must be placed there to keep the balls i"os inch apart ? Ans. I "6 mgr. 163<5. A small insulated sphere A charged with the quantity of + electricity 2 is at a distance of 25 mm. from a second similar sphere B charged with the quantity 5 ; the latter is momentarily touched with an unelectrified sphere B, of the same size, and the distance altered to 20 mm. What is the ratio of the repulsive forces in the two cases ? Ans. 25 : 32. 163c. Two insulated spheres whose diameters are respectively as 7 : 10 have equal quantities of electricity imparted to them. In what ratio are their electrical densities ? Ans. 100 : 49, 163d. Two such spheres whose diameters are as 3 : 5 contain respectively the quantities of electricity 7 and 10. In what ratio are their densities? Ans. 35 : 18. 164. A galvanometer offering no appreciable resistance is connected by short thick wires with the poles of a cell, and deflects 20°. By how much will it be deflected if two exactly similar cells are connected with the first side by side ? Ans. 47° '30. 165. By how much if the three cells are connected in series ? Ans. 20°. 166. Two cells each of i ohm resistance are connected in series by a wire the resistance of which is also i ohm. If each of these when connected singly by short thick wires to a galvanometer of no appreciable resistance deflects it 25°, how much will the combination deflect it, the connections being made by short thick wires? Ans. 17° -1 6. A Siemens' unit is equal to the resistance of a column of pure mercury a metre in length and a square mm. in cross section. It is equal to 0-9536 of an ohm or B A unit; or a B A unit equals i'0485 Siemens' unit, or equals a column of mercury i'0485 metre in length and a square mm. in cross section. 167. A single thermo-electric couple deflects a galvanometer of 100 ohms resis- tance 30'; how much will a series of such couples deflect it, the connections being made by short thick wires? Ans. 14° '40. 168. Suppose a sine galvanometer had been used in the last question, and the first reading had been 30', what would the second be? Ans. i5°'io. 169. The internal resistance of a cell is half an ohm ; when a tangent galvan- ometer of I ohm resistance is connected with it by short thick wires it is deflected 15° ; by how much will it be deflected if for one of the thick wires a thin wire of i^ ohm resistance is substituted? Ans. 7° •37. 886 Problems and Examples in Physies. 170. What will be the deflection if each of the wires is replaced by a thin wire of i^ ohm resistance ? Ans. 5° 5', 171. A ceU of one-third of an ohm resistance deflects a tangent galvanometer of unknown resistance 45°, the connection being made by two short thick wires. If a wire of 3 ohms resistance be substituted for one of the short wires the deflection is 30°. What is the resistance of the galvanometer? Ans. 3*42 ohms. 172. What would be the deflection if for the cell in the last question three exactly similar cells in series were substituted {a) when the galvanometer alone is in circuit ; ib) when both the galvanometer and the thin wire are in circuit ? Atis. a 66°- 10. b = 55° '30. 173. A galvanometer offering no sensible resistance is deflected 50° by a cell connected with it by short thick wires. If a resistance of 3 ohms be put in the circuit the deflection is 20°. Find the internal resistance of the cell. Ans. 1-49. 174. Suppose the results in the last question were produced by two exactly similar cells in series, find the internal resistance of each. Ans. 0-65. 175. Suppose they were produced by two exactly similar cells placed side by side, ^nd the internal resistance of each. Ans. 2-63. 176. If the resistance of 130 yards of a particular copper wire — - of an inch in 16 diameter is an ohm, express in that unit the resistance of 8242 yards of copper vnre — 12 of an inch in diameter. . Ans. 35*66. 177. One form of fuse for firing mines by voltaic electricity consists of a platinum wire f of an inch long, of which a yard weighs 2 grains. Required its resistance in terms of a Siemens unit. Specific gravity of platinum 22, and its conducting power 1 1 -25 that of mercury. Ans. o'l^i. 178. Express in ohms the resistance of one mile of copper wire | of an inch in diameter. Ans. 07577. 179. The whole resistance of a copper wire going round the earth (24800 miles) is 221650 ohms. Find its diameter in inches. Ans. — . 13 180. How much platinum wire 0-05 of an inch in diameter must be taken to get a resistance equal to i ohm, the specific resistance of platinum being taken at 5*55 that of copper? Ans. 14-26. 181. 160 yards of iron wire 0-0625 of an inch in diameter have the same electrical resistance as a mile of copper wire 0-0416 of an inch in diameter. Find the specific re- sistance of iron, that of copper being unity. Ans. 6. 182. Ten exactly similar cells in series produce a deflection of 46° in a tangent galvanometer, the external resistance of the circuit being 10 ohms. If arranged so that there is a series of 5 cells, of two abreast, a deflection of 33° '42 is produced ; find the internal resistance of the cell. Ans. ^ ohm. 183. On the bobbins of the new Post Ofiice pattern of a single needle instrument are coiled 225 yards of No. 35 copper wire o'oo87 inch in diameter, the resistance of which is about 92 ohms. Required the conducting power of the wire in terms of mercury. Ans. 56. 184. Ten exactly similar cells each of | of an ohm resistance give, when arranged in five series of 2 each, a deflection of 23^-57 ; but when arranged in 2 series of 5 each a deflection of 33^-40. Required the external resistance of the circuit including that of the galvanometer. Ans. \. 185. A cell in a certain circuit deflects a tangent galvanometer 18° 26' ; two such cells abreast in the same circuit deflect it 23° 57' ; two such cells in the same circuit diminished by i ohm deflect it 29° -2. Find the internal resistance of one cell and that of the circuit. Ans. R = r = i*66. 186. What is the best arrangement of 6 cells, each of | of an ohm resistance, against an external resistance of 2 ohms ? Ans. Indifferent whether in 6 cells of i each or in 3 cells of 2. 187. What is the best arrangement of 20 cells, each of 0*8 ohm resistance, against •an external resistance of 4 ohms ? Ans. 10 cells of 2 each. 188. In a circuit containing a galvanometer and a voltameter, the current which deflects the galvanometer 45° produces 10-32 cubic centimetres of mixed gas in a Problems and Examples in Physics. ^Zj minute. The electrodes are put farther apart, and the deflection is now 20° ; find how much gas is now produced per minute. Ans. 375 cc. 189. 100 inches of copperwire weighing 100 grains has a resistance of o'i5i6 ohm. Required the resistance of 50 inches weighing 200 grains. ' Ans. c'oiSgs. 190. A knot of nearly pure copper wire weighing one pound has a resistance of 1200 ohms at i5°"5 C. ; what is the resistance of a knot of the same quality of wire weighing 125 pounds? Ans. 9*6 ohms. 191. Find the length in yards of a wire of .the same diameter and quality as the- knot pound in 178, having a resistance of 2 ohms. Ans. 3-38 yards. 192. Find the length in yards of a wire of the same quality and total resistance as the knot pound in 178, but of three times the diameter. Ans. 18261 yards. 193. The specific gravity of platinum is 2J times that of copper ; its resistance 5^ 9 as great. What length of platinum wire weighing 100 grains has the same resistance as ICO inches of copper wire also weighing 100 grains? Ans. 7*2. 194. A cell with a resistance of an ohm is connected by very short thick wires, with the binding screws of a galvanometer, the resistance of which is half an ohm, and the deflection is 45° ; if the screws be also connected at the same time by a wire of i ohm resistance, find the deflection. Ans. 36° 52'. 195. The resistance of a galvanometer is half an ohm, and the deflection when the current of a cell is passed through it is 30°. When a wire of 2 ohms resistance is introduced into the circuit the deflection is 15° ; find the internal resistance of the cell. Ans. I '23. 196. When the current of a cell, the resistance of which is f of an ohm, is passed through a galvanometer connected with it by very short thick wires, the deflection is 45° ; when the binding screws are also connected by a shunt having a resistance of i the deflection is 33° "42. Find the resistance of the galvanometer. Ans. 2. 197. A cell whose internal resistance is 2 ohms has its copper pole connected with the binding screw A of a galvanometer formed of a thick band of copper. From the other screw B a wire of 20 ohms resistance passes to the zinc pole, and the deflection read off is 7°'8. Find the deflection when B is at the same time connected with the zinc pole by a second wire of 30 ohms resistance. Ans. 11 •6. 198. What would be the deflection in 185 if the second wire instead of passing from B to the zinc pole passed directly from the zinc pole to the copper pole ? Ans. 6° "43. 199. A Leclanch^ cell deflects a galvanometer 30° when 200 ohms resistance are introduced into the circuit, 15° when 50 ohms are introduced ; a standard Daniell's cell deflects at 30' when 100 ohms are in circuit and 15° when 250 additional ohms are introduced. Required the electromotive force of the Leclanch^ in terms of that of the Daniell. Ans. 1-48. 200. A Bunsen and a Daniell cell are placed in the same circuit in the first case so that the carbon of the first is united to the zinc of the Daniell ; and in the second case so that their currents oppose each other. The currents are respectively 30° "2, and in the second 10° '6. Required the electromotive force of the Bunsen in terms of the Daniell. Ans. \-?,(^. 201. A telegraph line constructed of copper wire, a kilometre of which weighs 30*5 kilogrammes is to be replaced by iron wire a kilometre of which weighs 135 '6 kilo- grammes. In what ratio does the resistance alter? Ans. The resistance of the iron wire will be i"i8 times that of the copper wire for which it is substituted. 202. A telegraph line which has previously consisted of copper wire weighing 30*5 kilogrammes to the kilometre is to be replaced by an iron wire of the same diameter which shall offer the same resistance. What must be the section of the latter, and what its weight per kilometre ? Ans. The section of the copper wire is 3*4357 sq. mm., that of the iron by which it is replaced is 2o'6 sq. mm., and its weight per kilometre is 160 '4 kilogrammes. i • INDEX. (THE NUMBERS REFER TO THE ARTICLES.) ABE ABEL'S electrical fuse, 746 Aberration, chromatic, 546 ; spherical, 501 Absolute expansion of mercury, 300 • Absorbent power of aqueous vapour, 909 Absorbing power, 397 Absorption, 139 ; of gases, 140; of gases by liquids, 175 ; of heat by liquids, 407 ; by vapours, 408 ; heat pro- duced by, 452 Acceleration of a force, 27, 74 Accidental haloes, 590 ; images, 589 ; magnetic variations, 656 Accommodation (of the eye), 583 Achromatism, 547 ; of the microscope, 555 Achromatopsy, 595 Acidometer, 123 Acierage, 805 Aclinic lines, 660 Acoustics, 208-272 Acoustic foci, 223 Actinic rays, 409, 538 Action and reaction, 39 Adhesion, 83 Aerial meteors, 900 Aerolites, 450 -^sculine, 545 Affinity, 82 Agents, 6 Agonic line, 654 Air, aspirating action of currents of, 186 ; causes which modify tempera- ture of, 929 ; heating by, 461 ; ther- mometer, 311 Air balloons, 177; chamber, 196 Air pump, 438 ; Bianchi's, 184 ; con- densing, 181 ; gauges, 182 ; rarefac- tion in, 181 ; receiver of, 181 ; Spren- gel's, 185 ; uses of, 189 AQU Ajutage, 203 Alarum, electric, 840 Alcarrazas, 349 Alcoholic value of wines, 354 Alcoholometer, 125 ; Gay-Lussac's, 125 ; centesimal, 125 'Alcohol thermometer, 285 Alloys, 317 Amalgam, 708 Amalgamated zinc, 768 Amber, 682 Amici's microscope, 5 54 ; camera lucida, 566 Ampere's memoria ' technica^ 772 ; theory of magnetism, 827 Amplitude of vibration, 5 1 Analogous pole, 691 Analyser, 618 Analysis, spectral, 540; of solar light, 403 Anelectrics, 683, 702 f Anelectrotonus, 779 Anemometer, 900 Aneroid barometer, 173 Angle of deviation, 512 ; optic, 580 ; of polarisation, 616 ; reflection and incidence, 480, 504 ; of repose, 39 ; refraction, 504 ; visual, 580 Angular currents, laws of, 808 Animal heat, 455 Anione, 791 Annealing, 87 Annual variations, 655 Anode, 791 Antilogous pole, 691 Anvil, 863 Aqueous humour, 575 Aqueous vapour, its influence on cli- mate, 909; tension of, 331, 332, 333 QQ 890 Index. ARA Arago's experiment, 167 Arbor Dianse, 801 ; Satumi, 801 Arc of vibration, 51 ; voltaic, 784 Archimedes' principle, 1 10 ; applied to gases, 176 Area, unit of, 22 Armatures, 678 ; Siemens', 858 Arms of levers, 40 Armstrong's hydro-electric machine, 712 Artesian wells, 108 Artificial magnets, 642 Ascent of liquids in capillary tubes, 129 ; between surfaces, 130 Astatic currents, 821 ; needle and sys- tem, 662 Astronomical telescope, 558 Athennancy, 407 Atmosphere, its composition, 146 ; crushing force of, 148 ; amount of, determination of, 152 ; electricity in the, 917, 918 ; moisture of, 374 Atmospheric electricity, causes of, 916, 919 ; pressure, 147 Atomic heat, 429 ; weight deduced from specific heat, 429 Atoms, 3 Attraction, capillary, 131 ; and repul- sion produced by capillarity, 131 ; molecular, 80 ; universal, 63 Attractions, magnetic, laws of, 665 ; electrical, laws of, 692 Atwood's machine, 74 Aura, 719 Aurora borealis, 656, 927 Aurum musivum, 708 Austral pole, 651 Avoirdupois, 23 Axis of crystal, 603 ; electric, 691 ; lenses, 519; optic, 580; of a mag- net, 643 ; of oscillation, 76 ; visual, 926 Azimuthal circle, 657 BABINET'S stopcock, 183 Bain's electrochemical telegraph, 838 Bad cond^tors, 378 Balancd^^j^^j beam of, 69 ; compensat- ing, -^98 ; delicacy of, 70 ; hydro- static, 117; knife edge of, 68 ; physi- cal and chemical, 71 ; torsion, 86, 666, 692 Ballistic pendulum, 78 Balloons, 177-180; construction and management of, 178 ; Mongolfier, 177 BOI Bands of spectrum, 541 Barker's mill, 205 Barometers, 153; aneroid, 173; Bunten's, 156 ; cistern, 154 ; correc- tions in, 159 ; determination of heights by, 165; fixed, 164; For- tin's, 155 ; Gay-Lussac's, 156 ; pre- cautions with, 157 ; wheel, 163 ; variations of height of, 160 Barometric formula, Laplace's, 165 ; height of, corrected for heat, 305 ; manometer, 172 ; variations, 161 Baroscope, 176 Battery, Bunsen's, 763 ; Callan's, 763 ; chemical effects of, 790 ; Daniell's, 761; electric, 729 ; gas, 798 ; gravity, 765 ; Grove's, 762 ; Leclanche's, 765 ; Leyden, constant, 760 ; charged by coil, 864 ; local, 825 ; luminous effects, 784 ; magnetic, 677; measure- ment of charge, 732 ; mechanical effects of, 789 ; Menotti's, 765 ; Marie Davy's, 765 ; postal, 825 ; Smee's, 764 ; sulphate of mercury, 765 ; tension of, 767 ; thermo-electric, 876 ; voltaic, 757, 758 ; Walker's, 764 ; Wollaston's, 758 Beam of a balance, 69 ; of a steam-en- gine, 438 Beats, 246 Beaume's hydrometer, 124 Becquerel's pyrometer, 880 ; thermo- electric battery, 876 ; electrical ther- mometer, 879 Bell of a trumpet, 223 Bellows, 229 ; hydrostatic, 98 Bennett's electroscope, 705 Berthollet's experiment, 174 Bertin's commutator, 818 Bertsch's machine, 714 Bianchi's air pump, 184 Biaxial crystals, double refraction in, 607 ; optic axes of, 607 ; rings in, 629 Bifurcation, 602 Binnacle, 659 Binocular vision, 584 Biot's apparatus, 638 Black's experiments on latent heat, 432 Bladder, swimming, 115 Block and tackle, 44 Blood globules, 15 Bodies, properties of, 7, 119 Bohnenberger's electroscope, 770 Boiler, 437 Boiling, 326 ; by cooling, 343 ; laws of, 339 Ifidex, 891 Bor Boiling point, influence of dissolved substances on, 341 ; of nature of vessel, 342 ; of pressure on, 343 ; in a thermometer, 281 ; measure of heights by, 345 Boreal pole, 651 Boutigny's experiments, 360 Boyle and Mariotte's law, 166-168 Bramah's hydraulic press, 105 Breaking weight, 88 Breezes, land and sea, 902 Breguet's thermometer, 288 Bridge, Wheatstone's, 886 British Association unit, 884 British imperial yard, 22 ; and French system of M'eights and measures, 1 22 Browning's regulator, 787 Brush discharge, 739 Bull's eye, 554 Bunsen's battery, 763 ; burner, 541 ; ice calorimeter, 423 ; photometer, 479 Bunsen and Kirchhoff's researches, 542 Bunten's barometer, 156 Buoyancy of liquids, 97 Burning mirrors, 393 C.^SIUM, 542 Cagniard-Latour's syren, 228 ; experiments on formation of va- pour, 346 Callan's battery, 763 Calorescence, 406 Caloric, AI9 Calorific effects of electrical discharge, 742 ; of current electricity, 780, 781 ; of RuhmkorfTs coil, 864 ; of the spectrum, 538 Calorimeter, 421; Bunsen's ice, 422; Black's, 422 ; Favre and Silber- mann's, 434 ; Lavoisier and La- place's, 422 Calorimetry, 418 Camera lucida, 557 ; Amici's, 566 ; obscura, 565 ; Porta's obscura, 483 Campani's eye-piece, 555 Capacity, specific inductive, 702 Capillarity, 128 ; attraction and repul- sion produced by, 131 ; correction for, 158 Capillary phenomena, 128-134 ; tubes, 129 ; ascent and depression in, 129 ; between parallel or inclined surfaces, 130 Capsule, of the eye, 575 CLO Cardan's suspension, 155 Carre's mode of freezing, 350 ; dielec- trical machine, 715 Carriage lamps, 503 _ Cartesian diver, 113 Cascade, charging by, 731 Cathetometer, 85 Catoptric telescopes, 561 Caustics, 501, 502 Celsius' scale, 282 Centesimal alcoholometer, 125 Centigrade scale, 282 Centimetre, 122 Centre, optical, 523 ; of gravity, 65 ; of parallel forces, 37 ; of pressure, 99 Charge of a Leyden jar, penetration of, 728 ; measurement of, 732 ; laws of, 733,; residual, 728 Charging by cascade, 731 Chatterton's compound, 832 Chemical affinity, 82 ; combination, 453 ; effects of the battery, 745 ; of electrical discharge, 745 ; of voltaic currents, 773 ; of Ruhmkorff's coil, 864 ; harmonicon, 262 ; hygrorpeter, 368; properties of the spectrum, 538 Chemistry, i Chevallier's microscope, 554 Cheval-vapeur, 444 Chimes, electrical, 718 Chimney, 457 Chladni's experiments, 266 Chlorophylle, 544 Chords, major and minor, 233 ; physi- cal constitution of, 248 ; tones dominant and subdominant, 233 ; vocal, 245 Choroid, 575 Chromatic scale, 236 ; aberration, 546 Chromium, magnetic limit of, 680 Ciliary processes, 575 Circle, azimuthal, 657 Circular polarisation, 631 Cirrocumulus, 905 Cirrostratus, 905 Cirrus, 905 Cistern barometer, 154 Clarke's magneto-electrical machine, 85 5 Cleavage, electricity produced by, 690 Clement and Desorme's experiment, 186 Climate, 932 ; constant 932 ; inrtuence of aqueous vapour on, 909 Climatology, 927-934 Clocks, 78 ; electrical, 841 Clouds, 905 ; electricity of, 920 ; for- mation of, 906 QQ?. 89? Index. COA Coatings, 724 ; Leyden jar with mov- able, 726 Cobalt, 680 Coercive force, 649 Coefficients of linear expansion, 292, 294 Cohesion, 81 Coil, primary, 837 ; Ruhmkorff's, 862 ; effects produced by, 864 ; secondary, 837 Cold, apparent reflection of, 395 ; pro- duced by evaporation, 349; expansion of gases, 464 ; by nocturnal radiation, 465 ; sources of, 463 Colladon and Sturm's experiments, 221 Collecting plate, 734 Collimation, 558 Collision of bodies, 55 Colloids, 136 Coloration produced by rotatory polari- sation, 637 Colour, 7 ; of (bodies, 555 ; of heat, 409 ; of thin pktes, 612 Colour disease, 595 Colours, contrast of, 5904 mixed, 536 ; simple, 532 ; complementary, 536 ; produced by polarised light, 624-630; by compressed glass, 630 Combustion, 453 ; heat diisergaged during, 454 Comma, musical, 234 Common reservoir, 685 Communicator, 832 Commutator, 833, 835, 856, 863 ; Berlin's, 818 Compass, correction of errors, 658 ; declination, 657 ; mariner's, 659; inclination, 660 ; sine, 776 ; tangeitt, 775 Compensating cube, 411 Compensation pendulum, 298; balance, 298 ; gridiron, 298 ; strips, 298 Complementary colours, 536 Component forces, 32 Composition of velocities, 48 Compound microscope, 52 Compressed glass, colours produced by, 630 Compressibility, 7, 16; of gases, 166; of liquids, 92 Concave mirrors, 392, 496 Concert pitch, 237 Concordant tones, 233 Condensation of vapours, 351 Condensed gas, 140 ; wave, 213 Condenser, 438, 713, 720 ; limits to ctm charge of, 723 ; of Ruhmkorff's coil, 863 ; Liebig's, 353 Condensing engine, 443 ; air pump. 188 ; force, calculation of, 722 ; electroscope, 734 ; plate, 734 ; hy- grometers, 369 Conical pendulum, 53 Conduction of heat, 377 ; of electricity, 684 ; lightning, 925 Conductivity of bodies for heat, 378 ; coefficient of, 378 ; of gases, 382 ; of liquids, 380 ; for electricity, 885, 888 Conductors, 684 ; equivalent, 885 ; good and bad, 378 ; lightning, 925 ; l^rime, 707 ; resistance of, 883 Congelation, 320 Conjugate mirrors, 393 ; focus, 493, 520 Connecting rod, 438 -^ Conservation of energy, 62 Constant currents, 760 Contact theory of electricity, 751 Contractile force, 297 Convection, 381 Convex meniscus, 128 ; mirrors, 494, 497 Cooling, method of, 426 ; Newton's law of, 390 Cornea, 575 Corpuscular theory, 469 Corti's fibres, 245 Cosine, law of the, 387, 478 Coulomb's law, 665 Couple, 36 ; terrestrial magnetic, 652 ; voltaic, 754 ; thermo-electric, 874 Couronne des tasses, 758 Coxwell's balloon, 177 Critical angle, 508 ; temperature, 346 Cross- wire, 558 Crutch of a clock, 78 Cryophorus, 349 Crystal, hemihedml, 691 Crystalline, 575 Crystallisation, 321 Crystalloids, 136 Crystals, 321 ; expansion of, 294 ; doubly refracting, 602, 614, 625 ; uniaxial, 605 ; positive and negative, 606 Cube, Leslie's, 396 Cumulostratus, 905 Cumulus, 905 Current electricity, 753 Currents, action on currents, 810, 811 ; action of magnets, 814 ; action of earth on, 820, 821 ; action on Index, 89s CUR solenoids, 822, 827 ; constant, 760 ; derived, 891 ; detection and measure- ment of voltaic, 771 ; diaphragm, 789 ; direct and inverse, 851 ; effects of enfeeblement of, 759 ; extra, 850, 851 ; of inclination, 893 ; intensity of> 777 j induction by, 843 ; laws of angular, 808 ; laws of sinuous, 809 ; local, 768 ; magnetisation by, 829 ; motion and sounds produced by, 831 ; muscular, 892 ; rotation of magnets by, 814 ; secondary, 759 ; terrestrial, 828 ; thermal effects of, 781, 782 ; transmissions by, 793 Curvature of liquid surfaces, 132 ; in- fluence of, on capillary phenomena, 133 Curves, magnetic, 666 Cushions, 707 Cyanogen gas, 356 Cylinder, 438 ; electrical machine, 71 1 DAGUERREOTYPE, 571 Daltonism, 595 Dalton's laM^s on gases and vapours, 358 ; method of determining the ten- sion of aqueous vapour, 332 Damper, 263, 848 Daniell's battery, 761 ; hygrometer, 370 ; pyrometer, 290 Dark lines of the spectrum, 539 ; of solar spectrum, 543 Davy's battery, 765 Davy's experiment, 394 Day, apparent, 21 Decimetre, 24, 122 Declination, compass, 657 ; magnetic, 653 ; of needle, 653 ; variations in, 654 ; of a star, 563 Decomposition, chemical, 790 ; of white light, 530 ; of salts, 792 Deflagrator, Hare's, 758, 780 Degrees of a thermometer, 282 De la Rive's floating battery, 815 ; ex- periments, 867 Delezenne's circle, 849 Delicacy of balance, 70 ; of thermo- meter, 286 Densimeter, 127 Density, 24 ; of the earth, 64 ; electric, 694 ; of gases, 312-314 ; maximum of water, 307 ; of vapours, Gay- Lussac's method, 361 ; Dumas's, 362 ; Deville and Troost's, 363 DOU Depolarisation, 627 Depolarising plate, 625 Depression of liquids in capillary tube, 129 ; between surfaces, 130 Derived currents, 891 Descartes' laws of refraction, 505 Despretz's experiment, 378 Developer, 572 Deviation, angle of, 512 Deville and Troost's method, 363 Dew, 911 ; point, 369 Diabetic urine, analysis of, 640 Dial telegraphs, 834 Dialyser, 136 Dialysis, 136 Diamagnetism, 870 Diapason, 243 Diaphanous iDodies, 470 Diaphragm, 554 ; currents 789 Diathermancy, 407 Dielectrical machine, Carre's, 715 Dielectrics, 702 Differential barometer, 1 72 Differential galvanometer, 773 ; ther- mometer, Leslie's, 287; Matthiessen's, 287 ; tone, 247 Diffraction, 473, 611 ; fringes, 609 Diffusion of heat, 410 ; of liquids, 136 Digester, Papin's, 347 Dioptric telescopes, 561 Diplopy, 594 Dip, magnetic, 660 • Dipping needle, 660 Discharge, electrical, 721 ; effects of the, 736 ; lateral, 925 ; slow and instantaneous, 721 ; universal, 736 Discharging rod, 721 Disc, Newton's, 533 Dispersion, 512 Dispersive power, 530 Dissipation of energy, 468 Distance, estimation of, 581 ; adapta- tion of eye to, 583 Distillation, 352 Distribution of free electricity, 693 ; of magnetism, 681 ; of temperature, 933 ; of land and water, 935 Diurnal variations, 655 Diver, Cartesian, 113 Dividing machine, 1 1 Divisibility, 7, 12 Dobereiner's lamp, 452 Dominant chords, 234 Doppler's principle, 220 Double action steam engine, 438, 439 Double refraction, 614 894 Index, DOU Doublet, Wollaston's, 549 Dove's law of storms, 903 Draught of fire-places, 458 Driving wheels, 441 Drummond's light, 569 Dry piles, 769 Duboscq's microscope, 569 ; regulator, 786 Ductility, 7, 89 Duhamel's graphic method, 231 Dulong and Arago's experiments on Boyle's law, 167 ; method of deter- mining the tension of aqueous va- pour, 333 Dulong and Petit's determination of ab- solute expansion of mercury, 300 Dulong and Petit's method of cooling, 426 ; law, 429 Dumas's method for vapour density, 362 Duplex telegraphy, 837 Duration of electrical spark, 747 Dutiochet's endosmometer, 135 Dynamical theory of heat, 402 Dynamic radiation and absorption, 415 Dynamo-magnetic machine, 860 EARTH, its action on currents, 819- 821 ; action of solenoids, 826 ; flattening of, by rotation, 79; magnetic poles of the, 660 ; magnetisation by, 674 Earth's magnetism, 663 Earnshaw on velocity of sound, 2 1 7 Ear trumpet, 225 Ebullition, 326 ; laws of, 339 Eccentric, 438, 439 Echelon lenses, 570 Echoes, 223 ; monosyllabic, trisyllabic, multiple, 223 Efflux, velocity of, 199 ; quantity of, 202 ; influence of tubes on, 203 Eff"usion of gases, 138 Elastic bodies, 55 Elastic force, 141 ; of vapours, 327 Elasticity, 7, 17 ; limit of, 17, 85; of traction, 85 ; modulus of, 85 ; of torsion, 86 ; of flexure, 87 Electrical machines, 706-715 ; precau- tions in, 708 Electrical attractions and repulsions, 692 ; resistance, unit of, 884 ; con- ductivity, 888 Electric alarum, 840 ; axis, 691 ; bat- teries, bottle, 741, 729; charge, 733; -ENE chimes, 718 ; clocks, 841 ; density, 694 ; discharge, 736 ; egg, 740 ; fish, 897; fuse, 746; glow, 739; light, 782-784 ; stratification of the, 865 ; pendulum, 683 ; pistol, 745 ; poles, 691 ; residue, 728 ; shock, 725, 737; spark, 717; telegraphs, 832- 842 ; whirl, 719; tube, 741 Electricity, 6, 682 ; application of, to medicine, 898 ; atmospheric, 916- 925 ; current, 753 ; bodies in contact, 696 ; communication of, 703 ; de- velopment of, by friction, 689 ; by pressure and cleavage, 690 ; distri- bution of, 693 ; dynamical, 749-891 ; disengagement of, in chemical actions, 745, 751 ; frictional, 689; loss of, 697 ; mechanical effects, 744 ; produced by induction, 699 ; velocity of, 748; theories of, 687 Electrified bodies, motion of, 688, 704 Electrochemical telegraph, 838 ; series, 791 Electrodes, 756 ; polarisation of, 759 Electrodynamics, 806 Electrogilding, 803 Electrolysis, 791 ; laws of, 795 P-^lectrolyte, 791 Electromagnetic force, 830 ; machines, 842 Electromagnets, 830 Electrometallurgy, 802-804 Electrometer, 705 ; Lane's, 732 ; quad- rant, 710 ; Thomson's, 735 Electromoter, 832 Electromotive series, 754 ; force, 755, 766, 777 ; determination of, 889 ; force of elements, 766 Electrophorus, 706 Electropyrometer, 880 Electroscope, 683 ; Bohnenberger's, 770 ; Volta's condensing, 734 ; gold leaf, 705 Electrosilvering, 804 Electrotonus, 779 Elements, electronegative and electro- positive, 791 Elliptical polarisation, 634 Emergent rays, 510, Emission theory, 469 Emissive power, 398 Endosmometer, 132 Endosmose, 135 ; electrical, 789 ; of gases, 137 Endosmotic equivalent, 135 Energy, 59 ; conservation of, 62 ; dis- Index. 895 ENG sipation of, 468 ; transformations of, 61 ; varieties of, 60 Engines, gas, 446 ; steam, 436 ; double action, 438 ; low and high pressure, 443 ; single action, 440 ; locomotive, 441 ; fire, 198 ; transformation of, 61 Eolipyle, 442 Equator, 643; magnetic, 660 Equilibrium of forces, 35 ; of floating bodies, 1 12 ; of heavy bodies, 66 ; of liquids, 103-104; mobile of tempera- ture, 388 ; neutral, 67 ; stable, 67 ; unstable, 67 Equivalent, endosmotic, 135 ; conduc- tors, 885 Escapement, 78 ; wheel, 78 Ether, 402 ; luminiferous, 469 Evaporation, 326 ; causes which accele- rate it, 328 ; cold due to, 349 ; latent heat of, 348 Evaporation and ebullition, 340 Exchanges, theory of, 388 Exhaustion, produced by air-pump, 184; by Sprengel's pump, 185 Exosmose, 135 Expanded wave, 213 Expansibility of gases, 141 Expansion, 275 ; appai-ent and real, 299 ; absolute, of mercury, 300 ; ap- parent, of mercury, 301 ; of liquids, 304 ; of solids, 292 ; of gases, 308- 310 ; linear and cubical, coefficients of, 292 ; measurement of linear, 293 ; of crystals, 296 ; applications of, 297 ; force of, 306 Expansion of gases, cold produced by, 464 ; problems on, 309 Expansive force of ice, 323 Experiment, Berthollet's, 1 74 ; Frank- Im's, 344 ; Florentine, 94 ; Pascal's, 151 ; Torricellian, 150 Extension, 7, 9 Extra current, 850, 851 ; direct, 851 ; inverse, 851 Eye, 575 ; accommodation of, 583 ; not achromatic, 591 ; refractive in- dices of media of, 576 ; path of rays in, 578 ; dimensions of various parts of, 577 Eye-glass, 512, 593 ; lens, 555 ; piece, 549, 553, 555 ; Campani's, 555 FAHRENHEIT'S hydrometer, 120; scale, 282 Falling bodies, laws of, 73 FOR Faraday's wheel, 588 ; theory of indue" tion, 701 ; voltameter, 795 Favre and Sil Hermann's calorimeter, 434 ; determination of Jbeat of com^ bustion, 453 ^ Field of a microscope, 554; of view, 556; magnetic, 669 Field lens and glass, 555 ; of micro- scope, 554 Figures, Lichtenberg's, 727 Finder, 558 Fire engine, 198; places, 457; works, 205 Fish, electrical, 897 Fishes, swdmming bladder of, 114 Fizeau's experiments, 477 Flame, 453^ Flask, specific gravity, 118 Flattening of the earth, 79 Flexure, elasticity of, 87 Float, 437 Floating bodies, 112 Florentine experiment, 13, 94 Fluid, 4 ; imponderable, 6 \ elastic 144 ; magnetic, 645 Fluidity, 7 Fluorescence, 545 Flute, 264 Fluxes, 317 Fly-wheel, 438 Focal distance, 392 Foci, acoustic, 223 ; of convex mirrors, 494 ; in double convex lenses, 520 Focus, 392, 493 ; conjugate, determi- nation of the principal, 495 ; of a spherical concave mirror, 493 Focussing the microscope, 550 Fogs, 904 Foot, 22 Foot-pound, 56, 444 Force, 26 ; conservation of, 62 ; coer- cive, 649 ; direction of, 30 ; elastic, of gases, 141; lines of magnetic, 669; of expansion and contraction, 297 ; electromotive, 755, 766 ; representa- tion of, 30 ; parallelogram of, 33 ; of liquids, 306 ; portative, 679 Forces, 6; along the same line, 31 ; equilibrium of, 38 ; impulsive, 57 ; magnetic, 660 ; molecular, 80 ; mo- ments of, 38 ; polygon of, 35 ; triangle of, 35 Formulae for expansion, 296 ; barome- tric, 163 ; for sound, 218 ; for spheri- cal mirrors, 498, 499 ; for lenses, 527 Fortin's barometer, 155 896 Index. FOU Foucault's determination of velocity of light, 476 ; experiment, 785 Fountain in vacuo, 189 ; at Giggles- wick, 193; intermittent, 191 ; Hero's, 190 Franklin's experiment, 344, 916; plate, 724 ; theory of electricity, 687 Fraunhofer's lines, 539, 540 Freezing, apparatus for, 350 Freezing mixtures, 324 ; point in a thermometer, 281 French weights and measures, 1 20 ; boiler, 437 Fresnel's experimentum crucis, 608 ; rhomb, 633 Friction, 26, 45 ; heat of, 447 ; hy- draulic, 203 ; development of electri- city by, 689 Friction wheels, 74 Frigorific rays, 395 Fringes, 609 Frog, rheoscopic, 894 Frost, 901 Frozen mercury, 349, 356, 360 Fulcrum, 43 Fulgurites, 923 Fulminating pane, 724 -Fuse, Abel's, 746; Chatham, 780, 781 Fusing point, 315 Fusion, laws of, 315 ; vitreous, 315 ; latent heat of, 432 ; of ice, 421 GALILEAN telescope, 560 Galleries, whispering, 223 Gallon, 122 Galvani's experiment, 749 Galvanometer, 773 ; differential, 773 ; vSir W. Thomson's, 774 Galvanoscope, 773 Galvanothermometer, 781 Gas battery, 798 ; engines, 446 Gases, absorption of, by liquids, 175 ; application of Archimedes' principle to, 1 76 ; cold produced by expansion of, 464 ; compressibility of, 143, 166 ; conductivity of, 382 ; diamag- netism of, 869 ; density of, 312, 314 ; expansion of, 142, 308-311 ; endos- mose of, 137 ; effusion and transpira- tion of, 1 38 ; Gay-Lussac's method, 308; index of refraction of, 518; laws of mixture of, 1 74 ; and vapours, mixtures of, 358 ; permanent, 356 ; problems in, 359 ; liquefaction of, 356 ; physical properties of, 141 ; HAM pressure exerted by, 145 ; radiation of 414 ; Regnault's method, 313 ; speci- fic heat of, 43 1 ; velocity of sound in, 217, 218, 219 ; weight of, 144 Gaseous state, 4 Gassiott's battery, 767 Gauge, air-pump, 182 ; rain, 907 Gay-Lussac's alcoholometer, 125 ; baro- meter, 156; determination and ex- pansion of gases, 308 ; of vapour- density, 361 ; stopcock, 358 Geissler's tubes, 185, 542, 866 Generating plate, 754 Geographical meridian, 653 Geometrical shadows, 473 Gififard's injector, 186 Gimbals, 659 Glacial pole, 933 Glaciers, 915 Glashier's balloon ascents, 177; factors, 372 Glasses, periscopic, 592 ; weather, 163 Glass, expansion of, 303 ; magnifying, 549; object, 553 ; opera, 560 Globe lightning, 923 Glow, electrical, 739 Gold leaf electroscope, 705 Goniometers, 502 Good conductors, 378 Gramme, 24, 122 Gramme's magneto-electrical machine, 861 Graphic method, Duhamel's, 231 ; Foster's, 782 Gratings, 610 Gravesande's ring, 274 Gravitation, 6, 79 ; terrestrial, 64 ; ac- celerative effect of, 27 Gravity, battery, 765 Gravity, centre of, 65 Gregorian telescope, 562 Gridiron pendulum, 298 Grimaldi's experiment, 608 Grotthiiss' hypothesis, 794 Grove's battery, 762 ; gas, 798 Guericke's air pump, 181 Gulf Stream, 930 HADLEY'S reflecting sextant, 490 Hail, 913 Hair hygrometer, 373 Haldat's apparatus, 98 Hallstrom's experiments, 307 Haloes, 590 Hammer, 263, 863 Index, 897 HAR Hardening, 87 Hardness, 7 ; scale of, 90 Hare's deflagrator, 758, 780, 781 Harmonicon, chemical, 262 Harmonics, 240, 257 Harmonic triad, 233 ; grave, 247 Harp, 265 Harris's unit jar, 733 Heat, 273 ; animal, 455 ; absorption of, by vapours, &c., 408, 412; diffusion of, 410 ; developed by induction, 868; dynamical theory of, 402 ; hypothesis on, 273 ; influence of the nature of, 408; latent, 318; mechanical, equi- valent of, 467 ; polarisation of, 641 ; produced by absorption and imbibi- tion, 452 ; radiated 377 ; radiant, 384; reflection of, 391; scattered, 397; sources of, 447-466; specific, 419 ; transmission of, 377 ; terres- trial, 451 Heaters, 437 Heating, 456 ; by steam, 460 ; by hot air, 461 ; by hot water, 462 Height of barometer, 154, 160; varia- tions in, 160 Heights of places, determination of, by barometer, 165 ; by boiling point, 345 Heliostat, 502 Helix, 44, 829 Helmholtz's analysis of sound, 241 ; researches, 244 Hemihedral crystal, 691 Hemispheres Magdeburg, 149 Henley's electrometer,'7 10 ; discharger, 744 Henry's experiment, 852 Herepath's salt, 620 Hero's fountain, 190 Herschelian rays, 403 ; telescope, 564 Hirn's experiments, 445 Hoar frost, 911 Holmes' magneto-electrical machine, 857 Holtz's electrical machine, 713 Homogeneous light, 537 ; medium, 472 Hope's experiments, 307 Horizontal line, 64 ; plane 64 Horse power, 444 Hotness, 276 Hour, 21 Howard's nomenclature of clouds, 905 Humour, aqueous, 575 Hyaloid membrane, 575 Hydraulic press, 105 ; friction, 203 ; tourniquet, 205 IND Hydraulics, 92 Hydrodynamics, 92 Hydro-electric machine, 712 Hydrometers, 116; Nicholson's, 117-; Fahrenheit's 120 ; with variable volume, 123; Beaume's, 124; of constant volume, 123 ; specific gra- vities, 116 ; uses of tables of, 122 Hydrostatic bellows, 98 ; paradox, JOO ; balance, 117 Hydrostatics, 92-95 Hygrometers, 367 ; of absorption, 373 ; chemical, 368 ; condensing^ 369 ; wet-bulb, 372 ; Mason's, 372 ; Regnault's, 371 Hygrometric state, 366 ; substances, 365 Hygrometry, 365 ; problem on, 375 Hygroscope, 373 Hypothesis, 5 Hyposometer, 345 ICE, 914"; method of fusion of, 421 Ice caloi-imeter, 421 ; Bunsen's, 422 ; expansive force of, 323 ; ma- chine, 464 Iceland spar, 621 Idioelectrics, 683 Image and object, magnitudes of, 528 Images, accidental, 589 ; condition of distinctness of, 550 ; formation of, in concave mirrors, 496 ; in convex mirror, 497 ; in plane mirrors, 482 ; of multiple, 485 ; magnitude of, 500 ; produced by small apertures, 474 ; virtual and real, 483 ; inversion of, 579 Imbibition, 139 ; heat produced by, 452 Impenetrability, 7 Imperial British yard, 22 Imponderable matter, 6 Impulsive forces, 54 Inch, 122 Incident ray, 504 Inclination, 660; compass, 661 Inclined plane, 42 ; motion on, 47 Index of refraction, 506 ; measurement of, in solids, 516; in liquids, 517; in gases, 518 Indicator, 832, 834, 835 Indices, refractive, table of, 518 Indium, 542 Induced currents, 843-855 Induction, apparatus founded on, 855 ; QQ3 8gS Index. IND by the earth, 849 ; by currents, 843 ; of a current on itself, 850 ; electrical, 699 ; in telegraph cables, 836 ; limit to, 700 ; Faraday's theory of, 701 ; heat developed by, 868 ; by magnets, 847 ; magnetic, 648 ; vertical, 675 Inductive capacity, specific, 702 Inductorium, 862 Inelastic bodies, 55 Inertia, 19 ; applications of, 20 Influence, magnetic, 648 ; electrical, 699 Ingenhousz's experiment, 378 Injector, 186 Insects, sounds produced by, 228 Insulating bodies, 685; stool, 717 Insolation, 598, 599 Insulators, 684 Instruments, optical, 548 ; polarising, 618; mouth, 254; reed, 256; stringed, 263 ; wind, 254, 264 Intensity of the current, 777 ; of the electric light, 788 ; illumination, 478 ; of reflected light, 488 ; of a musical tone, 232 ; of radiant heat, 387 ; of sound, causes vi'hich influ- ence, 214; of terrestrial magnetism, 663 ; of terrestrial gravity, 79 Interference of light, 608 Intermittent fountain, 191 ; springs, 193 ; syphon, 193 Interpolar, 777 Intervals, musical, 233 Intrapolar region, 779 Inversion of images, 579 lones, 791 Iris, 575 Iron, passive state of, 799 ; electrical deposition of, 805 Iron ships, magnetism of, 675 Irradiation, 590 Irregular reflection, 487 Isochimenal line, 931 Isoclinic lines, 660 Isodynamic lines, 663 Isogeothermic lines, 931 Isogonic lines, 654 Isotheral lines, 931 Isothermal lines, 931 ; zone, 931 I ACOBI'S unit, 884 Jar, Leyden, 725-735 r, luminous, 741 ; Harris's unit, 732 LEN Jet, lateral, ^00 ; height of, 201 ; form of, 204 Joule's experiment on heat and work, 467 ; equivalent, 467 Jupiter, 475 KALETDOPHONE, 588 Kaleidoscope, 485 Kamsin, 902 Kathode, 791 Kathelectrotonus, 779 Katione, 791 Keepers, 678 Key, 833, 849, 856, 863 ; note, 235 Kienmayer's amalgam, 708 Kilogramme, 24, 122 Kilogrammetre, 444 Kinetic energy, 59 Kinnersley's thermometer, 744 Kirk's Ice machine, 464 Knife edge, 68 Konig's apparatus, 242 ; manometric flames, 272 Kravogl's machine, 842 Kiilp's method of compensation, 679 Kundt's velocity of sound, 261 LACTOMETER, 126 Ladd's dynamomagnetic ma- chine, 860 Land and water, 935 Lane's electrometer, 732 Lantern, magic, 567 Laplace's barometic formula, 165 Laryngoscope, 529 Latent heat, 318 ; of fusion, 4;j2 ; of vapours, 433 Latitude, influence on the air, 929 ; parallel of, 79 Lavoiser and Laplace's calorimeter, 421 ; method of determining linear expansion, 293 Law, 5 Lead tree, 801 Leclanche's elements, 766 Ledger lines, 238 Leidenfrost's phenomenon, 360 Lemniscate, 629 Length, unit of, 22 ; of undulation, 213 Lenses, 519-527 ; achromatic, 545 ; aplanatic, 526 ; foci in double con- vex, 520; in double concave, 521 ; formation of images in double con- vex, 524 ; in double concave, 525 ; Index. 899 LEN formulae relating to, 527; lighthouse, 570; optical centre, secondary axis of, 523 Leriz's law, 845 Leslie's cube, 396 ; experiment, 349 ; thermometer, 287 Level, water, 106 ; spirit, 107 Level surface, 64 Levelling staff, 106 Lever, 40 Leyden discharge, inductive action of, 846 Leyden jars, 725-735 ; charged by Ruhmkorff's coil, 864 Lichtenberg's figures, 727 Liebig's condenser, 353 Ligament, suspensory, 575 Light, 469 ; diffraction of, 609 ; homo- geneous, 535, 537; intensity of, 478; interference of, 608 ; laws of reflec- tion of, 480 ; medium, 472 ; oxy- hydrogen, 569 ; polarisation of, 614 ; sources of, 597 ; theory of polarised light, 623 ; undulatory theory of, 469, 600 ; velocity of, 475-477 Lighthouse lenses, 570 Lightning, 921 ; ascending, 923 ; effects of, 923 ; conductor, 925 ; globe, 923 ; heat, 921 ; brush, 921 ; flashes, 921 ; zigzag, 921 Limit, magnetic, 680 ; to induction, 7(X) ; of perceptible sounds, 230 Line, aclinic, 660; of collimation, 558 ; isoclinic, 660 ; agonic, 654 ; isogonic, 654; isodynamic, 663 ; of sight, 558 Linear expansion, coefficients of, 292, 294 Liquefaction of gases, 356, 357 ; of vapours, 351 Liquids, 96 ; active and inactive, 638 buoyancy of, 97 ; compressibility of, 94 ; conductivity of, 380 ; calcula tion of density of, 104 ; diffusion of, 136 ; diamagnetism of, 870 ; expan sion of, 299 ; equilibrium of, 10 1 manner in which they are heated • 381 ; pressure on sides of vessel, 99 refraction of, 517"; rotatory power of, 638 ; spheroidal form of, 81 ; spheroi dal state of, 360 : specific heat of, 427 ; volatile and fixed, 325 ; ten sions of vapours of, 335 j of mixed liquids, 336 Lissajous' experiments, 268-270 Lithium, 542 Litre, 24, 122 MAG Local action, 759 ; attraction, 675 ', battery, 835 ; currents, 768 Locatelli's lamp, 401 Locomotives, 441, 442 Lodestone, 642 ^ Long-sight, 592 Loops and nodes, 253 Loss of electricity in vacuo, 698 ; of weight in air, correction for, 376 Loudness of a musical tone, 232 Luminiferous ether, 469 Luminous bodies, 470 ; effects of the electric discharge, 738, 784 ; of the electric current, 864 ; of RuhmkorfPs coil, 864 ; jar, 741 ; meteors, 916 ; pane, 741 ; pencil, 471 ; ray, 471 ; tube, 741 ; square, and bottle, 741 Luminous radiation, 405 ; heat, 407 MACHINE, Atwood's, 74 ; elec- trical, 706-715 ; Von Ebner's, 746 ; electromagnetic, 832 Mackerel sky, 905 Magazine, 677 Magdeburg hemispheres, 149 Magic lantern, 567 Magnetic attractions and repulsions, 664 ; battery, 677; couple, 652; curves, 668 ; declination, 657 ; dip, 660 ; effects of the, electrical discharge, 743 ; equator, 660 ; field, 669 ; fluids, 645 ; induction, 648 ; in- fluence, 648 ; limit, 680 ; meridian, 653 ; needle, 653, 654; observatories, 664 ; poles, 660 ; saturation, 676 ; storms, 656 Magnetisation, 670 ; by the action of the earth, 674 ; by currents, 829 Magnetism, 6,642 ; earth's, 663 ; of iron ships, 675 ; Ampere's theory of, 827 ; remanent, 830 ; theory of, 645 ; ter- restrial distribution of free, 681 • Magneto-electrical apparatus, 855; Gramme's, 861 ; machines, 857-860 Magnets, artificial and natural, 642 ; broken, 647 ; action of earth on, 65 1 ; equator of, 643 ; north and south poles of, 644 ; portative force of, 679 ; saturation of, 676 ; influence of heat, 680 ; induction by, 847 ; inductive action on moving bodies, 848 ; action on cun-ents, 815 ; on solenoids, 825 ; rotation of induced currents by, 867 ; optical effects of, 869 Magnification, linear and superficial, 900 Index. MAG 552 ; measure of, 552 ; of a telescope, 558 Magnifying power, 557 Magnitude, 9 ; apparent, of an object, 551 ; of images in mirrors, 550 Major chord, 233 ; triads, 234 Malleability, 807 Manganese, magnetic limit of, 680 Manhole, 437 Manipulator, 834 Manometer, 94, 169; open-air, 170 ; - with compressed air, 171 ; Regnault's barometric, 172 Manometric flames, 272 Mares' tails, 905 Marie Davy battery, 765 Marine galvanometer, 774 Mariner's card, 900 ; compass, 659 Mariotte and Boyle's law, 166 Mariotte's tube, 166 ; bottle, 207 Marloye's harp, 265 Maskelyne's experiment, 64 Mason's hygrometer, 372 Mass, measure of, 23 ; unit of, 23 Matter, 2 Matteucci's experiment, 846 Matthiessen's thermometer, 287 Maximum and minimum thermometers, 289 ; of tension, 709 Mean temperature, 928 Measure of force, 29 ; of work, 57 Measure of magnification, 552, 557 ; of mass, 23 ; of space, 22 ; of time, 21 ; of velocity, 25 Measurement of small angles by re- flection, 491 Mechanical equivalent of heat, 467 ; effects of electrical discharge, 744 Melloni's researches, 401 ; thermomul- tiplier, 385, 877 Melting point, influence of pressure on, 316 Membranes, vibrations of, 267 Memoria technica, 772 Meniscus, 129 ; in barometer, 158 ; Sagittaof, 158 Menotti's battery, 765 Mercury frozen, 349, 357, 360 ; pendu- lum, 298 ; coefficient of expansion, 301 ; expansion of, 300 ; pump, 187 Meridian, 21 ; geographical and mag- netic, 653 Metacentre, 112 Metal, Rose's and Wood's fusible, 317 Metals, conductivity of, 888 Meteoric stones, 450 MUS Meteorology, 899 Metre, 22, 122 Mica, 626 Micrometer lines, 557; screw, II Microscope, 12 ; achromatism of, 555 ; Amici's, 554 ; compound, 553 ; fo- cussing, 550 ; magnifying powers of, 557 ; photo-electric, 569 ; simple, 549 ; solar, 568 Microspectroscope, 544 Mill, Barker's, 205 Millimetre, 122 Mineral waters, 924 Mines, firing by electricity, 746, 780 Minimum thermometer, 289 ; deviation, 515 Minor chord, 233 Minute, 21 Mirage, 509 Mirrors, applications of, 502 ; burning, 393 ; concave, 392 ; conjugate, 393 ; glass, 484 ; parabolic, 503 ; rotating, 489, 747 ; spherical, 492 Mists, 904 Mixture of gases, 174; of gases and liquids, 175 Mixtures, freezing, 324 ; method of, 423 Mobile equilibrium, 388 Mobility, 7, 18 Modulus of elasticity, 85 Moisture of the atmosphere, 374 Molecular forces, 3 ; attraction, 8c ; state of bodies, 4 Molecular state, relation of absorption tor, 416 Molecules, 3 Moments of forces, 38 Momentum, 28 Mongolfier's balloon, 177 Monochord, 250 Monochromatic light, 535 Monosyllabic echo, 223 Morgagni's humour, 575 Morin's apparatus, 75 Morren's mercury pump, 187 Morse's telegraph, 835 Motion, 18 ; on an inclined plane, 47 ; curvilinear, 25 ; in a circle, 49, 50 \ rectilinear, 25 ; uniformly accelerated rectilinear, 46 ; quantity of, 29 ; of a ' pendulum, 51 Mouth instruments, 255 Multiplier, 773 Multiple echoes, 223 ; images formed by mirrors, 484, 485, 486 Muscular currents, 892, 893 Index, 901 MUS Music, 205 ; physical theoiy of, 232- 248 Musical boxes, 265 ; intervals, 233 ; scale, 234 ; temperament, 236 ; tones, properties of, 232 ; intensity, notation, 238 ; pitch, and timbre, 232 ; sound, 211 ; range, 238 Myopy, 582, 592 NAIRNE'S electrical machine, 711 Nascent state, 82 Narer's apparatus, 357 Needle, dipping, 660 ; astatic, 662 ; magnetic, 653 Negative plate, 754 Negatives on glass, 572 Nerve currents, 896 Neutral line, 699 ; equilibrium, 67 ; point, 699 Newtonian telescope, 563 Newton's disc, 533 ; law of cooling, 389 ; rings, 983, 612, 613 ; theory of light, 534 Nicholson's hydrometer, 117 Nickel, electrical deposition of, 805; magnetic limit of, 680 Nicol's prism, 622 Nimbus, 905 Nobili's battery, 875 ; rings, 800 ; thermomultipliers, 877 ; thermo-elec- tric pile, 401, 404, 875 Nocturnal radiation, 465 Nodal points, 253, 608 Nodes and loops, 253 ; of an organ pipe, 258 ; explanation of, 260 Noises, 209 Nonconductors, 684 Norremberg's apparatus, 619 Northern light, 927 Norwegian stove, 383 Notation, musical, 238 Notes in music, 233 ; musical, of women and boys, 245 ; wave length of, 239 Nut of a screw, 44 OBSCURE radiation, 405 ; rays, 406 ; transmutation of, 406 Object glass, 553 Objective, 553 Observatories, magnetic, 664 Occlusion of gases, 140 Octave 233 . PER Oersted's experiment, 772 Ohm's law, 777 Opaque bodies, 470 Opera glasses, 560 __ Ophthalmoscope, 596 Optics, 469 Optic axis, 570 ; axes of biaxial crystals, 607 ; angle, 570 ; nerve, 575 Optical centre, 523 ; effects of magnets, 869 ; instruments, 548 Optometer, 582 Organ pipes, 258 ; nodes and loops of^ 258 Orrery, electrical, 719 Oscillations, 5 1 ; axis of, 76 ; method of, 667 Otto von Guericke's air-pump, 181 Outcrop, 108 Overshot wheels, 206 Oxyhydrogen light, 569 Ozone, 745, 923 PALLET, 78 Pane, fulminating, 724 ; lumi- nous, 742 Papin's digester, 347 Parabolic mirrors, 503 ; curve, 57, 200 Parachute, 179 Paradox, hydrostatic, 1 00 Parallel of latitude, 79 ; forces, 36 ; centre of, 27 Parallel rays, 471 Parallelogram of forces, 33 Paramagnetic bodies, 870 Partial current, 890 Pascal's law of equality of pressures, 95 ; experiments, 151 Passage tint, 639 Passive state of iron, 799 Pedal, 263 Peltier's cross, 881 Pendulum, 51 ; application to clocks, 78 ; ballistic, 78 ; conical, 53 ; com- pensation, 298 ; electrical, 660 ; grid- iron, 298 ; mercurial, 298 ; length of compound, 76 ; verification of, laws of, 77 Penumbra, 473 Percussion, heat due to, 449 Periscopic glasses, 592 Permanent gases, 356 Persistence of impression on the retina, 588 Perturbations, magnetic, 654, 655 902 hidex. PHE Phenakistoscope, 588 Phenomenon, 5 Phial of four elements, 103 Phonautograph, 271 Phosphoi-escence, 598, 599 Phosphorogenic rays, 538 Phosphoroscope, 599 Photo-electric microscope, 569 Photogenic-apparatus, 569 Photographs on paper, 572 ; on albu- menised paper and glass, 574 .Photography, 571-574 Photometers, 479, 480 Physical phenomena, 5 ; agents, 6 ; shadows, 473 Physics, object of, i Physiological effects of the electric dis- charge, 737 ; of the current, 778 ; of Ruhm.korff's coil, 864 Piezometer, 94 Pigment colours, 536 Pile, voltaic, 757-770 Pipes, organ, 258 Pisa, tower of, 66 Pistol, electric, 745 Piston of air-pump, 181 ; rod, 438 Pitch, concert, 237 ; of a note, 232 ; a screw, 44 Plane, 44; electrical inclined, 719; wave, 605 Plants, absorption in, 139 Plante's secondary battery, 797 Plate electrical machine, 707 Plates, colours of thin, 612 ; vibrations of, 266 Plumb-line, 64 Pluviometer, 907 Pneumatic syringe, 143, 449 Poggendorff 's law, 745 Point, boiling, 342, 343 Points, power of, 695 Polar aurora, 927 Polarisation, 797 ; angle of, 616 ; current, 797 ; of electrodes, 759 ; by double refraction, 614 ; by reflec- tion, 615 ; by single refraction, 617; elliptical and circular, 631, 632, 634 ; of heat, 641 ; galvanic, 759, 797 ; of the medium, 701 ; plane of, 616 ; plate, 759 ; rotatory, 635 Polarised light, theory of, 623 ; colours produced by the interference of, 624, 630 ; rays, 624 Polariser, 618 Polarising instruments, 618 Polarity, 759; boreal, austral, 651 PYR Poles, 756 ; analogous and antilogous, 791 ; of the earth, 660 ; of a mag- net, 643 ; mutual action of, 644 ; precise definition of, 646 ; austral and boreal, 651 Polygon, offerees, 35 Polyprism, 512 Ponderable matter, 6 Pores, 13 Porosity, 7, 13 ; application of, 15 Portative force, 679 Positive plate, 754 Positives on glass, 573 Postal battery, 835 Potential energy, 59 ; of electricity, 752 Pound, 122 ; avoirdupois, 23, 29 ; foot, 56 Powders, radiation from, 416 Power of a lever, 40 ; of a microscope, 557 Presbytism, 582, 592 Press, hydraulic, 105 Pressure, centre of, 99 ; on a body in a liquid, 109 ; atmospheric, 147 ; amount of, on human body, 152 ; experiment illustrating, 189 ; in- fluence on melting point, 317 ; heat produced by, 449 ; electricity pro- duced by, 690 Pressures, equality of, 95 ; vertical downward, 96 ; vertical upward, 97 ; independent of form of vessel, 98 ; on the sides of vessels, 99 Prevost's theory, 388 Primary coil, 837 Primitive current, 891 Principal current, 891 Principle of Archimedes, no Prisms, 510-515 ; double refracting, 621 ; Nicols', 622 ; with variable angle, 512 Problems on expansion of gases, 309 ; on mixtures of gases and vapours, 359; on hygrometry, 375 Proof plane, 693 Propagation of light, 472 Protoplasm, 778 Protuberances, 543 Pulley, 41 Pump, air, 181 ; coixlensing, 188 Pumps, different kinds of, 194 ; suction, 195 ; suction and force, 196 Pupil, 575 Psychrometer, 372 Pyroelectricity, 691 Index. 903 PYR Pyrheliometer, 450 Pyrometers, 290; electric, 880 QUADRANTAL deviation, 675 Quadrant electrometer, 710 RADIANT heat, 484 ; detection and measurement of, 385 ; causes which modify the intensity of, 387 ; Melloni's researches on, 401 ; relation of gases and vapours to, 411 Radiated heat, 377, 384 Radiating power, 398 ; identity of ab- sorbing and radiating, 399 ; causes which modify, &c. , 400 ; of gases, 414 Radiation, cold produced by, 465 ; from powders, 416 ; of gases, luminous, and obscure, 405 ; laws of, 386 ; solar, 450 Radiative power, 909 Rain, 907 ; clouds, 907 ; bow, 926 ; fall, 907 ; gauge, 907 Ramsden's electrical machine, 707 Rarefaction in air pump, 181 ; by Sprengel's pump, 185 Ray, incident, 504 ; luminous, 471 ; ordinary and extraordinary, 604 Rays, actinic, or Ritteric, 335 ; divergent and convergent, 471 ; frigorific, 395 ; of heat, 384, 402 ; invisible, 402 ; obscure, 406; path of, in eye, 578; polarised, 624 ; trans- mutation of thermal, 407 Reaction and action, 39 Reaction machines, 442 Real volume, 14 ; foci, .520 ; focus, 493; image, 496, 524 Reaumur scale, 282 Receiver of air-pump, 181 Recomposition of white light, 533 Reed instruments, 256 Reeds, free and beating, 256 Reflected light, intensity of, 488 Reflecting power, 396 ; goniometer, 502 ; sextant, 490; stereoscope, 586; telescope, 561 Reflection, apparent, of cold, 395 ; of heat, 391 ; from concave mirrors, 392 ; irregular, 487 ; laws of, 390 ; verification of laws of, 393 ; in a vacuum, 394 ; of light ; 480-509 ; of sound, 222 ROT Refracting stereoscope, 587 ; telescope, 561 Refraction, 504-509 ; double, 602 ; polarisation by, 614; explanation of single, 601 ; of sound, 224 Refractive index, 506; of gases, 518; of liquids, 517 ; of solids, 516 ; table of, 518 ; indices of media of eye, 576 Refractory substances, 315 Refrangibility of light, alteration of, 545 Regelation, 914, Regnault's determination of density of gases, 313 ; manometer, 172 ; methods of determining the expansion of gases, 310 ; of specific heat, 425 ; of tension of aqueous vapour, 332, 334; hygrometer, 371 Regulator of the electric light, 786, 787 Relay, 835 Remanent magnetism, 830 Repulsions, magnetic, 665 ; electrical laws of, 690 Reservoir, common, 685 Residual charge, 728 Residue, electric, 728 Resinous electricity, 686, 687 Resistance of a conductor, 777 ; of an element, 887 Resonance, 223; box, 237 ; globe, 241 Rest, 18 Resultant of forces, 32-34 Retina, 575 ; persistance of impression on, 588 Return shock, 924 Reversion, method of, 658 Rheometer, 773 Rheoscope, 773 Rheoscopic frog, 894 Rheostat, 882 Rhomb, Fresnel's, 633 Rhumbs, 659, 900 Right ascension, 563 Rime, 901 Rings, coloured, 628 ; in biaxial crystals, 629 ; Newton's, 612, 613 ; Nobili's, 800 Ritchie's experiment, 399 Ritteric rays, 406 Rock salt, head transmitted through, 410 Rods, vibrations of, 265 Roget's vibrating spiral, 807 Rose's fusible metal, 317 Rotating min-or, 747 904 Itidex. ROT Rotation, electrodynamic and electro- magnetic, of liquids, 817 Rotation of the earth, 77 ; of magnets, by currents, 814 ; of currents by magnets, 816 ; of induced currents by magnets, 867 Rotatory power of liquids, 638 ; polari- sation, 635, 636; coloration produced by, 637 Rousseau's densimeter, 127 Roy and Ramsden's measurement of linear expansion, 294 Rubbers, 707 Rubidium, 542 Ruhmkorff's coil, 862 ; effects produced by, 864 Rumford's photometer, 479 Rutherford's thermometers, 289 SACCHARIMETER, 639 Saccharometer, 123 Safety-valve, 105, 347 ; tube 355 ; whistle, 437 Sagitta of meniscus, 158 Salimeters, 126 Salts, decomposition of, 792 Saturation, degree of, 366 ; magnetic, 676 ; of colours, 536 Saussure's hygrometer, 373 Savart's toothed wheel, 227 Scale of hardness, 90 Scales in music, 234 ; chromatic, 236 ; of a thermometer, 282 ; conversion of, into one another, 282 Scattered heat, 397 ; light, 487 Schehallien experiment, 64 Sclerotica, 575 Scott's phonautograph, 271 Screw, II, 44 Secondary axis, 523 ; batteries, 797 ; currents, 759 ; coil, 837 Second of time, 21, 25 Seconds pendulum, 76 Secular magnetic variations, 654 Segments, ventral and nodal, 204 Segner's water-M^heel, 206 Selenite, 626 Semicircular deviation, 675 Semi-conductox's, 684 Semi-tones, 235 Senarmont's experiment, 379 Serein, 909 Series, thermo-electric, 872 Serum, 12 Sextant, 490 SOU Shadow, 473 Shaft, 438 Shock, electric, 725-735 ; return, 924 Short sight, 592 Siemens' armature, 858 ; unit, 884 ; electrical thermometer, 890 Sight, line of, 558 Silver, voltameter, 795 Simoom, 902 Sine compass, 776 Singing of liquids, 339 Sinuous currents, 809 Sirocco, 902 Size, estimation of, 581 Sleet, 912 Slide valve, 438 Smee's battery, 764 Snow, 912 ; line, 915 Soap bubble, colours of, 612 Solar microscope, 568 ; light, thermal analysis of, 403 ; radiation, 450 ; spectrum, 530 ; properties of the, 538 ; dark lines of, 539, 543 ; time, 21 ; day, 21 Soleil's saccharimeter, 639 Solenoids, 822-826 ; action of currents on, 823; of magnets and of earth on, 824, 825 ; on solenoids, 826 Solidification, 320 ; change of volume on, 320, 323 ; retardation of, 322 Solidity, 4, 7 Solids, conductivity of, 378 ; index of refraction in, 516 ; diamagnetism of, 870; linear and cubical expansion of, 292, 297 Solids, formulae of expansion, 296 Solution, 319 Sondhauss's experiments, 224 Sonometer, 250 Sonorous body, 210 Sound, 209 ; cause of, 210 ; not propa- gated in vacuo, 211 ; propagated in all elastic bodies, 212 ; propagation of, in air, 213 ; causes which influ- ence intensity of, 214 ; apparatus to strengthen, 215 ; velocity of, in gases, 217-219 ; in liquids and solids, 221 ; reflection of, 222 ; re- fraction of, 224 ; transmission of, 216 Sound, Helmholtz's analysis of, 241 Sound, Konig's apparatus, 241 ; Kundt's, 261 Sounder, 839 Sounds, limit of perceptible, 230 ; synthesis of, 243 ; perceptions of, 245 ; produced by currents, 813 Index. 905 SPA Space, measure of, 22 Spar, Iceland, 621 Spark and brush discharge, 739 ; elec- trical, 717, 739 ; board, 747 ; dura- tion and velocity of, 747 Speaking trumpet, 225 ; tubes, 216 Specific gravity, 24, 116, 121 ; flask, 118 ; of solids, 117 ; of gases, 312 ; of liquids, 120 ; tables of, 121, 122 Specific heat, 419-432 ; compound bodies, 530 ; determination of, by fusion of ice, 421 ; by method of mixtures, 423 ; by Regnault's appa- ratus, 425 ; of solids and liquids, 427, 428; of gases, 431 Specific inductive capacity, 702 Spectacles, 593 Spectral analysis, 540 Spectroscope, 541 ; experiments with, 542 ; uses of the, 544 .Spectrum, calorific, 538; chemical, 538 Spectrum, 403 ; colours of, 532 ; pure 531 ; solar, 530, 542 Spectrum, dark lines of, 539 Spectrum, diffraction, 611 Spctrum, luminous properties, 538 Spectrum of aurora borealis, 927 ; pro- perties of, 538 ■ Specular reflection, 487 Spherical aberration, 501, 526 ; mir- rors, 492 ; focus of, 493 ; formulae for, 498 Spheroidalform of liquids, 81; state, 360 Spherometer, 11 Spiral, 829 ; Roget's vibrating, 807 Spirit-level, 107 Sprengel's air-pump, 185 Stable equilibrium, 67 Stars, spectral analysis of, 545 Staubbach, 73 Steam engines, 436 ; boiler, 437 ; double action, or Watt's, 438 ; pipe, 186; various kinds of, 443 ; work of, 444 ; heating by, 460 Steeling, 805 Stereoscopes, 585-587 Stethoscope, 226 Stills, 352 Stool, insulating, 717 Stopcock, doubly exhausting, 183 ; Gay-Lussac's, 358 Storms, magnetic, 656 Stoves, 459 ; Norwegian, 383 ' Stratification of electric light, 865 Stratus, 905 Stringed instruments, 263 TER Strings, 249 ; transverse vibration of, 249 Subdominant chords, 234 Suction pump, 195 ; and force pump, 196 ; load which piston supports, 197 Sulphate of mercury battery, 765 Sun, analysis of, 543 ; constitution of, 543 Sun spots, 663 Surface level, 64 Suspension, axis of, 68 ; Cardan's, 155 Suspensory ligament, 575 Swimming, 115 ; blader of fishes, 114 Symmer's theory of electricity, 687 Syphon, 192 ; intermittent, 193 Syphon barometer, 156 Syren, 228 Syringe, pneumatic, 143, 448 Synthesis of sounds, 243 TAMTAM metal, 91 Tangent compass, or galvano- meter, 775, 796 Telegraph, cables, induction in, 836 ; electric, 832 ; dial, 834 ; Morse's, 835 Telescopes, 558-564; astronomical, 558 ; Galilean, 560; Gregorian, 562; Herschelian, 564 ; Newtonian, 562 ; reflecting Rosse's, 564 Telluric lines, 539 Temper, 91 Temperature, 276, 419 ; correction for, in barometer, 159 ; critical, 346 ; of a body, 276 ; determined by specific heat, 428 Temperature, absolute zero of, 466 ; mfluence of, on specific gravity, 120 ; mean, 928 ; how modified, 929 ; dis- tribution of, 933 ; of lakes, springs, 934 Temperatures, different remarkable, 291 ; influence on expansion, 296 Tempering, 87, 91 Tenacity, 7, 88 Tension, 1 14, 694, 863 ; maximum ot electrical machine, 709 ; maximum of vapours, 329 ; of aqueous vapour at various temperatures, 333-337 ; of vapours of different liquids, 335 ; of mixed liquids in two communicating vessels, 337 Terquem's experiment, 693 Terrestrial currents, 828 ; heat, 45 1 ; magnetic couple, 652 ; telescope, 559 Terrestrial gravitation, 64, 79 go6 Index, TER » Terrestrial magnetic couple, 652 Tetanus, 778 Thallium, 542 Thaumatrope, 588 Theodolite, 10 Theory, 5 ; of induction, 701 Thennal analysis, 403 ; unit, 418, 454 ; springs, 934 Thermal effects of the current, 780, 781 Thermal rays, transmutation of, 407 ; unit, 418 Thermocrose, 409 Thermo-electric battery, 385, 876 ; couples, 874 ; currents, 873, 875, 878 ; pile, 385, 404, 875 ; series, 872 Thermo-electricity, 871 Thermo-element, 872 Thermometers, 277 ; Becquerel's elec- trical, 879 ; division of tubes in, 278 filling, 279 ; graduation of, 280 determination of fixed points of, 281 scale of, 282 ; displacement of zero, 283 ; limits to use of, 284 ; alcohol 285 ; conditions of delicacy of, 286 Kinnersley's, 744 ; Leslie's, 287 Matthiessen's, 287 ; Breguet's, 288 maximum and minimum, 289 Siemens' electrical, 890 ; weight, 302 ; air, 308, 309 Thermo-barometer, 345 Thermometer, electric, 744 Thermometry, 276-289 Thermo-multiplier, Melloni's, 877, Thermoscope, 287 Thomson's electrometer, 735 ; galva nometer, 774 ; apparatus for atmo spheri'c electricity, 917 Thread of a screw, 44 Thunder, 922 Timbre, 232 Time, measure of, 21 ; mean solar, 21 Tint, 536 ; transition, 639 Tones, combinational, 247 ; differential 247 Tonic, 234 Torricelli's experiment, 150 ; theorem 199 ; vacuum, 157 Torsion, angle of, 86 ; balance 86 666, 692 ; force of, 86 Total reflection, 508 Tourmaline, 620, 691 ; pincette, 628 Tourniquet, hydraulic, 205 Traction, elasticity of, 85 Trajectory, 25 Transformation of energy, 6i Transition tint, 639 VAP Transparency, 7, 470 Transparent media, 51 0-5 1 7 Transpiration of gases, 138 Translucent bodies, 470 Transmission of heat, 377 ; of light, 469, 510 ; by the current, 793 Transmission of sound, 216 Triad, harmonic, 233 Triangle, 265 Triangle of forces, 35 Trumpet, speaking, ear, 225 Tubes, Geissler's, 185, 866 ; luminous, 741 ; safety, 355 ; speaking, 216 Tuning fork, 237, 265 Turbines, 206 Tyndall's researches, 404, 910 UNANNEALED glass, colours produced by, 630 Undershot wheels, 206 Undulation, length of, 213, 600 Undulatory theory, 469 Uniaxial crystals, 603; double refraction in, 605 ; positive and negative, 606 Unit jar, Harris's, 733 ; Siemens', 884 ; thermal, 418 Unit of length, area and volume, 22 ; heat, 418 ; of work, 58 Unstable equilibrium, 67 Urinometer, 126 \ 7ACU0, loss of electricity in, 698 V Vacuum, application of, to construction of air pump, 181 ; ex- tent of, produced by air pump, 182 ; fall of bodies, in a, 73 ; formation of vapour in, 328 ; heat radiated in, 386 ; reflection in a, 394 ; Torri- cellian, 157 Valve, safety, 105, 347 ; chest, 437 Vane, electrical, 719 Vaporisation, 326 ; latent heat of, 347, 433 Vapour, aqueous, tension of, at various temperatures, 333-337 ; formation of, in closed tube, 346; latent heat of, 348 Vapours, 325 ; absorption of heat by, 408 ; absorptive powers of, 413 ; density of, Gay-Lussac's method, 361 ; determination of latent heat of, 432 ; Dumas's method, 362 ; elastic force of, 327 J formation of, in vacuo. Index. 907 VAR 328; saturated, 329 ;' unsaturated, 330; tension of different liquids, 335 ; of mixed liquids, 336; in communicating vessels, 337 Variations, annual, 655 ; accidental, 656; barometric, 160; causes of, 161 ; diurnal, 655 ; relation of, to weather, 161 ; in magnetic declina- tion, 653, 657 Varley unit, 884 Velocity, 25 ; direction of, 52 ; of efflux, 199 ; of electricity, 747 ; of light, 475-477 ; graphic representa- tion of changes of, 52 ; of sound in gases, 217, 218; formula for calcula- ting, 218; of winds, 900 Velocities, composition of, 48 ; ex- amples of, 25 Vena contracta, 202 Ventral and nodal segment, 204, 253, 258 Vernier, 10 Vertical line, 64 Vibrating spiral, Roget's, 807 Vibration, 210 ; arc of, 51 ; produced by currents, 831 Vibrations, 246 ; formulae, 259 ; of membranes, 267 ; laws of, 251 ; measurement of number of, 227 ; number of, producing each note, 237 ; of musical pipe, 259 ; of rods, 265 ; of plates, 266; of strings, 249, 251, 252 View, field of, 556 Vinometers, 126 Virtual and real images, 483; focus, .493 Vision, distance of distinct, 582 ; bino- cular, 584 Visual angle, 580 Vis viva, 56, 419, 467 Vital fluid, 749 Vitreous body, 575 ; electricity, 686 ; fusion, 315 ; humour, 575 Vocal chords, 245 Volatile liquids, 325 Volta's condensing electroscope, 734; electrophorus, 706 ; fundamental ex- • periment, 750 Voltaic arc, 784 ; couple, 754 ; cur- rents, 771 ; induction, 843 ; pile and battery, 757, 758, 783 Voltameter, silver, 795 ; Faraday's, 795 Volume, 22 ; unit of, 22, 24 ; deter- mination of, III ; change of, on solidification, 323 ; of a liquid and WOR that of its vapour, relation between, 364 Von Ebner's electrical machine, 746 WALKER'S battery, 764 Water bellows, 186 ; decom- position of, 120 ; hammer, 73 ; hot, heating by, 462 ; level, 1 06 Water, maximum density of, 307 ; spouts, 908 ; wheels, 206 Watt's engine, 438 Wave, condensed, 213 ; expanded, 213 ; lengths, 600 ; plane, 605 Weather, its influence on barometric variations, 160, 161 ; glasses, 163 Wedge, 43 Wedgewood's pyrometer, 290 Weighing, method of double, 72 Weight, 23, 79 ; of bodies weighed in air, correction for loss of, 376 ; of gases, 145 ; thermometer, 302 Weights and measures, 122 Wells, artesian, 108 Wells's theory of dew, 901 Wet bulb hygrometer, 372 Wheatstone's bridge, 886 ; photometer, 479 ; rheostat, 882 ; rotating mirror, 747 ; and Cooke's telegraph, 833 Wheel barometer, 163 Wheels, friction, 74 ; escapement, 78 ; water, 206 Whirl, electrical, 719 Whispering galleries, 223 Whistle, safety, 437 White light, decomposition of, 530 ; re- composition of, 533 W^hite's pulley, 41 Wiedemann and Franz's tables of con- ductivity, 378 Wild's magneto-electrical machine, 859 Winckler's cushions, 707 Windchest, 256 ; instruments, 254, 264 Winds, causes of, 901 ; direction and velocity of, 890, 929 ; law of rotation of, 903 ; periodical, regular, and variable, 902 Wines, alcoholic value of, 354 Wollaston's battery, 758 ; cryophorus, 349 ; doublet, 549 Wood, conductivity of, 378 Wood's fusible metal, 317 Work, 34, 56 ; measure of, 57 ; of an engine, 443 ; rate of, 443 ; unit of, 58 ; internal and external, of bodies, 9o8 Index. YAR 274; of a"voltaic battery, 783; re- quired ^r the production of elec- tricity, 716 YARD, British, 22, 122 Young and Fresni&l's experiment, 608 ZON ZAMBONI'S pile, 769 Zero, absolute, 466 ; aqueous va- pours below, 331 ; displacement of, 283 Zinc, amalgamated, 768 ; carbon bat- . tery, 763 Zone, isothermal, 931 % ^ -^. '/^ K. f^i Ux^ V • 1 w ^ y'lrs '': I187D P^y^"!f Tr! and ed. from I^K_ "^P^^it Elements de phys" .1. '"• ">* "°