UNIVERSITY OF CALIFORNIA SAN FRANCISCO LIBRARY PRINCIPLES OF PHYSICS AND METEOROLOGY. TatS. 7. Sindairslvflt PRINCIPLES OF PHYSICS AND METEOROLOGY, BY J. MULLEK, PROFESSOR OF PHYSICS AT THE UNIVERSITY OF FREIBURG. FIRST AMERICAN EDITION, REVISED AND ILLUSTRATED WITH 538 ENGRAVINGS ON WOOD, AND TWO COLORED PLATES. PHILADELPHIA: LEA AND BLANCHARD. 1848. Entered according to the Act of Congress, in the year 184S, by LEA AND BLANCHARD, in the Clerk's Office of the District Court for the Eastern District of Pennsylvania. PHILADELPHIA : T. if. AND P. G. COLLINS, PRINTERS. PUBLISHERS' ADVERTISEMENT. THE Treatise on Physics, by Professor Miiller, now presented to the American public, is the first of a series of works on the different branches of science, now passing through the press of Bailliere in London ; and which, from its thorough character and extended range, is much needed in this country. In preparing it, the American publishers have availed themselves of the ser- vices of a competent editor, who has made various alterations and additions. Among the changes considered necessary, the principal is the introduction of the English standard of weights and measures, in addition to the Continental system adopted by the author. Articles have also been added, on the electro-mag- netic telegraph, electrotype, steam engine, &c., with the necessary- illustrations, while various errors of importance, which had escaped the London editor, have been corrected. The publishers hope that the care exercised in the revision of the work, and the accuracy of the text, which it has been their aim to secure, will be deemed of sufficient importance to enhance the value of a work which has already received deservedly high commendation. PHILADELPHIA, January r , 1848. i* 4203.-J PREFACE. IN laying the following pages before the Public, it seems necessary to state that the design of them is to render more easily accessible, a greater degree of knowledge of the general princi- ples of Physics and Meteorology, than is usually to be obtained, without the sacrifice of a greater amount of time and labor than most persons can afford, or are willing to make. The subjects of which this volume treats, are very numerous more numerous, in fact, than at first sight it would seem possible to embrace in so small a compass. The Author has, however, by a system of most judicious selection and condensation, been enabled to intro- duce all the most important facts and theories relating to Statics, Hydrostatics, Dynamics, Hydrodynamics, Pneumatics, the Laws of the Motions of Waves in general, Sound, the Theory of Musical Notes, the Voice and Hearing, Geometrical and Physical Optics, Magnetism, Electricity and Galvanism, in all their subdivisions, Heat, and Meteorology, within the space of an ordinary middle- sized volume. Of the manner in which the translator has executed his task, it behoves him to say nothing; he has attempted nothing more than a plain, and nearly literal version of the original. He cannot, however, conclude this brief intro- ductory note, without directing the attention of his readers to the splendid manner in which the publisher has illustrated this volume. E. C. 0. LONDON, AUGUST, 1847. TABLE OF CONTENTS. PAGE INTRODUCTION . . ... 25 SECTION I. GENERAL PROPERTIES OF BODIES . . 29 SECTION II. EQUILIBRIUM OF FORCES. CHAPTER I. Equilibrium and decomposition of forces in the so called simple machines 43 CHAPTER II. Molecular equilibrium ....... 72 CHAPTER HI. Hydrostatics; or the theory of the equilibrium of liquids . . 76 CHAPTER IV. Molecular actions between solid and liquid bodies, and between the sepa- rate particles of liquids ...... 108 CHAPTER V. Of the equilibrium of gases, and of atmospheric pressure . . 116 CHAPTER VI. Attraction between gaseous and solid, as well as between gaseous and liquid bodies .... 145 X CONTENTS. SECTION III. OF MOTION AND ACCELERATING FORCES. CHAPTER I. PAGE Different kinds of motion . . . . . . 148 CHAPTER II. Laws of the motion of liquids . . . . . . 179 CHAPTER III. Motion of gases ........ 197 SECTION IV. ACOUSTICS. CHAPTER I. Laws of the motion of waves in general, and especially of waves of sound ........ 207 CHAPTER II. Laws of the vibrations of musical tones .... 227 CHAPTER III. Of the voice and hearing ...... 246 SECTION V. INTRODUCTION OF LIGHT ...... 252 CHAPTER I. Reflection of light ....... 258 CHAPTER II. Dioptrics ......... 270 CHAPTER III. Decomposition of white light ...... 285 CONTENTS. x i CHAPTER IV. PAGE Of the eye and optical instruments . . . 296 CHAPTER V. Phenomena of interference ..... 326 CHAPTER VI. Chemical actions of light .... 343 SECTION VI. MAGNETISM AND ELECTRICITY. PART I. MAGNETISM. CHAPTER I. Mutual action of magnets on each other and on magnetic bodies . 347 CHAPTER II. Of the magnetic actions of the earth .... 354 PART II. ELECTRICITY. CHAPTER I. Of electric actions . . . . . . 368 CHAPTER II. Electricity by induction ....... 375 CHAPTER III. Of electrical forces ....... 387 CHAPTER. IV. Of combined electricities ...... 390 CHAPTER V. Of electric light, and the motions of electrified bodies . . . 397 PART III. GALVANISM. CHAPTER I. On the electricity of contact, and on the galvanic circuit . . 402 CHAPTER II. Actions of the galvanic current . . . . . . 419 Xii CONTENTS. PART IV. ELECTRO-MAGNETISM. CHAPTER I. Magnetic actions of the current . CHAPTER II. Phenomena of induction . ... PART V. Thermo-electric currents and animal electricity . SECTION VII. OF HEAT. CHAPTER I. Expansion ..... CHAPTER II. Change of state of aggregation . CHAPTER III. Specific heat of bodies .... CHAPTER IV. Transmission of heat .... CHAPTER V. Different sources of heat SECTION VIII. METEO ROZOGT. CHAPTER I. Distribution of heat on the earth's surface .... 555 CHAPTER II. Of the pressure of the atmosphere and of the winds . . . 578 CHAPTER III. Of atmospheric moisture . . . . . . 589 CHAPTER IV. Optical phenomena of the atmosphere ..... 606 CHAPTER V. On atmospheric electricity ..... 616 PRINCIPLES OF PHYSICS AND METEOROLOGY. INTRODUCTION. General Idea. The grand spectacle that is ever present to our eyes in the vast realm of nature excites within us so ardent a thirst for knowledge, that we feel ourselves irresistibly impelled to the consideration of the combined causes that have produced these wondrous results. Such subjects fall within the department of natural philosophy, whose task it is to trace the connecting link between the different phenomena of nature, and, as far as this is possible, to unravel the causes from which they have originated. The combined natural sciences treat of bodies a word which we must not receive in the limited sense in which it is under- stood by the mathematician, who looks only to the relations of space, disregarding the matter that fills space ; while it is to the properties of this very matter that the natural philosopher devotes his especial attention. The interior of bodies is closed to our view, their external appearance being only made known to us by means of what we learn concerning them through our senses. Thus, a body, standing in no connection with our senses, has, so far as we are concerned, no existence ; and it is probable that there is still much passing around us in nature of which we have no con- ception, from the want of some additional sense by which we can recognize its existence. The province of the natural sciences is, therefore, to trace the connection existing between the phenomena brought within the scope of our knowledge by means of the senses, and so to arrange 3 26 INTRODUCTION. them, that they may elucidate each other, and manifest the mu- tual dependence existing between them. If we are able to trace a phenomenon in its connection with other phenomena, we have explained it; and a natural law is obtained as soon as the unchangeable link of connection existing between the natural phenomena is understood, even should we still remain ignorant of the final cause. Division. The vast department of the natural sciences divides itself into two great branches Natural History and Natural Philosophy. The former teaches us to know the nature of indi- vidual objects, and arranges them in systems according to their different characters; while the latter endeavors to lay open the natural laws of the material world. By the term physics, we understand that branch of the natural sciences which treats of phenomena which do not depend upon a change of the constitution of bodies ; the latter falling under the head of chemistry. As may be readily conceived, it is not always easy to trace with accuracy the line of demarcation between these two sciences. They are most intimately connected with each other, in some measure even forming one whole, which appears to have been divided chiefly owing to its embracing so wide and increasing a field of observation. Method. We must now point out the manner in which the student may attain to a knowledge of the laws of nature, and by what means the facts already ascertained have been acquired. The sources of knowledge, as well as the methods of acquiring it, are not and cannot be the same for all sciences. The mathematician may, starting from his own self-acquired conceptions, develop his science wholly out of himself; and we might even conceive the possibility of a man shut up within four walls, and separated from all communication with the outer world, constructing the whole science of mathematics from his own ideas of space and number.* * [We find the same idea expressed in nearly the same words in Herschel's beautiful Essay " On the Study of Natural Philosophy :" " A clever man, shut up alone, and allowed unlimited time, might reason out for himself all the truths of mathematics by proceeding from those simple notions of space and number, of which he cannot divest himself without ceasing to think. But he could never tell by any effort of reasoning what would become of a lump of sugar if immersed in water, or what impression would be produced on his eye by mixing the colors yel- low and blue." P. 76.] INTRODUCTION. 27 Seen from this point of view, mathematics is a purely speculative science, the very reverse of natural philosophy, which treats of objects that solely and alone come to our knowledge through the perceptions of sense and in the course of experience. The ancients were wholly unacquainted with any science of natural investigation that was based upon experience ; and hence their philosophical speculations upon the world in general, and upon the rise and origin of all material objects, are nothing but confused conjectures, and possessed of little value ; frequently, indeed, standing in direct opposition to fact and experience. Even in the middle ages the natural sciences were not much more developed, partly because the human mind was directed in other channels, and partly because the Aristotelian philosophy was held in such high esteem that all inquiries and progress were alike checked. Galileo was the first to enter the path of practical experiment, and Bacon showed that there was no other road that would lead to a knowledge of the laws of nature. The only source from whence we can draw our knowledge of nature is the perception of the senses, practical experience, observation. Hence we derive the materials which must be united and worked into a science by our mental activity. We derive our scientific perceptions either from changes effected by nature itself, or we designedly place bodies in those conditions that may call forth certain phenomena. In the first case we make observations; in the second, experiments. By means of good observations, and judiciously-conducted experiments, we learn to know the external connection of the phenomena of nature. And this connection is what we term a natural law. By the aid of experiments we may arrive at a knowledge of these laws, even while we remain w r holly unacquainted with their internal connection, and with the nature of forces. The law of the refraction of light was known long before any correct idea was formed as to the nature of light ; and, in the present day, we know the laws of the distribution of electricity, but we have little or no knowledge concerning the nature of electricity itself. It is only the external connection of things that can be discovered by perception ; and we can hazard nothing more than hypotheses 28 INTRODUCTION. as to the internal causes of phenomena, or the origin of the forces from which they are educed. These hypotheses are like questions which we put to Nature, but the answers she gives are not simply "yes" and "no;" but it can be so, or it cannot. Nevertheless, from these hypotheses deductions may generally be drawn, which can subsequently be confirmed or refuted by further observations. In proportion to the number of facts that can be explained by help of an hypothesis, and the more we can confirm it by new observations, the greater probability does it acquire. In all branches of physics we shall find examples of, and evi- dence favoring the correctness of these views. SECTION I. GENERAL PROPERTIES OF BODIES. As PHYSICS treats of bodies, it is most essential to form to one's self a representation of the nature of these bodies, and this object is the most readily attained by the consideration of those general properties which we observe to exist in all bodies, what- ever other differences they may manifest. Thus, it is essential to the existence of a body that it occupy a limited space, possess the property of extension, and that no other body occupy the same space at the same time; this latter con- dition indicating the property of impenetrability. Besides these two properties, without which we can form no conception of mat- ter, we observe other general properties, as divisibility, extensi- bility, compressibility, porosity, inertia, and gravity. Divisibility. As far as our experience goes, we find that all bodies are divisible ; that is, they may be divided into smaller and still smaller particles. Here the question arises : What are the limits of this divisibility ? And again : Do we by continued reduction arrive at particles which, although still perceptible to. the senses, are incapable of being further divided? Experience furnishes us with the reply, that divisibility continually oversteps the limits of sensible perception. As an instance of extreme divisibility we may adduce musk, which will continue year after year to fill an apartment with the most intensely-penetrating odor, without any perceptible loss of weight. Chemically, compound bodies afford the best evidence that divisibility passes the limits of sensible perception. In cinnabar, for example, which is composed of mercury and sulphur, and may easily be separated into these constituents, we are unable to distinguish small particles of sulphur and mercury from one another; even under the best microscope it appears to be a per- fectly homogeneous mass. 3* 30 PROPERTIES OF BODIES. But, although divisibility extends far beyond the limits per- ceptible to sense, it must not be assumed that it is wholly unlimited ; for to adopt such art assumption were, in other words, to admit that the size of the ultimate undivisible particle is null, while it is evident that, if the ultimate particle have no extension, it cannot enter into the composition of an extended body. It is upon these considerations that the natural philosopher bases the hypothesis that all bodies are composed of minute par- ticles, which cannot be further disintegrated, but are indivisible, and therefore termed atoms. This fundamental view of the constitution of bodies is now universally embraced by the natural philosopher, and the chemist, as the atomic theory. In speaking of small particles, without actually wishing to designate them as ultimate portions or atoms, we generally make use of the term molecules, which is synonymous with particles of a mass. Extensibility and Compressibility. A second general property is extensibility, on which depends compressibility. The same body does not always possess a similar volume, since it may be diminished by pressure and cold, and enlarged by expansion and heat. If, then, we assume that the atoms are invariably the same, we can only explain extensibility on the hypothesis that the atoms are not in immediate contiguity with each other, but are separated by interstices, according to the enlargement or diminution of which the volume of the body changes. Porosity. The interstices which occur between the different particles of bodies are named pores ; and, if we apply the same term to the interstices between the atoms of bodies, it is evident, from what has been already stated, that everybody is porous, and that porosity is therefore a general property. In common speech, however, we understand by the term pore an interstice sufficiently large to admit of the passage of fluids and gases; and, according to this definition, porosity is certainly not a general property. A sponge, all artificial textures chalk, pumice, &c. are porous in the restricted sense of the word. Different Nature of Atoms. After developing the fundamental idea of the atomic theory by the consideration of divisibility and extensibility, we will pass to the observation of the mode in which different bodies are formed from atoms, and next consider the remaining common properties of matter. ARRANGEMENT OF ATOMS. 31 We. find that there are in nature a number of bodies, the pro- perties of which are so different that we must necessarily assume that the atoms of which they are composed likewise differ in their nature. If, for instance, we consider sulphur and lead, we find that the relations of these two bodies are remarkably different, a fact which can only be explained by the hypothesis that the atoms of sulphur are not of the same nature as those of lead. Most bodies are not composed of homogeneous parts, but of such as differ among themselves, even where they appear to be of like nature, as we mentioned in the case of cinnabar, which is composed of sulphur and mercury ; and as in water, which we find to be a compound of oxygen and hydrogen ; and in common salt, which is composed of chlorine and sodium. Bodies such as these are said to be chemical compounds, in contradistinction to those which are not capable of being decomposed into different constituents, and which are, therefore, called simple bodies, or elements. There are fifty-five or six of such simple bodies or elements, which hitherto at least have not been found to admit of further decomposition. The consideration of these elements, and of the mode in which they enter into the composition of other bodies, falls within the province of chemistry. Aggregate Conditions. In addition to the above differences of bodies, we observe others, which depend, not upon a difference in their constituent parts, but upon the manner in which the particles are united. Thus one and the same substance may assume totally different forms, as water, which is solid when it appears as ice, fluid as water, and gaseous as steam. Without changing its composition, we may convert water into ice, and ice into water vaporize w r ater, and again condense it. All bodies with which we are acquainted are in one of these three conditions, either solid, fluid, or gaseous (aeriform). Solid bodies have, independently of the slight changes effected on them by heat, a constant volume and an independent form; and it requires a greater or less amount of force to divide a solid body. Thus it is impossible to compress a piece of iron to the half or the third of its volume, or make it fill a space twice or three times as great as it occupies, it being only by extreme force that we are enabled to change its form or to divide it. Fluids have, in the same sense as solid bodies, a constant volume ; that is, although they may be slightly compressed by 32 PROPERTIES OF BODIES. strong pressure, or somewhat expanded by the action of heat, the change of volume thus induced is very inconsiderable. We cannot compress the water which fills a quart bottle into a vessel of half the size, and, if we pour the fluid into one of twice the bulk, the vessel will only be half filled. But fluids differ from solid bodies in having no independent form, the. figure they assume being that of the vessel containing them, the surrounding solid body, while the liquid presents a horizontal surface where it intersects the sides of the vessel. Fluids also differ essentially from solid bodies in the least imaginable force being sufficient to separate their particles. Gaseous bodies have neither an independent form nor a definite volume; the space which they occupy dependingonly upon external pressure. A volume of air may easily be reduced to the half, the fourth, or even the tenth of its original bulk; and, conversely, we find that, on admitting the same volume of air into a vacuum twice, four times, or ten times as large, the air will completely fill it, thus proving that gaseous bodies have a tendency to expand as far as possible. Easy divisibility is alike common to gases and fluids. The external differences must, according to our views of the composition of bodies, depend upon the circumstance that in solid bodies the individual particles remain at certain distances from, and in fixed relative positions to, each other ; in fluids they remain at fixed distances, but may easily be displaced ; while in gaseous bodies the component parts show a constant tendency to separate. Molecular Forces. As a force is necessary to separate the particles of a solid body, and as also an external force is necessary to hold together the particles of a gaseous body, it is clear that bodies cannot be formed by means of a simple juxtaposition of their atoms, since they would then be nothing more than an un- connected mass somewhat in the condition of a sand heap. There must, consequently, be forces which hold together the particles of a solid body in their relative position, imparting to them a fixed internal structure and external form; and in like manner there must be forces which act repulsively amongstthe particles of a gas. These forces, which are continuously acting between the adjacent molecules of bodies, are termed molecular forces. The force which holds together the particles of a solid body is termed the force of cohesion, which we assume to be called forth by a mutual INERTIA. 33 attraction of the atoms. Now, if atoms mutually attract each other, it is not easy to understand how these can also mutually repel each other, and, therefore, in order to explain this repulsion observed in gases, we assume that there is another and an op- posite force, which we term the force of expansion. Solid bodies may be melted by heat ; that is, they may be transformed into a fluid condition ; and through the same agency fluids may be reduced to the state of vapor ; it follows, therefore, that heat is opposed to the force of cohesion, and hence we may assume it to be identical with the force of expansion. Let us suppose the molecules of a body to be surrounded by an atmo- sphere of heat which modifies the attraction of the molecules, and we shall then understand how the attractive and the repulsive forces proceed from one common centre. The preponderance of the expansive or of the repulsive force will determine whether a body be solid or gaseous, while an equilibrium of both forces cha- racterizes a fluid. Inertia. Throughout the whole kingdom of nature no change in the condition of things can occur without a special cause. Thus whatever change may occur in a body, w r hether it be relat- ing to rest or to motion, or to a change in its aggregate condition, must be occasioned by some force. If a body be at rest, a force is necessary to put it into motion, and, conversely, it cannot be reduced to a state of rest from motion without the agency of some force, for a body once put into motion, will continue that motion with unchanging velocity, in an unchanging direction, until its course be arrested by external impediments. This property of a body we term inertia. We find numerous examples in every-day life elucidating this law of inertia. Thus the wheel of an engine continues to pursue its course after the force which impelled it has been arrested, and it would continue to run on for ever if the motion were not constantly impeded by friction. In running fast the speed cannot suddenly be checked. A man standing upright in a boat will fall backwards when the boat is pushed from the shore, and will be urged forward as the boat touches the land. We shall subsequently have frequent opportu- nities of alluding to the influence of the law of inertia upon many phenomena of motion. According to the law of inertia a body must exercise a resistance against every force which removes it from a condition of rest to one of motion; or which hastens, 34 PROPERTIES OF BODIES. impedes, or tries wholly to arrest it when in motion. It is, therefore, clear, that the action exercised upon the condition of motion of a body must depend on the one hand upon the intensity of the force, and on the other upon the degree of inertia in the body. The larger the quantity of matter that is to say, the greater the mass is on which a force acts so much the greater will be the resistance it offers; and we judge of the mass of a body by the amount of resistance which it can oppose by its inertia to an accelerating or retarding force. This idea of inertia and mass cannot be rendered very clear until we have occupied ourselves somewhat with the study of the laws of gravity and motion. Gravity. If we remove a piece of stone or wood from the ground and throw it from our hands, it will, when left to itself, fall until it reaches the earth, or meets with any object to arrest its course. As matter is inert, it cannot of itself pass from a state of rest into one of motion. If, then, we see that a body at rest begins to move at the same moment that we deprive it of its support, we must ascribe this to a force, and to this force we apply the term gravity. Gravity is, therefore, the force which compels bodies to fall. We must not, however, suppose that its power is limited to this action, for we shall soon see that gravity produces other pheno- nomena, and other motions. The direction of rivers which flow into the sea, the rising of a piece of cork from the bottom of the water to the surface, the ascent of the air-balloon, are all the effects of this force. There is no better means of ascertaining the direction of the force of gravity than the following: Fasten a string at one extremity, and attach a small heavy weight at its other extremity; the direction of the thread, when it is tense and at rest, will j determine with accuracy the direction of gravity. This little ' instrument is called a plummet, and the line which the thread / forms in a state of equilibrium is the vertical. The direc- tion of gravitation is therefore identical with that of the plummet, and nothing can be easier than at all times, and in all places, to ascertain this direction of gravitation. As we shall see when we treat of hydrostatics, the upper surface of every fluid at rest must be at right angles with the direction of gravitation, or we may express the same thing differently FORCE OF GRAVITY. 35 by saying that the direction of gravitation is always at right angles with the earth's surface. Here, as may easily be supposed, we do not speak of the true surface of the earth with its hills and valleys, but of an ideal surface, of which we must form a conception in the following manner: If we assume that the Atlantic Ocean, the South Sea, and all other seas, were for a moment perfectly at rest, then their vast superficies would form a part of a spherical sur- face; and if, further, we assume that the different parts of this surface w r ere spread under the surface of the land, still retaining their curvature, they would form a spherical surface without hills or valleys. This partly imaginary and partly actual surface is what we term the level of the sea the horizontal line. When, therefore, we say that Mount Blanc is 14,690 feet above the level of the sea, we mean that a perpendicular dropped from the sum- mit of the mountain must measure 14,690 feet in order to reach this ideal surface. In Holland there are whole districts below the surface of the sea; that is to say, this imaginary level is at an elevation above the heads of the inhabitants. The force of gravity is always directed towards the central point of the earth, as we perceive from what has been already stated. The directions of the plummet at two different parts of the earth are, consequently, not parallel, for they make a certain angle with each other, the point of which coincides with the cen- tral point of the earth. Berlin and the Cape of Good Hope are two places lying in nearly the same meridian line. Berlin is 52 31' 13" north of the equator, and the Cape of Good Hope 33 55' 15" south of the same line; and if we draw two lines towards the central point of the earth, the one from Berlin and the other from the Cape, we find that they make an angle of 86 26' 28'', being the angle which the plummet at Berlin makes with the plummet at the Cape. If the experiments be made at two points lying within the circumscribed space of an apartment, or even at the extreme ends of a city, no deviation in the direction of the plummet will be perceived; the- reason of which is, that the central point of the earth (the focus towards which the two lines incline) is distant from the surface of the earth more than six millions of metres* (3960 miles) (the radius of the earth). Now, as 200 metres (218,72 yards) scarcely compose the 30,000th part * The metre is equal to 39.37 English inches. Tn. 36 PROPERTIES OF BODIES. of the earth's radius, it follows that two plummets placed at the distance of 200 metres from each other would form an angle of about 6.3 seconds. If the places at which the experiment is attempted were less removed from each other the angle would cease to be appreciable. If a body be impeded in its fall by the intervention of some other supporting body, the action of the force of gravity does not cease, but manifests itself in this case by pressure upon the intervening object. Gravity is a general property of bodies ; that is, it is common to fluids and gases, as well as to solid bodies. The falling of the rain drop proves the gravity of fluids, and we shall subsequently adduce instances of the gravity possessed by gaseous bodies, and consequently show that the whole atmosphere surrounding our globe presses upon the earth's surface. Weight. The amount of pressure exercised by a body upon another body upon which it rests is called its weight; this pres- sure increases with the number of material particles of the body. In order to compare the weight of different bodies, we make use of the balance, the application of which is familiar to all, and its arrangement we shall describe subsequently. In France the gramme is the legal unit of weight, and at the present day it is received almost universally as the unit measure in scientific researches. The gramme is the weight of a cubic centimetre of pure water in its state of greatest density. The French system of weights has this great advantage over others, that the units of weight and measure stand in a simple relation to each other, so that it is easy to judge of the weight of a body by its size, and vice versa.* * A measure can only be considered as unalterably fixed when it has been de- rived from some undeviating size or space in nature, as is the case with the French system of measures. Thus any certainty other systems now possess has been derived from a comparison with the system established in France. The undeviating length which has become the standard for this system is the earth's meridian that is, the circumference of a large circle of the globe, passing through both poles. The forty millionth part of this line is a metre. The length of a meridian of the earth was ascertained by a series of the most carefully conducted measurements, and for this purpose the old French unit of measure the toise was used for a basis ; it was in this way accurately deter- mined how many of these toises were contained in the earth's meridian, and con- sequently what was the exact length of the toise. As, however, it was resolved that an entirely new system of measures should be established, the forty millionth MASS. 37 Mass. According to the above explanation, the mass of a body is the quantity of matter of which it is composed ; and on this quantity depends its inertia ; consequently, the amount of this inertia gives the actual measure of the mass, and here gravity furnishes us with the best means of ascertaining the quantity we seek. The mass of a body is always proportional to its weight. This connection between the two is everywhere demonstrable by expe- riment, although we may readily conceive it to be not a necessary result. For, let it be assumed that there are bodies in nature on which gravity exercises no power, on this account they will not, therefore, the less continue to possess inertia ; further let it be assumed that the force of gravity acts unequally upon the particles part of the earth's meridian, expressed in toises, was taken as the new unit of length in short, the relation of the metre to the toise was then accurately deter- mined. As in the present day the French system of measures is referred to in almost all scientific works, we deem it desirable to give a table of the relations of foreign and English weights to those established in the French system, giving by way of intro- duction, a few facts referring thereto. The metre is divided into 10 decimetres, 100 centimetres, and 1,000 millimetres. The following diagram represents a decimetre, with its subdivisions, as accurately as we can represent them : Fig. 2. 10 The relation of the most important measures of length to the metre are given in the following table : 1 English foot = 304,79 millimetres. 1 Rhenish or Prussian foot = 313,85 " 1 Vienna foot = 316,10 1 Paris foot = 324,84 1 Toise = 6 French feet = 1,94904 metres. 1 German or geographical mile = 7407 1 English nautical mile = 1 Italian mile . . = 1852 " The measures for solid and fluid bodies and the weights are all derived from the measure of length in the French system. Thus the unit of the fluid measure is the litre (2,113 pts.) = 1,000 cubic centimetres. A cubic centimetre of water weighs 1 gramme (or 15.44 grains troy); 1,000 grammes make 1 kilogramme; 1 litre of water, therefore, weighs 1 kilogramme (2,679 Ibs. troy). One gramme is equal to 10 decigrammes = 100 centigrammes = 1,000 milli- grammes (15.44 grs. troy). The pound weight differs considerably in different countries, but it may on an average be said to correspond pretty nearly with the half kilogramme. The Baden 4 38 PROPERTIES OF BODIES. of different substances, and that a ball of lead is only heavier than a ball of wood of equal size because gravitation acts more espe- cially upon the particles of the lead, without, on that account, the mass of the leaden ball being greater than that of the wooden ball. Again, to make the subject clearer, let us suppose two equally large balls, one of lead, the other of wood, and let us assume that the mass or amount of inertia be the same in both, it clearly follows that in this case the leaden ball would fall with the greater velocity, for we know that it weighs some twelve times more than the wooden ball, and that, consequently, the force which impels the former is twelve times as great as that which and Hesse pound is exactly this weight, as the system of measures adopted in these countries has been derived from the French. This pound of 500 grammes is the standard measure used in the German Zollverein, or general customs. 1 London pound (troy weight) . = 373,202 grmes. 1 Vienna pound (trade weight) . = 572,880 " 1 Old French pound = 489,503 " 1 Prussian pound = 467,711 " [To render the comparison of the English and French weights still more evident, the following tables are subjoined. .015444 grains. .15444 1.5444 15.444 " 154.44 1544.4 15444. .03937 inches. .39371 3.9371 39.371 393.71 3937.1 " 39371. .061028 cubic in. .61028 6.1028 61.028 610.28 6102.8 61028. 1 Milligramme . . . Centigramme . . . Decigramme . . . Gramme WEIGHTS. = 0.001 grammes = 0.01 " = 0.1 = 1 = 10 = 100 " = 1000 " Decagramme . . . Hectogramme . . . Kilogramme . . . Millimetre Centimetre Decimetre Metre Decametre Hectometre Kilometre Millilitre Centilitre Decilitre Litre . . Decalitre Hectolitre Kilolitre MEASURES OF LENGTH. = 0.001 metres. = = 0.00 = = 0.1 = = 1 = = 10 " = = 100 " = = 1000 = MEASURES OF CAPACITY. = 0.001 Litre. = = 0.01 " = = 0.1 = 1 = 10 " = 100 = = 1000 = DENSITY. 39 acts upon the latter, and would, therefore, induce greater velocity, if equal resistance were opposed to both balls. We find, how- ever, that the leaden ball falls no faster than the wooden one, at least in vacuo, and hence we see that the force which impels the former, although twelve times as great, acts against a body pos- sessing twelve times the inertia of wood. And, as we find that the rapidity with which all bodies fall in vacua is equal, we con- clude, on the same grounds, that the mass of a body is always proportionate to its w r eight, and that, therefore, the weight of a body is a measure of its mass. Density. The density of a body is the relation of its weight to its volume, and thus conveys the idea of specific gravity, which is a constant characteristic property of every substance. As it was necessary to choose one body in particular as the unit of density, to which all others might be compared, water in its con- dition of greatest density has been made choice of for this pur- pose. The density, or specific gravity, of a body is, therefore, the number which indicates how much heavier a body is than an equal volume of water. A cubic centimetre of iron weighs 7.8, a cubic centimetre of gold 19.258 grammes, while an equal volume of water weighs only one gramme ; therefore 7.8 is the specific weight of iron, and 19.258 that of gold. Hence to find the specific gravity of a body, we divide its absolute weight by the weight of an equal volume of the water. Thus the data necessary to determine the specific gravity of a body are its absolute weight by the weight of an equal volume of water. These data are most readily obtained for fluids. If we take a narrow-necked vessel and fill it up to a certain marked line on the neck, first with water, and then with the fluid to be deter- mined, and weigh it each time in a balance, we obtain the rela- tive weight of the two fluids. Thus, if we wish to ascertain the specific gravity of oil of vitriol, we must first place the empty bottle on one scale and counterbalance it, then fill it to the gra- duated line with water. If we assume that the bottle contain exactly one litre, that is 1000 cubic centimetres, the water will weigh exactly 1000 grammes. If, now, we fill the bottle to the same point with oil of vitriol, it will require 1848 grammes to make the balance even. Since the oil of vitriol in) the flask weighs 40 PROPERTIES OF BODIES. 1848 grammes, while an equal volume of water weighs only 1000 grammes, the specific gravity of the former is =* 1.848. 1000 [This rule is applicable with some modifications when our usual weights are employed. Thus when the specific gravity of a fluid is to be ascertained, it can be readily accomplished by taking a bottle of convenient size, and carefully counterbalancing it. The weight of water required to fill it is then to be ascer- tained, and then the combined weight of the bottle and the fluid under examination ; on subtracting from the latter weight that of the bottle, the weight of the fluid will be afforded. If this weight be divided by that of water 1000, the quotient will be the specific gravity. For instance, a counterbalanced bottle holds 500 grains of water, and 412 grains of alcohol, then 412-^-500 = 0.824 for 500 : 1000 :: 412 : 0-824.] Owing to the difficulty of always obtaining sufficiently large quantities of the fluids to be weighed in so capacious a vessel, and the damage to a fine balance in support- ing such heavy masses, it is more expedient to make use of smaller vesssels. The form commonly employed is represented in Fig. 3. This vessel is made to contain from eight to twenty cubic centimetres, and has a ground glass stopper made of a part of a thermometer tube, in order to admit of the rising of por- tions of the fluid in case of expansion by heat through the slender opening without the stopper being raised, or the bottle burst. In order to determine the specific gravity of solid substances we must form from them a body of regular shape, as a cube or sphere, in order to estimate the more readily its cubic contents. The absolute weight of such bodies is found by the balance, and the weight of an equal volume of water is given by the known volume of the body. If a cube of marble weigh, for instance, 21.6 grammes, and each of its sides be two centimetres, its cubic contents will be eight cubic centimetres ; a cube of water of like size will thus weigh eight grammes ; and, consequently, the spe- 21 6 cific gravity of the marble is to that of water as =2.7 8 Take a sphere of dried beechwood weighing 25.79 grammes, SPECIFIC GRAVITY. 41 and, supposing its diameter to be four centimetres, we may easily compute its cubic contents, which we shall find to be 33.49 cubic centimetres. A sphere of water of equal size will, there- fore, weigh 33.49 grammes, and the specific gravity of the wood 9^ 7Q is therefore, ^11T = 0.77. ' 33.49 As, however, it is not always possible to obtain such large quantities of substances, and it is sometimes impracticable to form bodies of the regularity of figure necessary, other methods must be resorted to for ascertaining the specific gravity ; and the majority of these depend upon hydrostatic laws, the consideration of which we must postpone to a subsequent period. (Chap. III. Hydrostatics.) The following method, however, is not grounded upon these principles, and is often made use of to ascertain the specific gravity of such bodies as can only be obtained in small portions. We first fill the vessel (Fig. 3) with water, and bring it into equilibrium in the balance, then lay the granules beside it, and ascertain the absolute weight. This done, we remove both from the scale, and, throwing the granules into the water in the bottle, again insert the stopper. A quantity of water will then escape, equal in bulk to the granules which have displaced it. On weighing a second time, we ascertain the quantity of water that has been displaced ; or, in other words, the weight of a volume of water equal to the volume of the granules. By way of illustration, let us determine the specific gravity of platinum granules as they occur in nature : The glass vessel with water weighs . . 13.52 grms. The granules 4.056 " Both together 17.576 " If, after throwing the granules into the bottle, putting the stopper in, and weighing the whole together, we find it to be 17.316 grammes, the weight of the water forced out by the granules must be 17.57617.316 = 0.26 gram.; consequently the specific gravity of the granules is '. = 15.6. The same method may be pursued with larger portions of bodies if a suitable vessel be chosen for the experiment. 42 PROPERTIES OF BODIES. If the body to be weighed be soluble in water, some fluid must be chosen, as alcohol, oil of turpentine, or some other in which the body does not dissolve. By the above-described process, we find how much a certain quantity of fluid weighs which has the same volume with the body to be weighed, and when once the specific gravity of the fluid is known, it is easy to ascertain the weight of an equal volume of water. Let it be assumed that a piece of salt which is insoluble in oil of turpentine weigh 0.352 gram., and displaces when put into the glass 0.13 gram, of oil of turpentine. The specific gravity of this fluid is 0.8725 ; an equal volume of water will therefore weigh 13 -1 = 0.149, and the specific gravity of the salt is, therefore, COMPOSITION OF FORCES. 43 SECTION II. EQUILIBRIUM OF FORCES. CHAPTER I. EQUILIBRIUM AND DECOMPOSITION OF FORCES IN THE SO CALLED SIMPLE MACHINES. A BODY is in a state of equilibrium when all the forces acting upon it counteract each other, or when their action is prevented by any resistance. In a body suspended by a thread, the action of gravity is destroyed by the resistance of the thread. If the thread be not strong enough, it will break, and the body will fall to the ground. A body may often be in equilibrium without having any fixed point of support, and without any apparent resistance. The fish may be in a state of equilibrium in the water, and the balloon in the air, but here the gravity is counter- acted by a pressure, of which we shall further speak. It may be said that all bodies which appear to be in a state of rest are acted upon by many mutually counteracting forces. It falls to the department of statics to ascertain the conditions of equilibrium, while the subject of dynamics, on the other hand, investigates the law r s of the motions which result when the conditions requisite for the establishment of equilibrium are not satisfied. In order to measure forces we must assume some arbitrary force as unity. Two forces are equal when, in acting upon one point from opposite directions, they remain in equilibrium. Two equal forces acting in the same direction are equal to a double force. We should have a triple force if three equal forces acted in the same direction, and so on. 44 STATICS. Whatever be the number of forces acting upon one point, and whatever their direction may be, they can only impart one single movement in one definite direction. Hence we assume that there is a force which is capable in itself of producing the same action as these combined forces, and consequently of replacing them. This is termed the resultant. For example, when a ship is im- pelled by the combined action of the stream, the rudder, and the wind, it moves in a definite direction; but if the actions of the stream, rudder, and wind were to cease, we could evidently im- part the same motion to the vessel by attaching to it a rope or line by which a definite force might be made to bear in the direc- tion towards which the ship was impelled by the simultaneous action of the three forces. This then is the resultant of the three forces. The combination of forces which act together upon one point, we term a system of forces, or, when speaking of them in refer- ence to the resultant, we .call them component or lateral forces. It is evident that, if we were to add to the combined system of forces a new force, equal and opposed to the resultant, all the forces acting in concert must retain their equilibrium. If, for example, to abide by our former illustration, we had caused a force to act upon the line of the vessel which was equal, but op- posed, to the resultant force of the stream, rudder, and wind, the newly-applied force would induce a state of equilibrium, and the ship would remain at rest just as if it were lying at anchor. If two or more forces act in the same direction their resultant is the sum of the separate forces. When two forces act in opposite directions upon one point, the resultant is equal to the difference of the two, and will act in the direction of the greater. If the directions of two forces acting upon a material point, make an angle with each other, we find the resultant by means of a law known under the name of the parallelogram of forces, and established by means of the following simple consideration : Suppose two forces acting simultaneously on the point a, one in the direction a x, the other in the direction a y. Let one force be such that in a given time say a _ _ x ___ second it will by itself move the point from a to 6, while the other force will, in the same period of time, move it by itself from a to c. If PARALLELOGRAM OF FORCES. 45 now the point be exposed for a second to the simultaneous action of both forces, the effect is evidently the same as if the point were subjected for one second to the sole action of the one, and the next second to the sole action of the other force. The first force alone impels the point from a to b in one second ; and if the action of this force were to cease at the instant the point reaches by and the point be then solely subjected to the action of the second force, it would, at the close of another second, reach r. Hence, if both forces act simultaneously, the point a must, in the course of a second, reach the same point r. An illustration will make this more evident. A ship acted Fig. 5. upon simultaneously by two forces, the stream and wind, starts from the point A on the side of a river. Let us assume that the vessel will be urged obliquely across the river by the action of the wind alone, in a definite time, say a quarter of an hour, going from A to B ; and assume it to be borne during the same period of time by the force of the stream alone, if there were no wind from A to C ; then it would in the same period of time go from A to D, if both wind and stream acted simultaneously, that is, it must reach the point D in a quarter of an hour, when impelled by the simultaneous action of the two forces, as it would have gone from A to B in a quarter of an hour, if acted upon solely by the wind, and from B to D during the next quarter of an hour when impelled only by the stream. The line a r (Fig. 6) is the diagonal of the parallelogram a b r c, which by means of the law we have mentioned may be thus expressed. The resultant of two forces which simultaneously act at any angle upon a material point is such as to tend to move the point 46 STATICS. through the diagonal of the parallelogram, which we may con- struct from the lines corresponding to each of the component or lateral forces. As the line which a body passes over in a given time is pro- portionate to the force which impels it, and as in determining the resultant we only endeavor to find its direction and relations of size to both component forces, the law maybe thus expressed: "If two lines be drawn in the direction of two forces, and through their point of contact, and their length to be proportionate to the respective forces, the diagonal of the parallelogram which is determined by these two lines will represent the resultant both in magnitude and direction." As a state of equilibrium must be established between three forces, if each be equal and opposed to the resultant of the other two, we may easily, by means of an experiment pertaining to statics, test the correctness of the law of the parallelogram of forces. To the leaf of a table there are attached two vertical rods, each of which has a movable slide Flg> 7- bearing a pulley that turns easily upon its axis in a verti- cal plane. The rods must be so screwed on that the vertical planes of both pulleys coincide. If now we have a line over the pulleys, attaching at one end a weight a, at the other end a weight c, and lastly, a weight b between the pulleys, the whole will be in a state of equilibrium in any definite position of the threads; we have three forces acting upon the point o in the directions o p, o q, and o r, and it is easy to ascertain whether those relations between the amount and direction of the forces really exist, such as the law of the parallelogram offerees requires. Supposing by way of illustration, that a = 2 and c = 3 ounces, how great must be the force at b if the angle p o q be 75 ? According to the above law the resultant may easily be obtained, by construction, as in Fig. 8. If the angle r s t measure 75, and r s = 2 and s t = 3 (some unit being assumed), we shall find that the diagonal PARALLELOGRAM OF FORCES. 47 s p = 4. Thus, if the angle p o q = 75, the weight 6 must be equal to 4 ounces ; and if we at- tach a weight of 4 ounces to the string, we shall find that the angle p o q will measure 75; and this we may easily prove by holding a figure of larger dimensions behind the thread, r s cor- responding with o p, and s t with o q. If b had been made larger than 4, and all the other parts of the figure were left unaltered, the angle p o q would be less than 75 ; and the smaller we make the weight at 6, the larger will be the angle p o q. When both forces are equal, the resultant divides the angle which they make with each other into two equal parts. When the two forces are unequal, the resultant divides their angle into unequal parts, approaching more nearly to the direc- tion of the larger force. As we can find the resultant of two forces acting upon a point, so it is likewise easy to ascertain the resultant of any given number of forces, nothing more being necessary than to find the resultant of the two first forces, then their resultant with the third force, and so on. As two forces can be replaced by a single force, so conversely, we may substitute two forces for one ; and we see further, that an infinite number of different systems of forces may have the same resultant, and conversely, that one force may be replaced in innumerably different ways by a sys- tem of two forces. But if it were required that the force a r should be replaced by two other forces, one of which should have the direction a y, and the magnitude a c, the problem is perfectly definite, there being but one way to complete the parallelogram, and to find the component or lateral force a b. From the parallelogram of forces are derived the laws of equi- librium in all simple machines; and thes we now proceed to describe. Fig/9. 48 STATICS. The Inclined Plane affords a practical illustration of the decom- position of forces. When a weight rests upon a plane, which forms an angle x with the horizon, the gravity of the body acting in the direction a b is no longer at right angles to the plane, and, consequently, the latter has not to support the full pressure of the Fig. 10. weight of the load. In fact, the gravity of the body may be de- composed into two forces, the one of which acts at right angles with the plane, causing the pressure, while the other, acting parallel with the inclined plane, urges the body down it. The magnitude of these two forces may easily be obtained by con- struction. If a 6 represent the magnitude and the direction of gravity, we have only to draw a line at right angles with the in- clined plane through a, and another parallel with it, then join b and d, and drop the perpendicular b c. The line a d represents the amount of pressure which the plane has to support, a c the amount of force which impels the load down the inclined plane, or, in other words, the pressure upon the plane, and the force which tends to move the body parallel to the inclined plane are to the weight of the body as the lines a d and a c are to a b. But the triangle a b c is similar to the triangle jR S T and a b: a c = R S: S T, and, consequently, the force which urges the body down the inclined plane is to its weight as the height of the plane is to its length. If we denote by x the angle which the inclined plane makes with the horizon, then it is evident that a c = a b sin. x and b c = a b cos. x; and, therefore, if P repre- sents the weight of the body, the pressure which the plane has to INCLINED PLANE. 49 support is equal to P cos. x, and the force that urges the body down the plane is equal to P sin. x. We will attempt to make this point clearer by the following illustration. If we lay a load in a little carriage, and place it upon an inclined plane, it will roll down ; this may, however, be hindered by attaching to the carriage a line, passing round a pulley, and having the weight P suspended from its other ex- tremity. Supposing the little carriage and its load to weigh 100 ounces, and the angle x to be 30, then S T = J R S, and, consequently, a c = J a b; that is to say, the force which urges the carriage down the plane is equal to the half of its weight, and the carriage will, therefore, be prevented from rolling down, if we make the weight P equal to 50 ounces. If the angle x were 19 30', then would S T = J R S, and 100 then the weight P need only be = 33 ounces to prevent the o carriage from rolling down the plane. As sin. 14 30' nearly = J, that is to say, when the angle x = 14 30' S T= i R S, in this case P must = l = 25 4 ounces. In order to make' experiments with reference to different angles of inclination, we must use a polished board, which, by means of a hinge, is so secured to a fixed horizontal board as to admit of being placed at any angle of inclination that may be required. The pulley round which the line is passed may be secured to the board, but we may also easily make use of one of the rods in Fig. 7 for this purpose, as the slide may be pushed up and down to raise or depress the pulley to the elevation required. Instead of attaching the weight P directly on the line, we' lay it in a scale which has been weighed, and, together with its contents, must be made equal to the computed weight P. We daily see the practical application of the inclined plane. Every road leading up an ascent is an inclined plane, on which weights are lifted from valleys to the summit of hills ; for instance, in order to draw a loaded wagon up a hilly road, besides the force necessary to overcome the friction (which is likewise required upon even ground), we must apply another force to sustain the equilibrium with that portion of gravity acting parallel with the inclined plane, and which increases with the steepness of the road. 5 50 STATICS. For this reason it is preferable to make a road winding circuit- ously round a hill, instead of carrying it directly upward. It fre- quently happens in erections of almost every kind that the mate- rials for building are raised to the required height by means of inclined planes. This application of the inclined plane was known to the ancients ; and it is highly probable that the Egypt- ians availed themselves of it in order to raise the huge blocks of stone which they employed in constructing their pyramids. Fig. 11. Fig. 12. The Screw is an inclined plane wound round a cylinder. Let a b c, Fig. 12, be a rectangular piece of paper whose horizontal side, a 5, is equal to the circumference of the cylinder, Fig. 11, the paper be so wound around the cylinder that a b shall form the periphery of its base, the hypothenuse a c will wind round the cylinder in an uniformly ascending curved line, o p q r; if the point a coin- cide with the point o, b will also coincide with o, and c will be vertically over o at r. The curved line o p q r, which is repre- sented in our figure, is termed the thread of the screw ; and its reverse side has been drawn white in order to show that the entire curvature of the line from o to r, is the distance of two contigu- ous threads. If we imagine a triangle continued along the thread of the screw round the cylinder, we obtain a screw with a triangular thread, as shown in Fig. 13; and, if we suppose a Fig. 13. Fig. 14. parallelogram wound in like manner round the cylinder, we have a flat-threaded screw, as represented in Fig. 14. A screw cannot by itself be applied to remove or lift heavy weights, or to exercise any strong pressure ; for to effect these purposes it must be so com- bined with a screw-box or nut (which is a concave cylinder, on the interior of which a THE SCREW. THE WEDGE. 51 corresponding spiral cavity is cut), that the elevations of the one may accurately fit into the depressions of the other. If we suppose the screw to be fixed vertically, then every revolution must cause an elevation or depression of the nut. If a wqjght lying on the nut should be raised by the turning of the screw, it is evident that the same principles are at work here, as in an inclined plane of equal elevation. The steepness of the convolutions of the screw is inversely proportional to the distance between two contiguous threads as compared with the circumference of the cylinder. The screw is used partly to lift heavy weights, and partly to sustain great pressure, the resistance acting in some cases upon the screw itself, and in others upon the screw-box. In estimating the effect of a screw, we must not lose sight of the fact that fric- tion plays a conspicuous part in its action ; but of this we shall speak presently. In order to make use of the screw as a power- ful machine, the turning force is not applied directly to the cir- cumference, but to a lever, or arm, as we may observe in all screw-presses. The Wedge. Another form of applying the inclined plane is the wedge, which is used to cleave wood and masses of stone. By thrusting wedges under their keels, ships are raised for the purpose of being re- Flg> 15 ' paired in the docks. The wedge is the principal agent in the oil-mill. The seeds from which the oil is to be extracted are introduced into hair bags, and placed between pieces of hard wood. Wedges inserted between the bags are driven in by allowing heavy beams to fall on them. The pressure thus excited is so intense that the seeds in the bags are formed into a mass nearly as solid as wood. All our cutting implements, as knives, chisels, scissors, are nothing more than wedges. It must be perfectly clear to every one that the action of the wedge may be referred to that of the inclined plane. The Pulley is a round thin disc, hollowed out on its edges, and turning upon an axis passing through its centre at right angles with its plane. We divide pulleys into the fixed and movable. Fixed pulleys are such as have an immovable axis, and simply allow of things being turned round them. If a string or line be passed round a part of the circumference of a fixed pulley, and forces act at either 52 STATICS. Fig. 16. extremity, a state of equilibrium will not be brought about unless the force which stretches the line on the one side be equal to the force acting on the > other. Fig. 16 represents a pulley, c, mov- ing round a fixed axis, and the line stretched by forces acting in the directions a b and d e. If we suppose the lines d e and a b pro- longed to their intersecting point, m, it is evident that if m were a point connected with the pulley, we could change the points of application of the two forces from a and d to m without altering anything in the action ; and thus we should have two forces meeting at m, which could only be in equilibrium if their resultant were so. If the two forces meeting in m, and acting in the directions m b and m e, are equal, their resultant will bisect the angle b m e, and will then pass through the fixed central point c, and we shall have a condition of equilibrium. If one of the two forces be greater than the other, the resultant will no longer pass through the fixed point, and consequently equilibrium will not be main- tained. The pressure which the axis of the pulley has to sustain must clearly be equal to the resultant of the two forces ; and if the directions of the forces be parallel, as in Fig. 17, the pressure upon the axis is equal to the sum of the two forces, in which we might also include the weight of the pulley.* Fig. 17. Fig. 18. * It might be objected that this is arguing in a circle ; for we have already used the pulley as an experimental illustration of the correctness of the proposition of the parallelogram of forces, and now we derive the conditions of equilibrium in a pulley from the parallelogram of forces. This, however, is not so unreasonable as it may at first sight appear ; for, although the conditions of equilibrium between all the forces acting on a pulley can only be understood in all their bearings by means of the theory of the parallelogram of forces, we may easily perceive, even without any knowledge of these laws, that the powers acting on both ends of a string (the ten- sion of the string remaining constant) passed round a pulley must be equal if they THE PULLEY. 53 Fig. 19. Fig. 20. A movable pulley cannot be in equilibrium unless the forces by which the two ends of the string are stretched are equal to one another, for in this case only does their result- ant pass through the central point of the disc. The action of this resultant is not arrested owing to the fixed condition of the axis, but owing to there being a third power in the axis in the direction of the resultant, which is equal and opposed to it. This third power is usually applied to a hook fastened on the block. At Fig. 18 it is represented by a weight. When the two ends of the line passing round the movable pulley are parallel to each other, as in Fig. 19, it is evident that the force with which each end is drawn, is half as great as the weight hanging to the block. When two groups of pulleys, of which the one is fixed, and the other movable, are so con- nected by a line that the latter may pass from the one to the other, we have a system of pul- leys. Fig 20 represents a system consisting of three fixed and three movable pulleys. The weight q which is attached to the common block of the three movable pulleys is sup- ported by the six lines which connect the upper and lower pulleys ; and consequently, as the weight is equally divided between the lines, each is drawn by one-sixth of the weight q ; and if sixty pounds weight were suspended to the bottom, each line would be drawn upon by a force of ten pounds. If we observe the external line to the left side which connects the lowest of the mov- able pulleys with the highest of those that are are to be in equilibrium ; for, as each force tends to turn the pulley iu an opposite direction, a state of equilibrium can only be brought about when these forces are equal, as must already have been made evident to all in our illustration in Fig. 7. 5* 54 STATICS. Fig. 21, fixed, we shall see that this line runs round the top pulley, and hangs freely down on the right side. Now, in order to establish a state of equilibrium, it is necessary that the tension of the line should be equal on the two sides of the upper pulley ; and as we have seen that the line to the left is drawn with the force of one- sixth of the weight at q, it is necessary to attach a weight equal to one-sixth of q to the end of the line, in order to obtain a state of equilibrium. We may, therefore, again poise a weight of sixty pounds, by attaching to the line a weight of ten pounds. As the amount of weight bearing upon the lines depends upon their number, that is the number of pulleys composing the system, it follows that another relation will be established between the forces and weights, but this can readily be obtained by a similar mode of deduction. The Lever. Suppose a line passed round a pulley, to the end of which the weighty (Fig. 21) is attached ; whilst, on the other side, the line is drawn in the direction a 6, with a force equal to the weight p. Here, how- ever according to the theory of the parallelogram offorces, we may decompose the forces meeting at a, and acting in the direction a 6, into lateral forces, one of which acts in the direction of d from a, being a prolongation of the direction of the radius m a, while the direction of the other force a f is parallel with g p. If the pulley be fixed, the action of the force a d will be counteracted by the resist- ance of the fixed central point m ; we may, therefore, entirely remove the component force acting in the direction a d, without disturbing the equilibrium, and we may replace the active force a b by its component force acting in the direction of a f. If the line a c represent the force p acting in the direction a b, then the line a /will give the amount of the component force P, THE LEVER. 55 and, without further working out the relations of size between a c and a f or p and P, we see at once that P must be larger than p; we might, therefore, without disturbing the equilibrium, re- place the force p, acting in the direction a b by another force P, likewise acting at a, but in a vertical direction. Instead of letting the force P act directly at , we may, without disturbing the equilibrium, choose any part of the line a f as the point of application ; we may, for instance, let the force P act at the point A, where the lines af and g m intersect each other, and thus we have two rectangular forces p and P in a state of equili- brium, at the ends of a straight line h g revolving round m. The two forces are unequal, as their Fi 22 respective points of application at h and g are at unequal distances from the fulcrum m. We have now to ascertain the relation which exists between the magnitude of the forces p and P, and the lengths h m and g m. The triangles c af, Fig. 21, and a A m are similar to each other, and hence a c : af = hm : a m. But the lengths a c and a f are to each other as the forces p and P; thus we have p : P = h m : a m, and since a m = g m, p: P = h m : gm, or p:P=L:l . . . . (1), if we make the length h m = L and g m = I. Or, to express the same fact inwards, we may say that the forces P and p bear an inverse ratio to the distances of their points of application from the fulcrum m. A straight, inflexible rod turning on a fixed point is called a lever. If two opposite forces at right angles to its direction be applied at two different points of a lever, a state of equilibrium will be established when the above condition has been fulfilled. The distance of the point of application of a force from the fulcrum is called the arm of the lever ; and we may, therefore, thus ex- press the condition of equilibrium in the lever : Two forces tend- ing to draw the lever in opposite directions are in equilibrium when they bear an inverse proportion to the corresponding arms of the lever. If, for instance, the arm h m (Fig. 22) was half the length of 56 STATICS. g m, then P must be twice as large as p. A force p may be in equilibrium with a hundredfold larger force P if the arm m g be 100 times as long as the arm h m. From the proportion (1), it follows that P L = p I, that is to say, in order that two forces in a lever shall be in equilibrium, it is necessary that the products of the force and the distance at which it acts from the fulcrum be equal for both forces. If, for instance, the force p = 6 ounces, and the arm be 12 inches, it would be necessary, in order to bring them to a state of equilibrium, to have on the other side an arm three times shorter, that is, 4 inches, acted on by a force three times greater, that is, 3 X 6 = 18 ; it is evident that the product 6 12 is equal to the product 4 x 18. The product obtained by multiplying the force by the arm of the lever is called the static moment of the force. We may also define the static moment of a force as that force which, acting at an arm of one unit on the opposite side of the fulcrum, shall pre- serve the state of equilibrium. In Fig. 23, if we assume that the force to the right = 6, and the arm of the lever = 5, the 23 - static moment of the force will be -i \ H^ 5 x 6 = 30 ; then, if the force on the left hand is to be in a state of equilibrium with the former, the static moment of the two must be equal, and the force acting on the left side on an arm equal to 3 must have a value of 10. But, instead of letting the force 6 act on the arm of length 5, we might, with- out disturbing the equilibrium, apply a force of 30 on the arm of length 1 ; and, in like manner, the force 10 acting on the other side of the lever, which equals 3, may be replaced by a force ot 30 acting at an arm equal to 1. When several forces act on each side of the fulcrum, a state of equilibrium will be established, if the sums of the static moments on each side be equal. For example, in Fig. 24 m is the fulcrum, and on one side the force 5 Fig. 24. acts on the arm 2, the force 2 I I I J^ ' I ' I i I on the arm 4, and the force IB ran pj| Hi ill 4 on the arm 6, while on the s ^ other side the forces 10 and l STATICS. 57 3 act on the arm 3 and 4. Now, all these forces will be in a state of equilibrium, for the sums of the static moments of both sides are equal. The sum of the static moments on the one side is 5x2 + 2x4 + 4x6 = 42, and the sum of the same forces on the other side is 10 x 3 + 3 x 4 = 42. Instead of the force 5, which acts at the distance 2, we might have the force 10 at the distance 1 ; thus also the forces 2 and 4, acting at the dis- tances 4 and 6, may be replaced by two other forces, 8 and 24, acting at right angles to arm 1. We may likewise substitute the forces 10, 8, and 24, acting at the distance 1, for the forces 5, 2, and 4, acting at the distances 2, 4, and 6 respectively; or, in other words, we may replace the three forces 5, 2, and 4, acting on their different arms, by one single force of 42, acting at the distance 1. On the other side we may also substitute two forces, 30 and 12, acting at an arm 1, for the forces 10 and 3, acting at the distances 3 and 4 ; or we may make use of a single force of 42, acting at a distance 1. As the sums of the static moments are equal on both sides, a state of equilibrium must be maintained. The common steelyard furnishes us with a good example of the application of the lever, and Fig. 25 may serve to elucidate the principles of this machine. A lever is movable about Flg * 25> the point a, while a scale is suspended at r, to receive the weight acting upon the arm a r, and this weight is kept in equilibrium by a sliding weight at the other arm of the lever. The heavier the weight is, the further must the sliding weight be removed from the fulcrum r. In such a lever as we have been considering, the fulcrum has to sustain a resistance equal to the sum of the forces on both sides; it may also be in equilibrium when the fulcrum is not fixed, but is moved by a power acting in a con- trary direction, but equal to the sum of the other forces. Fig. 26 explains this. Let us assume that c is the fixed fulcrum of a lever m n, at the ends of which the forces P and P balance each other. Their equilibrium will not be disturbed by the fulcrum c ceasing to be 58 STATICS. fixed, if a force n be attached to it, which shall be equal to the sura of P and P', and act in an upward, as the forces P and P' draw in a downward direction. We may regard either of the three points m, c, or n, as fixed without disturbing the equilibrium. If one of the extreme points, n for instance, be fixed, we have a one-armed lever; that is, one in which the two forces JV and P act on the same side of the fulcrum n. The two forces have in this case opposite directions, and the pressure upon the point of support is equal to the differ- ence of the two forces P and JV. The arm of the force P is / + /', if we designate the length m c as /, and the length n c as /'; the arm of force Nis I'. If c had been the fixed fulcrum we should have had as a requisite condition of equilibrium : P' : P = / : I 1 , and, consequently, F + P ; P = I + I' : /', or, If, therefore, the forces N and P acting in opposite directions are to be in equilibrium, they must be inversely proportionate to the length of the arms at which they act. Fig. 27 shows the applica- Flg> 27 ' ^ tion of a single-armed lever. The valve j9, which closes the opening of a boiler, is forced up by the pressure of the steam, but this pressure is equipoised by a much smaller force, the weight n acting downwards, because r acts at a longer arm than the pressure on the under surface of the valve. Fi 2g The two extreme points (Fig. 28) m and n of the rod m n may be fixed, while a force N acts at e; so that the point m has a pres- sure J9, and the point n a pressure p' to sup- port. W^hen two men carry a load hanging to a rod, each one supporting an end of the rod on their shoulders, they have between them the whole weight to carry ; and when it hangs exactly in the middle of the pole, it will be equally divided between them ; but if the load should be hung nearer to one of them, he will have the most weight to support. Supposing \Yt J| * STATICS. 59 that the appended load weigh 100 Ibs., the pole be 5 feet long, and that the load hang 2 feet from one, and three feet from the other end, then the shoulders of one bearer will have to support a pressure of 60 Ibs., and those of the other a pressure of 40 Ibs. We have hitherto only considered, the forces acting at right angles to the lever ; equilibrium may, however, be established without this being the case. In Fig. 29 7i is the fixed point Fig. 29. of the lever a b ; at a the force o ^ p acts in the direction a c, and at b the force q in the direction a / b d, the forces p and q bearing the same relations to each other as the lines a c and b d. Ac- cording to the law of the pa- rallelogram of forces, p may be decomposed into two forces, of which the one p' acts at right angles to a 6, while the other acts in the direction of a b. In the same way q may be decomposed into two forces, of which one q' acts at right angles to a 6, and the other in the direction of that line. The action of the two component forces which act in the direc- tion of the line a b is evidently fully counteracted by the resist- ance of the fixed point n, thus leaving only the action of the forces j/ and q. 1 We may, therefore, substitute the component forces p' and q', acting at right angles to the lever, in place of the original forces p and q. A state of equilibrium will be established if p' and q' correspond in an inverse ratio to the length of their arms that is, if p f : q f = n 6, n a or if q' x n b = p' x n a. If we prolong the direction of the force p, and draw n o ( = 1) perpendicular to it, we have the triangle a o n, which is similar to the triangle whose hypothenuse is p, and one of whose sides is p' ; and from this it follows that p : p' a n : I and consequently that p x / == p f x a n. The force jt), acting obliquely on the arm a n, acts exactly the 60 STATICS. same as the component force p' acting at the same point a ; and also as if the force p acted at right angles to a shortened arm, which is found by letting fall a perpendicular from the fulcrum n upon the direction of the force. The moment of an oblique force is found by multiplying the force by the perpendicular let fall upon the direction of the force from the axis. Thus the oblique force q acts as if it met the arm of the lever n m at right angles, and the two forces p and q are in equilibrium when p x o n q x n m. Fi 3Q By the same process, we find the mo- ment of the forces when the lever does not form a straight line. When any fixed sys- tem turns round a fixed axis, the forces that tend to turn it round the axis follow N the laws of the lever ; and these we there- fore find applied in many machines, which may, therefore, be divided into more or less complicated systems of levers. In the windlass and capstan (Figs. 31 and 32) the weight r corresponds to the counteracting force p in an inverse ratio to the arms of the lever ; that is, inversely to the radii a b and c d. If, for ex- ample, the radius a b of the axle is four times less than the radius c d of the wheel, we may equipoise a weight of 100 Ibs. by a force of 25 Ibs. Fig. 31. Fig. 32. The capstan (Fig. 32) only differs from the windlass by having its revolving axis placed vertically, and thus a comparatively small force is required at p to move the weight r. When two parallel forces acting at right angles to a lever are equipoised, the equilibrium will not be disturbed if we increase or CENTRE OF GRAVITY. 61 diminish them in equal proportions, or if we keep the forces parallel to each other in altering their direction. If, for instance, the forces a b = p and c d = q, acting Fi 33 on the lever a c, are equipoised, the c ^ a equilibrium will not be disturbed if we let the forces act in the parallel direc- tions a e and c f, for the oblique force p acts in the same manner as its rec- tangular component p f , and the oblique force q as the rectangular force q' ; and p r q 1 will certainly main- tain a condition of equilibrium if it exists between the forces p and q, acting perpendicularly to the lever. Centre of Gravity. A heavy body, whatever be its size, may be regarded as a combination of innumerable material points, acted upon by gravity. All these forces, although innumerable, may be replaced by one single force acting at a fixed point. This single force, which is nothing more than the sum or the results of all the individual actions of gravity, is termed the weight of a body, and the point at which the resultant acts the centre of gravity. This definition is sufficient to prevent weight and gravity from being confounded. Gravity is the elementary force which acts directly upon all the particles of matter, while the weight of a body is the sum of the actions which gravity exercises upon this body. It is very important to be able to ascertain the weight of bodies and their centre of gravity, since we can then substitute one single force, namely, the weight, for all the elementary forces acting on the body ; and one single point, namely, the centre of gravity, for the collective points forming the body. We may thus consider a heavy mass, whatever be its size and form, as a single point, on which one single force acts. In a heavy body, possessing an extension of even some hun- dred yards, the direction of gravitation will be not only perfectly parallel for all the molecules, but also perfectly equal for all, because all the molecules will fall with equal velocity in vacuo. The centre of gravity is consequently nothing more than the centre of parallel and equal forces, where the position does not change when the position of the body with respect to the direction of quantity changes. 6 62 CENTRE OF GRAVITY. Fig. 34. We deduce from the laws of the action of parallel forces the fact that every solid body must have such a centre of gravity. If an immovable straight line a b (Fig. 34) be supported at its centre and loaded at both ends with equal weights, the whole will be in equilibrium, in whatever direction the line be turned round the point at which the central force acts, whether the line be in the position a b, or in the position a V . Let us assume that the two points a and b are two heavy molecules, connected by the straight rigid rod a b, supposed devoid of weight ; then it is clear that equilibrium must occur if only the point c be supported, whatever be the position of the line a b. The point c would be nothing more than the centre of gravity of the body consisting of the two molecules. We may regard the actions of the forces of gravity of the two molecules combined at the centre of gravity, without on that account the equilibrium being disturbed. If at the three angles of a rigid triangle, a b c (Fig. 35), supposed to be devoid of weight, three equal and parallel forces are at work, it is easy to ascertain the position of their central force. We may unite the two forces acting at b and c in the centre d of the line b c without disturbing the equili- brium, and thus the action of the three forces is reduced to the action of the two acting at the points a and d. The force acting at d is twice as great as that at a; if, therefore, we divide the line a d, pass- ing through the point m, into two parts, of which the one a m is twice as long as the remaining part d m, a state of equilibrium will necessarily be established between the parallel forces 2 p and jo, acting at d and a, if only the point m be supported, what- ever be the position of the line a d. But as the force acting at d is only the resultant of the parallel forces at b and c, we may take these forces themselves instead of their resultant ; and thus it is clear that the three parallel forces acting at a, 6, and c must be in equilibrium if the point m be supported, or if a force equal Fig. 35. CENTRE OF GRAVITY. 63 to 3 p, acting in an opposite direction, be applied at w, what- ever may be the position of the triangle in other respects. If we assume that a, 6, and c are three heavy molecules, which must necessarily always retain the same relative position towards each other, then the gravity of these molecules will act in the same manner as the weights attached at a, &, and c, and it is evi- dent that the body consisting of the three molecules will be in equilibrium if only its centre of gravity m be supported. Exactly as we can demonstrate that two or three firmly united molecules must have a centre of gravity, we can likewise com- prehend that every 4, 5, 6, &c., firmly-united molecules must have such a centre of gravity, and, further, that every solid body must have a fixed point of that nature, whatever be the number of molecules of which it is composed. The only requirement necessary to the equilibrium of a heavy body is that its centre of gravity should be supported. If, there- fore, the centre of gravity of a body be a fixed point, the body will always be in equilibrium, in whatever manner we may turn it. We may prove this by means of a homogeneous disc, made to revolve round a horizontal fixed axis, passing through its centre of gravity. If a body be supported at a point that does not coin- cide with its centre of gravity, it may still be in equilibrium, although only in two special positions, when the centre of gravity lies vertically above or below the point of support. This experi- ment is also easily made by means of a disc. From these considerations we may deduce a method which will enable us to show by experiment how to find the centre of gravity of a body. If we suspend the body at a Fig< 36 ' point a (Fig. 36), the di- rection of the thread sup- porting it will pass through a part c on the margin of the body. The centre of gravity must necessarily be in the line a c. Now if we suspend the body at the point b (Fig. 37), the centre of gravity will be again in the line of pro- 64 CENTRE OF GRAVITY. longation of the thread, that is, on the line b d. The centre of gravity lies, therefore, at the point of intersection of the lines b d and a c. It is easy to find the centre of gravity of homogeneous flat discs by this method, but it is difficult in other bodies to as- certain exactly the line of prolongation of the thread through the interior of the body. The centre of gravity of homogeneous bodies of regular form can be decided by simple geometrical considerations. The centre of gravity of a straight line lies evidently in the middle of its length. The centre of gravity of a homogeneous triangle (Fig. 38) is found by drawing straight lines from two of its angles to bisect the opposite sides. The point of intersection g of these two lines is the required centre of gravity. The truth of this assertion is easily proved. The point m is the centre of gravity of the straight line 6 c. If now we suppose any straight line drawn pa- rallel with & c in the triangle, it will evi- dently be bisected by the line am; on the line a m lie, therefore, the centres of gravity of all the lines in the triangle parallel with be; and a m is, so to speak, a line of gravity of the triangle, and the centre of gravity must evidently lie in a m. This reasoning shows, however, also, that the centre of gravity must lie in the line a b. The point g is so situated that g m = % a m, and gn = J bn. To prove this, let the line m nbe drawn, it is evident that m n \ b a. But the triangles g m n and g a b are similar, and hence it follows that g m : g a = m n : b a. Consequently, that g m Fig. 38. Fig. 39. The centre of gravity of a polygon (Fig. 39) is found by dividing the figure into triangles, and then determining the centre of gravity of each triangle. As the forces acting upon the centres of gravity of the triangles are propor- tional to the area of the triangles, we have only to seek the resultant of these forces by the rules already laid down. The centre of gravity of a triangular pyra- EQUILIBRIUM. 65 Fig. 41. Fig. 42. mid (Fig. 40) is found by drawing lines from the angle s and a towards the centres of gravity g- and g 1 of the opposite triangles. The point of in- tersection g" of these two lines is the centre of gravity. It is easy to prove that g g" = lg s. The centre of gravity of a cone (Fig. 41) with a circular base lies on the straight line, joining the apex with the central point of the base, and its distance from the central point of the base is J of the whole line. The centre of gravity of a regular prism, cylinder, or sphere, corre- sponds with the geometrical central point of each. Of Equilibrium. We have already seen that the only requirement for the equilibrium of a solid body is that its centre of gravity should be supported. But this condition may be fulfilled in various ways, according to whether the bodies are suspended at fixed points, or rest upon points of support. Let us suppose three holes, a, b, and c, in a homogeneous disc (Fig. 42), of which the one; a, passes through the centre of gra- vity. The disc will be in equilibrium in all positions, if a fixed axis is made to pass through the hole a. In such a case as this we have an indifferent equilibrium. If the axis passes through the upper hole, 6, the equilibrium is stable, for if we remove the disc from this position it will always tend to return to it. If we turn the disc a little round the axis 6, the centre of gravity is moved to the right or left along the arc m n; it is no longer sup- ported, because it no longer lies vertically below 6, and the gra- vity acting upon it draws it back to its position of equilibrium. If the axis passes through the lower hole, c, complete equilibrium is not established, but simply unstable equilibrium; for as soon as the centre of gravity is in the least removed from the vertical, 6* 66 EQUILIBRIUM. Fig. 43. passing through c, instead of returning, it describes a semicircle until it reaches a point vertically placed below the point c. We may thus generally express this result: A body attached to an axis may be in a state of stable, unstable, or indifferent equilibrium, according to whether its centre of gravity lies below, or above, or within the axis. Let us see what happens when a disc is placed upon a hori- zontal or inclined plane, and assume that the disc is so composed of lead and wood that its centre of gravity lies in the circle a b d. In this case none but a stable or unstable equilibrium can ex- ist ; the former when the centre of gravity rests at a, the lowest point in the circumfer- ence a b d, and the latter when the centre of gravity is at the highest point, 6, of this circle. If the same disc were placed on an in- clined plane (Fig. 44), equilibrium would be established if the centre of gravity lay in the vertical plane p 6, passing through the point of contact. Stable equilibrium will then be esta- blished when the centre of gravity is at the lowest point a, and unstable equilibrium when it lies at the highest point b. If we assume that the disc is in a state of unstable equilibrium, and were moved a Jittle towards the right side, it would roll up the inclined plane until the condition of stable equilibrium was again re-established. During this apparent elevation the centre of gravity nevertheless continues to approach the lowest points. When a body stands upon the ground, with a more or less wide base, the perpendicular drawn through its centre of gravity must fall within the base, if a state of equilibrium is to be established. Thus the inclined cylinder would be in equilibrium (Fig. Fig. 45. THE BALANCE. 67 45), if its height did not exceed the shaded part of the figure ; but it must fall if its height were such that the centre of gravity lay at b. The broader its base is, and the lower its centre of gravity lies, the firmer will a body stand. A four-footed animal stands firmly when the centre of gravity of his whole body lies over the paral- lelogram of which the four angles are indicated by the position of its four feet. If a man raise an arm, the position of the centre of gravity will be changed; and if a bird project its neck, the centre of gravity is thrown considerably forward. A man carry- ing a weight must change his position according to the manner in which he carries it. For instance, if he bears the load upon his back (Fig. 46), he must bend forward ; if he carry it in his left hand (Fig. 47), he must incline the upper part of his body to the Fig. 46. Fig. 47. right, otherwise the direction of the common centre of gravity of the human body and the load would fall beyond the line connect- ing the feet, and the man would fall. The Balance. The common balance consists essentially of a rod called a beam, which revolves round a fixed horizontal axis inserted in its centre. When there is no load at either end, the beam should be in a perfectly horizontal position. To either end of the beam, scale-pans are suspended, which serve for the recep- tion of the bodies to be weighed. If both pans are equally loaded, the beam will retain its horizontal position ; but, if an unit of weight is laid upon one of the pans, the beam will incline towards that side. 68 THE BALANCE. Fig. 48. We will now inquire how the conditions above mentioned can be satisfied. If we first suppose that the scale-pans are removed, and assume that the horizontal axis passes through the centre of gravity of the beam, we shall have a case of indifferent equili- brium, and the beam will be in equilibrium at any angle with the horizon. Such an arrangement will not, therefore, fulfil the first condition, namely, that the beam should assume a horizontal po- sition before the pans are loaded. This condition can only be fulfilled if the centre of gravity of the beam lie below the fulcrum. If we draw a line at right angles with, and bisecting the longer axis of the beam, this line must pass through the fulcrum of the beam, and through its centre of gravity. The suspension of the pans makes no difference in our reason- ing, for we may consider their weight concentrated at the point of suspension, and that they thus form an integral part of the beam. If we unite the points of suspension of the pans by a straight line, this line may pass through the fulcrum, or above or below it. It is most easy to take into consideration the first of these three cases, while it is likewise the most available for practical application ; we will, therefore, begin with this case. In Fig. 49 let a b be the straight line uniting the points of sus- Fig. 49. CENTRE OF GRAVITY SUSPENSION. 69 pension of the pans, whose weight we regard as concentrated at the points a and 6, and let c be the point at which the beam is suspended, that is to say, the point of support ; and s the centre of gravity of the beam. If equal weights P are suspended at a and 6, the beam will remain in a horizontal position ; for we may consider that one of the weights acts directly upon a, and the other directly upon b, and thus the common centre of gravity of the two weights P will correspond with the point c; and the com- mon centre of gravity of all the weights suspended at c, that is to say, of the beam and of the weights P, will meet at a point between c and s; this common centre of gravity lying vertically under the point of support, the equilibrium is not disturbed. If we apply an extra weight r on one side, the centre of gra- vity of the suspended weights, which we must necessarily con- sider as concentrated at the points a and 6, no longer corresponds with c, but falls on the line a 6, in the direction of the extra weight, somewhere towards d. The common centre of gravity of the beam and the weights will consequently be upon some point m in the line d s; but since, while the beam is horizontal, the com- mon centre of gravity m is no longer vertically beneath the point of suspension c, the whole beam must revolve sufficiently around the axis c to fulfil this condition. Hence the arm c a will neces- sarily rise, and the arm c b sink. The angle which, on the addi- tion of a slight excess of weight in either pan, the beam makes with an horizontal line is termed the angle of deviation. ' We shall now consider the points that must be attended to in the construction of the balance, in order to render it sufficiently sensitive ; that is to say, in order that a very slight preponderance of weight may give rise to a large angle of deviation. 1 . The centre of gravity of the beam must lie as closely as pos- sible below the centre of suspension; for if (the other conditions remaining unaltered) the centre of gravity s of the beam is raised upwards, the point m will also be elevated vertically, which must evidently produce an increase in the angular deviation of the beam. A contrivance has been applied to good balances by which the position of the centre of gravity is regulated. A fine screw is applied to the prolongation of the line c s, on which a weight corresponding to circumstances may be screwed up and down, by which a change in the position of the centre of gravity is manifestly effected. 70 SENSIBILITY OF THE BALANCE. If this weight were screwed up so far that s corresponded with c, we should have, either without a load or with an equal load on both sides, a case of indifferent equilibrium ; were we now to bring an extra weight r on one side, the point m would fall upon the line a b (see Fig. 49) ; that is to say, on the addition of the smallest extra weight the angle of deviation would become a right angle, the beam would be completely inverted, and, in short, the instrument would cease to be of any service. 2. The sensibility of the balance increases with the length of the beam. If (everything else remaining the same) we were to lengthen the beam, the distance c d would be proportionally greater, and the point m would thus also be removed further from the line c s in a direction parallel to a b, and consequently the line c m would make a larger angle with c s, and the angle of deviation would also increase. (It is easy to see that the angle m c s is equal to the angle of deviation.) 3. The beam must be as light as possible. We may suppose the weight of the loads 2 P-f r acting at the point d, and the weight of the beam, which we shall designate as g, united at s. The position of the common centre of gravity m will now evidently depend upon the amount of the forces acting at the ends of the line d s. If the weight g at s and 2 P + r at d be equal, m would fall in the middle of d s; but the smaller g becomes in comparison with 2 P + r, the more must m recede from d, and the larger pro- portionably will the angle of deviation be. In relation to the two last points, we are confined to certain limits which we cannot exceed, since too great a length of the beam would render the balance inconvenient for practical purposes, and too great a degree of lightness would deprive it of the necessary strength. As a matter of course, the greatest care must be had in the construction of the balance to render the two portions of the beam of equal length. As, however, slight errors cannot be avoided, we must endeavor to correct them by means of the method of weighing which is had recourse to. The best manner of proceed- ing in this respect is probably the following : The body to be weighed is laid upon one scale-pan, and equipoised by a sufficient quantity of sand, shot, or any other substance laid in the opposite scale-pan. This done, the body t6 be weighed is then removed, and in its place so many weights are substituted as to restore the SENSIBILITY OF THE BALANCE. 71 balance to equilibrium. These newly-applied weights will give the accurate weight of the body, whether or not the arms of the beam be equally long. The fulcrum is formed of a steel knife-edge, in order as much as possible to avoid friction, and the scale-pans are suspended from similar edges. 72 ELASTICITY. CHAPTER II. MOLECULAR EQUILIBRIUM. WE have already seen that, in order to explain the aggregate conditions of bodies, we assume the existence of molecular forces, which act continuously among the separate particles of bodies. As long as a body remains unchanged in its internal condition, and as long as the individual particles remain not only at un- changed distances but also in a relatively unchanged position, the molecular forces acting among the individual particles must re- main in equilibrium. The equilibrium established between the separate particles of solid bodies is stable, for a greater or lesser force is necessary to disturb this condition. As we have already seen, the force of cohesion preponderates in solid bodies, holding their particles together, and acting alike against their displacement and separation ; it being necessary to employ a greater or lesser force to bring about any such displace- ment or separation. Elasticity. When the particles of a solid body have been slightly drawn out of their relative position by an external force, the previously existing state of equilibrium is not on that ac- count entirely destroyed, for the particles may return to their former position when the disturbing force ceases to act. This property of bodies, by means of which the molecules return to their former position when the displacement occasioned by an external force does not exceed certain limits, we term elasticity. The elasticity of solid bodies proves that the molecules are in a state of stable equilibrium, since it is only under such circum- stances that a body returns to its position of rest, when the exter- nal disturbing force has ceased to act. All bodies are not equally elastic : there are some which perfectly assume their former posi- tion after even a very considerable amount of displacement, and such bodies are especially termed elastic, as, for instance, India- STRENGTH ABSOLUTE STRENGTH. 73 rubber, steel and ivory; others, on the contrary, as lead, glass, &c., are only elastic to a limited degree, not being able to bear any great displacement of their particles without the previous condition of equilibrium being disturbed. The displacement of the particles may either be occasioned by tension, compression, or rotation. When a proportionately large power is necessary to produce a displacement of the particles of a body, we term the latter hard. A body may be both hard and elastic, as is the case with ivory and steel ; glass, on the contrary, is hard and but slightly elastic. A body whose particles can be removed by an inconsiderable force, is called soft. Soft bodies maybe elastic, as India-rubber: or they may possess merely a small degree of elasticity, as is the case with moistened clay. The aggregate condition of such soft bodies may, in some measure, be considered as an intermediate state between perfect solidity and perfect fluidity. If the particles of a body are displaced beyond the limits of elasticity, the connection hitherto existing between them either ceases entirely, or the molecules arrange themselves in a new condition of stable equilibrium. In the first case we call the bodies brittle, in the next ductile. The external form of brittle bodies cannot be permanently changed by pressure, blows, &c. ; a perfect separation following, when, by means of such external causes, the molecules are displaced beyond certain limits ; the form of ductile bodies can, however, be permanently changed by such mechanical means, as we see, for instance, in the stamping of coins. Strength. The force with which a body resists the separation of its particles is termed its strength. The connection existing between the individual portions of a solid body may be removed by tearing, breaking, twisting, or compressing it. Absolute strength is the force by which a body resists being torn asunder when it is stretched lengthwise. This resistance evidently depends upon the diagonal section of the body to be severed, and is proportional to it, for the connection of two, three, four times as many molecules must be removed if the diagonal section or area of a body be increased twice, thrice, or four times. In order, therefore, easily to compare the absolute strength of dif- ferent materials, we must assume some unit for this area, and then 7 74 ABSOLUTE STRENGTH. ascertain how great a force is required to rend a body, the area of which is equal to this unit. If the area of the body submitted to the experiment be greater or smaller than the area assumed as the unit, the strength may be reduced to the measure of that unit. Muschenbroek has made numerous experiments concerning the absolute strength of different bodies. The following table gives, according to his calculations, the weight required to break a rod of different bodies whose diagonal section is one square centi- metre : about 1970 Ibs. 2190 " 1288 to 1992 2466 to 3143 2893 to 3400 2003 5965 7615 9962 583 979 7317 8969 304 to 501 750 to 1328 The great variation perceptible in the strength of rope depends upon the unequal character of the material of w y hich it is made. Thin ropes are proportionally stronger than thick ones, from being made of better hemp. Ropes have less firmness when wet than when dry. It will be most safe to assume for practical purposes that metals possess only J, and wood J, of the absolute strength ascribed to them in the above table. The force which a body opposes to the process of breaking is its relative strength. In order to break a body, the force must be applied at right angles to the direction of its long axis; the body to be broken being supported only at one, or at both, of its ex- tremities. Fig. 50 represents a prism, which is fastened at one end into a solid wall, while at the other extremity is attached the weight Q to break it. If K represent the absolute strength, that is, the force with which the body resists the force endeavoring to destroy it and acting upon it in its long axis, we may suppose this force Linden wood 918 kilogrammes, Fir (Pinus sylvestris) . White Pine (Pinus abies) Oak . 1021 . 601 to 929 . 1150 to 1466 1C Beech .... . 1349 to 1586 u Ebony Copper wire Brass wire . 934 2782 3550 (C it (C Gold wire . 4645 <( Lead wire . 272 H Tin wire 457 ll Silver wire 3411 4182 U u White glass Rope .... . 142 to 233 . 350 to 620 (C u EQUILIBRIUM OF SOLIDS. 75 concentrated at the centre of gra- Fig. 50. vity s of that diagonal section which corresponds with the plane of the solid wall. The weight Q mani- fests an effort to turn the whole body round the under edge of the prism ; and thus acts at the arm a b, while the resistance applied at s acts at the arm a s; if now the resistance shall exactly counter- poise the force, the resistance K must be inversely to the force Q as the arm a s is to the arm a b. If the height of the beam be represented by A, a s = J h, and if the length a & be represented by /, we have K : Q = I : % h or, K ' h The amount of strength K with which the body resists being rent asunder, depends upon the diagonal section of the beam. If we let k represent the absolute strength for one diagonal section of one square centimetre, while h is the height and b the breadth of the beam, then K = k b h, and therefore, k b h 2 From this formula, we see that the force necessary to break the body varies in a direct ratio with the breadth and the square of the height, and inversely with the length. If a beam be supported in the middle by a sharp edge (Fig. 51,) and be loaded at both its extremi- Fig. 51. ties with equal weights P, there will exist a tendency to break the beam at its centre ; in order to ef- fect this, the weight P acting at each end must be twice as great as the weight Q, which must be applied to the end of the same beam if projected its whole length from a solid wall, as in Fig. 50, since the weight P acts upon a lever only half the length of that supporting the weight Q. 76 EQUILIBRIUM OF SOLIDS. The pressure which has to be supported in the middle is evi- dently 2 P. If the beam be sup- 52> ported at each end as in Fig. 52, we may break it by attaching a weight 2 P to the middle. As P = 2 Q, we must ap- ply, in order to break a beam supported at each end, a force four times as great as would be necessary to break it if it projected its whole length from a solid wall, and the force acted upon the free end. The force necessary for breaking it is therefore 4*^. 21 By the length of the beam we understand, in the one case, the part projecting from the wall; and in the other, the portion lying between the two points of support. We have not taken into consideration in our calculations that the beams bend before they entirely break. By this bending, the relative strength is considerably modified, so that the value of the relative strength computed according to the above formulae, from the known absolute strength, may vary considerably from the reality. But, if these formulae do not serve to compute directly the amount of the relative strength, they yet serve for a compa- rison of the relative strengths of beams and rods, when formed of the same material, but of different dimensions ; for, however the amount of the absolute strength may be modified by flexibility, it is always directly proportionate to the breadth and square of the height, and inversely so to the length; therefore, in the for- mula nothing is changed by the flexibility but the value of the constant factor k, which must be replaced, not by the value of the absolute strength taken from the above tables, but by another factor, which must be obtained by experiment for each material. Experiments show that the force necessary to break a beam is four times as small as is given by the above formulae, if we substitute for k the number indicating the absolute strength. The influence exercised by flexibility upon the relative strength is also proved from this, ADHESION. 77 that, if a beam rests freely on both its extremities, it may be broken by a weight suspended from its centre, only half the amount of that necessary to break it when it is fixed at both ends, and, consequently, incapable of yielding. In woods, the direction of the fibres has naturally also much influence upon the strength. Mhesion. The same force which holds together the particles of a solid body, acts also in holding together the particles of two bodies already separated, if we are able to bring them within a sufficiently intimate contact with each other. Thus plates of mirrors, which are laid closely one upon another after being polished, often adhere so tightly that they cannot be separated without breaking. In the same manner two plates of lead, when pressed together, will adhere almost as closely as if they formed one single mass, provided always that the surfaces brought in contact are perfectly smooth and metallic. The force thus connecting two bodies is termed the force of adhesion. Adhesion is manifested not only between homogeneous, but also between heterogeneous bodies. Thus a plate of lead and a plate of tin, or a plate of copper and a plate of silver, combine to form an almost inseparable whole, when their polished surfaces are compressed by a heavy cylinder. The adhesion of heterogeneous bodies is most strongly manifested when a fluid is brought in contact with a solid body ; and the former is solidified by the cooling or evaporation of the dissolving medium, as we see exem- plified in the processes of pasting, gluing, and cementing. It often happens on joining together two pieces of glass with sealing wax, that on tearing the whole asunder, pieces are separated from the glass, instead of the glass being severed from the wax. If we rub a plate of glass with glue, the two substances often ad- here so closely together, that portions of the former will be torn away on the contraction of the glue in drying. If two bodies having smooth surfaces lie one upon the other, any attempt to push the one beyond the other will be opposed by the force of adhesion, which shows that this latter force has a share in the resistance of friction, which opposes itself wherever two bodies glide over each other, or where one body rolls over another. We shall subsequently treat more fully of friction. 7* 78 CRYSTALTZATION CRYSTALS. Crystalization. If a body pass from a fluid or gaseous form to a solid condition, the change is owing to the preponderance of the cohesive force, which fixes the hitherto moving particles in a relatively definite position. In this transition to a solid condition, .we see a tendency throughout all nature to produce a regular arrangement of the molecules, and the force exercising this tend- ency in inorganic nature is crystalization. Crystals are such solid bodies as have a regular form limited by plane surfaces. In nature we find a number of these crystals : for instance, quartz, calcareous spar, heavy spar, topaz, garnet, &c., are often found beautifully crystalized. A body almost always assumes the crystaline form on passing from a fluid to a solid condition. This transition is effected either by the cooling of a melted body, or by separation from a solution. If we pour melted bismuth into a warmed cup, a solid crust will, after a time, be formed upon the upper surface. If, now, we puncture this crust, and pour off the remaining fluid metal, we obtain large cubic crystals, measuring several lines in length, and filling up the cavity which is formed by the cooled and solid crust. We may obtain crystals from a melted mass of sulphur in a similar manner. On attentively observing a portion of water in the act of freez- ing, we see delicate needles of ice forming, and every moment spreading and ramifying. It is true, that we seldom see such regular crystaline formations in ice as in snow, but still it is suffi- ciently evident, that the formation of ice is a process of crystali- zation. Many bodies dissolve in fluids, as, for instance, in water; but only a definite quantity of any substance will dissolve in a definite quantity of water, although more is generally dissolved in hot than in cold water. If a solution be saturated at a high tempera- ture, that is, if, for instance, as much alum has been put into hot water as the definite quantity of the liquid will dissolve, the whole mass of salt will not remain wholly dissolved on cooling, but a portion will be again deposited, and in the form of regular crystals. Crystals will likewise be formed when the water gra- dually evaporates from a saturated solution. Crystals are not separated from aqueous solutions only; sul- phur, for instance, dissolves in bisulphuret of carbon, chloride of CRYSTALS. 79 sulphur, and oil of turpentine ; and we may obtain beautiful transparent crystals of sulphur from these solutions. The slower the cooling or evaporation, the larger and more regular will the crystals be. In rapid crystalization small crystals are formed which unite together in irregular groups, in which we can scarcely recognize the crystaline outline. Every substance has its own form of crystalization. Thus, for instance, the form of quartz is different from that of alum, and this latter varies again from that of sulphate of copper (blue vitriol). The investigation into the laws of symmetry which are found to enrol between the separate surfaces of crystals, as well as the description of crystaline forms in particular, are subjects which belong to the province of Crystalography. 80 HYDROSTATICS. CHAPTER III. HYDROSTATICS, OR THE THEORY OF THE EQUILIBRIUM OF LIQUIDS. HYDROSTATICS treats of the conditions of equilibrium in liquid bodies, and of the pressure which they exercise upon the walls of the vessels in which they are contained. The properties of liquid bodies are dependent upon two forces, namely on gravity, which acts upon them as upon all other bo- dies ; and on molecular attraction, the action of which is so modi- fied in them as to give rise to their liquid condition. We may easily separate in our minds the actions of these two forces, for we may form a conception of a mass of water devoid of weight, although not ceasing to be fluid. Such a mass left to itself would not fall ; it is evident that to be at rest it neither requires to be supported from below nor to be contained in any vessel. In this condition the fluid might sustain and propagate a pressure according to a law which we will at once consider. Principle of the equality of pressure. Fluids have the property of regularly propagating to all parts the pressure exercised upon a portion of their Surface. This principle is a physical axiom ; and, if it be not necessary to prove it, we may at any rate make it intelligible. Fi 53 Let abed (Fig. 53) represent a vessel containing a liquid supposed to be devoid of weight ; p is a solid plate, completely cover- ing the upper surface of the fluid, which we will also suppose to be devoid of weight. If the fluid is not pressed upon by any weight, j~ it evidently cannot suffer any pressure, and we might bore the vessel at any spot without the fluid escaping. But as soon as we load the plate with a weight, say, for instance, 100 Ibs., it will manifest a tendency to HYDRAULIC PRESS. 81 sink, and would sink if the fluid did not hinder it from so doing. The fluid, whether compressible or not, must now support the 100 Ibs. The upper surface x will, therefore, support the whole pres- sure, and would necessarily be pressed dowr, if it were not kept up by the layer y. The layer x presses accordingly upon the layer y with the same force with which it is pressed by the plate. Thus the layer y presses upon the next one z, and in the same manner the pressure is conveyed to the bottom, which is itself pressed upon, as if the plate rested immediately upon it. As now the whole bottom sustains a pressure of one hundred pounds, it is evident that the half of the surface of the bottom will bear only a weight of fifty pounds, and the hundredth part of the same sur- face only one pound. Hence it follows: 1. That the pressure is communicated from above downward to horizontal surfaces without diminution. 2. That it is equal at all points. 3. That it is proportionate to the extension of the surfaces con- sidered. The same occurs with regard to the lateral surfaces. If we were to make an opening in the lateral wall, the liquid would gush forth; and if we were to cut out of the wall a piece, the surface of which should equal that of the plate, we must have a counter pressure of one hundred pounds. If the plate itself had an opening, the water would gush forth from it, by which it is evident that the under surface of the plate is pressed upon, exactly the same as all the other portions of the walls. Fluids, therefore, communicate a pressure, exercised upon any part of their upper surface, equally in all directions. If we once understand this principle with regard to fluids devoid of weight, it can easily be applied to heavy fluids on each molecule of which, a pressure is exercised, arising from their own proper gravity. The Hydraulic Press depends upon the uniform communication of pressure by fluids, and consists of two main parts, a sucking and forcing pump, which exercise the pressure, and a piston with a plate to receive the pressure, and convey it to the bodies to be pressed. Fig. 54 is a section, and Fig. 55 a complete representation on a small scale of the hydraulic press. The piston s is raised by the lever /, and the water of the reservoir b pressing through the perforated vessel r lifts the valve i, and thus gets beneath the 82 HYDRAULIC PRESS. piston s. If we press down the lever J, the piston 5 goes down, the water is forced back, closes the valve i, raises the valve d, and runs through the tube t b u into the cylinder c c' of the press : Fig. 54. Fig. 55. here it presses against the piston p, which it lifts with the plate p' 9 and thus the body to be acted on is compressed between p f and the fixed plate e. The efficiency of the hydraulic press rests upon the principle that fluids communicate every pressure equally in all directions. If the piston s be pressed down by any force, each portion of the EQUILIBRIUM OF HEAVY FLUIDS. 83 surface of the walls of the vessel, which is equal to the diagonal section of the piston, has to sustain an equal pressure. But now we may regard the under surface of the piston p as a part of the wall of the vessel ; therefore, as many times as the diagonal sec- tion of the piston p is greater than the diagonal section of the piston 5, so many times will the force with which the piston p is elevated be greater than the force with which the small piston is depressed. If the area of a section of the piston s is r^oth of the area of the piston p, then p will be elevated with a force of 100 pounds, if s is pressed by a force of one pound. But with the help of the lever /, a man may easily exercise a pressure of 300 pounds on the piston s, and therefore raise the piston p with a force of 30,000 pounds. A portion of the force applied to the lever / is lost by the resist- ance of friction before it is transmitted to the piston p : the effect, therefore, will always be less than what it should be according to the above considerations. Equilibrium of heavy Fluids. Two conditions must be fulfilled in order that liquid bodies should be in equilibrium. First, their free surfaces must be at right angles with the direction of gravity ; and secondly, the forces of pressure acting on each particle must always be equal and opposed, the one to the other. If we assume that the upper surface of the fluid is not at right angles with the direction of gravity, but takes such a form as a b e d (Fig. 56), we may suppose an inclined plane laid through any two points, b and e; a. Flg ' 56> portion of the fluid lies on this inclined plane, and must necessarily glide off from the easy displacement of the particles. This will con- tinue until the whole upper surface is every- where at right angles with the direction of gravity. If we apply this to the upper surface of the sea, which we will consider as perfectly at rest, it is clear that if the force of gravity alone acts, and is always directed towards the central point of the earth, the superficies of all seas must be por- tions of a spherical surface, and that, therefore, the surfaces of seas connected together must be equally remote from this central point. 84 PRESSURE OF FLUIDS. If the molecules are attracted by other forces than terrestrial gravity, we may easily understand that their free surfaces must be at right angles to the resultant of gravity, and all the other simul- taneously acting forces. As the centrifugal force, which depends on the rotatory movement of the earth, continually acts with gravity upon all bodies, the upper surface of the waters must assume such a position as to be at right angles with the resultant of both forces. This is also the reason that the sea is flattened at the poles. At the foot of great mountains which cause the plummet to diverge, the surface of the water also deviates from the regular form. In the same way the attractive force of the moon, which acts upon the water, combines with gravity to create a resultant which is not vertical. The moving surface of the sea always strives to attain to a position of equilibrium, which is constantly disturbed by the motion of the moon, and hence the periodical oscillations of ebb and flow. We also observe deviations from the normal surface in fluids enclosed in vessels ; thus water in a glass is not even over its whole surface, but rises around the margin; the surface of mercury, on the contrary, is depressed at the sides, as if it dreaded coming in contact with the walls of the vessel. These pheno- mena depend upon the laws of capillary attraction, which we purpose, subsequently, to consider more fully. The second condition of equilibrium is self-evident, for the molecules that are in the interior of the fluid sustain a pressure from all the other molecules lying over them, which they transmit in all directions. But if the various pressures, acting in different directions upon one molecule, were not equal, it would be dis- placed by the strongest pressure, and consequeutly the fluid mass would not be in equilibrium. Pressure of Fluids. If fluid masses are in a state of equili- brium, they exercise upon themselves and on all solid bodies which they touch, a more or less considerable pressure, the amount of which we will now determine. In the first place we will exa- mine the pressure exercised from above downwards, or from be- low upwards, on horizontal surfaces, and then the pressure acting upon the lateral surfaces. The pressure exercised by a fluid from above downward on the bottom of the vessel in which it is contained is quite independent of the form of the vessel, and is always equal to the weight of a PRESSURE OF FLUIDS. 85 column of the fluid, whose base is the bottom of the vessel, and whose height is the vertical distance from the bottom to the sur- face of the fluid. The first part of this assertion is easily proved by help of the following apparatus : The apparatus (Fig. 57) consists of a bent tube, a b c fastened in a box, and so arranged that vessels of different form, as those at d ef g (Figs. 58, 59 and 60), may be screwed on at a. We pour mercury into the tube, and with the Fig. 57. Fig. 58. Fig. 59. Fig. 60. help of a moving index indicate the height n to which the mer- cury rises in the arm c. If now the cylindrical vessel d be screwed on at a, and filled with water to a definite height A, the mercury will rise in the tube c to a height p, which we must mark. The rising of the mercury n p evidently depends upon the pressure exercised by the water in the vessel d upon the surface of mercury which forms the true bottom of the vessel. When this has been duly observed, we empty the vessel d by the help of the cock r, and screw on in its place either the vessel e, widened at its upper margin, or /, tapering off towards the top. If we fill these vessels with water, as high as we before did the vessel d, the mercury in the tube c will again rise exactly to the height p. The pressure, therefore, which the bottom of these three differently shaped vessels bears, is precisely the same, if only the height of the fluid be the same. The pres- sure on the bottom is, therefore, as we before observed, inde- pendent of the form of the vessel, and only depends upon the size of the bottom, the height and nature of the fluid. The pressure is the same, whether the vessel be cylindrical, contain much (Fig. 61) or little (Fig. 62) fluid, be rectangular (Fig. 63) or inclined (Fig. 64). In order to prove the second part of the pro- 8 86 PRESSURE OF FLUIDS. position, it will suffice to remark, that the bottom of the cylin- drical vessel (Fig. 62) must bear the whole weight of the fluid, Fig. 61. Fig. 62. Fig. 63. Fig. 64. or, as the lateral walls are vertical, they are incapable of sup- porting the least part of the weight of the fluid. As, now, the bottoms of the inclined vessels, whether they are widened or con- tracted at their upper margin, sustain the same weight, it follows that in these vessels the pressure is no longer equal to the weight of the fluid they contain, but is equal to the weight of a straight column of water having the same surface and height. As all parts of the bottom are pressed upon with equal force, it is clear that the half, the third, fourth part, &c., must sustain J, J, J of the whole pressure. If we designate by g the portion of the bottom we are considering, by h the height of the smooth surface, and by d the density of the fluid, the pressure upon the surface s is equal to s X h X rf, for s X h is the volume of the straight column of fluid, and in order to obtain the weight we must mul- tiply the volume by the density. With a litre* of water weighing a kilogramme,! we may there- fore exercise a very small, or any unlimitably large amount of pressure upon the bottom of a vessel. If the pressure upon the bottom is to be exactly one kilogramme, we must take a straight cylindrical vessel of any base we choose, when the combined pressure upon the whole surface will always be one kilogramme ; only the pressure which each square centimetre of the bottom has to sustain will be large or smaller, as the vessel is wider or narrower. If we would exercise upon the bottom of the vessel a pressure of ro of a kilogramme with one kilogramme of water, we might take, for instance, a vessel whose bottom should measure a square * The litre is equal to 2.113 pints, or nearly equal to the English quart, f The kilogramme is equal to 15,444 grains, or rather more than two pounds avoirdupois (2.2. 4. 16). PRESSURE OF FLUIDS. 87 decimetre, and which was so widened towards the top, that a litre of water would only fill it to the height of one centimetre. If the pressure was to amount to ten kilogrammes, we might take a vessel of the same base (one square decimetre) so narrowed towards the top, that a litre of water would rise in it to the height of ten decimetres. With a similar weight of one kilogramme of water, we might with equal ease exercise a pressure of 7^, yoW, &c. part of a kilo- gramme, as one of 100, 1000, &c. kilogrammes. The pressure of fluids acts not only on the bottom of the vessel, but upon every point in the interior of the fluid mass. If we assume in the interior of a fluid mass a stratum m p parallel with the surface, all the molecules of this stratum will evidently be pressed upon by the fluid over it, bearing the weight of the fluid cylinder n v m p. The stratum must, however, sustain an equal pressure in an opposite direction from below up- wards. If now we consider a part a b of the said Fig. 65. Fig. 66. stratum, we find that the weight of the fluid column abed presses upon it from above downwards, while an equal force acts from below upwards. If, therefore, we immerse a solid cylinder in the fluid, its base will have to support a pressure from below which strives to raise it. This may be proved by the following experiment: Take a somewhat wide glass tube v (Fig. 66), whose lower margin has been smoothly polished : t is a perfectly smooth glass disc, secured in its centre by a thread passing through the tube, so that by drawing the thread, the disc may be made entirely to close the opening of the tube. When secured in this manner, we immerse the tube in the water. Now, it is no longer necessary to draw the thread in order to prevent the falling of the disc, for it is pressed upwards by the fluid. If we pour water into the tube, the glass disc will fall by its own weight as soon as the level of the water in the tube is almost equal to that of the water in which it is immersed, for now the glass disc sustains equal fluid pressure upwards and downwards. 88 PRESSURE OF FLUIDS. If, accordingly, we were to make an opening in a ship, the water would instantly enter the vessel : we must, in order to hinder this, exercise a counter pressure equal to the weight of a column of water, having the same base as the opening, and of the same height as the depth of the opening below the level of the water. The bottoms of large ships must, therefore, be very strongly built to sustain the pressure of the water from below upwards. If we assume that the bottom is horizontal, and has a superficies of 100 square metres (about 119 square yds.), this pressure would amount to 100,000 kilogrammes (214,500 Ibs.) if it were one (1 yd. 3 in.), and 300,000 kilogrammes (643,500 Ibs.) if it were three metres (3 yds. 9 in.) below the level of the sea. We may thus form an idea of the enormous pressure sustained by the living creatures inhabiting the depths of the seas and oceans. We shall again revert to this subject. The pressure which a given portion of lateral wall has to sup- port, is equal to the weight of a column of fluid whose height is equal to the depth of the centre of gravity of this lateral wall below the level of the fluid, and whose horizontal base is equal to the size of the given portion of the wall. The amount of lateral pressure may be obtained from the cor- responding horizontal pressure, according to the principle of the uniform transmission of pressure in all directions. The point m (Fig. 65) is a point in the horizontal layer m p; the pressure to which it is exposed transmits itself uniformly in all directions, therefore, also at right angles to the wall. Every point of the lateral wall sustains, therefore, the same pressure as every point of the equally high horizontal stratum of fluid. If, now, we con- sider any portion of the area of the lateral wall, whose highest point is so little elevated above the lowest point that the pressure sustained by both may, without any great error, be assumed as equal, then we find that the pressure sustained by this portion of the area is s X h X d, if s, h and d have the previously assumed significations. In a vat full of water, ten metres (10 yds. 2 ft. 9 in.) in height, the pressure upon a square centimetre of the lateral wall at the depth of one metre (1 yd. 3 in.) is equal to 100 grammes (3 oz. 6 drs. 12 grs.); and at two metres (2 yds. 6 in.) to 200 grammes (6 oz. 12 drs. 24 grs.); and at ten metres, that is at the bottom, to one kilogramme (2 Ibs. 2 oz. 4 drs. 16 grs.). The pressure sustained by any point of the vertical wall of a COMMUNICATING VESSELS. 89 Fig. 67. vessel filled with water may be made manifest by a diagram (Fig. 67). From a let a straight line be drawn a b, equal in length to the depth of the point a below the level of the water, a b will then represent the pres- sure which the point has to sustain. If we make the same figure for several points of the vertical line r s, the ex- tremities of all the horizontal lines of pressure will fall upon the line r t. It follows, therefore, that the combined pressure which the line r s of the vertical wall of the vessel has to sustain, is represented by the triangle r s t. The point of application of the resultant of all the elementary pres- sures sustained by a section of a wall is called the centre of pressure. It always lies deeper than the centre of gravity of the section, because the pressure increases in intensity downwards. The centre of pressure for the vertical line r s is easily obtained, for it is evidently the point c at w r hich the line r s is intersected by the horizontal line passing through the centre of gravity o of the triangle r s t. We have here only considered a line r s; but, if for this we substitute a broad band of the vertical wall, its centre of pressure will lie upon its vertical central line, and its height above the bottom will be one-third of the height of the level of the water above the bottom. Communicating vessels. The above developed conditions of equilibrium are valid equally for fluids contained in vessels that are connected together; that is to say, if both vessels contain the same fluid, the level must be the same in both. If we assume a horizontal partition wall to be applied at m to the vessel (Fig. 68), Fig. 68. Fig. 69. we obtain two vessels. According to the princi- ples advanced, the pres- sure which this partition wall sustains from below is jB A, if B designate the area of the partition, and h the height p v. If a b is the level of the fluid in the wider vessel, and h' represent the height a m, then the pressure which the partition wall has to support from above downwards is B h'. If, now, we suppose the partition wall again removed, the layer 8* 90 COMMUNICATING VESSELS. of water taking its place will have to sustain on the one side the pressure B h, and on the other the pressure B h'. Motion will necessarily occur as soon as h is not equal to h' . There can, therefore, only be equilibrium when h and h' are actually equal ; that is, when the level of the fluid is equally high in both vessels. If the fluids in the two vessels are dissimilar, the level will not be equally high in both. In the tube, for instance, (Fig. 70,) there is water in one side, and in the other mercury, the fluids meet- ing at g. Below the horizontal plane passing through g there is only mercury, which is per- fectly in equilibrium. The column of mercury over h has, therefore, to keep in equilibrium the column of water above g, and, that this may happen, the heights of the columns must be inversely to each other as the specific gravities of the fluids ; that is to say, the column of water must be nearly fourteen times as high as the column of mercury, because the specific gravity of water is nearly fourteen times less than that of mercury. Whatever be the fluids used, the heights of the columns must always bear an inverse ratio to their specific gravities. Thus a column eight inches high of concentrated sulphuric acid will equipoise one of water 14.8 inches high; and a column eight inches high of sulphuric ether will be in equilibrium with a column of water 5.7 inches high. We often see that heavy bodies move in an opposite way to the direction of gravity ; cork and wood, for instance, rise on the surface when they are immersed in water; in the same manner iron rises in mercury, and the air balloon in the air. All these phenomena depend upon the principle known by the name of the Archimedean principle, from having been discovered by Archimedes. This principle may be thus expressed: Jl body immersed in a fluid loses a portion of its weight exactly corresponding with the weight of the fluid displaced by it. Or, to express the same more correctly : If a body be immersed in a fluid, a portion of its weight will be sustained by the fluid, equal to the weight of the fluid displaced. W T e may convince ourselves of the truth of this principle by COMMUNICATING VESSELS. 91 Fig. 71. means of a simple experiment. Immerse a regular prism verti- cally in a fluid, as shown at Fig. 71, then every pressure on the sides of the prism is destroyed by an equal and opposite pressure ; but the upper surface sustains the pressure of a column of fluid having an equal base with the prism, and the height h. The under surface, however, is pressed upon from below up- wards by a force equal to the weight of a column of fluid of the same base, and of the height h'. The heights h and h' differ exactly by the height of the prism, and therefore it is clear that the pressure on the under surface exceeds that on the upper surface by the weight of a column of fluid equal to the volume of the prism. But, as this excess of pressure acts upwards against the gravity of the body, the action of the force of gravity of the body is evidently diminished in the way specified. If, for instance, the base of this prism be one square centimetre, its height ten centimetres, and the upper surface three centimetres below the level of the water, the upper has to sustain a pressure of a column of water whose base is one square centimetre, its height three centimetres ; consequently a weight of three cubic centimetres of water, that is, of three grammes. But the lower surface is thirteen centimetres below the level of the water, and has, therefore, to sustain a force acting from below upwards and equal to the weight of a column of water whose base is one square centimetre and height thirteen centi- metres, that is, thirteen grammes. If we deduct from these thir- teen grammes the amount of the pressure of the three grammes acting downwards upon the upper surface, there remain ten grammes for the force with which the prism is urged 'upwards by the pressure of the water. But ten grammes is the weight of a column of water of equal volume with the prism. If this prism were of marble, it would weigh twenty-seven grammes ; but, on being immersed in water, it has to sustain a pres- sure of ten grammes directed upwards, and, con- sequently, in the water it will be ten grammes lighter. If, in the place of one prism, we take several together, it is clear that each separate one will lose on being immersed in the water an amount of weight equal to an equal volume of water, and, consequently, the loss of weight sustained by the Fig. 72. 92 THE BALANCE. whole body composed of the several prisms will equal the weight of a mass of water of equal volume to the combined volume of the prisms. As, however, we may imagine any body decom- posable into a number of such vertically-placed prisms of very small diameter, the conclusion may be extended to any body we choose to take. A totally different mode of deduction leads us to the same result. If we suppose the space occupied by the body immersed in water to be filled with water, this body of water will float in the remaining mass of the liquid, neither rising nor sinking. If, now, we assume this body of water to be replaced by another which, with an equal volume, has also an equal weight, this latter will likewise float, its whole weight being sustained by the water in which it is immersed, whence it is clear that a portion of the weight of every immersed body is sustained by the water, and is equal to the weight of the fluid displaced. We may convince ourselves of the truth of the Archimedean principle by direct experiment. To one of the scale-pans of an ordinary balance (Fig. 73) is attached a hollow cylinder, c, Fig. 73. from which is suspended a massive cylinder, p, accurately filling the cavity" of the former. On the other scale-pan are placed sufficient weights d, to equipoise the whole. If, now, the cylinder p be immersed in water, it will lose a portion of its weight, and the equilibrium will be thus disturbed ; to re-establish this, the cylinder c need only be filled with water, which clearly proves SUBMERGED BODIES. 93 that p has lost as much weight by being immersed in the water as the contents of the cylinder c weigh. But the volume of water in c is equal to the water displaced by the cylinder^?, and the loss of weight of p is consequently equal to the weight of the displaced water. As we have already seen, there would be equilibrium if we could convert into water the immersed body. But this body of water would remain perfectly in equilibrium, whichever way it were turned, round its centre of gravity. The pressure of the surrounding fluid acting from below upwards is, therefore, a force whose point of application corresponds with the centre of gravity of the ideal body of water. This point may be termed the centre of pressure of the fluid. If, now, this ideal body of water be replaced by any other substance, as, for instance, cork, marble, or iron, the pressure which this body will have to sustain from the surrounding mass of water will be precisely the same as that which the ideal body of water has supported. A body immersed in water is, therefore, subject to the action of two forces, whose magnitude and point of application we now know. The first force is the gravity of the body acting from above downwards, and whose point of applica- tion is the centre of gravity of the body ; the second force acting from below upwards is equal to the weight of the water displaced, and its point of application is the centre of gravity of this mass of water. If an entirely submerged body is perfectly homogeneous, its centre of gravity will correspond with the centre of gravity of the water displaced. This upward pressure of fluids is designated by the term buoy- ancy. Conditions of equilibrium of submerged Bodies. For a perfectly homogeneous body submerged in water to keep itself suspended, nothing more is necessary than that its weight be exactly equal to that of the fluid displaced, the position of the body being entirely indifferent : here we have an instance of indifferent equilibrium. In order to prove this by an experiment, let us form a body of any shape from a mass composed of one part of finely pulverized cinnabar, and 226 parts of white wax. The constituents must be well worked together, that the mass may have the requisite uniformity. A body thus composed will float in water, and re- main in equilibrium in any position in which we place it. In 94 FLOATING BODIES. spirits of wine it will sink, while on a saline solution it will rise and float on the surface. If the immersed body be not homogeneous, so that its centre of gravity does not correspond with the centre of gravity of the water displaced, it may still float in the fluid, if its total weight is exactly equal to the weight of the water displaced ; but it can only be in equilibrium if the centre of gravity of the body and that of the water displaced be in a vertical line, and stable equilibrium can only be established if the centre of gravity of the body is in the lowest position. Conditions of equilibrium of Floating Bodies. If a body float, its whole weight is equal to the weight of fluid mass displaced by the immersed portion of the body : the condition of the stability of floating bodies differs, however, from that of submerged bodies. A ship, for instance, weighing one million kilogrammes is in equilibrium if it displace 1000 cubic centimetres of water ; and, if its centre of gravity and the centre of pressure of the water lie in a vertical line, we may have a condition of stability even if the centre of gravity do not lie below the centre of pressure, it being sufficient if it lie lower than another point, termed the meta- centre. The position of this latter point depends upon the form of the ship, and the position of the centre of gravity upon the manner in which the ship is loaded. Although a general determination of the metacentre would be hardly in place here, we must yet endeavor to give some idea of it: Let abed (Fig. 74) be the section of an immersed body, and, for the sake of clearer illustration, let us assume this section to be an elongated parallelogram. If the Fig. 74. , . . & . . .,., . body swim in a position ot equilibrium, it will sink as low as ef. The centre of gravity of the displaced mass of water is at m, and the centre of gravity of the body lies upon the vertical line, passing through m. If it be below m, the body will swim stably in every case, for we have a body suspended, as it were, at the point m in the water, and whose centre of gravity is deeper than its point of suspension, and consequently a pendulum that oscillates about the position of equilibrium. If the body be changed from the position of equilibrium to the HYDROSTATIC BALANCE. 95 one represented in Fig. 75, the triangle e g h is raised out of the water, while g If is, on the contrary, immersed ; but, as the quantity of the water displaced must always be the same, whatever be the position of the body, it follows that e g h = g if. But the form of the submerged por- tion differs from what it previously was, and, consequently, the centre of gravity of the displaced mass of water is no longer at m, but at another point o, whose position must be especially ascertained in each individual case. If we suppose a perpendicular drawn through o, it will intersect at a point g the perpendicular drawn in the position of equilibrium through m; the point q is the meta- centre. When the centre of gravity of the body lies below y, on the line m q, the weight of the body acting at o will turn it round o in such a manner as to make it return to a position of equili- brium. A floating body loses its stability entirely if its centre of gravity lie above the metacentre. The broader the immersed portion, and the lower its centre of gravity, the greater is the stability of a floating body. The Archimedean principle affords us excellent means of ascer- taining the weight of solid and fluid bodies. In order to compute the density of a solid body, we must know its absolute weight, and the weight of an equal volume of water. But in most cases it is very difficult, and even impossible, to obtain the volume of a body by measuring its dimensions. According to the Archime- dean principle, a single experiment gives us without anything fur- ther being necessary, the weight of a mass of water, having an equal volume with the body to be determined ; leaving us only to decide the loss of weight on immersion. In order to obtain this result easily by means of a balance, the instrument undergoes a slight alteration, by which it is converted into a hydrostatic balance (Fig. 76). We substitute for one of the usual scale-pans, one that does not hang down so low, and to the lower part of which a hook is attached, on which the body to be determined may be suspended. When this is done, we may ascertain the absolute weight g of the body by laying weights in the other scale-pan. If we now immerse the body, we must remove a part a of the weight g to restore equilibrium; a is con- 96 AREOMETER. Fig. 76. sequently the loss of weight sustained by the body from immersion, and 3- is, therefore, its specific gravity. Nicholson's Areometer (Fig. 77) may be used to determine the specific gravity of solid bodies, instead of the balance. To a Fig. 77. hollow glass or metal body v, a small heavy mass / (a glass or metal sphere filled with lead) is sus- pended, and superiorly there is attached to it a fine stem supporting a plate c, on which small bodies and weights may be laid. The instrument floats vertically in the water, because its centre of gravity is very low in consequence of the weight /. The instrument is so arranged that the upper part of the body v projects above the water. If now we lay the body w r hose specific gravity we would ascertain upon the plate c, the instrument will descend, and by adding additional weight, we may easily make it sink to the pointy marked generally by a line on the rod. We remove the mineral or other substance we have been using, and substitute in its place as many weights as will again make the instrument sink to/. If, in the place of the mineral, we have had to lay on n grains, the weight of the mineral is equal to n grains. If, in this manner, we have ascertained the absolute weight of the mineral, the n grains must be again removed, and the body AREOMETER. 97 laid in a basket placed between v and I. The instrument would now again sink to f if the body laid in the basket had not lost weight by being immersed in the water: we must, therefore, lay on the plate the weight m grains, that the body may be immersed to the mark. In this manner we obtain the absolute weight of the body n, and the weight of an equal volume of water m; the spe- 77 cific gravity we seek is, therefore, m. If, for instance, we have to determine the specific gravity of a diamond, we must lay it on the plate and add sufficient weight to make the whole sink tojT. If we find after removing the diamond, that we must lay on 1.2 grains to cause the areometer to sink again to the same point, the absolute weight of the stone would be 1.2 grains. These weights must be again taken away and the diamond laid in the basket ; then, in order to make the instrument sink toy, we must add 0.34 grains more; the weight of a volume of water equal in volume to the diamond is, therefore, 0.34 grains, 1 2 and the specific gravity required is -! =3.53. The specific gravity of liquids may also be determined by Ni- cholson's areometer. As the instrument always sinks so far that its weight, added to the weight upon the plate, is equal to the mass of liquid displaced, we may, by the aid of this instrument, ascer- tain how much a definite volume of water weighs. It is neces- sary, however, to know the weight of the instrument itself. Sup- pose this weight to be n, we must lay on some additional weight to make the instrument sink to f\ if we designate this addition by a, then is n + a the weight of water displaced. If we immerse the instrument in another liquid, we must lay on another weight b in the place of a, to make the whole sink to f-j b will be greater than a if the liquid be denser, and less than a if it be lighter than water. The weight of the liquid displaced is n + b ; but its volume is exactly as great as the volume of the mass of water, whose weight is n + a, because the areometer has sunk equally deep in both cases. Suppose the instrument weigh 70 grains, we must add 20 grains to make it sink in water, and 1.37, that it may sink to the pointy* in spirits of wine ; then the specific gravity of spirits of 70 + 1.37 wine is 2Q ~ 0.793. 98 AREOMETER. The delicacy of the areometer is proportionate to the slightness of stem in comparison with the immersed volume. It is always a somewhat tedious process to ascertain the specific gravities of liquids with this areometer, and we might effect our purpose as quickly and with much more exactness by means of the balance, in the manner already indicated. But it often hap- pens for practical purposes, that we desire to obtain by a short process the specific gravity of a fluid in as simple a manner as possible, in order to estimate its quality. In such cases, it is quite sufficient to obtain the specific gravity within a couple of decimal places, and this purpose is most readily effected by means of the graduated areometer, which we will now consider. The graduated Jlreometer. By means of Nicholson's areometer the specific gravity of a liquid is obtained by a comparison of the absolute weights of equal volumes. But the use of the graduated areometer is based upon the principle that, with equal absolute weights, the specific gravities are inversely as their volumes. Fig. 78 represents a graduated areometer. It usually consists of a cylindrical glass tube, which is enlarged at the bottom as represented in the drawing. The lower ball is partially filled with mercury, to enable the instrument to float upright. If we now suppose the instrument to be float- ing in the water, the weight of the water displaced is equal to the weight of the instrument. If we now im- merse it in another liquid, it will sink to a greater or less depth, according to whether the liquid is lighter or heavier than water. Supposing that the areometer weigh ten grammes, it will displace ten cubic centi- metres when floating in water. If we immerse it in spirits of wine, it will sink so low that the spirits of wine displaced will also weigh ten grammes. But ten grammes of spirits of wine occupy more space than ten grammes of water ; the instrument must, therefore, sink so deep that the volume immersed in the spirits of wine shall be inversely to the volume immersed in water as the specific gravity of these liquids. We may now well understand that, if the tube be properly divided, we may ascertain the specific gravity of a liquid by one single easily-conducted experiment. Amongst all the scales that AREOMETER. 99 have been applied to the areometer, the one proposed by Gay Lussac is incontestably the simplest and most efficacious ; we will therefore consider it first. We must suppose the point a of the tube of an areometer to be marked as being the point to which the instrument sinks in water, and, starting from thence, that a series of lines are so arranged that the volume of the portion of the tube intervening between two marks is y^ tn P art f tne volume immersed in the water. If, for instance, we assume that the volume of the sub- merged portion of the areometer is exactly ten cubic centimetres, then the volume of the portion of the tube intervening between the two marks would be 0.1 of a cubic centimetre. The watermark a is numbered 100, and the divisions are num- bered upwards. Areometers thus graduated are designated by the special term volumeters. Supposing that the areometer sank in any liquid to the mark 80 on the volumeter, we know that 80 parts of this liquid weigh as much as 100 of water; the specific gravity of this liquid is, therefore, to that of water as 100 to 80, and consequently = V/ or 1.25. If the volumeter were to sink in another liquid to the mark 116, we should find by a similar mode of deduction that the specific gravity of this liquid was yff or 0.862. In short, if the volumeter sink to a definite point j of the scale, we find the specific gravity s of the liquid, on dividing 100 by the number observed 1 00 upon the graduated scale; that is, s = The accuracy of such an instrument is increased in proportion to the distance of one mark from the other, and in proportion to the thinness of the tube in comparison with the volume of the whole instrument. In order to avoid having very long tubes, no volumeter is made applicable to all fluids, there being different ones that can be used either for lighter or heavier fluids. In the former, the watermark 100 is near the lower; and in the latter, near the upper extremity of the tube. Before the graduation is made, the quantity of mercury in the ball of the instrument must be so regulated that it will sink it in the water either to a point lying near the lower or upper end of the tube. When this is done, a second point in the scale must be obtained in the following manner: Suppose the instrument to be intended for heavy liquids, and, 100 AREOMETER. therefore, having the watermark at the upper end of the tube. We provide ourselves with a liquid whose specific weight is exactly 1.25, and which we can easily obtain by a mixture of water and sulphuric acid, its specific gravity being tested by means of the balance. In this liquid we now immerse the instru- ment, observing the mark to which it sinks. But the specific gravity 1.25 corresponds to the mark 80 of the volumeter scale. This last observed point is, therefore, to be marked 80, and the intervening space to be divided into twenty equal parts ; a similar graduation being carried on below the point 80. If the volumeter be designed for light liquids, and the mark 100 be consequently at the lower part of the tube, we find a second point in the scale on immersing the instrument into a mixture of water and spirits of wine, the specific gravity of which is accurately 0.8. This specific gravity 0.8 corresponds to the mark 125, and we must, therefore, divide the space between this mark and the watermark into twenty-five equal parts. The divi- sions are generally marked upon a strip of paper, and fastened to the interior of the tube. The relation existing between the different graduated points of the volumeter, and the specific gravity will easily be understood by looking at the accompanying diagram. The line a b (Fig. 79) represents a volumeter scale, ranging from the mark 50 to the mark 130. At every tenth point of division a per- pendicular is drawn, on which is marked the length propor- tionate to the corresponding specific gravity. Thus, if the perpendicular drawn through the point 100 is 1, that through 50 is 2, that through 120 is 0.83, and so forth; it is of course quite immaterial what unit we choose in the graduation of these perpendiculars. The summits of these perpendiculars are connected by a curved line, which represents the law connecting the points of the scale and the corresponding specific gravities. The curve ascends the more rapidly as it approaches the lower points of the volumeter 2 1.8 1.6 1.4 1.2 0.8 m a \ \ \ K X, "*-^ x l 8 G 4 2 08 50 60 70 80 90 100 110 120 130 AREOMETER. 101 scale lying near a. From this it is evident that the difference between the perpendiculars drawn through 60 and 70 must be greater than that existing between the equally distant perpen- diculars drawn through 120 and 130; or, in general terms, that an equal number of degrees on the lower end of the volumeter scale correspond with a greater difference of specific gravity than on the upper part. It further follows that, if the graduated points of the scale are to correspond to equal differences of the specific gravity, the distance between two points must be greater at the upper than at the lower part of the scale. Another excellent mode of dividing the areometer scale, pro- posed also by Gay Lussac, but previously made use of by Brisson and G. G. Schmidt, gives the specific gravities directly. The relation of this scale to the volumeter scale will be easily under- stood. If we mark on any of the perpendiculars (Fig. 79) the heights 0.8, 1, 1.2, 1.4, 1.6, &c., and draw horizontal lines through these heights to intersect the curve, and from these points of intersection perpendiculars down to the line representing the volumeter scale, or, as is the case in our diagram, to a line m n, lying somewhat above that of the volumeter scale, we obtain the degrees upon the scale coinciding with the specific gravities 1.8, 1.6, 1.4, &c. But we here see how unequal are the divisions of the scale, and how much they increase in size from the lower towards the upper parts. We have here only given the construction of this scale for the points from 20 to 20 p. c. of the specific gravity. If we wish to construct a scale according to this method, the figure must be drawn according to much larger proportions, and the points from at least 5 to 5 p. c. of the specific gravity must be obtained. The intervals may then be divided equally without any marked error. Another method of constructing these scales has been proposed by Schmidt. Although the specific gravity may be obtained directly by means of areometers of this kind, the volumeter has great advantages. In the first place, the completion of a volumeter scale is infinitely easier ; owing to the uniformity of the divisions, we may graduate the scale with much greater accuracy, while the calculations that have to be made to learn the specific gravity according to the volumeter scale, are so extremely simple that they 102 ALCOHOLOMETER. certainly cannot furnish any grounds of objection to the use of that instrument. In a practical point of view, our aim is not so much to learn the specific gravity of a liquid astto know the point of concentra- tion of a saline solution and the proportion of mixture in a liquid. These points certainly stand in such close relation to the specific gravity, that, if by help of the areometer we can ascertain the specific gravity of a liquid, we may also draw a correct conclu- sion as to its nature. Special areometers have been constructed for such liquids as are most frequently used, giving the direct proportions of mixture. We will only consider one of the most important of these the alcoholometer. This instrument serves to determine the amount of alco- Fig. 80. -j^j j n a m ixture O f wa ter and spirits of wine. The specific gravity of alcohol is 0.793 if we take that of water as unity; a mixture of water and absolute alco- hol will, therefore, have a density falling between 1 and 0.793, and approaching more nearly to either extremity as the water or the alcohol preponderates in the mixture. The density deviates, however, from the arithmetical mean reckoned from the proportions of the mixture. The reason of this deviation is to be sought in the con- traction occurring when we mix water and spirits of wine, and which we will first make evident by an expe- riment. If we take a glass tube, such, for instance, as is used in the Torricellian experiment, fill one-half with water and the remainder with spirits of wine, (for the Lecture Room, the colored spirit of wine is preferable,) we shall find the liquids do not mix, the spirits of wine floating on the water. When the open end has been closed by a cork stopper, so that no liquid can escape, a mixture of the fluids will occur by the sinking of the water as soon as we invert the tube. When the liquids are per- fectly mixed, we see that, instead of the whole tube being full, a vacuum has been formed, and occupying about half an inch of the tube. The accompanying figure (Fig. 81) represents the laws for the contraction of different proportions of mixture. The perpendicu- lars drawn at the different points of the horizontal bases of the parallelogram, and passing through its upper side, give the sums ALCOHOLOMETER. 103 of the mixed volumes, the part lying within the shaded portion of the figure showing the volume of the water, and the remainder the volume of the spirits of wine. Thus, the perpendicular line elevated at the point 20 is divided by the diagonal of the parallelogram in such a ratio that T 8 oths of its whole length fall with- in the shaded, and the remaining T yhs in the unshaded part of the figure ; it corre- sponds, therefore, to a case where we have a mixture of 80 parts water with 20 parts spirits of wine. But in this case, the mix- ture forms a volume only 0.982 of the sum of the mixed volumes, on which account the length of 0.982 is marked upon this perpendicular, counting from below (taking the whole length of the perpendicular as the unit). Thus the length 0.965 is marked at the point 60, because 40 p. c. of water mixed with 60 p. c. of spirits of wine coincide with 0.965, the sum of the mixed volumes. The numbers standing over every perpendicular give for each case the exact value of the volume according to the mixture, if the sums of the mixed volumes be 1000. A curve is drawn over the points marked in the way in- dicated on the different perpendiculars. The vertical distance between each point of this curve from the upper horizontal line represents the amount of the contraction. From these considerations it follows that the specific gravity of a mixture of water and spirits of wine must always be greater than the computed arith- metical mean. In Fig. 82, 0.793 is the length of the perpendicular drawn through the point 100, if we take the length of the perpendicular from the point o as the unity. The former represents the specific gravity of absolute alcohol, and the latter that of water. If we connect the upper points of these two extreme perpendiculars by a straight line, and draw through the points 90, 80, 70, &c., perpendiculars going to 10 this straight line, the length of these perpendiculars would repre- sent the specific gravity of a mixture of 90, 80, 70, &c., parts of Fig. 82. OOOO OOOOOOrH 80 60 40 20 104 ALCOHOLOMETER. spirits of wine with 10, 20, 30, &c., parts of water, if no con- traction occurred. But a length is marked upon every perpen- dicular corresponding to the true density of the mixture. The curve connecting those points in the different perpendiculars re- presents the law according to which the density of a mixture of water and spirits of wine changes, if the alcoholic contents increase from to 100 p. c. The number standing over each perpendicular gives the accu- rate numerical value of the specific gravity of the corresponding mixture. If by the numbers 100, 90, 80, 20, 10, 0, we designate those points on an areometer-tube that correspond with the specific gravities 0.793, 0.828, 0.857, 0.976, 0.985, and 1 ; and if, further, we divide the space intervening between every two points into ten equal parts, which may be done without any great inaccuracy, we obtain a per-centage areometer for spirits of wine ; that is to say, an instrument by which we can directly read off how many parts by volume of alcohol are contained in a mixture of water and spirits of wine. Such alcoholometers have been made in France according to the calculations of Gay Lussac, and in Ger- many according to those of Tralles, and have been officially adopted, in order that by their aid the alcoholic contents 100 of brandy, spirits of wine, &c., subject to excise duties, might be determined. Fig. 83 shows the main divi- sions of such an alcoholometer in their true proportions. We see, as we might suppose, that the divisions are of unequal magnitude. The volumeter may easily replace the alcoholometer, if we only have at hand a table in which the quantity of alcohol corresponding with the different degrees of the volumeter is given. As may easily be supposed, the alcoholometer is not applicable to any other fluid than the one for which it is - 50 designed. In a similar manner areometers have been 40 constructed for giving accurately the proportions of an J. so acid, a saline solution, &c. As, however, such instru- 10 ments are solely applicable to the single fluids for which they are constructed, it is better to make use of the vo- lumeter, and to seek in the tables constructed for the purpose, the proportions corresponding to the degrees observed on the volumeter. TABLE OF SPECIFIC WEIGHTS. 105 It now only remains for us to mention the older areometric gra- duations, which, however, are no longer of use for scientific pur- poses. Beaume fixed on a second point, in addition to the watermark, by plunging the instrument into a solution consisting of one part of common salt and nine parts of water. The space intervening between these two points he divided into ten equal parts, which he called degrees, the division being continued beyond the two fixed points. The water point is marked with for liquids heavier than water when the degrees are counted downwards, while for liquids lighter than water, the water point is marked 10, and the degrees are counted upward. It is easy to see that by such an instrument neither the specific weight nor the proportions of a fluid mixture can be ascertained. Cartier made an unimportant change in Beaume's scale by increasing the size of the degrees, fifteen of his degrees being equal to sixteen of Beaume's instrument. However little benefit may have been derived from this alteration, it has had the effect of handing down his name to posterity, since, in spite of its little value, Cat tier'' s scale is very generally known. In Germany, Meiszner has done much service to areometry, and his treatise, published in 1816, at Vienna, " On the Applica- tion of Areometry to Chemistry and Technology" is, perhaps, the most valuable work that we have on the subject. Meiszner's areometers consist of simple cylindrical glass tubes from six to eight millimetres in diameter, without enlargement at the lower end, which is filled with shot imbedded in fused sealing wax; the scale is at the upper end. The following table gives a view of the specific gravities of cer- tain bodies, the knowledge of which may frequently prove neces- sary, or' at least interesting. TABLE OF THE SPECIFIC WEIGHTS OF SOME SOLID BODIES. Platinum coined . . 22.100 Iridium 18.600 " rolled . . . 22.069 Tungsten .... 17.600 " fused .... 20.857 Lead fused . . . 11.352 " drawn into wire 19.267 Palladium .... 11.300 Gold coined . . . 19.325 Silver 10.474 " fused . . 19.258 Bismuth . 9.822 106 TABLE OF DENSITY OF LIQUIDS. Copper malleable . 8.878 " fused .... 7.788 " drawn into wire 8.780 Cadmium .... 8.694 Molybdenum . . . 8.611 Brass 8. 395 Sulphate of Lime (Crys- tal) 2.311 2.033 1.917 1.874 1.800 1.770 1.078 0.960 0.972 0.865 1.226 1.170 1.330 0.904 0.659 0.982 0.590 0.890 0.555 0.857 0.500 0.904 0.644 0.945 0.769 0.817 0.439 1.060 0.677 0.598 0.561 0.383 0.240 ISE 2.966 1.848 Sulphur (Natural) . . Ivory . Alabaster .... Anthracite .... Phosphorus .... Amber Arsenic .... . 8.308 Nickel .... . 8.279 Uranium . . . Steel . 8.1 . 7.816 Wax (White) . . . Sodium . Cobalt .... . 7.812 Potassium .... Ebony Iron wrought . . " cast . . . Tin . 7.788 . 7.207 . 7.291 Oak (Old) . . . . Box Antimony . . . Tellurium . . . Chromium . . . Iodine .... . 6.712 . 6.115 . 5.900 4.948 Maple Green . . . " Dry ... Beech Green . . . " Dry ... Pine Green . . . " Dry .... Alder Green . . . " Dry .... Ash Green . . . "Dry .... Hornbeam Green " Dry . . Linden Green . . " Dry ... Mahogany .... Nutwood .... Cypress . Heavy Spar .... 4.426 Selenium .... 4.320 Diamond .... 3.520 Flint Glass French . 3.200 " English .' 3.373 " Frauenhofer3.779 Bottle Glass . . . 2.600 Plate Glass .... 2.370 Tourmaline (Green) . 3.155 Marble 2.837 Emerald .... . 2.775 Rock Crystal . . Porcelain Dresden " Sevres . " China . DENSITY OF SOME Distilled Water . Mercury . . 2.683 . 2.493 . 2.145 . 2.384 LIQUIDS AT SPECIF . 1.000 , 13.598 Cedar Poplar Cork 32 F., UNLESS OTHERW TED. Bromine Sulphuric Acid TABLE OF DENSITY OF LIQUIDS. 107 DILUTE SULPHURIC ACID, ACCORDING TO DELEZEUNE, AT 59 F. 1.486 1.595 1.709 1.805 1.840 0.994 0.998 1.022 0.916 0.999 0.852 0.953 0.929 0.915 0.872 0.793 0.715 1.272 10 20 per cent, acid . tt . 1.066 . 1.138 60 per cent, acid . 70 30 . 1.215 80 40 tt . 1.297 90 50 tt . 1.387 100 DILUTE NITRIC ACID. 10 20 30 40 per cent, acid . u tt . 1.054 . 1.111 . 1.171 . 1.234 Wines Claret . . " Champagne " Malaga . " Moselle . 50 tt . 1.295 " Rhenish . 60 tt . 1.348 Oils Citron . . 70 . 1.398 " Linseed . . 80 90 tt . 1.438 . 1.473 " Poppy . . " Olive . . 100 Mill Sea tt . 1.500 . 1.030 . 1.026 " Turpentine . Alcohol, absolute . Sulphuric Ether Sulphuret of Carbon Water . . . 108 ADHESION BETWEEN SOLID AND LIQUID BODIES. CHAPTER IV. MOLECULAR ACTIONS BETWEEN SOLID AND LIQUID BODIES, AND BETWEEN THE SEPARATE PARTICLES OF LIQUIDS. Adhesion between solid and liquid bodies. The phenomena of adhesion occurring between solid and liquid bodies are similar to those between solid bodies ; that is to say, liquids adhere more or less strongly to the surfaces of solid bodies. If, for instance, we sprinkle a few drops of water on a vertical glass plate, they will partly remain hanging to it, instead of dropping down, as would be the case if the gravity of the drops were not counteracted by another force, namely, the attraction which exists between the particles of the liquids and the surface of the glass. This adhesion is also the cause of liquids so easily running down the outer walls of the vessels when we would pour them out ; and to avoid this, we either rub the outer rim of the vessels with fat, or let the liquid pass along a moistened glass rod. Capillary Tubes. It has been already mentioned that the upper surface of a liquid contained in any vessel is horizontal. This, however, is only true where the molecular action exercises no disturbing influence upon the walls of the vessel. In the vicinity of the walls, deviations from the normal surface always occur. If one end of a glass tube be plunged into a liquid, the level of the liquid in the tube will never be at the same height with the upper surface of the liquid outside. For instance, when plunged into water, the column of the liquid rises in the tube (Fig. 84) ; but if we plunge the tube into mercury, the Fig. 84. Fig. 85. r *. top of the column of mercury in the tube will be lower (Fig. 85). These phenomena of eleva- tion and depression are known as capillary phenomena, and the force producing them as capillary attraction, or simply capillarity. This force not only acts in the elevation or CAPILLARY TUBES. 109 depression of liquids in tubes, but is at work wherever liquids are in connection with solid bodies, or among themselves, or where solid bodies are in juxtaposition, or in general where the smallest particles of ponderable matter are in contact. It is easy to persuade one's self by experiment, that the difference of height between the surface of liquids in tubes, and that of the external fluid increases in proportion to the narrowness of the bore of the tube. If we plunge into water two tubes, of which one has twice as large a diameter as the other, the water will rise twice as high in the narrower tube ; if we plunge them into mer- cury, the liquid will be depressed twice as low in the narrower tube. The difference of the level of liquids within and without the tubes is inversely as the diameter of the tubes. The height of the raised columns depends in the above-given manner upon the diameters of the tubes ; but, if the walls of the tubes have been wetted, their thickness and substance are of no importance ; on the other hand, the height depends especially upon the nature of the liquid. The following is the elevation in a tube of .05 inches in diameter for three different liquids: Water (sp. gr. 1000) . . . 0.92 inch Alcohol (sp. gr. 0,8195) . . . 0.36 " Oil of turpentine (0,8695) . .0.39 " We must not omit to mention that when a liquid rises in a nar- row tube, the surface of the liquid column is always concave (Fig. 86), forming a hollow hemisphere having the diameter of the tube. If, on the contrary, there be a depression, the top of the liquid will assume a convex form (Fig. 87). These forms are essentially dependent upon the elevation or depres- sion, for if we pass any fatty substance over the minor walls of the tube, and then place it into water, we obtain a convex meniscus, exactly as if we had immersed an ordinary glass tube in mercury. It follows, therefore, that the differences of the level depend upon the form of the meniscus, and conse- quently, that all accidental causes which hinder the meniscus from assuming its regular form, also modify the height of the columns. If, for instance, a tube be not perfectly smooth and clean inter- 10 110 CONNECTION BETWEEN THE PARTICLES OF A LIQUID. nally, indentations will appear at the border of the meniscus, and we then obtain, on frequently repeating the experiment, very various results. The power of blotting-paper in taking up liquids, the action of the wicks of candles and lamps, the efflorescence of saturated solutions, &c., all depend upon the action of capillary tubes. The vessels of plants conveying the sap upwards from the roots are remarkably minute, *and act on this principle. Connection between the particles of a Liquid. Although liquids have no independent form, and although their separate particles admit of being most easily displaced, the connection existing between them does not cease, as we see exemplified in the case of the formation of drops. If we pour water upon a surface strewed with lycopodium seed, or mercury into a porcelain ves- sel, drops almost spherical will be formed. If no connection existed between the separate particles of the water and the mer- cury, they would fall asunder like dust ; in slowly pouring liquids from any vessel, they will not fall in separate drops; such a drop only falling if its weight be sufficiently great to effect at once a separation from the remaining mass of the liquid. The cohesion existing between the separate particles of a liquid can be directly measured. If a solid disc be placed upon the surface of a liquid, it can no longer be lifted up in a horizontal position with the same force as when hanging freely in the air ; a greater or smaller additional force being necessary to draw it up. We make use of the balance in order to measure this force. On the one side we hang a horizontal disc, and on the other we lay a balancing weight to establish equilibrium. If the whole be equipoised, we approximate the surface of a liquid to the under part of the disc until they meet, and then, without shaking the balance, we add weights to the opposite side, remarking the quan- tity necessary to separate the liquid from the disc. In order to remove a glass disc of 118 mm (4.6 in.) diameter, different weights are required for different liquids. As for in- stance : Water (sp. gr. 1.000) . . . 91 1.1 9 grains Alcohol . . . . . 478.76 " Oil of turpentine .... 525.05 " A disc of equal diameter, and constructed either of copper or any CONNECTION BETWEEN THE PARTICLES OF A LIQUID. HI other substance, wetted by a liquid, yields precisely the same results. Adhesion is, therefore, like capillarity, independent of the nature of the solid bodies, and depends only upon the nature of the liquids. It is easy to see the reason of this, for on drawing it up there always remains a layer of the liquid on the disc ; the liquid, therefore, has not been separated from the disc by the pre- ponderance of weight on the other side, but the molecules of the liquid have been severed from each other, and the cohesion of the liquid has been overcome. The experiments adduced, yield, there- fore, a measure for the cohesion of liquids, and for the attraction existing between their particles, and we thus see how considera- ble is this attraction, and that it changes with the nature of the liquids. If the upper surface of the disc be not moistened with the liquid, as, for instance, when we place a glass disc on mercury, the extra weight effecting the separation no longer expresses the cohesion of the liquid. It is necessary to use a force of about 200 grammes (3083 grs.) to raise a glass disc of the above dimensions. It follows, there- fore, that, even when a solid body is not moistened by a liquid, a greater or smaller attraction will still exist between the molecules of the liquid and those of the solid body, only in this case the cohesion of the liquid is greater than the adhesion between the liquid and the solid body. The phenomena here treated of may be considered in a theore- tical point of view, in the following manner: Mercury forms spherical drops upon paper, and water upon an unctuous or sprinkled surface. This phenomenon is usually explained by the universal attrac- tion of all molecules to one another, on the same principle that we explain the spherical formation of the heavenly bodies. But this explanation is not admissible, since molecular attraction acts very differently from universal gravity ; and since, from its acting only at imperceptible distances upon contiguous molecules, it cannot be so condensed as to form a central point of attraction similar to the central point of gravitation of the planets. The following seems to be a more correct mode of elucidating the subject: The molecules of a liquid must remain at such a distance that attraction and repulsion shall neutralize each other. This is only 112 CONNECTION BETWEEN THE PARTICLES OF A LIQUID. possible when the molecules are so placed in regular layers that each molecule is surrounded by twelve others, somewhat in the manner that cannon balls of equal size are wont to be ranged. This arrangement remains also undisturbed where the liquid ter- minates in a level surface. Every molecule is subject to perfectly equal actions from all sides, and all the molecules are perfectly equidistant one from the other. Such an arrangement may be termed the normal arrangement of the molecules. If a part of the limiting surface be curved, the reciprocal apposition of the molecules can no longer remain the same ; and such a disposition may be termed abnormal. As soon as the normal position of the molecules is disturbed by any external force, the hitherto perfect equilibrium of the whole will be disturbed, a tension will arise, striving to restore the dis- turbed parallelism of the layers, and bring back the particles of the liquid to their normal position as soon as the disturbing cause ceases to act. If we plunge a rod moistened by a liquid into the same, we may, by slowly drawing it out, form an elevation which will immediately be restored to a plane surface on entirely removing the rod. This certainly can only be the consequence of gravity; but the same thing occurs in the reversed position of the plane. If we fill with water a tube not exceeding three lines in diameter, and having one end open, we may revolve it without the water escaping. It forms a hanging plane, from which, as in the former instance, then arise elevations, which, after separation, in opposition to the action of gravity, return to the plane surface. A liquid strives, therefore, to terminate in a plane surface ; but a mass free on all sides cannot be surrounded by one single plane. If it were bounded by plane surfaces, the edges would be soon flattened by the tension of the molecules; but, if the mass were bounded by a curved surface, whose curves were not equal on all sides, a stronger tension would naturally also occur at the more strongly curved parts of the surfaces, tending to the perfect sphericity of the whole. The roundness of the air-bubble de- pends upon the same principle. The superficial molecules of a perfectly free liquid compose, therefore, a net-work, forcibly compressing the minor part. If we make a soap-bubble, it will retain its size as long as we keep the opening of the tube closed, but, as soon as this ceases to be done, the bubble will diminish CONNECTION BETWEEN THE PARTICLES OF A LIQUID. H3 more and more. If the air in the bubble were not compressed by the enclosing liquid, and if it were not denser than the sur- rounding atmosphere, it would remain in the bubble, and not be forced into the tube against the atmospheric pressure of the air. If mercury is put into a glass, it will stand off from the sides of the vessel, although, perhaps, not perceptibly; if, however, we add water or olive oil, either will fill the interval. In badly pre- pared barometers, air will also force itself through this interval into the Torricellian vacuum. The mercury forms a large drop lying free in the glass, and its form depends upon the walls of the vessel. It terminates superiorly in a horizontal surface, which, however, cannot reach to the sides of the vessel, owing to the sharp edge of the drop having been rounded off, as we have before, said. If a drop of mercury be poured into a perfectly cylindrical glass tube placed horizontally, the drop will form a cylinder rounded at either end. No motion can, however, arise, as the convexity is equal at both ends. But, if the tube be conical (Fig. 88), the mercury will be more curved at the narrower end ; the ten- sion of the abnormally placed mole- cules is, therefore, greater here than on the other side, and the consequence of this preponderating tension is, that the mercury moves to the wider end. If we entirely fill a narrow tube with mercury, and place it horizontally, letting the one end communicate with a drop of mercury at the extremity of the tube, the latter will increase until the mercury at length entirely leaves the tube, and is collected in one large drop. The reason of this is easily understood. By the strong 'curvature of the convexity at the end of the cylinder of mercury, there arises on this side a far stronger pressure on the mass than on the side of the drop. If a glass tube be plunged vertically into mercury, the liquid will be deeper within than without the tube, as the strong con- vexity of the cylinder of mercury acts depressingly in the tube. It is also clear that the narrower the tube, the greater will be the depression. If a liquid adhere to the walls of the vessel and wets them, it can no longer, as in the former instance, be regarded as a 10* 114 CONNECTION BETWEEN THE PARTICLES OF A LIQUID. large drop; the upper surface cannot, therefore, assume a con- vex form. The molecules of the walls of the vessel in contact with the liquid act upon the latter as the molecules of the liquid upon one another. The solid walls of the vessel are, therefore, only to be considered as a rigid continuation of the liquid. The air above the liquid in the vessel must, therefore, be regarded as a bubble, bounded inferiorly by the liquid, and on all sides by the walls of the vessel. If the surface of the liquid were perfectly even, the bubble would have a sharp edge where the fluid and the walls of the vessel came in contact, which would immediately be rounded off by the mutual attraction of the molecules of the wall and the fluid ; as, however, the molecules of the vessel are solid, the surface of the liquid must necessarily assume a concave form, while the molecules of the liquid ascend the sides of the vessel. In the bubble, however, the tension of the abnormally placed molecules of water exercises a pressure upon the enclosed air ; and then the concave surface of the liquid also exercises an upward pressure against the air of the bubble. A drop of water in a horizontal cylindrical glass tube will form a cylinder concave at both ends, and stationary, owing to the concavity being equal at both ends. If the tube be conical, the one concavity must necessarily be more strongly curved than the other, and, by the preponderating tension of the stronger curved extremity, the water will be drawn towards the narrower part of the tube (Fig. 89). In the same manner we may easily explain, by the action of concave surfaces, the rising of water in a tube plunged vertically into that liquid. If a hollow glass sphere swim on water, the liquid will begin at a distance of more than six lines to rise against the ball. If now we put a second glass sphere into the water, at about one inch from the former, the balls will begin to approach each other, at first slowly, then more and more rapidly, until they finally strike one another (Figs. 90 and 91). If both balls had been fixed, the water between the balls would have risen, in conse- Fig. 90. Fig. 91. ELASTICITY OF LIQUIDS. 115 quence of its striving to come to a level ; but, as they are move- able, the adhering water-surfaces sinking from the action of gravity must draw together the balls between which they were interposed. Elasticity of Liquids. Liquid bodies are also in some respects elastic, for they allow themselves, by means of a very strong pressure, to be reduced to a volume somewhat smaller than their original mass, and resume their former volume on the removal of the pressure. Oersted first, and subsequently Colladon and Sturm have made experiments upon the compressibility of liquids, but we should be drawn into too wide a digression were we to enter fully into a description of what they have done. The pressure of one atmosphere (an expression that we will explain in the proper place) compresses mercury to about three, and water to about forty-eight millionth parts of their volume. 116 AIR. CHAPTER V. OF THE EQUILIBRIUM OF GASES, AND OF ATMOSPHERIC PRESSURE. AIR is a body that does not act immediately upon the senses as solid and liquid bodies, but manifests itself by so many pheno- mena upon the land, and over the waters of the earth, that it will be unnecessary to seek for other proofs of its existence. There are thunderstorms in every climate, and storms on every sea ; the air, therefore, everywhere surrounds the whole globe of the earth, forming at all points a layer of great thickness ; for clouds driven by the winds pass alike over plains and hills. Above the clouds, we see the glorious color of the sky, evincing the height of the air, as the color of the ocean does the depth of its waters. If there were no air, the sky would be without color and brightness, ap- pearing but as a perfectly black vault, in which the stars would appear with the same splendor by day as by night. This vast mass of air spread over the earth, and stretching high over the summits of the loftiest mountains, bears the name of the atmo- sphere. The highest peak of the Himalaya scarcely stretches five miles above the level of the sea, while the air rises to a height at least six or seven times loftier. The chemical discoveries of the past century have taught us to know many bodies possessing the same physical properties as the air, although very different in their nature. They were termed airs, and were spoken of as mephitic, combustible, and fixed airs. In the present day, they are called gases, gaseous bodies, or elastic fluids. Gases are, like liquid bodies, subject to two different forces, gravity, and molecular forces. At a very remote period, even before the time of Aristotle, it was conjectured that air had weight. This truth was, however, first proved by Galileo, in 1640, and confirmed somewhat later by the beautiful experiments of Torricelli. The heaviness of the air AIR. 117 may be directly proved by the following experiment: Take a balloon provided with a cock, and from which the air has been removed by means of an air-pump ; hang it on one arm of a balance, and lay sufficient weight on the opposite side to establish equilibrium. If now we turn the cock, the balloon will again be filled with air, the equilibrium disturbed, and the balance inclined to the side of the balloon. We must now again lay on sufficient weight to equipoise the whole, and this will be precisely as much as the air in the balloon weighs. For a balloon of one litre, (61.028 cubic inches,) the difference of weight amounts to more than one gramme, (15.444 grs.,) from whence it follows, at a rough esti- mation, that, under ordinary circumstances, one litre of air weighs more than one gramme; that is, that water is not quite 1,000 times so heavy as common air. [The weight of 100 cubic inches of common air at 60 F., has been variously estimated. Thus Kirwan computes it at 30.92 grains, Davy at 31.10, Shuckburgh 30.5, and Brande at 30.199.] Instead of a balloon with a cock, we may use the following cheap arrangement, which has, further, the advantage of weighing much less under an equal volume than the former. We must take a balloon of not very thick glass, and not a very narrow neck (Fig. 92). The neck must be carefully closed with a tightly- fitting cork, perforated through the middle with an opening about two millimetres in diameter. The cork must now be tied down with oiled silk, as seen in Fig. 92, and on a larger scale in Fig. 93. In this manner, the inner part 92 Fjo . 93 of the balloon is completely secured from the access of ex- ternal air. Near the part co- vering the opening of the cork, we make two cuts into the oiled silk, as seen in Fig. 93, and then the balloon is to a cer- tain extent closed with a valve through which air may escape from the balloon, but cannot enter into it. In making this experiment we first weigh the balloon while full of air; we then bring if under the receiver of the air- pump, when, on exhausting it, the air in the balloon will also be removed; when thus emptied it must be re-weighed, when we shall find that it has become lighter. 118 AIR. Molecular forces act very differently in gases from what they do in solid and liquid bodies. We have seen that these forces hold firmly together the molecules of solid bodies, so that they cannot change their respective positions. They also hold together the molecules of liquid bodies, but only in such a manner as to afford them more freedom in displacing each other in all directions. In gases, however, molecular forces act repulsively, the molecules of gaseous bodies having a tendency to move reciprocally away from each other, and that to so great an extent that nothing but external impediments can hinder their further expansion. The air contained in a vessel presses, therefore, continually against its sides. This tendency in air to expand will be easily shown by the following experiment : We lay under the receiver of the air- pump an animal bladder, containing but little air, and, therefore, wrinkled, having its opening tightly secured. After a few strokes of the piston, the bladder becomes inflated, and at last is tensely stretched, as if air had been violently injected. If we suffer the air to return to the receiver, the bladder will again shrivel up. The air enclosed in the bladder has, therefore, really a tendency to expand, but meets with opposition from the surrounding air. Instead of a bladder we might have placed a thin, firmly-corked glass under the receiver, when the stopper would either have been forced out, or the glass would have been burst, provided the cork were not too firmly placed, or the glass too strong. This pres- sure exercised by the air upon the sides of the enclosing vessel is what we term its elasticity, power of tension, or force of ex- pansion. A feather only manifests elasticity if we compress it ; it loses its tension as soon as it returns to its original condition. But air has always an expansive force ; it cannot be said to have any original volume, for it always strives to occupy a larger space. If we were to admit one litre of common air into a vacuum of several cubic metres, it would distribute itself equally throughout the whole space, and would always manifest a tendency to expand, exercising, consequently, a pressure upon the enclosing walls. The construction of the air-pump, an instrument to which we have already repeatedly alluded, and which we purpose now describing more fully, depends upon the tendency manifested by the air of occupying as large a space as possible. If the air had PRESSURE OF THE AIR. 119 no power of tension, no elasticity, in the sense we have ascribed to the words, it could not distribute itself out of the receiver of the air-pump; without its tendency to expand, the air could not escape from the balloon, even if we removed the weight of air pressing from without upon the valve. It follows, from the expansive force of gases, that they cannot be bounded by a free even surface, as is the case with fluids. Two forces, gravity and the force of expansion, act upon the air of our atmosphere and counterpoise each other. By gravity the particles of the air are attracted to the earth: this force, therefore, exercises a tendency to condense the air upon the earth's surface, which is counteracted by the force of expansion. The atmosphere is, therefore, probably limited, as the expansive force diminishes so much at a certain degree of rarefaction, that the gravity of the particles of air is alone sufficient to hinder a further removal from the earth. Pressure of the Mr. If the common conditions of equilibrium be satisfied, we may prove by direct experiment that all the under layers of air are pressed upon by the upper, and that the amount of this pressure varies as we ascend more and more above the level of the sea. Let us place a glass cylinder, with some- Fig. 94. what thick sides, upon the plate of the air- pump, and cover the vessel with a bladder tightly stretched, and firmly tied over the top. The bladder suffers an equal pressure on both sides, and forms, therefore, a level surface. If now, by any means, we force additional air into the cylinder, the bladder will be arched outwards ; but if, on the contrary, we remove any of the air from the cylinder, the ex- ternal pressure of air will preponderate, and force the bladder in- wards. The latter may easily be shown by means of the air- pump. After the first few strokes of the piston, the bladder will already be curved downwards, and the more we exhaust the air the more this curvature increases. If we strike the bladder with any sharp body when it is thus stretched, it will be torn in a thou- sand pieces, with a noise like the report of a pistol. This sound is produced by the air forcing itself in ; and we may thus form some idea of the amount of the pressure of air resting upon the bladder. 120 MEASUREMENT OF ATMOSPHERIC PRESSURE. If we had so far altered the experiment as to have placed the bladder in an oblique position, or made the pressure of air act from below, we should have obtained the same result, as the air presses in all directions in an equal manner. This experiment appears very striking, when we think that the air in a room is able to exercise so enormous a pressure. This effect cannot arise from the weight of a column of air resting upon the bladder, and stretching from thence to the ceiling of the ' room, for even a column of water of this height could not produce such a result. If the experiment were made in the open air, the bladder would evidently have to sustain the pressure of a column of air whose height is equal to the height of the whole atmosphere. The same pressure acts in a room, for the air within the room is acted upon by the whole pressure of the atmosphere. Measurement of Atmospheric Pressure. As the air surrounds the whole earth, it presses upon everything as upon the bladder, upon the land as upon the ocean. If we plunge one end of a tube into a vessel filled with water, the fluid will rise as high within the tube as without, for the pressure of the air in the tube acts precisely the same upon the level of the fluid as without the tube. But if we abstract a portion of the air from the tube, the fluid will continue to rise as long as we remove the air. By this exhaustion the air within the tube is diminished, while the external pressure of the air remains the same. The preponde- rance of the external pressure of air raises the fluid within the tube, until the weight of this raised column of water equipoises the preponderance. If we entirely exhaust the air in the interior of the tube, the water must rise (provided the tube be high enough), until the weight of the raised column of water is equal to the weight of a column of air of the same base reaching to the limits of the atmosphere. In this manner we may ascertain the weight of a column of air, whatever be its height. We have to thank the mechanicians of Florence for the first germ of the discovery of this important law. On trying to raise water above thirty-two feet in a suction pipe, they found to their great surprise that the fluid would not rise beyond that altitude. The rising of a fluid was explained at the time by saying that Nature abhors a vacuum; but this reason did not satisfy Galileo, who, on hearing of the observations made by the pump-makers, at once came to the conviction that the gravity of the air was the MEASUREMENT OF ATMOSPHERIC PRESSURE. 121 true cause of the phenomenon. His pupil, Torricelli, gave con- vincing proofs of the truth of this conjecture, and arrived at nearly the following results. In order that two different columns of fluid should be equipoised, it is necessary that their heights must be inversely as their densities. Mercury weighs nearly fourteen times as much as water. If, now, the atmospheric air can sup- port a column of water thirty-two feet in height, it must also, according to the above view, be able to sustain a column of mer- cury -f|, that is, of twenty-eight inches in height. The experi- ment is easily made. We fill with mercury a glass tube of about thirty inches in length, and closed at one end, and, holding the finger over the open end, invert it. If, then, we plunge the end closed by the finger, into a vessel with mercury, and then remove the finger, the mercury will immediately sink some Fig. 95. inches, until the elevation of the mercury in the tube is as much beyond the level of the mercury in the vessel as follows from the above considerations. The column of mercury in the tube is to be regarded as an equipoise to the pressure of the atmosphere. This apparatus constitutes the barometer. The vacuum above the column of mercury is termed the Torricellian vacuum. We may express the above results more correctly. The vertical height of the level s in the tube above the level a b is called the height of the barometer. It is not the same in all places, or at all times. In the vicinity of the sea it averages 76 centimetres, or, what is nearly the same thing, 28 Paris inches.* Such a column of mercury, with a base of 1 square centimetre, has in cubic contents 76 cubic centimetres. As, now, 1 cubic centi- metre of mercury weighs 13.59 grammes, the pressure of the column on its base is 76 X 13.59 grammes = 1,033 kilogrammes. The column of atmospheric air, which at the level of the sea rests upon a base of 1 square centimetre, presses, therefore, on its sur- face with a weight of 1,033 kilogrammes.! We may carry this computation still further, and determine the weight of the whole mass of air composing the atmosphere. For instance, whatever Very nearly thirty English inches. TR. This is equivalent to a pressure of fifteen pounds on 1 square inch. TE. 11 122 CONSTRUCTION OF THE BAROMETER. number of cubic centimetres the earth's surface contains, so many times 1,033 kilogrammes does the mass of the air weigh. Fig. 96. Construction of the Barometer. Barometers have had various forms given to them, according to the several uses for which they are intended. Fig. 96 represents the ordinary barometer, consisting of a tube which is curved at the bottom, and terminates in a wide vessel, the whole being secured to a board. The graduated scale is generally made of metal. If the vessel be somewhat wide in comparison with the bore of the tube, the oscillations of the column exer- cise but little influence upon the level of the mercury in the vessel, so that in cases where extreme exacti- tude is not requisite, this level may be regarded as constant. In these barometers, which cannot be used in very nice observations, the scale is generally con- fined to the upper part of the instrument. In travelling, the syphon barometer of Gay Lussac is almost exclusively made use of, owing to the accu- rate results it yields, the facility of observing it, and, above all, the ease with which it can be carried. The open limb has only a capillary aperture of sufficient size to admit the air freely, and too small to allow of the mercury escaping. We may, there- fore, invert it, without fear of losing the mercury. In these barometers, the lower surface of the mer- cury which is exposed to the pressure of the atmo- spheric air has no fixed position. The zero point from which the height of the column of mercury must be measured, rises and falls. For the sake of safe and convenient transportation, the syphon barometer is generally fastened into a wooden case (Fig. 97), forming a staff or rod when closed. Whatever may be the form of the barometer, cer- tain conditions must be satisfied, if the instrument is to give the exact amount of atmospheric pressure. The height of the column of mercury must admit of being accurately measured, which can only be done if the tube be in a perfectly vertical position. The degrees of the scale are either marked upon a slip of Fig. 97. AMOUNT OF ATMOSPHERIC PRESSURE. 123 brass inserted in the board to which the tube is secured, or are engraved upon the tube itself. The space above the column of mercury must be perfectly free of air. The only way of effecting this object, is by boiling the mercury in the tube, and thus removing all particles of air and moisture, adhering to the sides of the glass. This process is one requiring much practice and skill. We may detect the presence of a particle of air in the Torricellian vacuum by the space not becoming entirely filled with mercury on inverting the tube, a little bubble of air remaining in that case at the top of the tube. The larger the volume of the empty space, the less importance is to be attached to the defect. Finally, the mercury must be perfectly pure, and the bore of the tube not too small. If the tube be too narrow, the adhesion and the friction of the mercury exercise so important an effect upon the sides of the glass, that the column of mercury often remains standing higher or lower than it ought, according to the height of the pressure of the air. If in such cases we strike the barometer, we may see the column of mercury instantly rise or fall, according to its previous position, as the hindrance to the motion has been overcome by the blow. Of the fluctuations of the barometer dependent upon the changes of the weather we will speak further. Amount of Atmospheric Pressure. We have already mentioned what must be the amount of pressure of air corresponding to 760 millimetres (30 inches) of the barometer. In the same manner the amount of atmospheric pressure may be reckoned at every height of the barometer. The results are given in the following table: 124 AMOUNT OF ATMOSPHERIC PRESSURE. Height of the Column of Mercury. Pressure upon One Square Metre. Height of the Column of Mercury. Pressure upon One Square Metre. Millimetres. Kilogrammes. Millimetres. Kilogrammes. 500 6793 650 8381 510 6929 660 8967 520 7065 670 9105 530 7201 680 9238 540 7336 690 9374 550 7472 700 9510 560 7608 710 9646 570 7744 720 9782 580 7880 730 9918 590 8016 740 10054 600 8152 750 10189 610 8287 760 10330 620 8423 770 10461 630 8559 780 10597 640 8695 790 10733 The surface of the human body measures about 2000 square inches ; we see, therefore, from these calculations, the enormous pressure we constantly have to sustain, and yet we do not feel it, owing to its acting uniformly on all sides, and because the air within our bodies perfectly equipoises the external pressure. On the summit of Mount d'Or, the barometric column is only 600 millimetres (23.5 inches); a weight of 2,173 kilogrammes (about 4,650 Ibs.) is, therefore, gradually removed from the traveller as he ascends higher and higher up the mountain, and still more on reaching the summit of Mount Etna or Lebanon. The diminished pressure of the air at higher elevations produces the most peculiar effects upon the human body, which is not made to endure so rarefied a state of the atmosphere. Even persons in good health experience lassitude, indisposition and oppression. [This decrease in the density of the atmosphere, as we ascend above the surface of the earth, is very rapid : thus, at an elevation of 3 miles, the pressure of the air is only \ of that at the level of the sea; at 6 miles J; at 9 miles \\ and at 15 miles ^V; this is shown by the subsidence of the mercury at the several eleva- tions. PUMPS. 125 At the level of the sea, it stands at At 5,000 feet elevation " 10,000 . " 15,000 " 3 miles .... " 6 " " 9 " . " 15 " 30 inches. 24.797 " 20.499 " 16.941 15.000 7.50 3.75 " 1.00 ] Pumps. A number of phenomena, of which we are daily wit- nesses, admit of being explained by the pressure of the air. If we suck the upper end of a tube immersed in water, the liquid will rise in the interior of the tube, owing to the air in the upper part being rarefied by the action of sucking, and the pressure of air acting on the external level of the water forcing the liquid into the tube. We may produce a similar rising of the water by inserting a piston in the interior of the tube, by the working of which the air will be likewise rarefied. Upon this principle de- pends the construction of pumps. The Suction Pump consists of a suction or feeding pipe a (Fig. 98), a cylinder 6, a piston p, an upper pipe s, and three valves r, t and /, opening up- wards. The valve r is at the bottom of the cylinder, t is in the piston, and / in the lower end of the upper pipe. The suction- pipe plunges into the w T ater we wish to raise, and the piston-rod moves air-tight through the box e. When, on the first movement, the piston is raised, t closes, but r and / are open: / owing to the condensation of air above the piston, and r owing to its rarefac- tion below the piston. As the pressure of air in the suction-pipe diminishes, the water rises in consequence of the preponderance of the external pressure. The lower valve closes as the piston descends. The air in the cylinder below the piston is compressed, and, opening the valve , passes through the piston into the upper part of the cylinder. On the second elevation of the piston, the water again ascends higher in the suction-pipe, while a quantity of air is again expelled through the valve I. At last, after a cer- 11* 126 HYDROSTATICS. tain number of strokes of the piston, the water ascends above the valve r and lifts up the valve t. Then, all the air being expelled from the pump, every valve is raised by the water alone. Every time the piston descends, a quantity of water passes through the valve t, and at each stroke a fresh supply is raised into the upper pipe and the suction-pipe. The force expended in raising the piston is partly lost in overcoming the friction, and in counteract- ing the pressure of a column of water w r hose base is equal to the surface of the piston, and whose height is equal to the vertical distance between the orifice at which the water escapes, from the upper tube over the level of the liquid, into which the suction- pipe is immersed. To make a pump efficient, the water must be able to reach the first valve r. The position of this valve depends upon the degree of rarefaction which can be produced between the valves t and r. If there were no space between r and t at the lowest position of the piston, an absolute vacuum might be produced between these two valves, and the valve r should be placed thirty-two feet above the level of the water of the reservoir. But, as it is impossible entirely to avoid interstices occurring below the piston, the valve r must not be elevated quite thirty- two feet above the level of the reservoir. Care must, however, be taken to make the space as small as possible in comparison with the contents of the cylinder. If, for example, the space occupied one half of the contents of the cylinder (excepting that filled by the piston), we could only rarefy the air between r and t to half the pressure of the atmospheric air, and consequently the valve r should not be elevated more than sixteen feet above the level of the water in the reservoir. The Suction and Forcing Pump (Fig. 99) Flg * ' (| consists of a suction-pipe a, an upper pipe s, a cylinder c, and a heavy piston p ; it has only two valves, r and /. On raising the piston, the water forces itself through the valve r\ on lowering the piston, r is closed, and the water raised up is forced through /. The Syphon. If we fill a drinking glass having a smooth edge (cut glass is the best) with water, cover it with a paper, and invert it, the water will not run out, the pressure of the air acting on the under surface of the paper, COMMON SYPHON. 127 and thus hindering the escape of the liquid. The paper is only so far necessary, as to enable us to invert the glass, and Fi I0a prevent the water from running out at the sides, and air- bubbles entering the vessel. When the lower opening is so small as to leave no fear of the liquid thus running out, as is the case with the form of syphon depicted in Fig. 100, the paper is unnecessary. This syphon is a common tubular vessel, constricted above and below, and open at both extremities. If we plunge it entirely into a liquid when both orifices are open, it will be en- tirely filled, and placing the thumb over one opening, we may lift the syphon up without any of the fluid contained in it escaping. The common syphon (Fig. 101) is a curved tube, b s b' 9 whose legs are of unequal length. If the shorter leg be plunged into a liquid, and the whole tube filled, the liquid will continue to run out at b', the end of the longer leg lying lower than b ; we, may, therefore, easily empty a vessel by means of a syphon. The action of the syphon admits of a ready explanation. On the one side the column of water s b f , and on the other the column of water from s to the level of the liquid in the vessel, have a tendency to fall, owing to their gravity. The gravity of the two columns of water in the different legs is, however, opposed on both sides by the pressure of air acting on the one side on the aperture &', but on the other on the sur- face of the water in the vessel, and thus hindering the formation of a vacuum in the interior of the tube, which would necessarily be formed at s if the columns of water ran down on both sides. As the pressure of air acts alike strongly on both sides, equili- brium would be established if the columns of water were equally high in the two legs; that is, if the opening b' were at the eleva- tion of the level of the water in the vessel ; as soon, however, as b' lies deeper, the column in the leg s b' preponderates, and, in proportion as the water escapes there, water is again forced into the tube on the other side by the pressure of the air, so that the 128 HYDROSTATICS. Fig. 102. Fig. 103. liquid continues to escape until the level of the water in the vessel has fallen to the height of the opening b f , or the opening at b has been set free. A suction-tube, a t (Fig. 102), is sometimes attached to the syphon to make it more useful and efficient. We fill a common syphon by sucking at b' ; as this pro- cess, however, is objectionable, owing to the diffi- culty of preventing the fluid from entering the mouth, which might be very dangerous in some cases, as, for instance, in emptying a vessel of sul- phuric acid, a suction-tube is indispensably neces- sary, as, by means of this, we may fill the whole leg s b f by sucking at t, without the fluid entering the mouth, if we close the tube at b'. The escape of the fluid begins as soon as we again open the end b' of the tube. Mariotte's Law. The volume of gases is inversely proportional to the pressure to which they are subjected. To prove this funda- mental law by experiment, we take a curved cylin- drical tube whose shorter leg is closed above, while the longer one remains open. At first we pour a little mercury into the tube, and then incline it somewhat that the air may escape from the shorter leg. By this means we can easily contrive that the mercury shall stand equally high in both legs. Then the air enclosed in the space a b (Fig. 103) is exactly counterpoised by the pressure of the atmosphere. If we again pour mercury into the open leg, the pressure to be sustained by the enclosed air is increased, and the latter is compressed within a smaller space. If the mercury rise in the shorter leg to the point m, half way between a and 6, the air will be compressed to the half of its former volume ; if now we mark on the longer leg the point n at an equal height with m, and measure how high the mercury has risen above n in the longer leg, we shall find that the height of the column of mercury s n is exactly equal to the height of the barometer; the air enclosed in b m has, therefore, to support the pressure of two atmospheres. If the open leg of this apparatus were long MARIOTTE'S LAW. 129 Fig. 104. enough, we might show in the same manner that a pressure of three or four atmospheres would compress the enclosed air to one-third or one-fourth of its original volume. Arago and Dulong have shown that for atmospheric air this law does not vary in its application at least up to a pressure of twenty-seven atmospheres. By this experiment the correctness of Mariotte's law is proved from the pressure of one atmosphere to the pressure of twenty- seven atmospheres; while for a pressure of less than one atmo- sphere we may confirm the principle by the help of the apparatus about to be described (Fig. 104). A somewhat wide glass tube, terminating above in a wider vessel, and closed below, .is so placed in a frame as to stand vertically. It is filled with mercury to about the line c n. We now fill a barometer-tube (as in the Torricellian experiment before described) with mercury, leaving, however, a space of an inch to two inches empty. If we now close the aperture with the finger, and invert it, the air-bubble will ascend into the upper part of the tube. If, now, as in the Torricellian experiment, the lower end of the tube enters the mercury of the vessel en, and we remove the finger from the tube, the column of mercury in the barometer-tube will fall to a certain point. But we shall immediately observe that the summit of the column of mercury does not stand so high above c n as the barometric height measures, because there is air in the upper part of the tube, and no vacuum as in the barometer. If we press down the tube until it reaches further and further into the mercury of the wide tube, the volume of the enclosed air will become smaller. We now press the tube so far down that the mercury in the tube stands exactly at the height of the level of the mercury en. In this case the enclosed air is submitted exactly to the pressure of one atmosphere. The height of the enclosed column of air exposed to the pres- sure of one atmosphere is now measured: it amounts to 1.96 inch. If we again draw up the tube, the volume of air increases, but at the same time the top of the mercury rises above the level en. 130 HYDROSTATICS. Provided we draw the tube so far up, that the enclosed air occupies a length of ten centimetres (3.93 in.) in the tube, the height of the top of the mercury above the level en will be exactly half of the height of the barometer observed at the moment. For instance, if the barometer stand at 760 millimetres, (30 inches,) the top of the mercury will be exactly 380 millimetres (15 inches) above en. The half of the atmospheric pressure is, therefore, counterba- lanced by the column of mercury under the enclosed air, and the pressure which the latter has to sustain is only equal to the pres- sure of half the atmosphere ; its volume, however, is twice as large as it was when supporting the pressure of one atmosphere. If, now, we raise the tube so far that the enclosed air occupies a length of fifteen centimetres, (5.89 inch,) so that its volume is three times greater than it was, the height of the column of mercury in the tube amounts to two-thirds of the barometric height : the enclosed air has, therefore, only a pressure of one-third of an atmosphere to sustain. Measurement of heights by the Barometer. If the air were not an elastic fluid, but were like water, it would be extremely easy to compute heights by the barometer. At the level of the sea, the barometer stands at 760 mm , as soon as we ascend 11, 5 metres, the barometer falls to 759 ram ; a column of air of 11,5 metres in height will, therefore, equipoise a column of mercury of l mm in height. From this we may calculate the density of the air, for it is to that of mercury as l mm is to 11,5, or as 1 to 11500, that is, the density of the air is th of that of mercury. The density of 11500 1 O CZ. the air is, therefore, ' , or nearly 0,0012 that of water, since 11500 water is 13,6 times lighter than mercury. If, now, the air were like water, the density of the strata of air lying above us would be equally great, and we should then only have to ascend 11,5 metres to have the barometer again to fall l mm ; and if, by con- tinued ascent, the barometer had fallen n millimetres, we should then have attained a height n x 1 1,5 metres. But the air is elastic ; the smaller the pressure weighing upon it, the less will be its density ; consequently, the higher we ascend, the more rarefied is the air. The law by which the density of the air diminishes by constant MEASUREMENT OF HEIGHTS. 131 ascent, and the relations existing between the height of the baro- meter and elevations above the soil, can be developed by Ma- riotte's law. Suppose the barometer to stand at 760 mra at any given spot. If we ascend 11,5 metres, the barometer will fall to 759 mm , or what is the same thing 760 . Without any serious error, we 760 may assume that the whole layer of air everywhere at a height >f 11,5 metre, is of equal density with that at the level of the sea. n Fig. 105, a is a point on the earth's surface, b is a point ying 11, 5 m higher, and each one of the several points c, d, e, &c., is 11, 5 m above the lower one. As the density of the air is proportionate to its pressure, the layer b c is less dense than the layer a b, and the densities of these layers will be as the height of the barometer at a and b; that is, the e layer a b. If, now, we ascend from b to c, the barometer h ' ' 7 ^(76b) Density f ^ e l a y er b c is . of the density of g f G59v 5 _\ 7(^Qram 60J does not fall so much as l mm , but only _ .The /759x4 760 \76oj height at which the barometer stands, is, there- -,/ 759 \ 3 f - Cfl 759 mm 759 759 2 -~ A /759\ 2 760( 7TO ) fore, 760 _ - - = _ = 760 (_) . c | 76o(^Vl n this manner we may further conclude that ' the densities of the layers b c and c d are as the /759\ ! b 760 ( ~^- n ) heights of the barometer b and c, and that conse- a 760 quently the layer c d is times lighter than 760 the layer b c. If, therefore, the layer b c could support a column 759 mm of mercury of , the layer c d can only bear a column of 760 _ x :rr = (^:r) millimetres; and if we rise from c to d, the 760 760 \760/ barometer must fall ( \ millimetres. At d, likewise, the height of the barometer is 760 ( j 132 HYDROSTATICS. It will easily be understood that formulae may be constructed from these considerations, by the aid of which the difference of height of two places may be computed, if the height of the baro- meter be accurately measured at both places. The Mr Pump must be ranked amongst the most indispensable and important instruments of the Natural Philosopher, and has undergone many alterations and improvements since its invention by Otto von Guericke. We will now consider it in its most simple form, in the small air pumps which are at present used in all chemical laboratories. We must suppose a hollow cylinder, perfectly closed below, and having a piston c closely fitting to the bottom. If now the piston be forcibly drawn up, a vacuum is formed below it, provided the friction be air tight against the sides of the cylinder. Nothing, however, can be done by means of this vacuum since we can neither see into it, nor put anything within. But if a canal lead from the lower part of the cylinder into a sphere, a balloon e, for instance, which, although filled with air, is fully closed against the external atmosphere, a por- tion of the air in e will enter the cylinder, owing to its elasticity, on lifting up the piston, and a rarefac- tion of the air in e will consequently follow. In order, however, that the air may not return into e on the descent of the piston, a cock s is attached by means of which the communication between e and the cylinder maybe interrupted, or again restored at will. This cock s is closed as soon as the piston comes over it. If we now press down the piston, the air in the cylinder will only be compressed, if we afford it no means of escape ; this, however, it will have, if we open a second cock t. When the piston is at the bottom, t is again closed, and s opened, while another drawing up of the piston produces another rarefac- tion in e. By frequent repetition of this operation, we may obtain a considerable rarefaction at e. The apparatus in this form is, however, inconvenient on many accounts. In the first place, the continual opening and shutting of the two cocks is extremely trou- blesome. But for the cock t we may substitute a valve which closes on the elevation, and opens on the de- pression of the piston. The lower part of the piston AIR PUMP. 133 Fig. 109. consists of a brass plate, with a screw screwed into Fi s- 108 - a piece of brass c c. The screw is perforated along its length, and a piece of silk r bound over the open- ing o. In the piece of brass to which the screw is fixed, there is an opening b. On the elevation of the piston, the air in the upper part of the cylinder forces itself through the opening b in the silk, and presses it tightly upon the opening o ; the piston acts, therefore, on rising, exactly as if it were solid: the air passes from the space e through the open cock s into the lower part of the cylin- der ; but if, after the cock s is closed, the piston be again pressed down, the air in the under part of the cylinder will be compressed, and raising the valve r, will escape through the opening b into the upper part of the cylinder. The piece of brass c is inserted into a cork bound round with fine leather. This leather is pressed against the sides of the cylinder by the elasticity of the cork. The cock s may also be dispensed with, if a second valve be applied to the part where the canal opens into the cylinder. This valve opens on draw- ing up the piston, and closes with its descent. The accompanying figure shows a very useful little air-pump, one- third of the natural size. It has been constructed in accordance with the plan of Gay Lussac. The canal goes ver- tically down from the lower end of the cylinder into a canal a b running hori- zontally. The cork at d should be closed, and the receiver from which the air is to be exhausted, screwed on at a; then on raising the piston, a portion of the air will pass first through the hori- zontal, and then through the vertical canal into the cylinder, and on pressing down the piston, will escape through its valve. To admit the air again into the receiver, nothing more is necessary than to open the cock at d. By means of the screw./, the air pump my be screwed on to a 12 134 AIR PUMP. table, or to a board secured to a table, and will thus remain fixed while being used. We designate by the term receiver, the space from which the air is to be exhausted. The best form for receivers of air pumps, designed for general experiments, is a bell made of glass, the under and somewhat broader edge of which must be made per- fectly smooth and polished, so that it may fit into a smoothly cut plate with such exactitude as to prevent the entrance of any air between the two. A perfect exclusion can, however, only be effected by rubbing the edge of the bell with tallow before placing it upon the plate. In Fig. 110 we see a receiver of this kind in conjunction with a Fi - no - little air pump. From the middle of the plate, a canal goes verti- cally down and then passes further on through a short hori- zontal tube. At the end of this short hori- zontal piece of tube, a glass tube is attached by means of an India- rubber tube, and is secured in a similar manner to the air- pump on the opposite side. The degree of rarefaction that can be obtained by pumping, may be measured by what is termed the barometric test. This is applied to the smaller air pumps in the manner shown at Fig. 110. A glass tube of about thirty inches in length is immersed at its lower end into a vessel full of mer- cury. Above it is curved, and secured to the pump by means of a short but wider piece of tube. If the cock d be opened, the mer- cury will ascend in the tube in proportion as the rarefaction is continued. If it were possible to create a perfect vacuum by means of the air pump, the column of mercury raised in the tube e, would be equal to the height of the barometer. With a well constructed apparatus of this kind, we may make most of the experiments of the air pump, with the exception per- AIR PUMP. 135 Fig. Ill, \c haps of some few, requiring very large receivers, or a very rapid and complete exhaustion. On this account, air pumps of this kind are to be recommended for all popular institutions, not pos- sessing the funds necessary to obtain the more highly finished apparatus, viz., when they are made four, five, or six times larger than the one represented in Fig. 109. Larger air pumps of various forms have been constructed, but all are based upon the same principles as the ones above described. We will consider more attentively one of the best arranged of these apparatuses. In a cylinder , which must be perfectly well finished, the piston b moves by means of the rod c, which must be per- fectly air-tight, no air be- ing able to escape between the piston and the cylin- der. In the piston there is a valve 5, which must move easily, and open up- wards. It rises when the pressure from below is greater than from above, but otherwise remains her- metically closed. The rod e d is the valve for the cylinder. If the piston be raised, the whole rod is lifted up, but d soon strikes the upper plate of the cylinder, and the piston moves with some friction along the whole rod. As soon as the piston descends, the trun- cated cone e is pressed into the conical opening below it, so that the upper surface of the cone e, and the bottom of the cylinder form a plane surface, and the piston may, therefore, rest perfectly on this bottom. From the above-mentioned conical opening, a canal goes on to v. Here there is a screw, to w r hich may be attached the balloons or receivers that are to be exhausted. The screw v is in the middle of a plate p, on which the bell h may be placed. Let us assume that the piston is on the lower plate of the cylinder. If then it be raised, a vacuum will be formed, provided all the valves remain shut ; but the valve e is 136 BAROMETRIC GAUGE. opened, and the air from the bell passes partly over to the cylin- der. But by this means, the air in the bell and in the canal of the bell is rarefied, consequently the valve s in the piston must remain closed. On the descent of the piston, the valve at e is shut, and all passage closed for the return of the air from the cylinder into the bell. The air thus shut in will escape through the valve s, until the piston reaches the bottom of the cylinder. Another upward stroke of the piston produces a fresh rarefaction in the bell. We may easily understand that an absolute vacuum can never be produced in this manner below the bell, however long we may continue the above-mentioned operation, because by every fresh stroke of the piston, the air below the bell is only re-rarefied; we may, however, easily manage to reduce the air until it has only a tension of two millimetres. The time required to produce a certain degree of rarefaction wil! 4 be shorter or longer, according to whether the volume of the receiver be small or large in compa- rison with the volume of the cylinder. If we have exhausted the pump sufficiently, the atmospheric pressure acting upon the piston is not counterpoised by any oppo- site pressure within. In order to raise the piston, we must apply a force of 1033 kilog. for every square centimetre of its surface, besides having to overcome the friction. In air pumps with two cylinders, the pressure on the one piston acts against that weighing down the other piston, and thus nothing but friction remains to be overcome. In the canal connecting the receiver with the sucker, a double- Fi H2 acting cock y is applied; that is to say, a cock having two openings, a common straight aperture connecting the receiver with the sucker, while the pump is being worked, and a lateral opening closed by a metal stopper 5, and turned towards the sucker, when the receiver is to be shut off. If we wish to let air again into the receiver, we must turn the cock in such a manner that the lateral opening is turned to the receiver, and then draw out the metal stopper. In these air pumps, the barometric gauge is generally differently constructed from the above-mentioned. It is usually a shortened barometer, closed in a long narrow bell r, Fig. Ill, and con- nected with the canal of the machine. This connection may be AIR PUMP. 137 cut off, or again restored by means of a cock. Fig. 113 repre- sents an isolated barometer gauge, seven inches in length. Fig. us. The mercury entirely fills the closed leg, and only begins to sink, when the pressure of air acting on the open leg is reduced to one-fourth of the atmospheric pressure. If this degree of rarefaction be obtained, the barometric test will always give the pressure of the air in the receiver, which is equal to the difference of the height of the two columns of mercury. As soon as air is again admitted, its pressure will drive the mercury forcibly back into the closed tube; we must, therefore, moderate the rush of air to prevent the top of the glass tube from being broken through. Otto von Guericke made, by means of the machine which he constructed, the remarkable experiment with the Magdeburg Hemispheres, which consisted in producing a vacuum in a hollow metal ball, the halves of which were only simply laid on each other. Before the vacuum is formed, it is easy to separate the parts, but when they have been entirely exhausted of air, and there is nothing to counteract the external atmospheric pressure, they adhere most extraordinarily close together. If, for instance, the radius of the ball were only 1 decimetre, a section through its centre would be 314 square centimetres, and consequently the ex- ternal pressure holding the two halves toge- ther would be more than 314 kilogrammes. [In other words, they will be pressed together by as many 15 pounds as there are square inches of surface.] Fig. 115. Fig. 114. 138 AIR PUMP. In order to make the contact more perfect, the edges of the hemispheres are rubbed with fat, like the bell before it is placed on the plate ; the cock c, which is open while the pumping goes on, is closed before the united hemispheres are taken off the air pump, and the re-entrance of air is thus prevented. The air pump is used in many experiments. By this means it may be shown that burning bodies are extinguished in a vacuum ; that smoke falls to the ground like a heavy body; that air, as it were, is dissolved in water ; that a layer of air intervenes between fluids and the sides of the vessels in which they are contained, for its presence is manifested by a number of little globules that increase in proportion as the air diminishes. By the aid of an air pump, we may cause cold water to boil. A glass cylinder about one yard in height, and having a 116 diameter of about eight inches, whose upper and lower edges are carefully smoothed, is placed upon the plate of the air pump ; the upper aperture of the cylinder is closed by a metal plate (as exhibited in Fig. 116) hermetically attached to the polished glass edge by being rubbed with fat. Through the middle of this plate, there passes an air-tight metal cone (almost like a cock), that may be turned at will. Two horizon- tally secured rods s revolve with this metal cone. On each of the rods there is a little metal plate t fastened to a rod projecting from the metal plate by means of a horizontal pin, round which it must revolve easily. When the rod s is turned so far from the position indicated in the diagram, that the little plates t are no longer supported, the latter will turn round, throwing off whatever may have been laid upon them. It is better that the two plates t should not turn round simultaneously. We lay then a piece of metal, and a little feather on each plate; and if we let the one plate turn over before we have done pump- ing, the piece of metal will fall much faster than the feather. But when the air is quite exhausted, and the second plate is turned over, the feather will fall as rapidly as the piece of metal. CONDENSING PUMP. 139 The Condensing Pump serves to condense the air. It differs essentially from the air pump, in having valves Fi s- 117 - that open and shut in op- posite directions, as exhi- bited in Fig. 117. When the piston descends, it compresses the air, driving it into a receiver ; when it ascends, the external air opens the valve of the piston, and presses into the cylinder, while the compressed air in the receiver keeps the bottom valve of the cylinder shut. Another depression of the piston re-opens the bottom valve, and closes the piston valve, when a new supply of air is forced into the receiver, &c. Fig. 118. Fig. 119. 140 CONDENSING PUMP. The barometer gauge of the condensing machine is a straight tube, closed at the top and filled with air, having its lower open end plunged in a vessel of mercury. On beginning the experi- ment, the air into the tube is below the pressure of one atmo- sphere, if the levels of the mercury in the tube and the vessel are of equal weight. The more the pressure increases, the higher the mercury rises in the tube. From the height of this column of mercury, and the compression of the air in the tube, it is easy to determine the degree of condensation in the receiver. In this machine, the receiver must be screwed tightly on the plate to prevent its being raised by the compressed air. Condensing pumps have been so contrived as to screw on the apparatus in which air is to be compressed. They have only one cylinder, and one piston without a valve. On the one end of the cylinder, the reservoir is screwed on, in which the air is to be compressed ; on this there is a valve, through which air may enter, but cannot escape from the reservoir. In order to admit fresh air into the cylinder, after a portion has been compressed into the reservoir, the cylinder has either a lateral aperture as in Fig. 118, or a lateral valve like Fig. 119. The latter is particularly appli- cable when we want to compress a special gas, for it is then only necessary to put the glass reservoir in connection with the tube of the lateral valve. The first of these condensing pumps is mainly used for loading air guns, the construction of which will be made clear by the accompanying figures. When by help of the condensing pump, Fig. 120 HERO'S BALL. THE FIRE ENGINE. 141 we have compressed the air in the piston of the air gun to the density of 8 or 10 atmospheres, a barrel is screwed on, along which the ball is directed. If the valve closing the piston be opened by the trigger, a part of the enclosed air will escape with great violence, carrying the ball with it; but the valve closes immediately. A good air gun may give as much speed to a ball as a musket can do. Many shots may be discharged without reloading, the number being in proportion to the size of the piston. Hero's Ball. We can also force fluids out of vessels with great violence by means of compressed air, as is the case with Hero's Ball. A tube passes nearly to the bottom, through the neck of a vessel partially filled with water. The tube termi- nates above in a point with a fine aperture. If the air in the upper part of the vessel have in any way been compressed, the pressure which it exerts on the surface of the water will drive the fluid out of the fine aperture after the manner of a fountain. We may make use of a flask, closed by a cork, through which passes a glass rod drawn out to a fine point. If the glass rod does not penetrate far into the vessel, we obtain, by this arrangement, the dropping bottle with which chemists commonly wash their precipitates. The air in this may be com- pressed by blowing with the mouth through the tube. If the air enclosed in the apparatus be of equal density with the sur- rounding atmosphere, and we place it under the bell of the air pump, it will begin to burst as soon as we have exhausted the air. This apparatus is often constructed in large dimensions en- tirely of metal. In that case, the neck is furnished with a cock, above which the thin tube may be screwed on. The air is compressed by means of a condensing pump screwed on in the place of the pointed tube. When the vessel is charged, we close the cock, remove the pump, and screw on the pointed tube. As soon as the cock is opened, the water rushes out to the height of from 30 to 100 feet, if the air has been compressed to 2, or from 5 to 6 atmospheres. The Fire Engine. Fig. 124 represents the combination of the forcing pump with Hero's Ball ; the cylinders, of which we will consider the one to the right hand, stand in a trough filled with 142 HERO'S FOUNTAIN. Fig. 124. water. If thepiston^/be raised, the valve d rises, and the water presses into the cylinder e. On the descent of the piston, the valve d closes, the valve c is opened, and the water is forced through the narrow tube 6, into the air chamber a. This air chamber is no- thing more than a large Hero's Ball, and the more water is pumped into it, the more is the air in its upper part compressed. The tube h reaches almost to the bottom of the air chamber ; at g a tube with a narrow opening is screwed on. A strong jet of water is driven from the aperture by the pressure constantly exercised upon the water by the air compressed in the chamber. A leather pipe, with a metal spout, may be screwed to an opening in the side of the air chamber near the bottom ; this pipe, also, throws out a jet of water which can be more easily directed, and brought nearer to the burning parts than the stream from the aperture g. The raising and lowering of the piston are managed by a lever, w T hose fulcrum is m. Both rods of the pistons are so attached to this lever, that the one ascends as the other descends, and a fresh supply of water may, therefore, be uninterruptedly conveyed to the air chamber. Hero's Fountain. The most simple mode of constructing Hero's Fountain by means of glass tubes, and a glass-blower's lamp is shown in Fig. 125. The column of water in the tube a com- presses the air in 6 ; the compressed air presses upon the sur- face of the water in c, and consequently the water must gush out MEASUREMENT OF THE PRESSURE OF GASES. 143 at d. According to the same Fi s- 125 - Fi s- 126 - principle, Hero's Fountain in Fig. 126 is composed of glass tubes, glass flasks, and a funnel. It is evident that the vessel c must be supported in some way. When the apparatus is set into action, the vessel c is filled with water, and its neck closed with a cork, through which pass the tubes b and d. Water is then poured into the funnel /, on which the water begins to gush from the tube d. Measurement of the Pressure of Gases. There are two means by which we may measure the pres- sure of gases, viz., by columns of liquids, and by valves. An appa- ratus designed for this purpose is termed a manometer. The baro- meter gauge upon the air pump, and the condensing machine are manometers. Safety tubes belong, in some respects, to mano- meters, for they measure the pressure of the gas in the apparatus to which they are attached. If their tension be equal to the atmospheric pressure, the fluid will stand at the same level in both limbs, (Fig. 127;) if this be not the case, the pressure may be determined in the interior of the enclosed space by the difference of the columns of liquid in the two limbs, provided the density of the liquid in the safety tube be known. These safety tubes were invented by Welter, and are of the greatest utility in many chemical operations, by preventing explosions, as well as the forcing back of enclosed liquids by the air's pressure when absorption takes place. In Figs. 128 and 129 there are two loaded or safety valves re- presented. If the weight be known that will load such a valve, and the size of the surface of the valve which has to support the vertical pressure of the gas, the tension of the gas at the moment Fig. 127. 144 MEASUREMENT OF THE PRESSURE OF GASES. 129- when it is able to raise the valve may be calculated. For instance, if the load- ing of the valve be 100 kilog., and the area of the value 25 square centimetres, each square centimetre of this area will have to bear 4 kilogrammes. As now the pressure of the atmosphere upon each square centimetre amounts to 1,0325, the tension of the gas able to lift this valve will be equal to - - =3,87at- 1,0325 mospheres, to which must be added one atmosphere more, on ac- count of the pressure of the air, borne by the valve besides its other load. This apparatus is applied to liquids as well as gases, and by its means, the boilers, tubes of communication, and the cylinders of the steam engine are proved. ATTRACTION BETWEEN SOLID BODIES. 145 CHAPTER VI. ATTRACTION BETWEEN GASEOUS AND SOLID, AS WELL AS BETWEEN GASEOUS AND LIQUID BODIES. THE following experiments prove most evidently that a con- siderable attraction exists between the particles of solid and gaseous bodies. If we place a piece of glowing char- Fi 130 coal under mercury, and then let it ascend into a cylinder, whose upper part is filled with carbonic acid, shut off by means of the mer- cury from any communication with the exter- nal air, and whose volume is about 20 times greater than that of the charcoal, the carbonic acid will in a few minutes be so condensed by the charcoal, that the mercury will rise to the top of the cylinder. The whole mass of the carbonic acid, which before filled all the upper part of the cylinder, is now condensed by the attraction existing between the gas and the pores of the charcoal, the former having been absorbed. A similar experiment succeeds with many other gases. If the char- coal have lain any length of time in the air, the experiment does not prove quite successful, as we may easily understand, if we reflect that it absorbs atmospheric air and the vapor distributed through the air, and that its capacity for absorbing other gases is consequently diminished. If charcoal that has absorbed gas be brought under the air- pump, or kindled, it will liberate the absorbed gas. Absorption of gases is at all times accompanied by a develop- ment of heat, which is more considerable in proportion to the amount of absorption. In the manufacture of gunpowder, the charcoal is triturated to a very fine powder, which absorbs atmospheric air with such 13 146 ATTRACTION BETWEEN SOLID BODIES. avidity that a considerable degree of heat takes place in the mass, and frequently gives rise to combustion. If a fine jet of hydrogen gas be thrown upon spongy platinum, absorption of the gas follows with such violence as to make the platinum red hot, and inflame the hydrogen gas. On this prin- ciple Dobereiner's lamp is constructed. Absorption is considerably promoted when the solid body is in a finely divided condition, as is the case with charcoal powder and spongy platinum, because of the increased number of points of contact between the solid bodies and the gas, but this finely porous condition is not indispensable to effect a condensation of the gas ; it also occurs if the solid body has a perfectly smooth, or metallic surface ; in this case, however, the condensation is less considerable. If we put a piece of platinum, having a perfectly smooth metallic surface, into a mixture of oxygen and hydrogen, both gases will be so much condensed as gradually to combine and form water. Not only platinum and charcoal, but all solid bodies, exhibit in a greater or less degree this remarkable relation to gases. Every solid body is as it were surrounded by the condensed atmosphere of some gas, which it is often very difficult to separate from it, and which, even if its surface be perfectly freed from it, will again adhere after a time, if the body come into contact with gases. Thus, for example, glass is always surrounded by a coating of condensed air, which, in the construction of barometers, can only be removed by the boiling of the mercury in the tube. If water be poured into a glass flask, and placed over the fire, there is soon seen a number of bubbles forming on the bottom long before the water boils. This is owing to the layer of air, which, from its great condensation, was before imperceptible, but now forms bubbles after its expansion by heat. Similar bubbles appear if the vessel with water be placed under the receiver of the air-pump, and then exhausted. Such gaseous bodies as easily pass over into a fluid condition (vapor) are rendered liquid by their attraction for solid bodies. Thus chloride of calcium attracts the vapor of water with great rapidity, condenses it to water, and at length dissolves in the water. Common salt also attracts the vapor of water from the air, and becomes moist. It is the same with potash and many other bodies. ABSORPTION OF GASES BY LIQUIDS. 147 Bodies that attract the vapor of water from the air are called hydroscopic bodies ; to these belong, besides those we have men- tioned, wood, hair, whalebone, &c. Absorption of gases by liquids. Liquids exhibit a similar rela- tion to gases as that we have just considered in solid bodies. This may be made evident by so far altering the experiment given in Fig. 130, as to substitute ammoniacal gas for carbonic acid, and water for charcoal. The ammoniacal gas is so eagerly absorbed by the water, that all the gas disappears at once, and the tube becomes filled with water. The water absorbs 700 times its volume of ammoniacal gas, and 500 times its volume of muriatic acid gas. The power of absorp- tion of liquids depends upon the temperature and degree of pres- sure. Liquids absorb larger quantities of gas at a low tempera- ture, and under strong pressure, than a high temperature, and under less pressure. Water almost always contains a tolerably large quantity of absorbed air, from which it can only be freed by prolonged boiling. Carbonic acid, amongst other gases, is pretty freely absorbed by water, as, for instance, beer, champagne, and certain mineral waters. 148 REST AND MOTION. SECTION III. OF MOTION AND ACCELERATING FORCES. CHAPTER I. DIFFERENT KINDS OF MOTION. Rest and Motion. A body that changes its position with respect to another is in motion; it is at rest if no such change occur. Every form of rest or motion observed by us is only relative, absolute. The trees are at rest in relation to the neighboring hills ; trees have an unchangeable position on the earth's surface but trees and hills are not on that account in a state of absolute rest ; they with the whole earth on which they stand traverse the vast orbit of our planet. Although we know that we fly throu^ the space of heaven with the earth, as it revolves round the sui we cannot say anything definite respecting our own absolute motion, as we know not whether the sun is an immovable centi of the world. Everything, however, seems to imply that the sui itself is only a planet revolving round another sun, which in it turn is not fixed; but we are not able to determine or even conjecture what the centre of all motion is. There are two essential points regarding motion that we mus consider, viz., direction and velocity. If a body move continually in one direction, its course is in a straight line ; but if the direc tion of its motion constantly change, its motion is curvilinear. If we draw a tangent to the curve at a point of the curve occu- pied by the body at any given instant, this tangent will show the direction of the motion of the body at that moment. Uniform motion. A body has a uniform motion if it pas over equal spaces in equal times. If a body moving in a straight UNIFORM MOTION. 149 line, advance equally far, sixty feet for instance, in each minute, thirty feet in every half minute, and one foot in every second, it moves uniformly. As the spaces traversed in equal times are equal, it follows that the relation between time and space remains constant. This relation we term the velocity of uniform motion. If we take double or triple the time, the space traversed will be doubled and tripled ; and the relation consequently remains the same. The number expressing the velocity depends upon the units chosen for space and time. If we were only to express the velocity by a number, without giving the units employed, the velocity would then be wholly undefined. The simplest mode of expressing velocity is by giving the space traversed by the body in a unit of time, as a minute or a second. Thus, for instance, a man walks, as a general rule, with the velocity of 2.5 feet in a second. An ordinary wind has a velocity of 3.28 feet in the second; a hurricane 118.08 in a second. [The following table from the Ann. de Bureau des Longitudes, 1828, gives the rapidity of the motion of the air per second in different winds. 1.64 feet . . . Scarcely perceptible wind. 3.28 "... Sensible breeze. 6.56 "... Moderate wind. 18.04 "... Brisk " 32.80 " . . . Strong " 65.60 "... Violent " 73.80 "... Tempest. 88.56 "... Violent tempest. 118.08 "... Hurricane. 147.60 "... Violent hurricane.] These two last named velocities admit of comparison, as they are expressed in the same units ; thus the velocity of the hurri- cane is 45 times as great as that of an ordinary wind. If we would compare the speed of a man with the velocity of an hurri- cane, we must first reduce both to a like unit. As matter is inert, a body once having a uniform motion would continue to move in the same direction, and with the same velocity, unless a second force were to act upon it, changing its direction alone, or its velo- city alone, or both ; for by itself a body can change nothing in this respect, either with regard to its conditions of rest or motion. Thus we are to understand the law of inertia, and not as the 13* 150 ACCELERATED AND RETARDED MOTION. older philosophers, who maintained, that matter had a prevailing tendency to rest. If we see that the motion of a body be in any way changed, if, for instance, its velocity increases or diminishes, its motion ceases, or changes its direction, then must this change always be occasioned by some external cause. A stone thrown towards the sun would continue its course till it reached the sun, were it not prevented by the resistance of the air, and by the force of gravity drawing it back to the earth. Accelerated and retarded motion. A constant change of velo- city can only be effected by a constantly acting force, termed accelerating or retarding, according as it augments or diminishes motion. If at any moment of the varying motion, all the accele- rating or retarding forces were to cease to act, the motion would become uniform from that moment. The velocity of a varying motion in a given moment is determined by computing how far the body would move in the unit of time, if all acceleration and retardation were to cease from the said moment. A motion is termed uniformly accelerated, or uniformly retarded if the velocity increase or diminish equally in equal times. Such motions are produced by forces acting continually with the same intensity as is the case with gravity. A heavy body falls with an uniformly accelerated velocity. If we set out with the supposi- tion that the intensity of gravity is the same at the different places traversed by the falling body, (and experience justifies us in this assumption at least within certain limitations,) all laws of freely falling bodies may be developed by a simple mode of reasoning. As gravity acts in the same manner at every moment of a fall, the velocity of the falling body must also increase equally, on equal terms, that is, the motion must be a uniformly accelerated one. If the falling body attain, in the first second of its descent, a velocity g, it must after 2, 3, 4 ... t seconds have attained to a velocity of 2g, 3g, 4g . . . t . g-, which may be thus generally expressed in words : the velocity of a freely falling body is always proportionate to the time elapsed during its fall: or it is v=g.t if v represent the velocity acquired by the body during its fall in t seconds, and g its velocity at the end of the first second. What space will, therefore, the body fall through in 1, 2, 3, 4 .... seconds? At the beginning of the first second, its velocity is equal to o; at the end of the same, it is g. As now the ACCELERATED AND RETARDED MOTION. 151 velocity increases uniformly, the space fallen through in one second must clearly be the same as if the body were during one second moved by a velocity ranging half way between the beginning and ending velocity ; that is between o and g. But this medium velocity is ^g, and a body falling during one second with a velocity of J g, passes over a space J g. In the same manner, we may find by deduction, the space passed through by a body falling during two seconds. The starting velo- city is o ; the closing velocity 2g; the medium velocity is conse- quently i. and a body moving during two seconds with this velocity, passes through a space equal to 2.2? . In three seconds the body passes through a space equal to 3.3 ? 9 for the starting velocity is 0, the closing velocity 3 g, and the medium velocity is consequently equal to 3 ?. ; and a body must & move uniformly with this velocity during three seconds, if it tra- verse the same space through which a heavy body will fall in the same time. We will express this generally: If a body fall during t seconds, it must traverse a space equal to what it would have done during the same time with a uniform motion, if its velocity cr were a medium between o and g . t, that is ^ . t. But a body mov- er ing t seconds with a velocity equal to 5 t traverses a space or, expressed verbally : the spaces described are proportional to the squares of the times. Experiment, however, can alone prove whether these premises be correct, and whether gravity actually be a uniformly accele- rating force. This question cannot be directly solved, since the velocity with which bodies fall, augments so rapidly, that after the first few moments it becomes impossible to determine accurately the spaces passed through in given times. But although we cannot find this by direct experiment, we may arrive at the result by indirect means. The most simple method is Galileo"* s inclined 152 GALILEO'S INCLINED PLANE. plane; but the one possessed of the greatest degree of accuracy is Jitwooffs falling machine. Galileo's Inclined Plane. -Galileo studied the laws of descent by rolling easily moving bodies down an inclined plane. To fol- low his experiments, it is best to make use of a canal of wood, about 10 or 12 feet in length (Fig. 131), polished as smoothly as pos- Fig. 131. sible in the interior, and divided into feet and inches. The canal must be inclined by being supported at one end. If it were placed perfectly horizontally, a ball laid upon it would re- main at rest, owing to its gravity being entirely counterpoised by the resistance of its horizontal support. If the canal were placed vertically, the ball would fall freely with the whole force of its gravity; but if the body be inclined, the force of gravity will be diminished in a certain fixed relation. It follows from the prin- ciples of statics, that we obtain the amount of accelerating force urging the ball down the inclined plane, if we multiply the accelerating force of gravity with the sine of the angle of inclina- tion of the plane. Whatever may be the relation in which a force is diminished, whether it be reduced to the half, the third, or the fourth part of its original amount, the absolute amount of the mo- tion produced will alone be changed, while the relations of the spaces traversed in given times will remain the same. The laws derived from experiments with the inclined plane, are therefore the true laws of gravity. If we slip a ball at a definite moment from the upper end of the canal, and note the spaces traversed in 1, 2, 3, seconds, we shall find that the spaces are as the squares of the time necessary to traverse those spaces. Gravity is, there- fore, really a uniformly accelerating force. Jltwootfs Falling Machine consists essentially of a pulley revolving round a horizontal axis, and fastened to the top of a vertical column, about 7 feet in height (Fig. 132). A string is slung over the pulley having equal weights m at its extremities. If we attach an extra weight n on the one side, equilibrium will be disturbed; the weights m and n will sink on one side, and the weight m on the other \vill be raised up. The velocity with which this takes place is much less considerable than in a free ATWOOD'S FALLING MACHINE. 153 Fig. 132. fall, because the moving force, the force of gravity of the extra weight n, has not only to set in mo- tion the mass m, but also the mass 2 m + n. If, for example, each of the weights m were 7 oz., but n 1 oz. only, the extra weight of 1 oz. would have to put a mass of 15 oz. in motion; the motion will follow the same laws, as in a free fall, with this difference only, that the intensity of the accele- rating force is here 15 times smaller. If, therefore, a freely falling body traverse 15 feet of space during the first second, the space traversed in this case, in the first second, will be only 1 foot. It is easy to see that the motion will be slower, the smaller the extra weight n is in relation to mj and we may, therefore, by proper alterations in Uj make the motion as slow as we choose. The vertical column has been di- vided into feet, for the greater con- venience of measuring the spaces of falling. The upper point is the zero of the scale. Two slides, one of which is perforated, can be secured to any part of the scale. It is necessary to know thus much of the apparatus in order to understand the experiments. In the first place, it is easy to prove, by means of this machine, that the space is as the square of the time of falling. Let n be so chosen that the descent in the first second is 1 inch. If the lower end of the weight m, carrying the extra weight, be at the zero point of the scale, the weight will be at the first mark below zero, in the course of one second from the time of the commencement of motion. If the space traversed during the first second of falling be 1 inch, it must be 4 inches during the two first seconds ; if, there- fore, we move the slide to 4 inches below zero, the weight that 154 ATWOOD'S FALLING MACHINE. began its motion at the point zero, will strike at the end of two seconds. If we let the motion always begin from the same point of the scale, viz., from zero, the slide must be fixed at 9, 16, 25, 36, 49, 64 inches below that point, if the weight is to strike in 3, 4, 5, 6, 7, 8 seconds. This experiment fully confirms the law, that the spaces traversed in falling are as the squares of the time of falling. We have shown above, that this law follows from the assump- tion that the velocity is proportionate to the time of falling. The truth of the inference proves also indirectly the correctness of the assumption. The relation existing between the time of falling and the velocity of the body at any given moment, cannot be directly ascertained either in a free descent, or by means of the inclined plane, since, in order to obtain this result, it would be necessary that the velocity of the body should not increase from that moment ; consequently we must be able suddenly to destroy the action of gravity on the body. By means of the falling- machine, we may arrest the accelerating force at any moment. The accelerating force is only the gravity of the extra weight n ; if, now, we give to the excess of weight n, the form represented at Fi 133 ^S' 1^> we ma y arres * ft by means of the perforated rm . slide at any moment, while the mass m continues to 'Ka)^ 1 progress with uniform velocity from the time it ceased to be acted upon by an accelerating force. We may, therefore, by help of this contrivance, determine directly the velocity at any one moment by the space traversed in the next second. We have seen that if g be the velocity of the body at the end of the first second of falling, the space traversed in the same period of time will be ^ g. If, now, we have so arranged, that 1 inch is traversed in the first second, the closing velocity of the first second will be 2 inches ; that is, if at the close of the first second the accelerating force cease to act, the body will traverse in the next second a space of 2 inches with uniform velocity. It is easy to demonstrate that this relation actually exists be- tween the time and velocity of falling. Let us, for instance, so place the weights m + n before motion begins, that the under surface of n may stand at zero upon the scale ; the perforated slide must also be so arranged that its upper surface stand at 1 inch, and the lower slide so that its upper surface may be as much ATWOOD'S FALLING MACHINE. 155 below the mark, 3 inches, as the height of the weight m requires. If, now, we start the weights at a definite moment, the extra weight will strike in 1 second, and the weight m in 2 seconds. The upper point of the weight m has, therefore, traversed the space from zero to 1 with accelerated velocity in the first second, and has passed in the next second from 1 to 3 with a uniform degree of velocity. That the velocity is really uniform after the removal of the extra weight, we see from this, that if, without altering anything else, we lower the slide 2, 4, 6, 8, or 10 inches, the contact occurs 1, 2, 3, 4 or 5 seconds later; consequently that a space of 2 inches is t traversed in every succeeding second. If we had so arranged the extra weight n that 2, 3, 4, 5, &c., I inches were traversed in the first second, a space of 4, 6, 8, 10, I &c., inches would be passed over, provided we removed the extra [ weight at the end of the first second. We have assumed above that if the velocity be g at the end of the first second, the closing velocity in 2, 3, 4 seconds will be 2 g, 3 #? 4 g. Experiment fully confirms this. If we again assume that the extra weight n be so arranged, that in the first second 1 inch will be traversed, and consequently in the next two seconds, 4 inches, there will be a space of 4 inches passed over in each succeeding second, provided we take off the extra weight at the close of two seconds ; if we did not take off the extra weight before the close of the 3d and 4th second, that is, when a space of 9 or 16 inches had been passed over, the motion would continue from that time with a uniform velocity of 6 or 8 inches. In a free fall the value of g may be taken at somewhat more than 30 feet. When we come to speak of the pendulum, we will ive a more accurate estimate of its value. In a free fall, there- fore, according to the above proved laws, the space passed over in the first second of falling must be about 15 Paris feet,* while in 2, 3, or 4 seconds, it must amount to 60, 135, 240, &c. Galileo himself made experiments regarding the free descent of bodies, which were subsequently repeated by Riccioli and Grimaldi from the Tower Degli Asinelli in Bologna; Dechalles has, however, made the most accurate experiments on the subject. The observed spaces through which bodies fall are always smaller * A Paris foot is 1.066 ft. English. 156 ATWOOD'S FALLING MACHINE. than we might be led to expect from theory. This difference depends, however, solely upon the resistance of the air, which increases as the square of the velocity. In the falling machine, and the falling-canal, the resistance of the air does not influence the results. It is frequently important to be able to compute directly the velocity corresponding to given heights of descent. A formula, according to which this calculation may be made, is obtained from the following equations : v=g,t and s = t 2 . By the elimina- tion of t we find that The velocities are, therefore, as the square roots of the spaces. If, for instance, a body had fallen from a height of 100 feet, its velocity would be, according to this formula, as follows: v = v/2.30.ioo = 77,4 . . feet (without taking into account the resist- ance of the air). When a body is projected by any force vertically upwards, it ascends with decreasing velocity ; after a time its upward motion ceases, and it then begins to fall. The laws of this motion follow immediately from the foregoing. Suppose a body to be thrown upward with a velocity of 150 feet, it would ascend 150 feet in every second, provided gravity exercised no influence upon it. But as gravity imparts to a falling body in 1,2, 3, 4, 5 seconds, a velocity of 30, 60, 90, 120, 150 feet, opposed to the direction of the upward motion, it is evident that the velocity of the ascending body is at the end of the 1st second 150 30 = 120 feet ; at the close of 2 seconds this velocity is 150 60 = 90 feet ; at the close of 3 seconds 150 90 = 60 feet ; in 4 seconds 150 120 = 30 feet; and finally at the end of the 5th second 150150 = 0; and now consequently the body begins to fall. We have here an illustration of a uniformly retarded motion, for the velocity of the ascending body diminishes about the same in every second, viz., about 30 feet. Let us put this in general terms. If n be the velocity at the beginning of the ascent, the velocity of the body will after t seconds be v = n g't. The body ceases to ascend, when n = g t, that is, when the ATWOOD'S FALLING MACHINE. 157 velocity acquired in falling during t seconds is equal to the velo- city with which the body began to ascend. The time required by the body to reach the highest point of its course, is f-5. 8 Let us now endeavor to ascertain the height attained by an ascending body in a given time. According to the above given illustration, the body would have attained a height of 150, 300, 450, &c., feet, in 1, 2, 3, &c., seconds, provided gravity had not drawn it down. But as we have seen, gravity draws it down 15 feet in 1 second; 4 . 15 = 60 feet in 2 seconds; and 9 . 15 = 135 feet in 3 seconds. The height at the end of 1 second is, therefore, 150 15 = 135 feet; at the end of 2 and 3 seconds, 300 60 = 240 feet, and 450 135 = 315 feet. In 5 seconds it would have reached a height of 750 feet, but being drawn down 15 X 5 2 = 375 feet by the force of gravity, it is actually at an elevation of 750 375 = 375 feet, and now begins again to fall. Let us consider this more generally. In t seconds the body would ascend to the height n t, owing to its original velocity n ; but having been drawn down ^ t 2 by gravity, its actual height is h = nt 2 f t 2 . A The body ascends as long as n t is greater than ? t 2 . As the highest point of its course is attained when t = -, we g find the elevation of the body at this moment, if in the above given formula for h, we substitute this value in place of ; we then have T n 2 g n 2 _n 2 n 2 n 2 ~g ~2g~*~g '~2g~2g' But in - seconds a body, falling free, traverses a space o g n 2 n 2 2 ? ~ %' Hence it follows that the body requires exactly as much time to fall as to rise. 14 158 PROJECTILES. CENTRAL MOTION. Let us seek the velocity with which the falling body regains the point from whence it began its ascending motion. We shall find it from the formula v = g tj but as the time of falling t = - o it follows that v n 9 that is, the body comes down with the same velocity with which it began to rise; or, in order to impel a body vertically to a height h, we must impart to it an initial velocity exactly as great as that acquired by it, in its free fall from the height h. Projectiles. If a body be thrown in any other than a vertical direction, it will describe a curved line, the form of which may be easily deduced from the laws of falling. Let us assume the simplest case, for instance, that the body be impelled by any force in a horizontal direction. If there were no such force as gravity, the body would continually move in a hori- zontal direction, and with an uniform velocity. By reason of the first impelling force, it would traverse the space a b in 1 second, the equally large space b c in 2 seconds, and so on, and must conse- quently, at the end of the 1st, 2d, 3d, &c., second, have reached the points 6, c, d, &c. But it has sunk from the force of gravity; in the first second it fell 15 feet, consequently at the end of that time instead of being at 6, it will be 15 feet below it. At the end of the next second, it is 60 feet below c; at the end of the third, 135 feet below d, &c. The curved line described by the body, in this manner, is a parabola. If an impulse be given in any other direction, the course de- scribed may in like manner be obtained by construction. The course described by a projected body varies, in consequence of the resistance of the air, from a true parabola. Central Motion. We must now consider motions produced by gravity, where the directions of the force of gravitation in various points of the course are no longer parallel. Motions such as these are observed in the revolution of the moon round the earth, and of the planets round the sun. CENTRAL MOTION. 159 If we suppose the point a (Fig. 135), to have received an im- pulse in the direction a b from any momen- tarily acting force at the beginning of its course, while it is driven towards the point m by a constantly acting force of attraction, it will neither move in the directions a b nor a c, but in another direction a d, which may be ascertained by the law of the parallelo- gram of forces. In order to make the con- sideration more simple, we will assume that the constantly attracting force directed towards m, acts by im- pulses at short intervals, and this will be found the more nearly to approach the truth, the smaller we imagine these intervals to be. If the laterally directed impulse alone would drive the ma- terial point in a short space of time t from a to b, and the attract- ing force, acting alone, would urge it in the same time to c, it would move under the influence of both forces in the instant of time t, from a to d. Arrived at c?, it would move further in the direc- tion de, and in the time t, the space de would be exactly as great as a d, if the attracting force did not act again in such a manner, as if the body had received an impulse in d, which, acting alone, would have led it in the time t from d iof. By this second action of the attracting force, the body is again turned from the direction d e, and urged to g. From this we can easily understand, that if the body have re- ceived at a a laterally directed impulse, while the attracting force acts at small intervals, it must describe a polygon, which ap- proaches more nearly to a curved line in proportion to the small- ness of the intervals. When the attracting force constantly acts, as it does in nature, the course will truly be a curved line, the nature of which will depend upon the relation of the influencing forces. The force that constantly urges a body towards a central point of attraction, is designated the centripetal force. If, at any mo- ment, the centripetal force were to cease acting, the body would from that instant continue to move in the direction of a tangent, and the force thus acting is named the tangential force. The figure described by the course of a body will be a circle, an ellipsis, &c., according to the relation between the tangential and centripetal forces. 160 CENTRAL MOTION. Fig. 136. Let us seek to determine the amount of the centripetal force, that urges the moon in its motion round the earth towards the central point of the latter. The earth's circumference is 40 mil- lions of metres (24,880 miles); but as the radius of the moon's orbit is equal to 60 radii of the earth (237,600 miles), the circum- ference of the moon's orbit is 2400 millions of metres (1,493,485 miles). This course it traverses in 27 days, 7 hours, 43 minutes, or, what is the same thing, in 39,343 minutes. In every minute, therefore, the moon passes over a space of ?12P> OQO ' QQO =6 1,000 39,343 metres (66,810 yds.). Fig 136 represents the arc a b of 61,000 metres, traversed by the moon in one mi- nute ; a c is, therefore, the amount of space through which the moon would approach the earth in one minute by the force of gravity, if the action of the tangential force were suddenly destroyed. We may compute the magnitude of the distance a c, by assuming that the arc a b is a straight line, from which it actually deviates but slightly ; a b n is then a right angled triangle, b c is a perpendicular let fall from the right angle upon the hypo- thenuse; and, under such circumstances, in accordance with a known proposition of geometry, a b is a mean proportional be- tween a c and a n\ consequently and hence ab* a c an Now we have seen that a 6=61,000 ra ; but a n, the radius of the moon's orbit, is 763,950,000 m . If we put this value in the place of a b and an into the last equation, we have a c =4,87 , that is, we find the attraction of the moon towards the earth amounts to 4,87 metres in a minute. But what is the force producing this action? Is it the same force that makes the stone fall to the earth? If we assume that the force of gravity observed upon the surface of the earth, extends CENTRAL MOTION. 161 its influence beyond our atmosphere, acting even on the moon, we can easily comprehend that its intensity must diminish with the distance from the earth. By a simple mode of deduction, which we shall consider more attentively when we treat of light, we find that the intensity of all actions emanating from one point stands in an inverse relation to the squares of the distance. Con- sequently, at double, triple, quadruple the distance from the earth's centre, the intensity of the force of gravity will be dimin- ished 4, 9, 16 times. At the moon it is, therefore, 60 2 or 3600 times weaker than at the surface of the earth, because the moon is removed 60 times farther from the earth's centre. If, according to this, the space fallen through in the first second on the earth's surface were 4,9 metres, the space fallen through by the moon towards the earth in 4 9 one second would be metres, and consequently in a minute, 60 2 4 9 that is sixty seconds, it would be -^-. 60 2 = 4,9 metres. That is the space by which the moon approaches the earth in one minute must be as great as the space fallen through in the first second of fall upon the earth's surface. If we compare the space, viz., 4,9 metres, calculated for the fall of the moon towards the earth in a minute, with the 4,87 metres deduced from astronomical observations, we shall really only find a very small difference, which would wholly disappear if we had not, for the sake of the simpler computation, taken only approximating values into consideration. Thus we have entirely neglected the seconds in giving the time of the moon's revolution, and have assumed the distance of the moon from the earth to be equal to 60, although it really is 60,16 radii of the earth. In this manner the motion of the planets round the sun may also be explained, and it is thus one and the same force that urges the stone to the earth, and, acting through the whole space of the hea- vens, maintains the harmony of our planetary system. For the knowledge of this vast law of general gravity, we are indebted to the penetration and the unwearying industry of Newton. Had he done nothing more, this single discovery would have sufficed to immortalize his name. In the same manner in which we have developed the amount of the centripetal force in the motion of the moon, we may also 14* 162 CENTRAL MOTION. obtain a general expression for these forces. Let us assume, as a measure of the centripetal force, the space a c, through which the body in its central motion, in a unit of time, will be urged towards the centre of attraction, and let us designate it by p\ then, as has T o been already proved, p = . Now the arc a & is that which the an body actually describes in the unit of time, therefore, a b = -, If if r be the radius of the spherical orbit, and t designate the time of revolution. Further, an is the diameter of this orbit, and conse- quently equals 2r. If we substitute these values of a b and a n in the above equation, we find that n = t* That is to say: if two bodies move in different orbits, and with different times of revolution, the centripetal forces will be as the radius of the circles described) and inversely as the squares of the times of revolution. If a small sphere, which we must suppose devoid of weight, be fastened to the end of a string at m, and turned round the point c, so that it describes a circle round the centre c, the string will constantly have to sustain ..''" \ a tension increasing with the speed of the revolution. If, at any moment, the string were severed, the ball, instead of moving on in a circle, would by reason of its inertia fly off at a tangent from its former path. The cause of the tension sustained by the string is designated centrifugal force. But as the resistance of the string produces the same effect as the centripetal force considered under the head of central motion, it is clear that the centrifugal force is equal, and opposed to the centripetal force, and that all that has been said of the latter applies equally to the former, that is, that the centrifugal force increases in the ratio of the radius of the orbit, and inversely to the square of the period of revolution. As a matter of course the tension of the string, and consequently the centrifugal force, must be proportional to the revolving mass. Centrifugal force prevails wherever there is a rotation round a fixed axis, and the separate particles are prevented in any way OF THE PENDULUM. 163 deviating from this axis. Such a centrifugal force must, therefore, be occasioned by the rotation of the earth round its axis. As the time of rotation is the same for all points of the earth, while the different points are not equi-distant from the axis of rotation, it is clear that this centrifugal force is not equal upon the earth's sur- face, but must be as the distances from the earth's axis ; conse- quently, it is at its minimum at the poles, and at its maximum at the equator. This centrifugal force which is greatest at the equator, and diminishes as it approaches the poles, acts against gravity, and lessens its intensity. We may easily compute the amount of velocity with which the earth must rotate on its axis, in order that the centrifugal force engendered at the equator may fully counter- act the effect of gravity. The .apparatus represented at Fig. 138, is particularly well cal- culated for experiments con- cerning the centrifugal force. We will, however, limit our- selves to one experiment, explaining the flattening of the earth at the poles. By help of the handle m, the horizontal disc below it is made to revolve. The rotation of the disc is trans- mitted by the thread d to another disc of a smaller radius. It will of course be evident that the smaller disc must make more revolutions than the larger one in the same period of time, these bearing the same relation to each other as the radii of the two discs. The vertical axis c, fastened in the middle of the smaller disc, turns with it. A spring a b fastened by its lower end to the axis, but admitting of its other extremity being freely moved up and down, and which in a state of rest forms a spherical figure, will by rapid revolution assume an elliptical form, owing to the centrifugal force acting with the greatest intensity upon those points of the spring that are the furthest removed from the axis. Of the Pendulum. The common pendulum consists of a heavy ball suspended to the end of a flexible thread. If we disturb the equilibrium of the pendulum, that is if we remove it from its 164 LAWS OF THE OSCILLATIONS OF THE PENDULUM. vertical position, it will, when left to itself and without receiving any impulse, continue to oscillate in a Fig. 139. ., i i rr- i ,n f . vertical plane. If we bring the pen- dulum into the position f a, the ball will describe an arc a I, reaching / with such velocity as to be carried forward as high as b on the other side, that is to say to the elevation of the point a ; from 6, the pendulum again traverses in a reversed direction the arc b I , and in this manner continues its oscil- lations. The velocity of the pendulum constantly increases with its descent and diminishes with its ascent ; at the moment, therefore, in which the pendulum passes the point of equilibrium it has attained its greatest velocity. The motion from a to 6, or from b to a is termed an oscillation, from a to / is a semi-descending oscillation, from / to b a semi- ascending oscillation. The amplitude of an oscillation, is the magnitude of the arc a b expressed in degrees, minutes, and seconds. The time of an oscillation is the time necessary for the pendu- lum to traverse this arc. At the first glance we might conclude from this experiment that the motions of a pendulum must always continue, for if starting from a it be borne up to an equal height b on the other side, it must, starting from b, also ascend to #, and thus continue the same course, a second, third, and fourth time, and thus on to eternity. This deduction would be perfectly correct, if b were absolutely at an equal elevation with a ; but the friction at the point of sus- pension/, and the resistance of the air that must be displaced by the ball, hinder the latter from ascending exactly to the same height from which it descended. This difference becomes only appreciable after a series of oscillations, and instead of wondering that the motion does not continue for ever, we ought rather to be surprised that it lasts so long, for a pendulum can go on oscillat- ing for hours together. Laws of the Oscillations of the Pendulum. The laws of the oscillations of simple pendulums, are as follows : LAWS OF THE OSCILLATIONS OF THE PENDULUM. 165 1. The duration of the oscillation is independent of the weight of the ball and the nature of its substance. To prove this, we must construct several pendulums of equal length, the ball of one being of metal, of another wax, of a third wood, &c., and we shall then find that all have equal durations of oscillation. When gravity makes a pendulum oscillate, it acts upon every atom of the matter composing the ball; each atom of the ball is acted upon by its own gravity, and consequently an increase of the atoms can have no influence on the velocity of the oscillations. If we could suspend a single atom of iron to a thread devoid of weight, it must oscillate just as fast as if we attached to it two or three atoms, or even a ball of iron. Gravity, however, might act otherwise upon a molecule of wax than upon a molecule of iron. That it does not do so, that gravity acts alike on a molecule of gold, platinum, wax, iron, &c., is proved by the experiment with the pendulum. The already mentioned experiment on falling in a vacuum is but a rough illustration of the fact, as we have only to observe the action of gravity during an extremely short period of time. The pendulum, however, enables us to watch the in- fluence of gravity upon different bodies during many hours toge- ther. 2. The duration of small oscillations of the same pendulum is independent of their magnitude. If, for example, a pendulum vibrates 4 5, the duration of the oscillation is the same as if it vibrated only 1. This law may be thus developed. If the angle of deviation be not too large, the inclination of the course towards the horizon will be pro- portionate to the distance from the point of equilibrium. If we suppose a tangent drawn at c to the arc of the circle, it will form an angle with the horizon twice as great as the angle made with the horizon by the tangent at c', provided the arc c' a be half as great as the arc c a. If, therefore, the pendulum begin its motion at c, the accelerating force is twice as great as when it begins its descent 166 LAWS OF THE OSCILLATIONS OF THE PENDULUM. from c'; the arc c d which we will assume to be so small that ill may be considered a straight line, and the arc c f d' only half the I size, will, therefore, be traversed in an equal period of time, i I motion begin at one time in c, and at another in c'. If we suppose two equal pendulums suspended to an axis, the'i one raised to c, the other to c', and both going off simultaneously. ; they will reach the points d, and d f at the same time. But the accelerating force at d is twice as great as that at d f , besides which, the pendulum reaches a point d with twice as great a velocity as that with which the other passes the point d', and hence it follows, that also in the next short interval of time, the one pendulum will have traversed twice as much space as the other. By pursuing this mode of deduction', we at last find that both pendulums must arrive simultaneously at a. This reasoning may also be applied if the relation of the angle of deviation be not exactly between 1 2, since the accelerating force is always proportionate to the distance from the position of equilibrium for small angles of deviation ; and thus it may gene- rally be proved, that within certain limits the deviation of the oscillation is independent of the magnitude of the angle of devia- tion. In order to confirm this law by experiment, we must accurately determine the time necessary for a pendulum to make several hundred oscillations. If this observation be made at the beginning of the motion, when the amplitude is 4 5, subsequently when it only amounts to 2 3 G ; and lastly when the oscillations have become so small as to require the aid of the lens for detecting them, we shall find that the oscillations are truly isochronous at these three stages. 3. The durations of the oscillations of two pendulums of un- equal length are as the square roots of the lengths of the pen- dulums. We must suppose the arc a b described by the oscillation of a pendulum to be divided into so many parts that each division may be considered as a straight line. If now the angle of deviation of a longer pendulum is equally large, the arc of oscillation c d must be to the arc of oscillation a b as the lengths of the pendulums to each other. If we suppose the arc d c to be divided in an equal number of parts as the arc a 6, these separate parts will be to each LAWS OF THE OSCILLATIONS OF THE PENDULUM. 167 other as the lengths of the pendulums. If, Fi s- 14L therefore, one pendulum be four times longer than the other, the subdivisions of the arc d c will also be four times larger than those cor- responding divisions of the arc a b. The angles made with the horizon by the first, second, and third divisions of the arc a 6, are equal to the angles made with the horizon by the first, second, and third divisions of the arc c c?; the accelerating force is, therefore, also the same on the corresponding parts of a b and c d. But if different spaces be traversed with equal accelerating forces, we know from the formula s = t 2 , that the times of falling are as the square roots of the spaces; if, therefore, each of the parts of c d were two, three, or four times as large as the cor- responding divisions of a 6, the time in which a division of c d will be traversed, must also be \/2, >/3, \/4, \/n times as long as the period occupied in traversing the corresponding portions of a b. But as this is true of all the parts, so it is also true of their sums, or, in other words, the duration of the oscillation is propor- tionate to the square root of the length of the pendulum. In order to confirm the accuracy of this third law by experi- ment, we will take three pendulums of different lengths. If, for instance, the lengths are as the numbers 1, 4, 9, the corresponding times of oscillation will be as the numbers 1, 2, 3. The most convenient mode of exemplifying this, is by attaching the balls to a double thread as seen in the accompanying figure. While a pendulum four feet in length makes one oscillation, the pendulum which is four times smaller than the former makes two oscillations, and whilst a pendulum, one foot in length moves three times backwards and forwards, another, nine feet long, will only make one backward and forward motion. The length of a simple pendulum oscillating seconds, is 994 millimetres ; if, therefore, the length of a second's pendulum had been taken as the unit of length, it would have deviated but little from the metre. Fig. 142. 168 QUANTITY OF MOTION. Quantity of Motion. Most forces that set bodies in motion act only directly upon a small portion of the molecules composing the body. In striking a billiard-ball we only touch a few points of the surface. If the wind drive a ship, it only presses upon the sails, and when a ball is discharged by powder, the gases which give the impulse on being liberated, press only upon half the surface of the ball. Notwithstanding this, all parts of the body move, whether they be directly acted upon or not. Motion must, therefore, be uniformly distributed to all the molecules, as all move simultaneously. The molecules directly struck, impart an impulse to those nearest them, and so on, until the whole mass is set in motion. A certain, although inappreciably small portion of time is necessary for the transmission of motion from one mole- cule to the whole mass. If a force act upon a body, it will have produced its effect as soon as motion has been distributed to all portions of the mass, and these latter move with a common velocity, the force being then transferred, as it were, to the body, and diffused through it. If, therefore, a body be projected by the hand, by the release of a spring, by a quick push, or by means of a sudden explosion, it will continue to move on after the force has ceased to act upon it. If nothing were to oppose it in its course, neither air, water, nor any other body, and if no force whatever were acting upon it, it would move in the direction of the first impulse with uniform velocity after a hundred years in the same manner that it did after the first second. We may say that the activity of such a body is momentary, while its effect lasts for ever. Thus the body to a certain extent absorbs the force acting upon it, and we can, therefore, easily understand how the same force acting upon different bodies must call forth very different motions. A quantity of powder, sufficient to discharge a musket-ball, would scarcely raise a bomb; while a bow capable of sending a light arrow to a great distance, would not be able to send off a heavy one with as much speed. We say commonly that the gravity of the body gives rise to this difference, but this is an incorrect assertion, since we might be erroneously led to conclude that if a body were to cease to be heavy, the same force would move all bodies with equal velocity. Let us suppose, for a mo- ment, that bodies are without gravity, and assume that there is QUANTITY OF MOTION. 169 no air present, or other hinderance of motion ; the musket ball would still be urged on faster than the bomb, because the same force must produce a degree of speed, smaller in proportion as the mass of matter to be moved increases in size. It is one of the fundamental principles of machines, that the same force, acting upon different bodies, imparts to them a velocity inversely propor- tionate to their masses ; that is to say, in an inverse ratio to the quantities of matter composing them. If, therefore, the same force discharged in succession leaden balls, whose volumes, and like- wise whose masses were as the numbers 1, 2, 3, 4, &c., it would impart to them the velocities 1, J, J, J, &c., so that a mass ten times larger would only have T Vth the velocity. On multiplying each of these masses with its velocity, we always obtain the same product for the first 1 X 1 = 1 for the second 2 X J = 1, &c. The quantity thus obtained by multiplying a body by its velocity is termed quantity of motion. The same force also produces always the same quantity of motion on whatever body it acts. In order to obtain a clear idea of the mode of action of various machines, we must compare the quantity of motion, which the applied force is capable of producing, with the effect obtained by means of the machine. It would be a vulgar error to regard a machine as a source of force, or to believe that the quantity of motion could be increased by machinery. By machines the nature of the motion is simply changed, without its quantity being in the least increased thereby. A weight of twenty-five pounds may be easily lifted two feet and a half in a second, by means of a rope swung round a simple pulley. But if the rope, pulled by the workman, were passed round a wheel (Fig. 143), and the load attached to an axle of four times smaller diameter, a fourfold larger weight might be raised by an equal application of force, although with a speed four times smaller. If we ex- amine the mode of action of other machines, as the screw, the pulleys of various wheel works, we shall always attain to the same results, viz., that what we gain on the one side in force, 15 170 THE MATERIAL rENDULTM. Ave lose on the other in speed, and that consequently the quantity of motion is not at all increased by machines. If a body in motion come into contact with another at rest, but which is easily moved, it will impart to the latter a portion of its motion; but the total quantity of motion is not thereby altered; and if the striking body rebound in consequence of elasticity, and the impulse were centrally applied, both bodies will move on in the same direction after coming into contact. If the mass of the body at rest be equal to that of the one striking it, the speed of motion will be diminished to the half after contact, as the mass has been doubled. From this we may easily see that, in order to find the relation of the speed before contact to that of the speed subsequently manifested, we have only to divide the mass of the body moved by the sums of the masses of the body moved and the body at rest. If, for instance, a musket ball of ?V Ib. wr strike, with a speed of 1300 feet in a second, a ball of 48 Ibs. at rest, but easily movable and suspended to a long line, the com- mon speed after the blow would be to 1300 as V is to 48 -f ^V* 1 '300 or as 1 to 961 ; that is, it would be only about - or about 1 J feet in a second. If a similar musket ball were to strike against a large block of stone or a rock, it would also impart a motion to it, but the speed would be very inconsiderable; for, if the block of stone were 500 Ibs., the common speed after the contact, as may easily be reckoned, would be only one inch in the second. But friction, however, soon destroys this motion, which by degrees distri! itself to all neighboring bodies, and finally to the whole earth, and thus entirely disappears. Motion, therefore, distributes itself to other bodies, but is not lost. If it appear wholly destroyed, the reason is, that, b\ gradual distribution to other bodies, it finally becomes imper- ceptible. Motion is necessary to destroy motion; resistance only scatters without destroying it. The (material) Pendulum. The above developed laws apply, strictly speaking, only to an ideal pendulum. Such a pendu- lum we may conceive, but we cannot construct, for it must consist of a simple thread devoid of all weight, and having a extremity only a heavy point. Every pendulum not corresponding with both these conditions THE MATERIAL PENDULUM. 171 is a compound pendulum. An inflexible rod devoid of weight on which are two heavy molecules, m and n, would consequently be a compound pendulum. The molecule m nearer to the point of suspension than n, has a tendency to vibrate more rapidly, but as both molecules are combined, m will hasten the motion of n, and conversely n will retard that of m\ the vibrations will, on that account, move with a velocity varying between j the degrees of velocity with which each of the molecules m and n would oscillate alone. They are equal to the oscillations of a simple pendu- um longer thanf m, and shorter ihanfn. It s the same with every material pendulum. / Fhose parts lying nearest the central point of j ribration in the pendulum have their motion / etarded by the most remote, while the latter '-. e accelerated by the parts most contiguous the point of suspension. There must, consequently, be a point every compound pendulum, which is not acted upon by the st of the mass of the pendulum, vibrating exactly as fast as a mple pendulum, whose length is equal to its distance from the int of suspension. This is called the centre of oscillation. If e speak of the length of a compound pendulum, we understand f the term the distance of this point from the point of suspension, , what is the same thing, the length of a simple pendulum of an [ual time of oscillation. A pendulum, consisting of a fine thread, at whose lower end a dl, or a double cone, of a substance of great specific gravity, is tached, approaches most nearly to the simple pendulum. If the read be somewhat long, and the diameter of the ball somewhat nail, in proportion to the length of the pendulum, w r e may, without y serious error, take the centre of gravity of the ball as the point oscillation of the pendulum, or, in other words, we may take ich a pendulum for a simple one. In every actual pendulum, however, which differs more consider- )ly from the form of a simple pendulum, the centre of gravity is IT no means the centre of oscillation ; it is, in most cases, a diffi- ilt problem to ascertain by calculation where the centre of oscil- tion lies in an actual pendulum, because, in a computation of is kind, we must not only have regard to the accelerating force 172 THE PENDULUM CLOCK. of gravity of the individual points lying at different distances from the point of suspension, but also to the resistance opposed to an acceleration of motion owing to the inertia of their mass. The simplest way of seeing that the centre of oscillation of an actual pendulum cannot coincide with its centre of gravity, is by observing a pendulum in which a portion of the mass lies above the point of suspension. Such a pendulum vibrates considerably slower than it would do, if its centre of gravity were the centre of oscillation. Fig. 145 represents an evenly divided rod, provided in the middle Fig H5 w ^ an ec * e s i m *l ar to w hat forms the fulcrum of the beam of a balance. If, now, we fasten a leaden mass, weighing two pounds, one decimetre above, and another of the same weight equally far below this edge, and place the edge upright on its support, the rod with its weights will be in a condition of indifferent equilibrium, for the centre of gravity of the system corresponds with the fulcrum ; as soon, however, as we attach a small extra weight to the lower end of the rod, the whole becomes a pendulum. But the oscillations of this pendulum are much slower than those of a simple pendulum of the length a /, for the only force that sets the whole system in motion is the gravity of the lower leaden weight ; this, however, has not only its own mass to move, but also the masses of the weights at c and d. We thus easily perceive why the beam of a balance, which may be considered as a pendulum, vibrates so slowly, although its centre of gravity is close to the point of suspension, and why it must vibrate very rapidly if the centre of gravity were really the centre of oscillation. The Pendulum Clock. The most important application of the pendulum is for the regulation of clocks. Every clock must have an accelerating force to produce and maintain motion. From what has been said, however, concerning accelerating forces, it is evident, that, if some other equal force, or hinderance of motion, do not oppose the accelerating force, motion cannot remain uniform, but will become faster and faster, as in a falling body. In our large upright clocks, this accelerating force is produced by weights, hung to a line passed round a horizontal axle. If the weight be drawn down by its gravity, the axle will be turned by the line, and THE PENDULUM CLOCK. 173 the whole machinery set in motion. But the motion of a falling weight is an accelerating one ; consequently the check must at first go slowly, then more and more quickly, unless its course were regulated, and this regulation is effected by means of the pendulum. * Fig. 146 exhibits the manner in which the pendulum regulates the going of a clock. A toothed wheel is fastened to the axis to Fig. 146. which the line with the weight is attached. The axis, round which the pendulum vibrates, is above this wheel, and to this axis is secured a beam a 6, which catches the teeth of the wheel on either side. The figure represents the pendulum in the position where it is at the extreme left side. The wheel is turned by the weight in the direction of the arrow, but cannot go on, having the tooth 1 held by the tooth 6 of the lever : as soon, however, as the pendulum vibrates back again, b rises, and the tooth 1 is suffered to pass ; but the mo- tion of the wheel is again im- mediately arrested, because the tooth a at the other end of the lever now descends, pressing against the tooth 2 of the wheel : thus the wheel can move one tooth at every oscillation, and the same every time the pendulum returns, and thus the motion of the wheel is regulated by the movements of the pendulum. Such a contrivance is called an escapement. In watches, the weight is replaced by a tensely drawn steel spring, and the pendulum by a fine spring vibrating, owing to its elasticity, round its point of equilibrium. Clocks made in Paris, 15* 174 IMPEDIMENTS TO MOTION. and which there went quite well, were found to lose when brought near the equator, so that it was necessary to shorten their pendu- lums. Hence it follows that the same pendulum goes more slowly at the equator than near the poles, and consequently, that the action of gravity is less at the equator than at the poles. This is owing to two causes : first, the flattening of the earth ; and secondly, the centrifugal force produced by its rotation round its axis, and which is stronger at the equator. Impediments to Motion. A resistance already often spoken of, and which exercises a considerable influence upon almost all motions, is friction. In order to propel a load of moderate size along a horizontal plane, a considerable application of force is necessary, arising entirely from the resistance of friction. If the plane, on which the mass is to be propelled, as well as the under surface of the load, be perfectly hard and smooth, (which is never the case in nature,) the smallest force might set a very large mass in motion, and once impelled, the load would move on with uniform speed on the horizontal plane. Friction arises, incontestably, from the elevations of one of the surfaces entering into the depressions of the latter. If, now, motion is to occur, the projecting parts must be torn away from the mass of the body, or the one body must be continually lifted over the inequalities of the other. The first occurs if one or both the rubbing surfaces are very rough. If, however, the rubbing surfaces can possibly be smoothed, the last named mode of action almost exclusively takes place. The accompanying figure may serve to explain the manner in Fi 147 which resistance to motion arises, if a body must be lifted over small inequalities. The lifting of the body A is effected by raising the lowest points of the projections of A to the summit of the inequa- lities of the under layer, whence they must again slide down, and the same raising and lowering be repeated. The resistance op- posed here by Ji to the motion, is no other than what must be overcome to draw it up an entirely smooth inclined plane. If this view of friction be correct, the laws relating to it must admit of being proved by experiment. IMPEDIMENTS TO MOTION. 175 In order to overcome friction, we must, exactly as in drawing the body up an inclined plane, apply a force equal to an aliquot part of the load. The number that gives the relation of the force to the weight is termed the co-efficient of friction. It naturally depends upon the peculiarities of the rubbing surfaces, and can be determined by experiment. If, for instance, we would propel a load of one cwt. upon a horizontal layer of iron (on the line of a railroad, for instance), and if the under surface of the truck were also iron, a force of 27,7 Ibs. would be necessary ; that is to say, the same expenditure of force that would be requisite for lifting 27,7 Ibs. vertically up. When iron rubs on iron, the resistance of friction is, as we see, 27,7 per cent. ; and the co-efficient of friction, in this case, is 0,277. In order to ascertain the co-efficient of friction for different bodies, we may make use of an apparatus as seen at Fig. 10. The board R S is placed in a horizontal position. Suppose this board to be of oak, we lay a block of oak upon it, whose under surface must also be well planed, weighing 1000 grammes (15,444 grs.); a line is attached to this block of oak, and passed round a pulley as in the experiments of the inclined plane, carrying a light scale-pan. This latter will not be sufficient to produce motion, w r hich will not begin before the weight of the scale-pan, and of the weights toge- ther, amount to 418 grammes (6,456 grs.). We obtain, by this experiment, the co-efficients of friction of oak upon oak, and find them to be 0,418. If we alter the substance of the body to be moved, as well as of the body supporting it, we may ascertain the co-efficient of friction of different bodies. The following table contains some of the most practically important co-efficients of friction. Iron upon iron .... 0,277 Iron upon brass .... 0,263 Iron upon copper .... 0,170 ( 0,418 = Oak upon oak . . . Oak upon pine .... 0,667 Pine upon pine .... 4,562 The resistance of friction maybe diminished by the application of well chosen oleaginous substances. Oil is the best for metal, while tallow answers best for wood. 176 IMPEDIMENTS TO MOTION. In woods it is by no means a matter of indifference which way the fibres run ; friction is much less considerable where they run across (+) than where they are parallel (=). From what has been said, it is directly shown that friction is always proportionate to the weight. If, for instance, in the above experiment, we had taken a block of oak weighing 2000 grammes (30,888 grs.), we should have had to attach 836 grammes (12,912 grs.) to the rope, in order to overcome the friction. The size of the surface in contact cannot, according to the above views, exert any influence on the amount of friction ; this may be also proved by experiment. Suppose that the block of wood have lateral surfaces of different size, no difference will be found in the result, whichever surface of the block touch the wood. The above described kind of friction is termed sliding friction, in order to distinguish it from the rolling friction, which we pro- ceed to consider more attentively. Sliding friction always occurs where pins or axes revolve in their supports. In order the better to take into account the effect of friction in this case, we need only consider that it acts precisely like a corresponding weight suspended to a string passed round the same axle. Let us, by way of illustration, examine the effect of friction on the windlass. Let the weight of the axle, with every thing that is fastened to it, be about 751bs., the stone to be raised 100 Ibs., and the force acting on the circum- ference of the wheel, be 25 Ibs., then the combined pressure sustained by the props of the axle will be 75 + 100 + 25 = 200 Ibs. If the props be of brass, but the extremities of the axle be of iron, the resistance of fric- tion acting on the circumference of the ends of the axle, will be 26,3 per cent.; the effect of friction is, therefore, the same as if in place of this we had passed a line round the ends, in the same direction as the line bearing the weight, and had attached to it a weight 200 X 0,263, or 52,6 Ibs., or as if the load acting at the circumference of the axle had been 52 6 - or 10,5 Ibs. larger, provided that the diameters of the rods o were y of that of the axle. Thus about 10 per cent, of the force IMPEDIMENTS TO MOTION. 177 applied, is lost in this windlass, in overcoming the resistance of friction. It now remains to notice rolling friction. Rolling friction occurs where a round body, as a ball, or a cylinder, rolls along a surface. Here the supporting under surface comes always in contact with new points of the rolling body. The resistance that arises here is by far less than the resistance of sliding friction, as may be seen from the following consideration. If we wish to propel the round body Jl over the surface on which it rests, we must begin by drawing it to a little inclined plane c b, when its centre of gravity will be raised as much as c lies below Flg ' 149> b. But by rolling on the body ./?, it will turn round the point 5, by which its centre of gravity will only be raised from d to e. The difference of height, however, between d and e, is much less than the difference of height be- tween c and b. Let us suppose a spheri- cal arc to be drawn round the central point d, and through the points a and 6, the lowest point of this arc will be as much below &, as d is below e. But as the lowest point of the arc a b still lies high above c, we may easily understand that the alternate rising and falling of the centre of gravity, is much less considerable in rolling than in sliding friction. We also, however, perceive that the resistance of friction depends mainly here upon the radius of the rolling body. The larger this radius is, the smaller will be the resistance. In other respects, resistance is here likewise proportionate to the load. In the wheel of a carriage there is rolling friction at the cir- cumference of the wheel, but sliding friction at the axles. Both resistances become smaller in proportion to the larger diameter of the wheels. In both kinds of friction, adhesion has considerable influence. In a locomotive, the middle wheels, the so-called driving wheels, are turned by the force of the steam-engine ; the whole carriage rolls on in consequence of this, for, if it were to remain at rest, the wheels could not revolve without the occurrence of a considerable sliding friction between the wheels and the iron on which they 178 IMPEDIMENTS TO MOTION. ran, whilst by rolling on, the incomparably smaller rolling friction has alone to be overcome. If a locomotive be attached to a number of carriages, a certain resistance of friction must be overcome during the continuance of motion rolling friction at the circumference, and sliding friction at the axles. All these resistances must be overcome if the carriage is to be drawn onward. It is evident that the number of oarriages attached, might, at last, be so increased, that the locomotive would no longer be able to draw them ; in this case, therefore, the wheels of the locomotive would revolve without its being borne forward, when the con- siderable friction of the sliding friction, at the circumference of the driving wheels, would have to be overcome by the force of the machine. The train, therefore, can only proceed if the sum of all the resistances of friction of all the carriages is smaller than the resistance of the sliding friction from the rotation of the driving wheels of the locomotive at the circumference which would exist were there no forward motion. From these considerations, it follows, that the load which a locomotive is capable of drawing, depends not only upon the force of its steam-engine, but always upon its weight. If we as- sume that two locomotives have equally strong machines, but that the one is heavier than the other, a larger weight may be pro- pelled by the heavier of the two. LAWS OF THE MOTION OF LIQUIDS. 179 CHAPTER II. LAWS OF THE MOTION OF LIQUIDS. IF we make an opening in the lateral wall, or the bottom of a vessel filled with liquid and open at the top, and if the aperture thus made be small in comparison with the dimensions of the ves- sel, the liquid will flow out with a velocity whose intensity will be in proportion to the depth of the opening below the surface of the liquid. The connection existing between the velocity of the escaping liquid, and the height of the pressure, may be most simply expressed in the following manner: The velocity of the escaping liquid is exactly as great as the velocity a freely falling body would acquire, if it were to fall from the surface of the liquid to the aperture through which the liquid escapes. This proposition is known by the name of the Toricellian theorem. It may be explained in the following manner : If the liquid layer abed (Fig. 150) imme- diately above the opening a b, were to fall down without being accelerated by the liquid pressing over it, it would flow from the opening with a velocity corresponding to the height a c, which we will designate as h. This velocity is c = %/ 2 g h. But now the escaping stratum is not only accelerated by its own gravity, but by the gravity of all the liquids pressing upon it. The accele- rating force of the gravity g is, consequently, to the accelerating force g f y actually propelling the liquid particles, as a c is to af, or as h is to s if the height of pressure be designated by s, that is h : s = g : g 1 , and, therefore, the accelerating force g f , acting upon the liquid layer flowing out, is = - s. But if the accelerating force acting h upon this layer be g' and not g, then its velocity c' = \/ 2 g f h- } 180 THE VELOCITIES OF EFFLUX. and if we add the value of g' to this value of c', we obtain as the value of the velocity of the escaping fluid c' = N/ 2 g s. But this is the same velocity as that acquired by a body falling freely from a height s. From this proposition it immediately follows that : 1. The velocity of the efflux depends only upon the depth of the aperture below the surface, and not upon the nature of the liquid. At equal heights of pressure, water and mercury will, therefore, flow out with equal velocity. Every layer of mercury will cer- tainly be driven out by a pressure 13,6 times greater than that acting on water, but then the mass of a particle of mercury is 13,6 times heavier than that of an equally large particle of water. 2. The velocities of efflux are as the square roots of the heights of pressure. The water must, therefore, flow with ten times greater velocity from an opening 100 inches below the level of the liquid, than from a depth of only one inch below the same level. In order to determine the velocity of efflux, the simplest way is to observe a jet issuing vertically or horizontally from the vessel. We will first consider the vertically directed jet. If the water spring forth from the opening o (Fig. 151) with the same velocity as if it Fig. 151, Fig. 152. were to fall from the level of the liquid in the vessel to the height of the opening 0, the jet of water must rise again to the elevation of the liquid-level. We may easily show this by the help of the ap- paratus represented in Fig. 152, letting the water flow from the opening c; and we shall then find that the as- cending jet of water does not attain to anything like the height that might be expected. The impediments to motion are, however, the sole cause of the water not attaining the height yielded by theory ; the water fall- THE VELOCITIES OF EFFLUX. 181 ing back from the top exerts an essential influence in hindering the free ascent of the succeeding water; and consequently the jet rises the higher, immediately the aperture of efflux is so turned, that the water flowing out may make a small angle with the ver- tical, that is, that the ascending and descending jets may be close to each other. In this case, the jet may, under favorable circum- stances, that is, where there is the smallest possible friction, attain an elevation 0,9 of the height of the pressure. . A stream of water flowing out in a horizontal direction describes a parabola, the form of which depends upon the velocity of its efflux. Supposing that the p . 153 opening a (Fig. 153) were 0,l m below the water level, the velocity of efflux would be .according to the Toricellian law, v/ 2.9,8.0,1 = l,4 m . If, therefore, a particle of water were at any moment to flow from the opening, it would in one second be l,4 m from the vertical wall of the vessel, and 0,28 ra in ^ of a second. But in 0,2 of a second, the water falls 0,196 (we find this on substitut- ing the value 0,2 for 1 in the equation s H t 2 ) ; if now we mea- 2 sure the length a6=0,196 m downwards from the opening a, a horizontal line drawn from b towards the jet of water will intersect the latter at a distance of 0,28 m . In making the experi- ment, the distance b c will be somewhat less than 0,28 m , owing to the action of friction. According to theory, the water should flow from a second opening d 40 cm , below the surface, with a velocity double that at a; if, therefore, we measure 196 mm from d downward, and then suppose a horizontal line drawn towards the jet, it must intersect the latter at a distance of 0,56 m . The quantity of water issuing from an opening, in a given time, depends evidently upon the size of the opening, and the velocity of the efflux. If all the particles of water passed the opening with the velocity corresponding according to the Joricellian law with the height of the pressure, the water flowing out in one second would form a cylinder whose base would be equal to the opening, 16 182 THE VELOCITIES OF EFFLUX. and its height equal to the distance described by a particle of water (owing to its velocity) in a second. This distance is, how- ever, the velocity of the efflux itself, and therefore, \/2gs 9 and designating the area of the opening by/, the quantity expelled in a second will be If we assume that the apertures m and n are circular, and that their diameter is 5 mm , the area of the opening/= 19,625 square millimetres, or 0,19625 square centimetres, if the height of the pressure be ten centimetres, the velocity of the efflux will be as we have already computed 1.4 m = 140 cn % and therefore m= 0,19625 X 140 = 27,475 cubic- centimetres. In a minute, therefore, 1648,5 cubic-centimetres, or 148,5 cubic-centimetres, more than 1J litres must flow out. An aperture of equal size lying 40 cm below the water-level, must yield double as much in one minute ; that is, 3 litres and 297 cubic-centimetres of water. If we make the experiment, we find that the upper opening only yields about 1 litre and 55 cubic-centimetres, and the lower one 2 litres and 110 cubic-centimetres. This difference, between the theoretical and the actually ob- served quantity of the discharge, proves incontrovertibly that all the particles of water do not pass the aperture with a velocity corresponding to the height of the pressure. In fact it is only those particles of water lying in the centre of the opening that have this velocity, while that of the particles flowing nearer to the edge of the opening, is much less considerable, as we shall see from the following observations. [The experiments of Bossut show that the actual quantity of water discharged from orifices of the same dimensions, under dif- ferent degrees of pressure, is much less than is inferred by calcu- lation; this is exemplified in the following table: Weight of fluid Computed discharge per Actual discharge above the orifice, minute in cubic inches. per minute. Per cent. 1 foot 4,427 2,812 63.5 5 feet 10,123 6,277 62.0 10 " 14,317 8,860 61.8 15 " 17,533 10,821 61.1 ] In a wide vessel having a narrow opening, the whole liquid mass, with the exception of the parts in the vicinity of the aper- INFLUENCE OF CONDUCTING TUBES. 183 ture, may be regarded as at rest. The layers that successively flow out, do not begin their motion simultaneously, the foremost having attained the maximum of their velocity, whilst the most bsrckward are beginning their motion. The consequence of this would be a breaking up of the successive layers if vacua could be formed; as this, however, cannot occur, the separate layers become more elongated while their diameter diminishes ; but in the proportion that the diameter of these layers diminishes, other particles of water must flow on from the sides ; as these, however, only begin later their motion at right angles to the opening, it is clear that they must reach the opening with less velocity than the central lines of water. Whilst the nucleus of the jet has a velocity corresponding to the height of the pressure at the moment of its leaving the aper- ture, it is surrounded by lines of water, whose velocity diminishes in proportion as they approach the edge of the aperture: whence it follows, that the quantity flowing out must be less, than if all the particles left the opening with the velocity of the nucleus of the jet. The water flowing out is not perfectly cylindrical, but contracted at the opening as seen in Fig. 154, in consequence of the central lines of water Fl s- 154 - at their passage through the opening having a greater velocity than the parts near the edges, and in consequence of the latter being possessed of a velocity directed towards the centre of the jet. At c d the diagonal section of the stream is about equal to two-thirds of the area of the opening. In like manner the actual quantity of water expelled is about two-thirds of the theoretical. Influence of conducting tubes upon the quantity of liquid dis- charged. If the efflux does not take place through openings made in a thin wall, but through short tubes, remarkable modifi- cations occur, which we purpose considering. If a conducting tube have exactly the form of the free jet from the opening to the part where the latter contracts, and exactly the length between these two points, it will exercise no influence upon the quantity of liquid discharged. In cylindrical pipes, the water either pours freely out as from 184 INFLUENCE OF CONDUCTING TUBES. an opening of equal diameter, in which case no influence is exer- cised upon the quantity of liquid, or the water adheres to the walls of the pipes, so that the liquid fills the whole pipe, and flows forth in a stream having the diameter of the pipe ; in this case the pipe considerably influences the quantity discharged. Whilst an opening in a thin wall yields theoretically 0.64 of liquid, w r e obtain by such a cylindrical conducting pipe of like diameter 84 p. c., provided the length of the pipe is equal to four times its diameter. The stream always adheres to the pipes at lower, while it is free at greater pressures. Where there is a medium pressure, it may be made free or adherent at pleasure ; an inconsiderable impediment will occasion adhesion, while a very slight touch is often sufficient to render the stream free. A conical conducting pipe acts in case it discharges when full, in the same manner as a cylindrical pipe, excepting that it occa- sions an increased efflux. The speed of the efflux is diminished in cylindrical or conical conducting pipes in the same proportion as the quantity of dis- charge is increased. We must now examine how it happens that conducting pipes increase the quantity of liquid discharged, while on the contrary they diminish the velocity of the efflux. The water suffers a contraction on entering the conducting pipe, in the same manner as if it were discharged from an open- ing in a thin wall, but besides this, as soon as the walls of the pipe are wetted, adhesion acts in such a manner on these walls that the conducting tubes become entirely filled, and the diagonal section of the stream thus increases, being at its exit from the pipe larger than at the place of con- Fig. 155. Fig. 156. traction, as may be seen at Fig. 155. That such a contraction actually oc- curs in the tube is proved by this, that if we give the conducting tube the shape of a contracted stream as in Fig. 156, the efflux is precisely the same as if the conducting tube were cylindrical. If the particles of water filling the whole section of the tube leave it with the same velocity with which they pass the most contracted part, a breaking up of the succeeding layers of water must necessarily occur. The separation of the particles of water, LATERAL PRESSURE OF LIQUIDS IN MOTION. 185 and consequently the formation of vacua is, however, hindered by the pressure of the air which accelerates the motion of the liquid while flowing into the tube, but retards its efflux from it. By atmospheric pressure, the particles of water flowing out are so much retarded that a full efflux is produced. That the pressure of the air really has this effect is especially proved by the quantity of the discharge not being increased by putting on conducting pipes where water flows into a vacuum. If we make a hole in the lateral wall of a conducting pipe, the air will be drawn in through this opening, and the stream will cease to be continuous. If a bent tube x y, Fig. 155, whose lower end opens into a vessel of water, be inserted into the lateral wall, the water in the tube x y will be sucked up by the tendency manifested by the water to form a vacuum in the conducting pipe. This pheno- menon proves likewise the influence exercised by the air in the above experiments. As a conical conducting pipe gives a larger discharge than one that is cylindrical, it must also draw up more liquid, that is, under otherwise similar conditions, the column of water drawn into the tube x y by a conical conducting pipe will rise to a greater height than in a cylindrical pipe. Lateral pressure of liquids in motion. If water flow through pipes out of a reservoir, the lateral walls of the pipes would not have to support any pressure, if there were no resistance of friction to overcome ; this, however, under some circumstances may be so considerable, that the greater part of the hydrostatic pressure is lost in overcoming this resistance, and proves of no avail in aiding the motion. Instead of the plate with the opening c in Fig. 152, let us insert into the apparatus a cork, in which is a glass tube three feet in length, and give the tube a horizontal direction, when the water at the end of the tube will then flow out much more slowly than if the efflux had occurred through the opening c. If we apply several equally long tubes of different diameters to exhibit this experiment, we shall see how the velocity of the dis- charge diminishes with the narrowness of the tubes. Supposing we find that the velocity of the efflux for one of these tubes is only half as great as we should expect from the amount of height of the pressure, then the one-half of this pressure is neces- 16* 186 REACTION CREATED BY THE EFFLUX OF LIQUIDS. Fig. 157. sary to overcome the friction, and the other half only is available for motion. If the water in the tube a c (Fig. 157) were to move with a velocity cor- responding to the height of the pressure in the reservoir, the walls of the tubes would have no pressure to support; but if the water in the reservoir produces in the tube a motion corresponding only to a part of the height of the pressure, the remainder must act upon the walls of the tubes as hydrostatic pressure. The pressure sus- tained by the walls is, however, not equal in all parts of the tube, being less, the nearer it approaches the opening c. In many cases, the pressure to be supported by the walls of the tubes from within may be less than the pressure of air acting upon them from without; this is everywhere the case where the conditions are fulfilled in which the phenomenon of suction occurs. Reaction created by the efflux of Liquids. If we suppose a vessel filled with water, the whole will be at rest, as every lateral pressure is counteracted by a perfectly equal, but opposite one. But if we make an opening at any part of the wall from which the water may flow forth, the pressure will evidently be removed at this spot, whilst the portion of the wall diametrically opposite and corresponding to it will be pressed upon as strongly as before. The pressure, therefore, on the wall of a vessel through which the opening has been made, is less than that acting on the opposite side, consequently the whole vessel must move in a direction opposed to the direction in which the stream of water flows out, if this motion be not hindered by friction or some other cause. This may be compared to the recoil of fire- arms. The reaction manifested on the escape of water may be shown by an apparatus known by the name of Segner's Water-wheel. It con- sists of a vessel v turning round a vertical axis, and having at its upper extremity a cock r, which need only be turned in order to put Fig. 158. REACTION CREATED BY THE EFFLUX OF LIQUIDS. 187 the apparatus into motion. By means of the reaction of the streams of water, issuing from the end of the horizontal and curved tubes t and t f , and at a tangent to the circle described by the end of the tubes, the apparatus receives a rapid rotatory motion. Vertical Water-wheels. If water continually flow from a more highly elevated to a lower spot, it may be applied as a moving force. If during a unit of time, as a second, a mass of water whose weight is M, flow, or fall from a height h, M h is the quantity of motion, or the mechanical moment of this mass of water. In whatever way we may turn the motion of the water to another body, the effect can never exceed the mechanical momentum of the fall, that is, we can by means of the fall, at most raise to an equal height, a weight equal to the mass of water falling from the same height in the same unit of time, or effect some other similar action. If, for instance, a mass of water of 800 Ibs. fell from a height of twenty-four feet in one second, the absolute maximum of the effect of this fall is 19,200, that is, a result might be pro- duced by this fall, supposing all forces to come into action without there being any loss by friction or other resistance, which would be equal to the force necessary to raise a weight of 19,200 Ibs. in one second to an elevation of one foot. If we assume that a horse working with medium force and medium speed can raise a load of 100 Ibs., four feet in one second, the absolute maximum of the effect of that fall might be compared, or would be equal to a forty- eight horse-power. In what follows, we will designate the absolute maximum of a fall by the letter E. In order to avail ourselves of the mechanical momentum of a water-fall, we generally make use of water-wheels, that is wheels, on the. circumference of which the water acts by means of pres- sure or impact. Ordinary water-wheels turn in a vertical plane round a hori- zontal axis. We distinguish three main kinds of vertical water- wheels, under-shot, over-shot and middle-shot. In under-shot wheels the float-boards are at right angles with the circumference of the wheel. The lowest float-boards are im- mersed in the water, which flows with a velocity depending upon the height of the fall. The flowing water sets the wheel in motion, and imparts to it 188 VERTICAL WATER-WHEELS. a velocity which may be greater or smaller according to circum- stances. If the impact of the water is to impart to the wheel a velocity equal to that with which the water would flow if there were no wheel, there must be no resistance opposed by the wheel to this motion, it must therefore not be loaded ; or in this case there can be no mechanical action produced, and the effect will be null. On the other hand, we might load the wheel so strongly by a counterpoising weight, that the strike of the water would not impart any motion to it, the falling water exercising only a static pressure, and keeping the whole in equilibrium. In this case, the effect is also null. From this consideration it follows that where the wheel is to do any work, it must move with a velocity less than that of the freely flowing water; theory and experience show T that the most advantageous effect is produced, if the velocity of the wheel be half as great as that corresponding to the height of the fall. Hence it follows that only half of the mechanical momentum of the fall comes into action in an ordinary under-shot wheel, while the water flows off with half the velocity with which it came on the wheel ; the effect of such a wheel can, therefore, never exceed the value of \ E. Even this effect cannot be practically obtained, as a part of the force is lost by the adhesion of the water to the walls of the channel, resistance of friction, &c. Carefully con- ducted experiments have yielded the value e = 0,3 for under-shot wheels moving in a channel, where no lateral efflux of the water could take place. But in unconfined wheels, as those applied to ship-mills, where the water may escape laterally, the effect is still more remote from the absolute maximum. Under-shot wheels are applied where there is a considerable mass of water, but where the fall is of small elevation. As the mechanical momentum of the fall is turned to little ac- count in the above described under-shot wheels, where the water strikes the float-boards at right angles, Poncelet has constructed an under-shot wheel with curved float-boards, the effect of which approaches far nearer to the absolute maximum. In order to have the water come upon the wheel without a sudden stroke, the float-board at the circumference of the wheel HORIZONTAL WATER-WHEELS. 189 must correspond with the direction of the tangent ; but if they were so constructed, the water would be hindered in falling from the wheel ; besides which, the water must not expend all its velocity on the w r heel, since in that case, it would have none left for flow- ing off. Thus a certain loss of power, independently of the natu- ral impediments, is unavoidable even in Poncelefs wheel. Wheels w r ith curved float-boards are computed to yield an effect equal to two-thirds or even three-fourths of the absolute maximum. This result is explained in Poncelet's wheels by the water losing its velocity as it ascends the curved float-boards, and yielding it almost entirely to the wheel. The over-shot Wheel is applied where there is a high fall of an inconsiderable quantity of water, as in small mountain streams. The water in running down upon it fills the cells on one side of the wheel, which is turned by this very addition of weight. Near the lower part of the wheel the water again flows out of the cells. There is also a portion of the mechanical moment lost in over-shot wheels, because the cells cannot keep the water down to the lowest point of the wheel, but begin sooner to let it flow out. A well constructed over-shot wheel ought to produce an effect amounting to 75 per cent, of the absolute maximum, provided that it turn slowly, for in rapid turning the water does not remain in a hori- zontal position in the cells, in consequence of the centrifugal force, but rises exteriorly, so that it falls sooner from the cells. The middle-shot wheel is a kind of medium between the over and the under-shot wheel. Horizontal Water-wheels. Earlier attempts were made to con- struct water-wheels, but it is only recently that they have been practically applied by Fourneyron. The horizontal wheels he invented are known by the name of turbines. Fig. 159 represents one of these constructed for a high fall of water. The whole mass of the falling w r ater is collected in a wide cast iron tube, connected with a cast iron reservoir by the opening o. A hollow tube passes through the middle of the reservoir con- necting the upper lid with the bottom. This horizontal bottom does not, however, touch the vertical walls of the vessel, there being between it and the lateral walls an annular interval from which the water flows in a horizontal direction. This water thus streaming out sets the horizontal wheel with its 190 HORIZONTAL WATER-WHEELS. vertical spokes in motion ; a a is the vertical axis, round which the wheel turns, passing through the shell con- necting the bottom and the cover of the reservoir. To this axis the plate b b is fastened, opposite to the opening of the reser- voir bearing the rim of the wheel with the float- boards. The float-boards are curved as seen in the sectional view in Fig. 160 ; in order, however, to make the w r ater strike the float-boards of the wheel in the most advan- tageous direction, con- ducting curves made of tin are fastened to the plate of the reservoir to give a determined direc- tion to the water. It would detain us too long were we to enter into a particular descrip- tion of the most advan- tageous curvature for float-boards, and con- ducting curves. Fourneyron^s turbines, if well constructed, ought to produce an effect, amounting to 75 p. c. of the absolute maximum. Gadiat has simplified them by leaving out the con- ducting curves, and thus lost 5 p. c. more of the absolute maxi- mus effect, so that his turbines yield but 70 p. c. Turbines are particularly useful for high falls which do not admit of the use of vertical wheels. Attempts have been made to enlarge upon the Segner water- wheel, in order to work machinery with it, but hitherto with very HORIZONTAL WATER-WHEELS. 191 little effect ; a very small motive power being invariably produced. The reason of the want Fig. 160. of success attending these attempts did not arise from the active moving power being too small, but because the lower of the two pivots around which the apparatus turns has to bear the whole weight of a large mass of water, in conse- quence of which, there is a disproportionally large amount of resist- ance from friction to be overcome. This objection has been ingeniously set aside by Jllthans of Sayn, who has made such an alteration in the apparatus, that the water enters the horizontal arms from below, and not from above. The most essential part of the arrangement is shown in Fig. 161. The reservoir is formed by a cast Fi * 16L iron conducting: O pipe, which is curved horizon- tally below, and ends in a verti- cally rising piece of tube a. From the opening at a, the water flows into the neck b attached to the end of the tube a in such a manner that it can turn round it as round a pivot. The water passes through the neck b into the horizontal arm c, and flows out of the openings at o. The motion of the wheel is transmitted by the axis d. 192 WATER-COLUMN MACHINES. The friction to be overcome by such awheel in revolving round the pivot a, must be very inconsiderable, for the weight of the wheel with all that is fastened to it is almost entirely supported by the pressure of the column of water, so that the pivot a has scarcely any pressure to sustain. In the apparatus seen at Fig. 161, a large portion of the mecha- nical momentum of the fall must be lost from reasons similar to those affecting the under-shot wheel with flat float-boards, for if the water imparts all its velocity to the wheel, and falls from the opening without any velocity, and if, therefore, the wheel rotate with a rapidity corresponding to the operation of the fall, the pressure backwards, and consequently the mechanical effect will be null also. The water must still retain a portion of its velocity of motion. Much may be gained here by curving the arms, somewhat in the manner represented in Fig. 162. The water imparts its velocity gra- dually to the wheel, flowing through the tube, and pressing against the curved walls, so that it falls at the opening almost devoid of all rapidity. In Scotland such turbines of reaction are much used, on which* account they are often called Scotch turbines. Water-column Machines. In these machines the acting column of water, pressing upon a piston that moves in a cylinder, imparts to it a forward and backward motion which is farther transmitted by the piston. Water-column machines are generally applied for the purpose of raising water to a considerable height. In this manner, for instance, the salt spring at Reichenhall in Upper Bavaria is con- ducted by a circuitous course about one hundred and twenty miles to Rosenheim, and other intermediate places for the purpose of being boiled. On this road there are nine of these water-column machines, constructed by Reichenbach, to raise the springs over the mountainous heights. Although all these machines depend upon the same principle, their mode of action is in many respects different; we will here consider with attention one of nine of those most simply arranged, that at Nesselgrabe. The pipe Ji leads the impelling water to the machine, it enters WATER-COLUMN MACHINES. 193 alternately into the upper and lower part of the cylinder B, where it drives the piston C alternately up and down. Fig. 163. 17 194 WATER-COLUMN MACHINES. In order to produce this alternation, on the entrance of the water, an arrangement has been applied precisely similar to the contrivance used for governing steam-engines. Three connected pistons move in the cylinder d, the two lower ones are alike, while the upper one has a smaller diameter. In the position of the piston as represented in the drawing, the impelling water passes through the pipe e into the large cylinder, and raises the piston C. The water above C flows through the pipe/* into the pipe d, and from thence passes away through the pipe g. When the piston C is raised, the pistons must be so displaced in the tube d, that the impelling water may enter the large cylinder. This is effected by the pistons descending so far in d, that the piston i stands below the tube/", and the piston m below e; then the impelling water passes from the tube A through h andyinto the upper part of the cylinder B, drives down the piston C, whilst the water below C passes through e into the tube d, flowing off through the tube g. The elevation and depression of the pistons in the tube d are effected in the following manner. The tube h is connected by the tube n with the upper part of the tube d: at the joint of the tube n, a cock r is applied, which, according to its position at one time, connects the upper part of the tube d with A, and at another, cuts off this connection and puts the upper part of the tube d in communication with the external air. If, now, we suppose the cock to be so placed that the impelling water can enter from h by means of this cock into the upper part of d, the piston s will be pressed upon above and below by an equal power of water; be- sides this, the water presses above on the piston i, below on the piston m\ the pistons, therefore, are exposed to equal water- pressure from above and below, and descend by their own weight. When the pistons are to rise, the cock r is so arranged that the communication between h and the upper part of d is interrupted. Now no pressure of water acts upon s, the water above s escaping from the machine by the cock. The water-pressure from above against i, is counteracted by the pressure from below against m, and the pressure of the water from below s, to which there is no counter pressure, raises the pistons. The turning of the cock is effected by the machine itself. At the upper end of the rod fastened to the piston C, a round disc is WATER-COLUMN MACHINES. 195 applied, which strikes against the oblique surface t on the rising of the piston, and against the oblique surface u on its sinking, pushing them sideways, and thus causing a revolution about the axis x. The arm y is fastened to this axis, and the arm z, by its rotation, causes the cock to turn. Let us now further consider how the motion of the piston C is transmitted and applied to the other parts. The piston a is connected with the piston C by means of a rod passing through a stuffing box, and has a much smaller diameter than C; the elevation and depression of the piston cause, there- fore, a similar motion in the piston a ; but when a rises, a rare- faction of air takes place in the chamber 6, the lower valve opens, and water is raised through the suction pipe JVinto the chamber 6. By the rising of the piston a, water is pressed into the chamber c, the lower valve closes, the upper one opens, and the water is thus raised through the piston into the reservoir R, and from this into the ascending pipe S. On the descent of the piston, the valves which were open, close, and vice versa ; water is sucked up into the chamber c, and raised from b into the reservoir, and the ascending pipe. If the diameter of the piston C be two, three or four times greater than that of the piston a, we may raise a column of water (disregarding friction and other impediments) two, three, or four times as high as the height of the impelling water. In the water-column machines we have been considering, the height of the impelling water is 140 feet ; it raises the brine to a height of 346 feet ; but this column of salt water corresponds to a column of fresh water of 397 feet ; the diameter of the piston C is 20J, that of the piston a 10 inches, the larger one having almost four times as great a diameter. The reason of the height of the raised column of water not being four times greater than the height of the impelling water, that is, not 560 feet, is owing to a considerable force being necessary to overcome friction and other resistances. This machine yields, therefore, about 70 per cent, of the absolute maximum, for 397 is to 560 nearly as 70 to 100. The water-column machine at Esang, also between Reichenhall and Rosenheim, which is somewhat differently constructed, raises the spring to an elevation of 1218 feet, equal to the raising of a column of fresh water to a height of 1460 feet. The diameter of 196 WATER-COLUMN MACHINES. the larger piston is 25 feet 8 lines, that of the smaller, 11 feet 3J lines. Great difficulties present themselves in converting the back- ward and forward motion of the piston, in these water-column ma- chines, into a uniformly circular motion, as seen in steam engines, owing to the water not being elastic like steam. But Reichenbach has ingeniously met this difficulty in the construction of a small machine at Toscana, by applying a guiding or directing piston ; we cannot, however, here enter further into the consideration of this subject. MOTION OF GASES. 197 CHAPTER III. Fig. 164. MOTION OF GASES. IF a gas be enclosed in a vessel having any kind of opening, it will escape through the opening as soon as the gas in the vessel is more strongly compressed than the air in the space communicat- ing with the aperture. The laws of the passage of gases through openings in thin walls, and through conducting pipes, are analo- gous to those bodies of liquid with which we have become ac- quainted. The term gasometer is applied to an apparatus serving to maintain a constant discharge of gas. In chemical laboratories, the form most commonly used for gasometers is represented at Fig. 164. A is a cylinder of lacquered tin, about 16 to 18 inches in height, and 10 to 12 inches in diameter, having its upper cover vaulted. On this cover stands a second cylinder 5, open at the top, resting upon three supports, and only \ of the height of the lower one. The upper cylinder is connected with the lower by means of two tubes, of which the one b is exactly in the middle of the cover. This must not quite enter the lower cylinder. A second con- necting tube a reaches almost to the bot- tom of the lower cylinder. In each of the tubes there is a cock, by means of which we may at pleasure establish or interrupt the communication of the two cylinders. At e there is a short horizontal tube, which may also be closed by a cock, and to which a screw is attached, in order to admit of other pipes and openings being connected with it. Near the bottom of the lower cylinder, there is an opening at d directed upwards, that may be closed by 17* 198 MOTION OF GASES. means of a screw or cock. If we wish to fill the lower cylinder with a gas, we first fill it with water in the following manner. The opening at d must be closed, the three cocks opened, and then water poured into the upper vessel. The water flows into the lower cylinder, and, as soon as this is filled to e, we close the cock. The remainder of the air, still in the cylinder, escapes through the tube b. When the lower cylinder is thus filled with water, the cocks of the connecting pipes are closed, and the screw or cork at d taken off. Water cannot flow thence because no bubbles of air are able to enter. But if we insert a gas-conducting tube at d, the water will flow out in its vicinity, whilst bubbles of gas continually ascend from it into the upper part of the receiver. In this manner, the lower cylinder fills itself more and more with gas. We may see how far the cylinder is filled with gas by the glass tube f, which is so connected above and below with the vessel, that the water stands as high in it as in the cylinder. When the whole reservoir is filled with gas, the opening at d is closed, and the cock of the connecting tube a is opened. As soon as the cock e is opened, the gas escapes with a rapidity corresponding to the pressure of the column of water in the tube a. Large gasometers used for gas illumination, are constructed on a different principle: a cylinder closed at the top dips into a large reservoir filled with water, (Fig. 165). This cylin- der is made of tin, is ten yards in dia- meter, contains 100 cubic yards of gas, and weighs, as we will assume, 20,000 pounds. It does not sink in the water, in consequence of its being filled with gas ; but its whole weight presses upon this gas with a force greater than the pressure of the atmosphere. Accord- ing to our assumption, this excess of pressure amounts to 20,000 pounds upon a circular area of ten yards in diameter, which is Fig. 165. BLOWERS. 199 about equal to the pressure of a column of water of 4 inches ; the water must, therefore, stand 4 inches higher without than within the cylinder. Ascending from below, a pipe passes into the cylinder, having its upper end open above the level of the water; this pipe sepa- rates into a number of narrower ones, leading to the mouths of the separate gas pipes, from which the gas pours out with a velo- city corresponding to the pressure in the gasometer. This velocity is constant, because the gasometer, even though it sank more deeply into the w r ater, only loses a little of its weight, as it is only the wall of the gasometer that is here to be taken into account. The pressure upon the gas is modified and regulated by a counter weight. In order to fill the gasometer, the cock in the distribut- ing pipe is closed, while the cock of another pipe is opened, con- necting the interior of the gasometer with the apparatus in which the gas is prepared. Blowers or blowing machines, of various modes of construction, are used in forges. The most applicable kind, and that now generally used, is the cylindrical blower as represented at Fig. 166. Fig. 166. In a well bored cast iron cylinder *#, in which an air-tight piston c may be moved up and down, the piston-rod a passes air-tight through the stuffing box in the centre of the upper cover. The upper and lower parts of the cylinder communicate at the opening 6 and d, with the external air; while the openings at g and/ con- 200 BLOWERS. vert the cylinder with a square box E. At b and d are valves opening inwards, at g and/ valves opening outwards. When the piston descends, the valve at d closes, while that at f opens, all the air being driven from the lower part of the cylinder into the space E. But in the meanwhile the valve at g is closed, while the air presses through the valve at b from without into the upper part of the cylinder. When the piston again rises, b closes, and all the air forced in by the descent of the piston, is carried through the opening at g into the box 6, while/ is closed, and the under part of the cylinder is again filled with air passing through the open valve d. The air compressed in E passes to the space occu- pied by the fire through a tube applied at m. The velocity of the piston is greatest when it passes the middle of the cylinder ; it diminishes the more the piston approaches the upper or lower limit of its course. Hence it follows that the blast yielded by such a cylinder does not pass out in a uniform man- ner at m. As, however, a uniform current is necessary for most smelting processes, care must be taken to regulate it. This is effected either by applying three cylinders to the same air box E, whose pistons do not simultaneously pass the middle point of their course ; or by suffering the air to enter from E into a receiver, whose area is very large in proportion to the volume of the cylinder. The larger this air receiver is, which is termed the regulator, the less influence will the irregularity of the movements of the piston exercise upon the regularity of the current of air passing out of the regulator. As a regulator for a blower, there is used either an air-tight balloon of sheet iron, whose contents are from forty to fifty times as large as that of the cylinder, or else the water regulator represented at Fig. 167, which is quite identical in its nature with the gasometer, as used for gas lighting. In the box .B, consisting of iron plates secured together so as not to admit of the entrance of air, and whose contents far exceed those of the cylin- der, the air pours through the tube D from the cylinder, escaping through the tube C. The air in the box B is enclosed below by water, whose level r r necessarily stands lower within the box than the surface v v without. BLOWERS. 201 Fig. 168. On the difference of the heights of the levels of the water, depend the degree of compression of the air at JB, and the velocity of the discharge through the tube c. In order to determine the pressure of the air in the different parts of the blowing apparatus, a manometer is used, which, when applied to this especial purpose, is termed a wind-measurer. A section of a very well constructed instrument of this kind is repre- sented at Fig. 168. A hermetically closed block-tin box is partly filled with water. A tube a passes through the bottom of the box, having a screw below, by which it may be secured to the blower. The apparatus com- municates by means of this tube with the upper, part of the tin box, where the air is consequently as strongly compressed as in that portion of the apparatus to which the wind-measure is screwed. A graduated glass tube b is connected with the lower part of the tin box. Water is poured through an open- ing in the cover of the box, until the water in the tube stands exactly at zero of the graduated tube, when the opening is closed by a cork stopper. As soon as the air is compressed in the upper part of the tin box, the water rises in the tube without any marked sinking of the level of the water within the box ; the rising of the column of water above the zero point of the glass tube indicates, therefore, the pressure sustained by the air within the apparatus. By means of the cock, the communication between the tin box and the glass tube may be interrupted at pleasure. The most simple form of the bellows is sufficiently well known, but with bellows thus constructed, we are unable to engender a continuous current of air, such Fi lgg as is necessary in forges and in chemical laboratories. For such purposes compound bellows are used, as represented at Fig. 169. If the upper division a of such bellows be filled with air, compressed by the weight resting 202 LAWS OF THE FLOW OF GASES. upon the upper cover, it can only escape by the opening at c, for the valve between a and b closes as soon as the air becomes more strongly compressed in a than in b. When the lower surface of the space b rises, the air is compressed in b, raises the valve leading to a, and presses into the upper space. On the descent of the lowest side, the valve between a and b closes; the valve communicating from b with the air opens, b is again filled with air, which is again forced into the upper space. It will be readily understood that the pouring forth of air from a through the opening c is not interrupted while b supplies itself with air. Laws of the flow of Gases. The same laws apply to the velocity of the efflux of gases that we have given for liquids, that is to say, the velocity of the efflux is c = v/ 2 g s, if s represent the height of pressure. Here, however, s is a mag- nitude not directly given by observation as for liquid bodies ; s designates the height of the column of fluid, whose pressure occasions the discharge, and which is of the same nature and density as that flowing out. Gases contained in a vessel are not, however, at any time compressed by a column of air of equal density, and well defined height, for even if the gas were only compressed by the pressure of the atmosphere, the column of air producing this result is neither of uniform density, nor measurable height. Therefore, even in this case, s cannot be directly obtained from observation. The pressure driving the air from a reservoir is, however, usually measured by the height of a column of water, or mercury, observed by means of a manometer. The value of s, which must be substituted in the above formula for the velocity of the discharge, may, therefore, always be computed from the circumstances observed. [Bernouilli gives the following expression for the velocity of an escaping current of gas: v = ^% k (p-p') P v = velocity of the gas; p = internal, and p' = external pres- sure; and 2 k = a co-efficient equal to 155,610 for gases at 32 F.] The simplest case that can be adduced, is that of air being forced into a vacuum by atmospheric pressure. The medium atmospheric pressure equipoises a column of water 32 feet in LAWS OF THE FLOW OF GASES. 203 height, or 10,4 metres. But the density of the air having to sustain this medium pressure is 770 times less than that of water ; a column of air, therefore, having this density throughout, must have a height of 770 X 10,4 = 8,008 metres to counterpoise the pressure of the atmosphere. For this case, therefore, s 8,008 m , and consequently c = V 2 X 9,8 . 8,008 = 396 ra . If the air pour into a vacuum from a reservoir in which it has been compressed by the pressure of only half an atmosphere, the velocity of the discharge will be precisely as great as in the last case, namely 396 m . The reason of this is easily understood, for although the discharge is produced here by a pressure of only half the quantity in the former case, the air flowing out has here only half the density. Besides, the velocity with which the air rushes into a vacuum is always the same, whilst the pressure on which this velocity depends may be very various. If the discharge be directed towards a space already containing air, although of inconsiderable tension, the tendency to escape will necessarily depend upon the difference of the two tensions. If we designate this difference by a column of air of the height H, and of the density of air more compressed, the velocity of the discharge will be c = v/ 2 g H. We will endeavor to determine the value of H in a case where air more compressed is discharged into atmospheric air of the ordinary tension. Let the compression of the air in the reservoir be measured by a column of water, whose height we will desig- nate by h. This height h gives the difference between the ten- sion of the inner and the outer air, and we have only to determine what must be the height of a column of air of the density of the air in the reservoir, to enable it to counterpoise a column of water of the height h. If we had to do with air of medium atmospheric pressure, we might substitute a column of air of the height of 770 h for the column of water of the height h. In order, however, to equipoise the same column of water, we want a column of air of smaller height if the air be denser, the requisite height bearing an inverse relation to the density of the air. Atmospheric air of average pressure, which is 770 times lighter than water, is likewise compressed by a column of water of 32 feet or 10,4 metres, whose height may be designated by 6, whilst 204 LAWS OF THE FLOW OF GASES. the air in the reservoir has to sustain the pressure of a column of water of the height b f + h, if V designate the height of a column of water corresponding exactly to the then height of the baro- meter. The density of air of average pressure is, therefore, to the density of the air in the reservoir as b : b' + h ; the air in the reservoir is, therefore, - times as dense as the air of average atmospheric pressure; instead, therefore, of a column of air of the height of 770 h of this more rarefied air, we must substitute a column of the height - ^ of this more rarefied air, and this b' + h value of ~ ' we must put in the above equation in the b' + h> place of H; for a column of air of the height - , and the density of the air in the reservoir would entirely counterpoise the column of water of the height h. The velocity of the efflux is, therefore, in this case We should obtain the quantity discharged in a second, if we multiplied the area of the opening by this value of c, provided that the particles of air flowed out in every part of the diagonal section with equal velocity. The quantity discharged in t seconds would be according to this *_,., Experience, however, shows, as we have seen in liquid bodies, that the actual quantity discharged is far smaller than what is yielded by theory, and we must multiply the theoretical quantity by a definite factor ^ in order to obtain the actual amount. For water, this factor is 0,64, and is almost entirely inde- pendent of the height of the pressure, increasing only very inconsiderably when the height of the pressure diminishes. For gases, however, the value of /* is very variable. According to Schmidt, who was the first to direct particular attention to this subject, /* is equal to 0,52 at a height of pressure of three feet (water) ; while d"* Aubuissori* s experiments yield the value of /* as equal to 0,65 at heights of pressure, varying between from 0,1 to 0,5 of a foot. LATERAL PRESSURE OF GASES. 205 The difference between the theoretical and actual quantity discharged, depends upon causes analogous to those affecting liquid bodies, and we may, therefore, conclude that a contractio venae, must occur, although it does not admit of direct obser- vation. Cylindrical as well as conical conducting pipes, whether the wide opening be turned inwards or outwards, increase the quan- tity of the gas discharged. Lateral pressure of Gases in the flowing out. When air moves through conducting tubes, there is a resistance to be overcome from friction, for which a portion of the tension of the compressed gas must be employed, and thus be lost to the motion. The pressure sustained by the walls of the tube from the ten- sion of the air passing through, diminishes in proportion as it approaches its mouth, as we may see by applying manometers to different parts of the tube. This is quite analogous to the phe- nomena observed in the motion of liquids passing through con- ducting tubes. The phenomenon of suction takes place in the motion of gases precisely in the same manner as in the efflux of liquids. If we make an opening of one or two inches in diameter in the bottom of a vessel containing compressed air, the air will escape with great force. If we connect a disc of wood or metal, seven or eight inches in diameter, with the opening, it will not be pushed off after the first resistance has been overcome : it will oscillate quickly, approaching and retreating from the opening within very short intervals. The air in the mean time will escape with much noise between the disc and the wall. On attempting to remove the disc, we must use as much force as if it were cemented fast to the wall. This phenomenon is explained in the following manner : the stream of air leaving the open- ing, must spread itself in a thin layer between the disk and the wall (Fig. 170). The density re- maining unchanged, it must extend in proportion as it approaches the edge of the disc ; it finds itself consequently in the same case as a liquid stream which is to fill up the constantly increasing 18 206 LATERAL PRESSURE OF GASES. diagonal section of a conical conducting pipe. Between the disc and wall, a vacuum is formed, in consequence of which, the atmospheric air pressing from below against the disc forces it against the wall. We may make this experiment on a small scale by blowing air with the mouth through a tube, at the end of which is a flat smooth disc. If we put a card while blowing to the opening of the tube in the middle of the disc, we shall observe the above- mentioned phenomenon. Faraday has suggested the most simple mode of making this experiment. On laying the fingers of the open hand closely together, a series of intervals will still remain from joint to joint : whilst the hand is held thus horizontally, with the palm turned downwards, we must apply the lips to the space intervening between the index and middle finger (near the roots), and blow with as much force as possible. If then a piece of paper, of three or four square inches, be applied to the opening, through which this current of air passes, it will neither be blown away by this current, nor will it fall by its weight until we cease blowing. ACOUSTICS. 207 SECTION IV. ACOUSTICS. CHAPTER I. LAWS OF THE MOTION OF WAVES IN GENERAL, AND ESPECIALLY OF WAVES OF SOUND. Vibratory Motion. If a pendulum be brought out of its position of equilibrium, and then left to itself, it will in the first place be carried back to a state of equilibrium by its gravity, but having returned to that point, it cannot remain at rest, because it reaches it with a velocity that drives it out of its position of equilibrium ; and hence the pendulum makes a number of oscillations, the laws of which we have already mentioned. The mutual position of the particles remains unchanged in the motion of the pendulum. If, however, the relative position of the particles of a body be disturbed by any external cause, and if any forces be present, tending to restore' the original state of equilibrium, they will also take up an oscillatory motion, which differs essentially from the motion of the pendulum by the mutual position of the particles changing every moment ; we have here, therefore, to consider not only the oscillatory motion of an indivi- dual particle, but also the changes in the relative positions of the particles. Fig. 171. \ 208 ACOUSTICS. The oscillatory movement of the individual parts of a body may be of such a kind that all particles simultaneously come into motion, simultaneously pass the point of equilibrium, simulta- neously reach the maximum of their oscillation, and simulta- neously begin their retrograde motion. Such are the vibrations of a steel bar fastened at one end, Fig. 171, and of a cord ex- tended between two fixed points (Fig. Fig. 172. 172). Such vibrations are termed by '"";:.- Weber, "standing vibrations." If the motions of the individual parts are of such a kind that vibratory motion proceeds from one par- ticle to another, so that each makes the same oscillations as the preceding one, with the sole exception of the motion beginning later, we have progressive vibrations. By progressive vibrations, waves are formed. The motion, the advance of the wave, is to be regarded as essentially distinct from the oscillations of individual parts. Examples of wave-motion are afforded by a quiet surface of water, on which we drop a stone ; by a long tense line, near one end of which we strike with a sharp blow, the waves of sound in the air, &c.; we will consider these various wave-motions more particularly. The vibratory motions may be greater or smaller, according to the cause of the disturbance of the equilibrium, and the nature of the force, striving to restore the particles to their former condition of equilibrium ; so that the external form of the body may in con- sequence suffer either well-marked or inconsiderable changes ; the vibrations may be slower or faster: they may be so slow as to enable us to follow them with the eye, and count the several oscillations; while, on the other hand, they may be so fast as no longer to admit of being distinguished. If the vibratory motion of a body exceed a certain degree of velocity, its combined effect may produce a certain impression by creating undulatory motions in the surrounding media, by means of which, they are conveyed to peculiarly adapted organs of sense, occasioning to these latter a characteristic sensation. Thus, vibrations whose rapidity lies within certain limits, which we purpose speaking of more fully, occasion waves in the air, or in other elastic media, which, consisting in alternate condensations and rarefactions, are conveyed to the ear, and received by that organ as sounds. WATER-WAVES. 209 Incomparably more rapid vibrations of the particles of a body conveyed to the eye, produce the impression of light, by means of the undulatory motion of a peculiarly elastic fluid, which we term ether. As the vibrations of sound as well as those of light are trans- mitted by undulatory motions, we will at once proceed to consider the most important laws connected therewith, beginning with water waves, as in them is incorporated the idea of a wave, and because a right comprehension of these will help to elucidate other undulatory motions, as, for instance, sound-waves, which furnish especially interesting matter of consideration. Water-waves. If we throw a stone into the water, circular waves will be formed, spreading themselves from a centre (the spot where the stone fell), in all directions, with uniform velo- city, when unopposed by any impediment. The waves consist of alternate elevations and depressions succeeding each other pretty quickly, and continuing to spread outward from the centre. When a wave elevation proceeds outward, the individual par- ticles of water do not share in this advancing motion, for we see when a piece of wood swims on the water, that it is alternately raised and lowered as the wave elevations and depressions uni- formly glide away from under it. The force by which the water-waves are propagated, is gravity, for if, from any cause, an elevation or a depression be produced on the horizontal surface of the water, the gravity of the separate particles of water will endeavor to restore the disturbed horizontal plane, by which means an oscillatory motion is produced, which by degrees is propagated from one particle to another. As soon as regular waves have been formed, the separate par- ticles of water on the surface describe, during the advance of the wave, curves returning into themselves, which, in cases of extreme regularity, are circles, while in cases where the front of the wave elevation is not equal to the succeeding one, the individual par- ticles of water describe curves which are not closed, but such as we have represented at Figs. 173 and 174. Let us now consider somewhat more ^J_^ attentively, the connection between the (^_^/ \^? motion of the individual particles of water and the propagation of the wave. Let us assume that a regular undulatory motion, advancing 18* 210 WATER-WAVES. from left to right, spread itself to the particle of water in Fig. 175, obliging it to describe a circular course. Now while the particle completes, for the first time, its circular course, motion is propagated to a certain distance. Let the particle marked 12 Fig. 175. 12 15 be the one to which the vibratory motion is propagated from 0, while performs its revolution ; then will 12 begin its first revo- lution at the moment that enters upon its second. If we now suppose the circumference of the circle described by the particle to be divided into 12 equal parts, as well as the space intervening between and 12, the undulatory motion in the direction from towards 12 will always advance one division further, whilst the particle describes T Vth of its circular course. While the particle describes the first 12th part of its course, the undulatory motion extends to 1 ; and while is passing over the first quarter of its course, the same motion is transmitted to 3. Fig. 176 represents the moment in which the particle has Fig. 176. o i traversed the quarter or ^ths of the circle ; the particle 1 has at that moment passed over -&ths ; the particle 2 T Vth ; while the particle 3 is not yet displaced from its position of equilibrium. Fig. 177 shows the moment in which the particle has traversed Fig. 177. half its course ; the particle 1 T 5 2 ~ths ; the particle 2 T \ ths ; and the particle 3 f'jths of their course ; while the particles 4 and 5 WATER-WAVES. 211 are in the same position as the particles 1 and 2 of the former figure. The particle 6, although not removed from its equilibrium, is about to begin its motion. The particle 3 has reached its lowest point; here is the centre of a wave-depression. If, now, -rath of the time necessary for a particle to complete its circuit be passed, the particle 3 will have come into such a position with reference to its original place, as is now the case with the particle 2; and the particle 4 will have reached its lowest position, being J of the circle removed from its position of equili- brium ; the wave-depression has, therefore, advanced from 3 to 4 in this interval of time. Fig. 178 represents the moment in which the particle 0, having Fig. 178. traversed f ths of its course, has reached the highest point of its circuit ; here, therefore, is the summit of a wave-elevation. The particle 1 has traversed Aths; the particle 2 -rVhs; and 3 -j^ths of its course ; the particles 4, 5, 6, 7, 8, are in the same position as 1, 2, 3, 4, and 5 of the former figure. From the moment re- presented in Fig. 177 to the moment shown in Fig. 178, the wave- depression has moved from 3 to 6. Whilst the particle is traversing the last quarter of its course, the wave-elevation advances from to 3, and the depression from 6 to 9 ; while, at the same moment that has ended its course for the first time, and is entering upon a second circuit, the particle 12 begins its course for the first time. This moment is represented in Fig. 179, which needs no further explanation. Fig. 179. 212 WATER-WAVES. Fig. 180 represents the moment in which has traversed its Fig. 180. course a second time ; at this time 12 will have made its first circuit ; motion been transmitted to 24, a wave-elevation is seen at 3, another at 15 ; one wave-depression at 9, and another at 21. If the undulatory motion continue uninterrupted, the individual particles of water will likewise pursue their circuits ; the wave- elevations, as well as the wave depressions, advancing uniformly from left to right, while one particle after the other reaches the highest and lowest point of its circuit. Thus the wave-elevations and depressions advance owing to the same circular motion being imparted to all the particles of water, each entering upon that motion successively. The distance between two adjacent particles in similar con- ditions of vibration, is called the length of a wave; as the distance between and 12, and between 12 and 24, these particles begin- ning their oscillation simultaneously, and reaching simultaneously their highest and lowest points. According to this, the distance from the summit of one elevation to the next, as from 3 to 15 in our figure, or from the middle of one depression to the middle of the next, as from 9 to 21, constitutes, likewise, the length of a wave. Those particles that are removed J of the length of a wave from each other, as and 6, 3 and 9, 9 and 15, are always in opposite conditions of vibration. The particle 9, for instance, forms the lowest point of a depression ; 3 and 15, on the contrary, the summit of wave-elevations. The particles and 6 are certainly both in their position of equilibrium, but the motion from is directed downward, while that from 6 is directed upward. The time required by a particle to complete an oscillation is termed the time of an oscillation ; whilst a particle is completing an oscillation, the wave advances a length. Linear-Waves. As has been already remarked, the courses of LINEAR-WAVES. 213 the particles of water are not always strictly circular, as we have assumed them to be in our figures, or even curves returning into themselves. This circular course is often converted into an ellip- tical form; sometimes the horizontal, sometimes the vertical diame- ter being the greater. If the horizontal diameter were null, the separate particles would merely oscillate up and down at right angles to the direction in which the waves are propagated. This kind of motion propagates the waves along a stretched cord. We shall, on a future occasion, have more to say regarding this kind of undulatory motion when we enter upon the theory of light. Fig> 181 . The lines marked from 1 to 6, in Fig. 181, are designed to illustrate the transmission of such linear waves. These lines cor- respond accurately with the Figs. 176 to 180, be- ing derived from the lat- ter, on setting down the horizontal part of the mo- tion as null ; and they will not, therefore, require any further ex- planation. If a linear- wave, advancing towards one fixed point, reach that point, it will be reflected returning to the other end, and will pass many times backwards and forwards. But if new waves be con- tinually formed, they will, in meeting the reflected waves, form standing waves, from the combined action of the two systems of waves. We will not here pause to consider any further the formation of standing waves by the combined action (interference) of the direct, and the reflected wave-system, since we purpose treating more fully, and on similar principles, of the formation of standing air- waves, depending on the interference of a direct and reflected 214 LINEAR-WAVES. wave system ; at present, we will limit ourselves to the conside- ration of the kind of motion manifested in a line or cord during such standing vibrations. The most simple case is where the line vibrates throughout its whole length as represented in Fig. 182. This motion may be 182 . brought about by removing the centre of a moderately tensely drawn line, somewhat out of its equilibrium (which is best done by moving it somewhat to the right or left), and then leaving it to itself. All the particles are simultaneously on one and on the other side of the position of equilibrium ; they simul- taneously attain the maximum of their distance from the point of equilibrium on the right side, and simultaneously come to the extremities of their course on the other side. The particles, there- fore, whose points of equilibrium are /, d, and g, simultaneously reach /', d f , and g f ; and simultaneously passing their point of equilibrium, moving in the same direction, they simultaneously come to/", d", and g". While all the particles are always, at the same time, in similar conditions of equilibrium, the amplitude of their oscillations is alone different, being greater for the particle d than for/ and g. The oscillations of a tense string disturbed from its position of equilibrium, or those induced by a bow drawn across the middle of its length, are of the same kind. But the vibrations of the string are so rapid, that the separate oscillations can no longer be distinguished, but, on the contrary, only a tone is produced. We shall have once more further to consider the vibrations of the cord with reference to this tone. The vibrations of a somewhat loosely strung cord are slow enough to be counted ; it is difficult, however, to produce a wholly regular oscillatory motion in the manner indicated, if we bring the middle of the line out of its equilibrium from below, since in that case not only the elasticity of the line will bring back the particles to their conditions of equilibrium, but gravity will also act ; but if we move the middle of the line out of its equilibrium to the right or left, the motion is partially that of the pendulum, because if the line be not too tightly strung, the middle always LINEAR-WAVES. 215 hangs somewhat down ; if, however, we draw it tighter, the vibra- tions become too rapid to be distinguished. These regular vibrations in a string are best distinguished, if one of its extremities be fastened, while the other is held in the hand, and made to describe small circles with uniform velocity. When we find the right degree of rapidity for the motion of the hand, which is easily done, the string will fall into such motion, that its centre will describe a large circle around its point of equilibrium. All the other points of the line then turn likewise in circles round their positions of equilibrium ; the circles being smaller, the nearer the points lie to the extremities. If we accelerate the motion of the hand, the regularity of the motion of the string will be disturbed ; it is easy, however, so to accelerate the rapidity of the motion of the hand, that there shall be a point of rest in the middle of the string. Each half will vibrate exactly as did the whole line in the former case; the middle of each half describes larger circles than the other points, and here, therefore, a belly is Fig. 183. formed. In Fig. 183 we have represented two ventral points, and one node, for thus we term the resting point k, separating the two vibrating portions. When / reaches its highest point, m attains its lowest position, and conversely. By increased rapidity of the hand, we can easily succeed in producing two nodes, and three bellies as represented at Fig. 184. Fig ' ] In the same manner the line may be divided into many parts, always separated by a node. The nodes may also be observed in tense cords. Fig. 185 represents a tense cord from which J of the length has Fi ^ 185 - been separated by means of '^::::^Z:::::'-^^:CZl^:--' ;n -:C^'i:r^- J a bridge, which so divided the cord into two parts, that the one is twice as long as the other. On touching the smaller parts with the bow, the other portion will fall into vibrations, and one node at , and two bellies at v and v' will be formed. The position of these nodes is proved 216 LINEAR-WAVES. by little figures of paper remaining fixed at these points, which fall off at other parts of the cord. If we so arrange the bridge, that the string is divided into two parts, of which the one is only ^th the length of the other, we shall have two nodes and three bellies on touching the string with the bow. In metallic plates, bells, &c., regular vibrations may also be produced. In order to make plates vibrate, we may use the vice 186> shown in Fig. 186, which must be firmly fastened. The plate is placed between the cylinder a and the screw 6, both of which terminate in a piece of cork or leather. If the plate be sufficiently well screwed on, we may produce vibrations by strokes of the bow. We may thus cause plates of wood, glass, metal, &c., to vibrate, whether they be triangular, square, round, elliptical, &c. The vibrating plates produce like the vibrating cords, tones which are sometimes high, and sometimes low. It is observed further, that the plates may be separated into vibrating parts, and lines of repose or nodal lines for each one of these tones. In general, the extension of the vibrating parts diminishes, and consequently the nodal lines become more numerous as the tone rises. In order to prove the existence of these nodal lines, we may strew fine dry sand on the upper surface of the plate, when the sand will rise and fall during the tone, and at last accumulate upon the nodal lines. In this manner arise the sound-figures as they were named by their discoverer Chladni. A number of different figures may be produced by means of the same plate, according as we move the bow more or less violently, or with more or less rapidity ; or, again, according as we change the point of support of the plate, and touch various parts of its edge. At Figs. 187 and 188, a number of sound figures are repre- sented as produced with a square plate. For example, in order to obtain the cross whose arms unite the middle points of the parallel sides of the square (see the first figure) we must fix the middle of the plate, and move the bow at one corner. By fixing the middle of the plate, and moving the bow in the middle of one TRANSMISSION OF SOUND THROUGH THE ATMOSPHERE. 217 Fig. 187. Fig. 188. side of the square, we form a cross, whose arms unite the oppo- site corners of the square, Fig. 188. Triangular and polygonal plates yield similar results. Transmission of Sound through the atmosphere. The vibratory motion of any body surrounded by air gives rise in it to an undu- latory motion, which, on being transmitted to the ear, produces the sensation of sound. Generally speaking, it is by means of the atmosphere that the sound-waves are transmitted to our organs of hearing, but still all other elastic bodies, solid as well as fluid, are capable of conducting sound more or less perfectly. Sound can- not, however, be transmitted in a vacuum. Let us lay a small cushion of wool or cotton in the middle of the plate of the air- pump, on the top of this a piece of clock-work provided with a little bell, and which can be made to strike. Over the whole is placed a bell glass, provided above with a leather cap, through which a rod passes, by whose turning the clock-work is set into action. At the instant the works begin to act, the clapper strikes at the intervals upon the bell; no sound, however, will be heard, if the bell have first been exhausted. On gradually admitting the air, we distinguish the tone becoming louder and louder as the bell becomes more filled with air. Sound cannot, therefore, be propagated through a vacuum. The loudest noise on earth cannot, therefore, penetrate beyond the limits of our atmosphere, and in the same manner not the faintest sound can reach our earth from any of the other planets; thus, the most fearful explosions might take place in the moon, without our hearing anything of them. Saussure asserts that the discharge of a pistol makes less noise on the summit of Mont Blanc, than the report of a small toy 19 218 TRANSMISSION OF SOUND THROUGH THE ATMOSPHERE. cannon fired off in the valleys below ; and Gay Lussac found that when he had risen in his balloon to an elevation of 700 metres, (758 yds.,) and was consequently in a highly rarefied atmosphere, his voice had lost very much of its intensity. Sound may diffuse itself not only through the atmosphere, but through all kinds of gases and vapors. To prove this, we will Fi 189 hang a little bell to an untwisted hemp line in a large balloon (see Fig. 189). If the air be ex- hausted in the balloon, we shall no longer hear the sound of the bell ; as soon, however, as a few drops of a volatile fluid, as, for instance, ether, be intro- duced into the balloon, vapor will be immediately formed, and the tone will again become audible. Sound is readily transmitted in water; the diver can hear what is said on the shore, while persons on the shore can distinguish the noise made by the concussion of two stones at great depths below the surface. Solid bodies can not only produce, but also transmit sound. If we apply the ear to one extremity of a beam, 20 or 30 yards in length, we can clearly hear a slight tap made at the other end of it, although the sound may be so indistinctly conveyed by the air that the person causing the noise may be scarcely conscious of it. In order to comprehend the way and manner in which vibra- tions of sound are transmitted through the atmosphere, we will suppose the air at one end of an open tube to be put into a con- dition of oscillation by the vibratory motion of a piston applied at the other extremity. Fig. 190 represents such a tube; the lines drawn at equal distances designate strata of air of equal density; p is the piston which moves rapidly backwards and forwards along the distance a g, Fig. 191. Fig. 191. Fig. 190. Fig. 192. Fig. 193. 3 6 9 12 15 18 21 369 12 15 16 21 24 TRANSMISSION OF SOUND THROUGH THE ATMOSPHERE. 219 I Fig. 194. HM _ > ^ MI 3 6 9 12 15 18 21 24 Such an oscillating motion cannot, as we have already said, be uniform. Let us suppose the time necessary for the piston to move backwards and forwards, that is, from a to g, and again from g back to a, to be divided into twelve equal parts ; it will traverse in the first of these periods the distance a b, in the second the dis- tance b c, in the third c , a condensation would again occur at the same moment at c', and a rare- faction at a', consequently there would be like conditions at a and c', and opposite conditions at c.and a* '; but now the wave is reflected at b, c f therefore coincides with c, and a' with a ; condensation and rarefaction will conse- " quently cease at c as well as at a ; there being nothing at these points but a simple motion backwards and for- wards of the layers of air, without any marked change of density. Let us now see what goes on at c?. I va. - If the maximum of density be advanced from a to d, it would also have gone on from c f to d f , if there were no reflection at 6; at d and d 1 there are consequently always equal conditions of oscillation ; but by the reflection at 6, d' is thrown upon d ; hence the maximum of the density of the incident and reflected waves, and \ an undulation N later, the maximum of the rarefaction of both, coincide; and consequently there will be here alternately an in- creased condensation and rarefaction. If, now, we investigate the condition of oscillation of a layer of air at d, we shall find that it has no motion, for if the waves advanced beyond 6, there would be equal conditions of oscillation at d and d', which w r ould always move towards the same side with uniform velocity ; but if the wave system be reflected, the reflected wave of the layer of air d will impart an opposite motion to that which it would have imparted without any reflection of the layer of air d' d is, therefore, always affected by both wave- systems with equal, but oppositely directed velocities; and consequently this layer of air must remain at rest. The Figs, from 206 to 208 show the air-waves formed in a tube fths of the length of the incident sound- - wave. In Fig. 206 we see a maximum of condensation at d, and a maximum of rarefaction at the bottom of the tube at 6; all the 232 LAWS OF THE VIBRATIONS OF MUSICAL TONES. Fig. 206. Fig. 20' Fig. 208. layers of air lying to the left of d, simultaneously begin their motion in the direction indicated by the arrow; whilst the layers lying to the right of c?, begin to move towards the right. After J of an undulation, the separate layers have reached such a position that the air is of uniform density throughout the whole tube, as intended to be represented in Fig. 207 ; after another J of an undulation moving in the direction indicated, the condition represented in Fig. 208 will occur; now there is the greatest condensation at b, and the greatest rarefaction at d. From this moment the separate layers of air again begin to move towards d, and then the condition represented in Fig. 206 recurs after J of an undulation. The layers of air lying to the right and left of e?, either move simultaneously away from, or simultaneously towards d, which has no motion; the layer of air d forms, therefore, a node of oscil- lation. The point c and a, where there is neither rarefaction nor con- densation, but where the layers of air oscillate with the greatest amplitude, are termed bellies. In order to put the air within a closed tube, into such standing vibrations, it is only necessary to bring an oscillating body before the open extremity of the tube, which may give such a tone, that the length of the tube is equal to J, f, |, &c., of the wave length of the tone. We may use for this purpose an ordinary tuning-fork, holding it over a glass tube of about two inches in length, closed below; or we may take a glass or metal-plate in the same manner as LAWS OF THE VIBRATIONS OF MUSICAL TONES. 233 when used to produce Chladntfs figures by the help of the bow of a violin, holding a tube, closed below, under it. If the tube be of the right length, the enclosed air, being thrown into a state of standing vibrations, will become resonant, considerably increasing thereby the intensity of the tone, as may be clearly perceived by passing the sounding body backwards and forwards before the opening of the tube; the tone becoming alternately stronger and weaker as the body is brought to the opening or beyond it. If the tube should be too long for the sounding body that is used, it may easily be brought in accordance with it by pouring water into it; that is to say, it may be thus shortened until it have the length proper for the sounding body. In order to throw the enclosed air into regular vibrations, or to make it resonant with the sounding body, it is not indispensably necessary to bring a sounding body before the opening of a tube. Thus, in organ pipes, there is a current of air flowing past the open end of the tube, breaking against the edges, and creating, by its impulses, waves that are reflected on the bottom, and interfere with the newly incident waves. Although these impulses are at first not quite regular, they are soon regulated by the accession of reflected waves, provided the tube sound well, so that regularly standing waves are formed, by means of which the air in the tube becomes resonant. The notes yielded in this manner by a tube, are of the same kind as those which must be given forth by another sounding body brought to the opening of the tube for the purpose of inducing spontaneous sound in the enclosed air. The simplest way of making air sound in a small tube is by holding it in a vertical position before the mouth, turning the closed end downwards, whilst the open extremity is held to the lower lip, arid we blow obliquely towards the edge of the tube. Notes are naturally higher in proportion to the shortness of the pipes. Organ pipes have generally the arrangement represented in the following figures. We divide them into the pedal, yielding the wind, the mouth and the tube containing the column of air, the vibrations of which produce the note. The pedal is hollow, (Figs. 209 to 213,) and through this cavity the wind passes by means of a fine slit into the tube. The mouth-piece b b' is more or less open, that is to say, its upper part is more or less removed 20* 234 OPEN PIPES. from the lower, and not unfrequently the former is movable, so as to open or close the mouth-piece at will. Fig. 209. Fig. 210. Fig. 211. Fig. 212. Fig. 213. I The organ pipes are filled with wind by means of bellows. If air be blown into the pedal of the tube, there will be a thin layer formed at its passage from the air-hole, breaking against the upper lip, and thus imparting those impulses to the air in the tube, which occasion the notes. The same tube closed at one extremity, may yield many notes. The deepest having a wave-length four times as great as the length of the tube ; the higher notes of the pipe correspond to a wave- length three times, five times, &c. as short as the wave-lengths occasioned by standing vibrations, having threet imes, five times, &c. as short a duration of oscillation as the deepest note of the pipe. The pipe yields the deepest note with a faint wind, and the highest notes with a strong wind. Open Pipes. A stronger condensation of air may occur at the end than in the middle of the pipe, as the air cannot escape laterally from the former. If, now, the condensed portion of a wave arrive at the open extremity of the tube, the layers of air may easily escape in all directions on their passage from the tube, and a rarefaction thence arise ; which, being reflected, as it were, from the open end of the tube, traverses it in an opposite direction, and so standing waves are here formed. OPEN PIPES. 235 The returning wave is naturally not so intense as the original one. As a condensation always coincides with a rarefaction at the open extremity of the tube, a belly must necessarily arise here, while nodes of oscillation can only be formed in the interior of the tube. If a wave-length I belong to the note of the body by which the air in the tube is to be brought to sound, the length of the shortest open tube corresponding to this note will be ; that is to say, the tube is half as long as the wave-length of its note. If, there- fore, the deepest notes of one open and one covered pipe are to be equal, the open pipe must be twice as long as the other. A node of oscillation occurs in the middle of the length of an open tube in forming the deepest note, and a belly at each ex- tremity, as represented in Figs. 214 and 215. Fig. 214. Fig. 215. Fig. 214 represents the moment when the greatest condensation takes place in the middle of the tube; while the layer of air re- mains at rest in the tube, the air begins to move away on both sides from the middle, as indicated by the arrow ; rarefaction is at its maximum half an undulation afterwards in the middle of the tube, and now the layers of air begin to move towards the middle from both sides. In the next highest note, a belly occurs in the middle of the tube, and nodes at the points a and b, which are J of the length of the tube from the extremities. If condensation be at its maximum at a, as represented in Fig. 216, then the Fig. 216. < 272> sequently divergent, this divergence is greater after their pas- sage through the glass than was the case with the parallel incident rays; the nearer the luminous point is to the lens, the nearer the point of divergence, or focus, therefore, approaches to the glass. We have still to consider the case in which the incident rays are convergent. If the incident rays converge towards the focus F on the other side of the glass, the refracted rays emerging from the lens are occasionally parallel to each other, this being the SECONDARY AXES. 281 converse of what is represented in Fig. 272. If the incident rays converge more strongly, they will still converge after being refracted ; but if the incident rays converge towards a point t, Fig. 273, lying at a greater distance from the glass than the chief focal point, they will still diverge as if they came from a point before the glass, as seen in the figure. The consideration of this Fig. 273. last case is important to the right understanding of Galileo's tele- scope, of which we purpose shortly to speak. Secondary axes. Hitherto we have only considered those lumi- nous points that lie on the axis of the lens ; it now remains to show that what has been said applies also to points not lying in the main axis, provided that the secondary axes make only a small angle with the main axis. By the term secondary axis, we designate the line we may imagine to be drawn from a point, not lying on the main axis, through the middle of the lens. Let H, Fig. 274, be a luminous point not situated upon the main axis ; then all the rays of light issuing from it will be united Fig. 274. in a point ff, lying in the secondary axis M N f , and as far re- moved from the lens as the point of union T of the rays issuing from a point T 9 which lies upon the main-axis, and is as far re- moved from the lens as H. This is easily proved. The central ray H M f passes unbroken through the lens; further, H c = T c and the angle c TM= c H M' (if not exactly, still very nearly so) ; and since the ray 7 c diverges as strongly at c as He, therefore the angle He H 24* 282 IMAGES PRODUCED BY LENSES. T c T ; consequently the triangle H c H = to the triangle T c T, and thus T T = H H ; H is therefore as far removed from the lens as T. The same result is obtained by a comparison of the triangles Id T audHdH'. The field of a lens is the angle which two of the secondary axes make together; this definition will not materially affect the cor- rectness of our proofs. Of the Images produced by Lenses. Let Jl B, Fig. 275, be an object on one side of the lens V W 9 but further removed from it Fig. 275. than the focal point F. The rays emitted from A are united at a point a upon the secondary axis drawn from # through the mid- dle of the lens ; a is therefore the image of */?, and b is the image of B, consequently a b is also the image of the object A B; the image is in this case inverted, and is a true convergent image. Seen from the middle of the lens, the image and object appear at the same angle, for the angle b o a is equal to the angle B o A, being angles at the vertex ; the greater size of the image or of the object depends upon which of the two is furthest removed from the glass. If we assume that the object lie twice as far as the focal distance from the glass, the image will be formed on the other side at an equal distance; in this case, therefore, the image and the object are equal in size. If the object approach nearer to the glass, the image will recede, becoming, consequently, larger. We therefore obtain inverted enlarged images of objects stand- ing further from the glass than the focal distance, yet not as far IMAGES PRODUCED BY LENSES. 283 as twice that distance ; thus the image a b in our figure is larger than the object A B. If the object be further removed from the glass than twice the focal distance, the image will be nearer; we therefore obtain inverted diminished images of distant objects. If, for instance, a b 9 Fig. 275, were an object lying more than twice the focal distance from the glass, we should have the diminished image AB. If we term the size of the object g, that of the image g 7 , the distance of the object from the glass 5, and the distance of the image m, we have g : g' = b : m, that is, the image and object are to one another as their distances from the lens. In a lens of short focal distance, the images lie nearer to the glass than in one of greater focal distance ; lenses give images, therefore, small in proportion to the shortness of the focal distance ; and, conversely, lenses give enlarged images of small objects lying near their focal point ; at an equal distance from the lens, the images will be larger in such lenses as have a small focal distance, because in that case the object approaches nearer to the lens. If the object be within the focal distance of the lens, no con- vergent image of Ji can be formed, because the rays emitted from a luminous point, which lies nearer to the glass than does the focus, still diverge after their passage through it. Let Ji JB, in Fig. 276, be an object lying within this focal distance ; then the rays pass- ing from A will diverge after emerging from the glass as if they Fig. 276. 284 IMAGES PRODUCED BY LENSES. came from a. We may easily find the distance of the point a from the glass by the constructions already given. The rays coming from B diverge, after their passage through the glass, as if they came from b ; if, now, there be an eye at the other side of the glass, it will receive the rays of light issuing from the object Jl B in the same manner as if they had proceeded from a 6; a b is, therefore, the image of Jl B. As the object and image both lie within the same angle a o 6, but the former is nearer to the glass, the image is evidently, in this case, larger than the object. If we use a lens as a microscope to observe small objects, the en- larged image seen, is of the kind described. We shall subse- quently revert to this subject. Concave glasses do not give convergent images, but only such as arise from convex lenses Flg> 277 ' when the object lies within the focal distance. As a con- cave lens causes the rays emitted from a point to diverge as if they came from a point lying nearer to the glass, it is evident that concave glasses yield diminished images of objects, as we may easily see from Fig. 277, where A B is the object, and p q the image. DECOMPOSITION OF WHITE LIGHT. 285 CHAPTER III. Fig. 278. Fig. 279. DECOMPOSITION OF WHITE LIGHT. White Solar Light is composed of different colored rays. To prove this, we need only form a solar spectrum in the manner already indicated. In Fig. 278, let m be a mirror, which, placed before the shutter of a darkened room, throws the rays of the sun into it through the opening o; p is the refracting prism, and t a wall on which the images are thrown. Before apply- ing the prism, we see a white, round image at g, but through the prism we obtain an elongated colored image r u. Fig. 279 exhibits the appear- ance observed upon the wall t. This colored, elongated, solar image is called the spectrum. The length of this spectrum increases, cteteris paribus, in pro- portion to the refracting angle of the prism. It also depends upon the substance of which the prism is formed. By the illustration given at Fig. 278, we shall easily see that a white band is formed in the middle of the spectrum, provided its length is, at least, not twice as great as its breadth ; if, how- ever, the spectrum be very much elongated, the white will totally disappear, and we shall distinguish seven principal colors in it, in the following order : red, orange, yellow, green, blue, indigo and violet. These colors are termed prismatic, and simple colors of the rainbow. We shall soon see that there are actually a very great number of different colors in the spectrum, but that among these the eye distinguishes the seven above named. 286 DIFFERENT COLORED RAYS. The red end of the spectrum is always turned towards the side at which the round, white sun-image g, Fig. 279, would appear, if the prism did not intervene ; the red rays suffer, there- fore, the least amount of deviation. If the opening in the shutter be about -^th of an inch in dia- meter, when the refracting angle of the prism is 60, and the spectrum is received at a distance of 6 yards, we shall obtain a perfect separation of the colors ; that is, the spectrum will every- where appear vividly colored, without showing any trace of white in the centre ; the separate colors appear, however, purer when the opening is smaller. In order to see the prismatic image, it is not necessary to pro- duce a solar spectrum by means of a prism on a white wall, it being sufficient to look through a prism towards a bright, narrow object. If, for instance, we look at the flame of a candle through a prism held vertically, it will appear considerably extended, and colored in the manner we have mentioned. If we cut a small opening of about iVth of an inch in diameter, in the shutter, we shall see the clear sky through this opening; that is, a light disc upon a dark ground. If, then, we look at this disc through the prism, we shall perceive, instead of the white circle, a very much elongated colored image, to which all that we have said of the spectrum cast upon the wall, equally applies. The differently Colored Rays are unequally refrangible. This follows from white light admitting of being decomposed by the prism into rays of different colors; the red rays, after passing through the prism, form an angle with the violet, the violet rays deviating more from their original direction than the red. The violet rays are most strongly refrangible, and the red the least so. The green rays are more refrangible than the red, and less so than the violet, because in the spectrum they lie between the red and violet. If we were to suppose for a moment that white light contained only red and violet rays, it is evident that, instead of the spectrum, we should only have two solar images separated from each other, of which the one would be red, the other violet. We can, in fact, make such separate images apparent: many bodies, for instance, have the property of not admitting all colored rays to pass equally well through them ; they, consequently, absorb certain rays. To these belong colored glasses and colored DIFFERENT COLORED RAYS. 287 fluids. If, for example, we fill the intermediate space between two parallel glass plates with a solution of sulphate of indigo, and look with a prism through this solution towards an opening in the shutter, we shall see two divided images of the opening, one red and the other blue. We obtain the same result by using a piece of dark blue glass in the place of the indigo solution. The whole spectrum consists of a series of circularly formed images succeeding one another, and partly overlapping each other. The smaller the opening is through which the white rays fall upon the prism, the smaller will be the separate round images, while, at the same time, the cen- tres of the separate co- lored images do not ap- proach nearer, and, con- sequently, the different colors less overlap one another ; the smaller the opening is, the purer will also the sepa- rate colors appear. Each color of the Spectrum is simple. Every color is simple if it does not admit of being further decomposed into other colors. We will now show that this property is really characteristic of the prismatic colors. If we receive a spectrum upon a wall, and make a hole some- where about the spot on T-- i ^i i f n Fig. 281. which the violet rays fall, we shall arrest all the other colors, while only one co- lored ray passes through the opening ; this ray does not admit of being in any way further decomposed; and, if it be again suffered to pass through a prism, the color remains unchanged. Newton applied the term homogeneous to simple light ; a name that has been generally adopted. White light may be recomposed from the simple colors of the spectrum. If we receive the spectrum on a lens /, the variously 288 ON WHITE LIGHT. Fig. 282. colored rays will be united by it in a point f, and if the sun's image be received upon a ground-glass, or a paper screen, it will again appear dazzlingly white, notwithstanding the different- ly colored rays that fell upon the lens. If, instead of holding the screen at the focal point jf, we remove it further from the lens, we again obtain an inverted spectrum / u f , Fig. 282, a proof that the differently colored rays cross each other at f, and if we apply a mirror at that point, the re- flected rays will again form a spectrum u" r". We may also use a concave mirror instead of a lens for these experiments. That the combination of prismatic colors yields white, is proved by the extraordinary experiments made by Newton, that the long prismatic image, seen through a second prism, will, under favora- ble circumstances, again appear as a perfectly white and round disc. Let v w be a spectrum, Fig. 283, produced by the prism, and caught on a white wall. If, now, a second prism B be so placed that it would produce the same spectrum r v in the same place, if a ray of solar light fell upon it in the direction o n, it is clear that the rays falling from the spectrum on the prism B will emer e in the di ' rection n o ; thus an eye at o must see a round white image of the co- lored spectrum in the direction on s. The position that must be given to the prism B may easily be ascer- tained by experi- ment. If, now, we divide a circular disc into seven sectors, and paint them with colors that most nearly approach the prismatic hues, Fig. 283. COMPLEMENTARY COLORS. 289 the disc, if made to rotate rapidly, will no longer appear to be colored, but will look whitish, and it would appear wholly white, if the sections could be painted with purely prismatic colors, and if the breadth of the separate colored sectors stood exactly in the same relation to each other as the breadths of the corresponding parts of the spectrum. Munchow combined the prism with clock- work, in order to be able to make experiments with pure prismatic colors on this principle, by setting the prism into rapid oscillating motion. By this motion of the prism, the spectrum moves rapidly backward and forward on a screen, and then there appears, in- stead of the colored spectrum, a white band of light, slightly colored at the ends. The eye rapidly receives at each of the points of the screen the impressions of all the separate colors suc- cessively ; these separate impressions vanish, however, and pro- duce the sensation of white. Of the Complementary Colors, and the Natural Colors of bo- dies. As all simple colors, combined in proper proportions, (that is, in the proportion given by the spectrum,) produce white light, it is sufficient to suppress one or more of the simple colors, or even simply to alter their proportion, to form any shade of color from white. If, for instance, we suppress the red of the spectrum in white light, while all the colors remain unaltered, we shall have a bluish tint, to which we need only add red, in order to restore the white. Two tints of color fulfilling these conditions, that is, giving, when combined, white, are termed complementary colors. Each color has its complementary color, for if it be not white, it is deficient in certain rays that would aid in producing the white, and these absent rays compose the complementary color. Violet, which passes more or less into red, is the comple- mentary color of different shades of green. We have already seen that a solution of sulphate of indigo in a prism yields a blue and red image of a white object. The red image is very sharply defined, the blue not so much so, passing somewhat more into violet, and less into green ; the light transmitted through a solu- tion of indigo is therefore wholly deficient in yellow and orange, and almost so with respect to all the green, and a portion of the violet. These absent colors form, however, when taken together, a mixture, in which yellow predominates to a considerable extent ; yellow is consequently the complementary color to blue in the indigo solution ; as yellow shades of color are complementary to 25 290 NATURAL COLORS OF BODIES. blue. The more the image approaches the green, the more will the complementary yellow merge into red. We shall subsequently have another opportunity of speaking of complementary colors. The prism we have made use of to decompose solar light, will also serve to analyze the natural colors of bodies ; and for this purpose, we need only cut off narrow strips from colored bodies, and look at them through the prism. We glue a row of colored strips of paper, about 1 millimetre (0.039 in.) wide, and as seen at Fig. 284, upon a piece of black Fi 284 paper: let 1 be white; 2, yellow; 3, orange; 4, scarlet; 5, green; and 6 blue; the best paper for the purpose is that used by book- binders for the titles of the back of books, as the colors are generally clear, and well defined. If, now, we look at these colored strips from the distance of several feet, through a prism whose axis is parallel with the direc- tion of the length of the strips, they will natu- rally appear moved out of their places ; at the same time, however, all the colors will be de- composed into their elementary colors. The white paper will give a perfect spectrum with all colors, from the extreme red to the extreme violet. The colored image given by the yellow paper approaches most nearly to the perfect spectrum. Red, orange, yellow and green are present; the lower blue and violet end alone is wanting ; consequently the color of the yellow paper requires only blue and violet in order to produce white. The colored image of the piece of paper No. 3 (orange) is much less complete; here the green rays are wanting as well as the violet and blue. The colored image of the red paper, No. 4, is the least dispersed, showing besides red, only a little orange ; the red of this paper is, therefore, almost a pure prismatic red. In the colors of the paper we have hitherto considered, red was contained in 1 to 4 ; the limits of these four colored images coincide, therefore, above in a straight line, while below they are cut off like gradu- ated steps. The colors of the papers 5 and 6, green and blue, contain but very little red, on which account there is scarcely any red end to the colored images they yield ; and hence it follows DISPERSING POWER OF DIFFERENT SUBSTANCES. 291 that the two last images appear much more removed from their true position, than the image of the red paper, No. 4. If we look through the prism at a broad, instead of a narrow piece of paper, we shall see it white in the middle, and only colored at the edges. Supposing that we look at the white strip of paper a b, in Fig. 285, through a prism whose axis is at right angles to the direction of length of the paper, the different colored images of the band will appear par- tially to overlap each other. The red image of the band extends, for instance, from r to /, the orange from o to . // COMPOSITE EYES. 297 mosaic composite eyes of insects and Crustacea, and, 2, the eyes of vertebrata provided with convex lenses. Composite Eyes. Muller was the first to throw any light by his classical investigations upon mosaic composite eyes. There are a very great number of transparent small cones, standing rectangularly upon the convex retina, and only those rays falling in the direction of the axis of the cone can reach its base on the retina. All laterally incident light is absorbed, because the lateral walls of the cone are invested with a darkly- colored pigment. In Fig. 288,fcbg is a section of the convex retina, with the trans- parent cylinders upon it. It is evident that the rays passing from the luminous point A can only strike the retina in c 6, the base of the truncated cone \ a b c d-, the bases of the two cones con- tiguous to a b c d are no longer struck by the rays passing from A ; a luminous point B sends its rays to another spot of the retina, and so on. All the light coming from points, lying on the pro- longation of the cone, will naturally act upon the basis of such a transparent cone, and the impressions of light from all points, sending light on the basis of the same cone, will also blend together; from which we see that the distinctness of an image on the retina is greater in proportion to the number of cones. Muller* charac- terizes the sight of such eyes with striking accuracy, when he says: "An image formed by several thousand separate points, each of which corresponds to a distant field of vision in the ex- ternal world, will resemble a piece of mosaic work, and a better idea cannot be conceived of the image of external objects, which will be depicted on the retina of beings endowed with such organs of vision, than by such a comparison." The size of the field of vision of such eyes, naturally depends upon the angle made by the axes of the external cones, that is, upon the convexity of the eyes. The transparent membrane covering the eye exteriorly, the cornea, is generally divided into facettes, each separate facette corresponding to the above men- Miiller's Physiology, translated by Baly, vol. ii. p. 1091, 298 SIMPLE EYES WITH CONVEX LENSES. tioned transparent cone. The number of the facettes of such an eye is generally very great, a single eye containing often from 12 to 20,000 such facettes. All insects have not such mosaic composite eyes; spiders, for instance, have simple eyes with lenses, entirely formed like the eyes of the vertebrate animals ; there are, also, many insects which, besides the mosaic composite eyes, have also simple eyes with lenses, but the construction, as well as the position of these, would lead us to conjecture that they are only intended for seeing the most contiguous objects. Simple Eyes with Convex Lenses. The image is formed upon the retina of eyes having collective lenses in precisely the same manner as the images of ordinary convex lenses ; the rays issuing from one point of the object, and striking the anterior surface of the eye, are refracted by the transparent media of that organ towards a point of the retina. Fig. 289 represents the section of a human eye. The whole globe of the eye is surrounded by a firm, hard membrane, only transparent at the front part ; this transparent portion is called the cornea, and the white opaque part, the tunica sclerotica; the transparent cornea is more strongly curved than the rest of the globe. Behind the cornea lies the colored prismatic membrane, the iris, which is plane, cutting off, as it were, the curvature of the transparent cornea from the remaining parts of the eye. In the middle of the iris, at s s r , there is a circular opening, which, seen from the front, appears perfectly black; this opening bears the name of the pupil. Behind the iris and pupil is the crystaline lens c 320. an d suspended in a horizontal posi- tion. If we bring one pole of a magnet near either of the two poles a and b of another magnet, the pole a will be attracted while b will be repelled. We term the poles a and b opposite poles, because they act in different ways upon the same pole if brought near them. If, now, we invert the magnet which we hold in our hand, in order to bring its opposite pole to the suspended magnet, the reverse will take place, a will be repelled and b attracted. The two poles of the magnet in the hand are, therefore, also of different natures, and are consequently opposite. In a similar manner we may show that the two poles of every magnet are opposite. If we bring two different magnets to the suspended magnet, it will be easy to find which of the two attracts the pole a of the suspended magnet, and repels b. If we designate this pole of the first magnet as n, and the pole of the second magnet acting simi- larly as n', n and n f will be the similar poles of these two magnets. If the second pole of the first magnet be m, and that of the other m r , the pole m as well as m! will repel the pole a of the suspended magnet, and attract the pole b. The two poles m and m! are like- wise similar. If, now, we suspend the magnet whose poles are designated m and m!, in such a manner as to admit of its turning readily in a horizontal plane, and bring the other near it, we shall find that the poles m and m! will repel each other, as will also the poles n and n' ; similar poles consequently repel each other. While the poles m and n' and n and m! being dissimilar poles, attract each other. There are, therefore, in the two halves into which a magnet is divided by the neutral line, two forces, which, although appearing at first sight to be of similar nature, from their acting similarly INFLUENCE OF A MAGNET. 349 upon iron are actually two opposite forces. The neutral line is, consequently, the boundary between two opposite forces, forming the transition from one to the other, and herein lies the reason of their neutral character. For reasons which we shall presently better understand, one pole of the magnet is termed the south pole, and the other the north pole. Under the influence of a Magnet, iron itself becomes magnetic. In order to show this property of iron, we must make the experi- ment represented in Fig. 321. Let an iron cylinder f be sup- ported by a magnet a b ; if we bring iron filings to the lower part of this cylinder, they will continue suspended to it in the form of a little tuft hanging as long as the little cylinder continues to adhere to the magnet ; but, as soon as the cylinder is removed, the iron filings will fall off, and no further attractive force be per- ceived. We cannot ascribe this phenomenon to the force of the magnet acting at a distance, for, if the small cylinder were not of iron, we should not observe the phenomenon ; of this we shall be still better convinced by observing, 1, that the threads of iron filings diminish gradually from the extremity of the cylinder ; 2, that there is a point towards the upper end where the filings do not adhere, consequently, that the small cylinder has a neutral magnetic line ; 3, that the filings adhere again above this point, but that they have an opposite direction. The little cylin- der is, therefore, a real magnet, attracting iron filings, having two poles, and a neutral magnetic line; the latter, however, does not coincide with the geometrical middle. Instead of bringing iron filings to the suspended cylinder, we may attach to it another cylinder (as in Fig. Fig 322> 322) which will also be supported ; to this a third, fourth, and so on ; in this way a chain may be formed, of which the magnet is the first link. If we remove this link, the whole :hain will fall apart, there being no power to hold the links to- gether. Magnetic Fluids. To explain the various phenomena of mag- letism, we assume that there are two different magnetic fluids, listributed in the magnet in a manner which we must consider nore particularly; the particles of both of these fluids repel each 350 MAGNETIC FLUIDS. other, but attract those of the other fluid. The magnetic fluids are present in equal quantities in every molecule of iron and steel; but they cannot pass from a magnet to a piece of iron, or from one molecule to another, the magnetic condition depending only upon the manner in which the magnetic fluids are distributed in every individual molecule. We must suppose a magnet, or a magnetized iron rod (as seen in Fig. 323) to be composed of small particles, each of which contains both fluids, although in a state of separation ; the mag- netic fluids being distributed in each particle in such a manner Fi 323 that the similar fluid is turned towards the same side in all the particles. There is, therefore, only one fluid present at the left ex- tremity of the magnet represented in Fig. 323, while the right extremity is solely occupied by the other ; the polarity of the magnet is thus explained. We can easily understand from this explanation that a magnet may be broken into two parts, and each separate portion remain a perfect magnet. If, therefore, a piece of iron be magnetized by the influence of a magnet, no magnetic fluid will pass from the magnet to the iron, but the approximation of the magnet will simply occasion a dis- tribution through the iron of the magnetic fluids which have not hitherto been separated in each molecule, and directed towards a definite side, but distributed quite uniformly over the whole. Iron only retains its magnetic properties so long as the con- tiguity of a magnet keeps the magnetic fluids separated ; on the removal of the magnet the separated fluids again combine, and the iron returns to its natural condition. A horizontal magnet a b supports at one end an iron massy, the I weight of which is nearly as great as the magnet is capable of supporting. We now bring another . magnet a f b r over a b in such a manner that the contrary poles a and b' are turned towards each other. If we bring the second magnet gradually nearer, in the manner specified, the piece of iron i f will fall off. The two magnets combined cannot j therefore, support as much as each one separately. We may easily understand the cause of this; for the second magnet disturbs the[ MAGNETIC ARMATURES. 351 actions of the first, whilst it decomposes the fluids of the mass of iron f in an opposite sense. Steel resists the magnetizing influence of a magnet much better than iron, that is to say, a piece of steel, if it be tolerably large, is not magnetized so strongly or immediately by contact with a mag- net as is a piece of iron ; and in order perfectly to magnetize a rod of steel, it is necessary that it should be for a longer period in con- tact with the magnet, or that the latter should be drawn repeat- edly over it in the proper manner ; when, however, steel is once magnetized, it does not lose this property very easily, but retains the magnetic character even after the magnet has been removed; we may, consequently, form permanent magnets of steel, but not of iron. Perfectly hardened steel admits least easily of being mag- netized ; but when once it has acquired the magnetic property, it does not readily lose it. When tempered steel loses its hardness by being annealed, it assimilates more nearly to soft iron in its relation to magnetism. Red hot iron is not attracted by a mag- net, and a steel magnet entirely loses its magnetic properties on being heated. Besides iron, nickel and cobalt may also become magnetic. Magnetic Jlrmatures. A magnet may gradually lose its force, owing to various causes. To prevent this, the so called arma- tures are made use of: this term is applied to pieces of soft iron, brought into contact with the magnet in order to preserve its power by means of the magnetic decomposition going on in the soft iron. The following method, for thus arming magnetic bars, | is the best, and will be seen exemplified in Fig. 325. Two like magnetic bars are laid parallel to each other, in such a manner that the north pole of the one is directed to the same side as the south pole of the other, to these are attached two pieces of soft iron ; a b and c d y in order to complete the parallelogram. Each of these pieces of iron naturally becomes a magnet of itself, reacting in such a manner upon the magnetic rods JV S and N f S f , that the separated fluids are fixed at the corresponding extremities. Magnetic needles, and bars lying in the direction of terrestrial magnetism, may be considered as in some degree, armed by the earth. 352 COULOMB'S PLAN. A magnetic battery is a combination of several individual magnets. Fig. 326 represents one constructed according to Fig. 326. Coulomb's plan. It consists of 12 separate magnetic bars, form- ing 3 layers each, composed of 4 bars. The bars of the middle layer are about 2, 5, or 3 inches shorter than those of the other layers, and project about 15 to 18 lines at either side. All the bars are of exactly the same thickness, and are fastened into pieces of irony serving as armatures. The brass bands c d serve to hold the rods and armatures together. Such large magnetic bundles remain horizontally fixed, when made use of for the pur- pose of magnetizing. The smaller ones, employed for friction, are constructed on similar principles. Fig. 327 represents a horse-shoe magnet. It consists of several horse-shoe shaped curved plates of steel, lying immediately on one another, and held together by two screws a and a, made of iron or brass. Each plate is separately magnetized, before it is used for constructing the apparatus. A ring n n' serves to sus- pend the magnets, and a piece of soft iron p p f , the anchor, forms the armature. Good horse-shoe magnets are capable of sustaining from 10 to 20 times their own weight. Fig. 327. Fig. 328. Fig. 329. MAGNETIZATION OF STEEL NEEDLES AND BARS. 353 The armature of natural magnets is represented in Figs. 328 and 329. The parts / and V are the wings of the armature, and p p' the feet. The wings are made nearly as broad as the mag- net, and about one line in thickness. The dimensions of the feet depend upon the strength of the magnets. A remarkable phenomenon is observed in natural as well as artificial magnets, which has not as yet been satisfactorily ex- plained, we mean the weakening which occurs on overloading. Let us assume that a magnet can bear 40 pounds. If, now, we daily add a small weight, we increase its power of bearing until the load amount to 60 or 80 pounds ; as soon, however, as the lifter is severed by the application of too large a weight, the strength of the magnet diminishes considerably, scarcely, at last, supporting more than 40 pounds, the weight from which we started. But if we attach a smaller weight, increasing it with caution, we shall find that, after some time, the magnet has recovered its former strength. Magnetization of Steel Needles and Bars. The so-called method by separated touch, is managed by placing two strong bundles of magnets, see Fig. 326, in such a manner that the axis of the one coincides with the line of prolongation of the axis of the other, and that the opposite poles are inclined towards each other, as seen in Fig. 330, where f represents the one pole of one bundle, and !/' the opposite pole of Fjg 330> i the other. The needle | to be magnetized is now laid upon a piece of wood /, to which it may be se- cured to prevent its be- ing displaced. We now take the two touching magnets g and g*, each in one hand, and holding them at an inclination of about 25 or 30 degrees towards the horizon, place them in the middle of the rod to be magnetized, moving them gently and regularly in such a manner that g g' simultaneously reach the opposite extremities of the needle, and this process is repeated several ! times. It will, of course, be understood that the touching magnet must touch the needle with the same pole towards which we direct | it. This method is especially well adapted to magnetize regularly 'and perfectly such magnets as are used for compasses, or steel bars which are not more than 1 or 2 lines in thickness. 30* 354 DIRECTION OF MAGNETS. The double touch is applied to prepare steel bars which exceed 1 or 2 lines in thickness ; in which case, the method above de- scribed is inadequate to the purpose. The double touch is thus managed. The bar to be magnetized is laid between two bundles of magnets, which are placed over its centre as described in the for- mer method; the magnets must, however, be less inclined, form- ing only an angle of from 15 to 20 degrees with the horizon. Besides this, the frictions are not made towards opposite poles, but both magnets are moved towards one extremity of the rod, and then back the whole length. After the magnets have been moved together sufficiently long, they are again raised from the middle of the rod. In order to manage this process more conve- niently, we may fasten the two rubbing magnets to a kind of tri- angle of wood or brass ; there must, however, at all events, be a space of about 2 or 3 lines between the lower parts of the mag- nets ; this is best effected by the insertion of a bit of wood, brass, or lead, as represented in our Fig. at /. The double touch communicates a very strong degree of mag- netism, but it cannot be safely applied to magnetize needles for compasses, or bars intended for nice experiments, since it almost always gives poles of unequal strength, thus occasioning succes- sive stoppages. CHAPTER II. OF THE MAGNETIC ACTIONS OF THE EARTH. Direction of Magnets, Declination, Inclination. A mag- netic rod, horizontally suspended by a silk thread, or a magnetic needle, revolving easily upon a point in a horizontal plane, (this needle is generally made in the form of a rhomboid, as seen in Fig. 332, and has in its centre an agate cap, which reposes upon the steel point forming the pivot,) is not in equilibrium in all po- DECLINATION INCLINATION. 355 Fig. 332. sitions, but takes a definite position, directed towards one definite point of the horizon. It will always return to this position after a series of oscillations, if removed from it. The force urging the needle back to this position is magnetic; since no phenomenon of the kind is exhibited in the case of an unmagnetized needle. This remarkable property of magnetism is observed everywhere; in all parts of the world, on all seas, on the loftiest summits of mountains, as in the deepest mines, the mag- netic needle assumes a definite direction, to which it will inva- ^^ riably return if removed from it. There must, consequently, be a magnetic force which acts at all points of the earth's surface, for magnetic needles can no more take up a direction of themselves, than a body can set itself into motion ; in both cases the influence of some foreign force is re- quired. We may prove, by means of a simple experiment, that this directing force acts as a magnet, and not as a mass of iron. If we entirely invert the poles of a magnetic needle, they will not be in equilibrium in their new position, but will each describe a complete semicircle in order to return to the state of equilibrium, and reassume their original direction. The directing force, con- sequently, distinguishes the two poles, attracting the one, and re- pelling the other like a magnet, whilst iron will equally attract the poles of a magnet. When we combine all the different observations that have been made in different places, we are, in truth, led to regard the earth as one great magnet, whose neutral line is situated in the region of the equator. Hence we have a means offered us of giving fitting terms to the two poles of a magnet. The two poles of the great terrestrial magnet lie in the vicinity of the poles of the earth's axis, on which account we name the one the magnetic north pole, and the other the magnetic south pole. These contrary poles attract each other, however, and thus a mag- netic needle will turn its south pole to the north, and its north pole to the south. 356 THE MAGNETIC MERIDIAN. This designation is not, however, universally received, since some designate the poles of a magnetic needle in a totally oppo- site manner, giving the name of north pole to that pole which turns towards the north. If we suspend two magnetic needles at the same place at such a distance that they exert no influence on each other, each will assume a direction parallel with that of the other. This paral- lelism does not, however, prevail for places separated by the dis- tance of several degrees of latitude or longitude from each other. It is of the greatest importance to be able to determine the direc- tion of magnetic needles, that is, to compare them with lines of unvarying position, in order to ascertain the variations, occurring in the course of time, at one and the same place in the direction of the magnetic needle, and the relations existing between the direction of magnetic needles at different places. The Magnetic Meridian is the vertical plane, we may suppose, passing through the line of direction of a horizontal magnet, or simply the section of this plane with the earth's surface. The magnetic meridian of a place makes with the astronomical meri- dian an angle, termed the declination or deviation. The declina- tion is east or west, according as the magnetic needle deviates towards one or the other side of the astronomical meridian. In Fig. 333, for instance, s n represents the meridian of a place, and a b the direction of the horizontal magnetic needle at the same place. The western declination amounted to 18 37' 30,55" at Gottingen in January, 1837. We shall presently see that the de- clination varies with the time. There are places on the earth where the direction of the magnetic needle exactly coincides with Fig. 333. Fig. 334. THE MAGNETIC MERIDIAN. 357 the meridian. At these places the declination is, of course, null, at 0. very apparatus serving to measure declination is termed a lination compass. ig. 334 represents a compass of simple construction. The .t to which the needle is suspended is the centre of a gradu- ated horizontal circle, which may revolve about a vertical axis in its own plane. To the side of the box a telescope is attached, whose axis runs parallel with the line which we may suppose drawn from on the graduated circle, through its central point, to the line marked 180. On revolving the horizontal circle in its plane, the extremity of the magnetic needle points towards other lines of the circle. If we place the apparatus in such a manner as to let the needle point to of the scale, the axis of the tele- scope will be parallel with the needle, coinciding with the mag- netic meridian ; but in every other position the needle will point to that number of the circle marking the number of degrees of which the angle consists, which the direction of the needle makes with the axis of the telescope ; if, therefore, we bring the telescope exactly into the astronomical meridian, we shall see on the gradu- ated circle the angle made by the magnetic with the astronomical meridian. This instrument serves especially for the measurement of angles, since we can, at all times, make use of it to determine the angle which the optical axis of the telescope (or rather its izontal position) makes with the magnetic meridian. The declination compass, generally used at sea, is known by e name of the Mariner's Compass. On the whole, the direction of the magnetic needle inclines more to the north and south than to the east and west; hence, it is usual to say, that the magnetic needle points to the north. The magnetic needles we have been considering, are suspended in such a manner as only to revolve in a horizontal plane, that is, about a vertical axis. In the mode of suspension, represented in Fig. 320, and also in Fig. 332, the horizontal position is main- tained by the centre of gravity of the needle being below the point of suspension. As soon, however, as we suspend a magnetic needle in its centre of gravity, it will not remain equipoised, but will make, with the horizon, an angle, which is termed the inclina- tion. The apparatus, represented in Fig. 335, is well adapted to 358 THE MAGNETIC MERIDIAN. show the inclination of the magnetic needle. In a brass frame, suspended by a thread, there is a horizontal axis a b which moves Fig. 335. Fig. 336. very readily, passing through the centre of gravity of the magnetic needle. We see that a magnetic needle, thus suspended, can easily move round a vertical or a horizontal axis, and, therefore, that it can freely follow the directing influence of the earth. The needle places itself in such a position, that its line of direction coincides with the magnetic meridian ; but the extremity of the needle, turned towards the north, dips; consequently, the line of direction of the needle, makes an angle with the horizon, which, in our part of the world, amounts to about 70. If the needle of inclination be applied to a graduated vertical circle, whose planes coincide with the plane of rotation of the needle, as seen in Fig. 336, we may ascertain the amount of inclination on this circle, by making the plane of the vertical circle coincide exactly with the magnetic meridian. An apparatus serving to measure the amount of inclination, is termed a dipping needle, or a compass of inclination. The inclination generally increases as we approach nearer to the north ; in many places the dipping needle assumes an almost vertical position; thus, for instance, in the year 1773, Captain Phipps observed, at 79 44' north latitude, an inclination of 82 9', and Parry, an inclination of 88 43', in latitude 70 47'. Captain THE MAGNETIC MERIDIAN. 359 Ross has, at last, reached the magnetic north pole of the earth. At 70 5' N. lat., and 263 14' E. long., from Greenwich, he found the inclination, or dip, to be 90. The inclination of the magnetic needle is so considerable in high latitudes, that the compass loses much of its practical utility, as has been shown in the late North Polar Expedition. The further we advance towards the south, the more the incli- nation decreases, and at the equator we come to a point where it is absolutely null, where, consequently, the needle of inclination is perfectly horizontal ; as we advance further to the south, we again observe an inclination, but it is in an opposite direction, the extremity of the needle pointing to the south being the one that now dips. This inclination increases likewise with the increase of southern latitude. In the vicinity of the south pole of the earth, there is, therefore, a second point at which the dipping needle stands perfectly vertical, and this is the south magnetic pole. At whatever degree of geographical longitude we may pass this equatorial zone, we shall always find one point where the needle will be perfectly horizontal. These places where there is no inclination form a curve all round the earth, termed the magnetic equator. The magnetic equator does not coincide with the terrestrial equator, or form any regular circle of the earth's sphere. It attains its greatest southern latitude on the Atlantic Ocean at about 28 W. of Paris, (25 40' W. of Greenwich,) where it is then about 14 degrees south of the terrestrial equator. The two equators approach each other as they incline to the west, meeting at 120 W. of Paris (117 40' W. of G.); here, however, instead of turning to the northern hemisphere, it again inclines to the south about 160 W. of Paris (157 40' W. of G.), in order to reach a second southern maximum of 3 75'. At 174 long, it cuts the terrestrial equator, and remaining within the northern hemisphere, intersects the terrestrial equator again at 18 E. of Paris (20 20' E. of G.). The magnetic equator has a N. lat. of 11 47' at 62 E. of Paris (64 20' E. of G.); while it is 7 44' at 150 E. of Paris (152 20' E. of G.), and 8 57' at 130 E. of Paris (132 20' E. of G.). These data will suffice to define, in general terms, the position of the magnetic equator, and the irregularity of its course. The total action exerted by the earth upon a magnetic needle, 360 VARIATIONS OF DECLINATION AND INCLINATION. is simply directive , not attractive, since, if it were the latter, a magnetic needle would necessarily weigh more than before it was magnetized. If we lay a magnetic needle upon a cork swim- ming in water, it will move into the magnetic meridian, without evincing any tendency to float towards the north, as we might expect. If we bring a magnet near a floating needle, either attraction or repulsion will occur, according to the pole of the magnet nearest it ; the needle either approaching to, or receding from the magnet. Why does not the needle move towards the north magnetic pole, if the earth be nothing more than a large magnet? The reason is this: the force of magnetic attraction diminishes with the distance, as we shall soon see. If we direct a magnet towards the floating needle, the two poles of the needle will not be equally distant from the pole of the magnet ; consequently the repulsive or the attractive force must preponderate, and forward motion be produced. The north magnetic pole of the earth is, however, so extremely remote from the floating needle, that the length of the needle does not bear any appreciable proportion to the distance ; the one pole of the needle is, therefore, as much attracted as the other is repulsed. Variations of Declination and Inclination. The declination, like the inclination, is variable ; thus, in the year 1580, the decli- nation at Paris was 11 30' E., it then diminished, and was null in the year 1663; from this time the declination inclined to the westward, increasing constantly till the year 1814, when it attained its maximum west, amounting to 22 34', and again began to decrease. The inclination of the magnetic needle at Paris has constantly diminished from the year 1671, when it amounted to about 75, it being now about 67J [The declination in London was 11 16' in 1580, and was null in 1660, and then inclining to the west- ward, gradually increased in that direction until 1818, when it attained 24 30' since which it has decreased. The inclination of the needle at London was 74 30' in 1680, since which it has gradually lessened to about 67.] These gradual changes of declination and inclination are called secular variations; they are not, however, the only changes to which the direction of the declination is subject. If we carefully observe the declination needle, we shall find INTENSITY OF TERRESTRIAL MAGNETISM. 361 that it continually makes small oscillations, moving alternately from east to west from its position of equilibrium ; these oscilla- tions are sometimes regular and periodical, sometimes accidental and abrupt. The former are termed the diurnal variations, the latter perturbations. In general, the north end of the needle continues its onward motion westward from sunrise, and begins its retrograde motion about 5 P.M. The amplitude of the diurnal variations, that is, the angle be- tween the eastern and western limits, varies ; being sometimes only 5 or 6 seconds, and sometimes amounting to J minute. The inclination is likewise subject to similar variations. The needle of declination makes very strong irregular oscilla- tions, amounting often to more than a degree, on the appearance of an aurora borealis in the heavens. Earthquakes and volcanic eruptions also appear to act upon the magnetic needle, producing frequently a permanent change in its position. Intensity of Terrestrial Magnetism. If a needle of inclination be drawn out of the magnetic meridian, terrestrial magnetism will endeavor to restore it to its position of equilibrium ; it is only on leaving the needle entirely to itself, that it will, after a series of vibrations, resume its position of rest. The period necessary for each one of these vibrations depends upon the mass of the needle, the strength of the magnetism developed, and likewise the force of terrestrial magnetism. Thus, the same needle will vibrate with more or less rapidity, according to the force of the terrestrial mag- netism acting upon it. We have thus a method of comparing the force of terrestrial magnetism, as manifested at different pi aces on the earth; it being only necessary to observe the number of oscillations made in a definite time (as 5 minutes for instance), in different parts of the earth by the same needle of inclination, and by this mode of observation we may easily reckon how the force of terrestrial magnetism stands at one place with regard to that exhibited at another, for the intensities of terrestrial magnetism are as the squares of the number of oscillations made in an equal period of time. The observations made on the oscillations of a needle of incli- nation can never yield very accurate results, and, therefore, the experiments made on the oscillation of horizontal needles or rods 31 362 INFLUENCE OF TERRESTRIAL MAGNETISM UPON IRON. are preferable. The force causing the needle of declination to vibrate, is only a portion of a horizontal lateral force, itself but a part of the magnetic terrestrial force acting in the direction of the needle of inclination; if, however, the horizontal intensity and the amount of the inclination be known, we may easily compute the whole intensity. When the horizontal intensity of the terrestrial magnetism and of the inclination is known, we may easily find the whole intensity by construction. In Fig. 337, a b is the horizontal intensity. If now we make the angle i equal to the inclination observed at the Fig. 337. same place, and draw a perpendicular from 6, a c a 6 will represent the whole intensity. If I = o, the direction of the terrestrial magnetic force will be in a horizontal plane ; this, as is well known, is the case at the magnetic equator, the horizontal intensity being here equal to the whole intensity. The horizontal portion of the magnetic terrestrial force becomes larger, the nearer we ap- proach the magnetic equator ; at the magnetic poles of the earth, where the needle of inclination stands in a vertical position, the horizontal portion of the terrestrial magnetic force is null. On comparing the results of the observations that have been made on the amount of intensity at different places on the earth's surface, we arrive at the following general result, that the total intensity is smallest in the vicinity of the magnetic equator, increasing the further we move away from it towards the north or south. In the vicinity of the magnetic poles it is about 1,5 times greater than at the equator. The intensity varies also at the same place, and, like the declination and the inclination, is subject to diurnal variations. Influence of Terrestrial Magnetism upon Iron. If we hold a rod of soft iron, from 20 to 30 inches in length, in the direction of the dip, it will become magnetic by the influence of terrestrial magnetism, its lower end becoming a south pole, and its upper end a north pole, as may be easily seen by bringing a small sen- sitive magnetic needle successively in the vicinity of the ends of the rod. The same pole of the needle is attracted by the one end of the rod, and repelled by the other; by which circumstance we may at once perceive the polar magnetic condition of the rod. INFLUENCE OF TERRESTRIAL MAGNETISM UPON IRON. 363 On inverting the rod we find its poles have changed, the lower end being again a south pole, and the upper one a north pole. The same, although somewhat modified action is also produced by terrestrial magnetism on a vertically suspended iron rod, or, indeed, on any iron rod, let the angle it makes with the direction of the needle of inclination be what it may; the action being, however, less in proportion as it recedes from the direction of the needle of inclination. Terrestrial magnetism exercises more or less strongly the same influence on all masses of iron ; all soft iron must, therefore, assume a polar magnetism under its influence, as may be shown with more or less distinctness, according to cir- cumstances. If a rod of iron be magnetized by the influence of terrestrial magnetism, a few strokes of the hammer will suffice to fix the magnetism, and, therefore, to convert the rod into a perma- nent magnet; by striking the iron, a coercive force is consequently imparted to it, which hinders the union of those fluids that have separated in the iron by the influence of the earth. We may thus understand how almost all tools in the workshop of a locksmith become magnets. It appears that chemical changes act similarly to mechanical disturbances in fixing the magnetism imparted by the earth to the iron, for we find that iron rods, after being for any length of time in a vertical position, and becoming rusted, acquire a permanent magnetism. A certain individual, named Julius Caesar, a surgeon at Rimini, first observed in the year 1590 that an iron rod on the tower of the Church of St. Augustin had become magnetic from the influence of the earth. At a subsequent period, in the year 1630, Gassendi made a similar observation with regard to the cross on the steeple of the Church of St. John, at Aix, which had been struck down by lightning. It was strongly rusted, and had all the properties of a magnet. Since that time numerous observations of this kind have been made, and it has been generally found that iron which is somewhat rusted, is always more or less magnetic. On dipping a horse-shoe magnet into iron filings, the latter will arrange themselves in a tuft between the poles ; if we then moisten them with oil, and expose them to a red heat while they remain under the influence of the magnet, a partial oxidation of the iron will take place, and we shall obtain a tolerably compact mass, the composition of which is similar to that of natural magnets, and which, also, will remain permanently magnetic. 364 DIMINUTION OF MAGNETIC FORCE BY DISTANCE. Diminution of Magnetic Force by Distance. Since we have now learnt to know the magnetic action of the earth, we may also in- vestigate the laws by which the strength of magnetic attractions and repulsions diminishes as the distance increases. It will be readily understood that magnetic actions, like all other actions emanating from one point, must stand in inverse relations to the squares of distance, that is to say, at 2, 3, or 4 times the distance, the actions will be 4, 9, or 16 times less. When we endeavor to confirm this law by experiment, we labor under the peculiar difficulty of being unable ever to try the expe- riment on one magnetic pole, without having to contend with the counter influence of the other pole ; we must, therefore, endeavor to make the distance between the poles so great as to destroy the disturbing influence exercised by the one over the other. Let us suppose a magnetic needle so suspended by a thread of untwisted silk, as to be able to oscillate freely in a horizontal plane, while it is sufficiently protected from disturbing currents of air. This needle must be first left to oscillate under the sole influence of terrestrial magnetism. Let n be the number of oscillations ob- served in a minute, and m the horizontal portion of the magnetic terrestrial force acting upon it. Let, now, one pole of a highly magnetized steel bar act upon the needle. This steel rod is to be brought into the magnetic meridian of the needle 7i 5 in a vertical position, so that the pole s of the needle is to be turned towards the pole JVof the bar, on which it will act attractively. The bar NS must be so large that the distance s JV* may be as small as possible, in comparison with the distance s S, so that we may neglect the action of the pole S on 5, without committing any serious error. If we designate by n' the number of oscillations of the needle for the case, where the pole JVof the bar NS acts upon the needle from a definite distance, and call the force accelerating the motion of the oscillating needle^/*', we shall have, in accordance with the ft n t2 former experiment, J - = . / n Supposing the needle, under the sole influence of terrestrial magnetism, to make 15 oscillations in one minute, and 41 when DIMINUTION OF MAGNETIC FORCE BY DISTANCE. 365 pole JV* of the bar is removed 4 inches from the needle, we shall have i~ = f 15 2 We must now remove the bar to twice as great a distance, so that JV* is 8 inches from the needle, and then observe the number of oscillations ; supposing we find their number in one minute n" = 24, we shall have, if we designate asjf" the force acting in fi 242 this case upon the needle, J = f 15 2 The amount f is evidently the sum of the terrestrial magnetic force, and of the attractive force exercised by the pole JV* at the distance of 4 inches upon the needle ; the latter is, therefore, evidently f f. In like manner, the attractive force exercised by the rod at a distance of 8 inches upon the needle, is f" f. By the combination of the two latter equations, we shall have the ,, f f 41 2 15 2 1456 lowing result: J j^ f ~ wH&" 351 = ' *> 1 ' This experiment shows, therefore, that the attractive force of a magnetic pole acts with nearly four times less intensity when removed to twice the distance. Weber has indirectly proved the truth of this proposition by his investigations, not merely on the action of a single pole, but on that of the whole magnet at greater distances. He has shown that if a magnetic bar be small in comparison with the distance at which it acts, the total action of the magnet must diminish in an inverse ratio to the third power of the distance, provided the action of a single pole really stand in an inverse relation to the squares of the distance. In Fig: 339, a b is a magnetic bar, 1 decimetre (3.93 in.) in length, whose centre is 10 decimetres Fi 339 (1 yd. 3 in.) from the point c; the dis- c tance of the pole b from c is, therefore, ^ I 9,5, (1 yd.,) and that of the other pole 10,5 dm , (1 yd. 1 ft. 6 in.) If, now, c be a magnetic pole, and if we designate as 1 the force with which the poles b and c would attract each other, supposing them to be l dm from one another, the attractive force will be A_ = _, if the attracting action 9,5 2 90,25 of the pole stand in an inverse relation to the squares of distance. From the same data, the value of the repulsive action of the poles 31* 366 DIMINUTION OF MAGNETIC FORCE BY DISTANCE. b and c is _ _; the total action exercised by the mag- 10,5 2 110,25 net a b upon c is, therefore, 1 1 _ 20 90^25 110,25 9950* If, now, we remove the magnet to double the distance of c, that is, if we place it in such a manner that the middle is 20 th11 from c, the distance b c being equal to 19,5, the distance a c will be 20,5 dm , and, consequently, the total action of the magnet will be as follows : 1 1 1 1 40 19,5 2 ~~ 20,5 2 = 380,25 "" 420,25 ^ 159800* If, therefore, we move the magnetic bar to a distance of 20 dm , instead of 10 dm only, its action must diminish in the relation of to , provided the action of each separate pole stand 9950 159800 20 in an inverse relation to the squares of distance. But 9950 40 l 2 1598 = 8, at double the distance, 159800 995 15980 1990 the total action of the magnet is 8 times weaker, and 8 is the third power of 2. What we have shown here by particular examples, may also be generally proved, as it admits of a general proof that the total action of a magnet must be in an inverse ratio to the third power of the distance, if the action of one single pole stand in an inverse relation to the squares of the distance. We will now adduce an experiment, by which the total action of a magnetic bar is shown to be as the third power of the dis- tance, provided the magnet be small in comparison with this distance. A bar 3 feet in length, and divided into inches, must be so laid that its direction may be at right angles to the magnetic meridian. A small compass is then placed in the middle, as represented in Fig. 340. The needle of this compass will stand at 0, if the magnetic terrestrial force be the only one acting upon it. If, however, a magnet be laid sideways upon the rod, the needle will be turned aside ; and then this deviating force will be proportional to the tangent of the angle of deviation. Let us now lay a magnetic bar 3 inches in length, in such a DIMINUTION OF MAGNETIC FORCE BY DISTANCE. 367 manner (as seen in Fig. 340), that its middle may be 15 inches from the middle of the compass. In such an experiment the deviation will amount to If the magnetic bar n s be now placed in such a manner that its centre is 10 inches from the centre of the compass, the devia- tion will amount to 35J. The distances here are to each other as 10 to 15, or as 2 to 3 ; the tangents of the angles of deviation must, therefore, be as 2 3 to 3 3 , 27 or as 8 to 27 ; and here we shall have = 3,375. 8 ut the tangent of 11J = 0,2034, the tangent of 35 = 0,7115, and !?']?***? = 3,49 ; the tangent of the angles of devia- tion are, therefore, very nearly as 8 to 28, or as the third powers of the distances. 368 ELECTRICITY. PART II. OF ELECTRICITY. CHAPTER I. Fig. 341. OF ELECTRICAL ACTIONS. There are bodies which, by friction, acquire the property of attracting Light Bodies. We may easily convince ourselves that bodies, in their ordinary condition, do not possess the property of attracting light bodies, as gold-leaf, sawdust, paper-cuttings, balls of the pith of the elder, &c. ; but if we rub a glass rod, or a piece of sulphur, or sealing-wax, or amber, &c., with a woollen or silk substance, these bodies will immediately acquire this remarkable property. This attrac- tive force is so great, that, even at the distance of more than a foot, light bodies are drawn towards the attracting body (Fig. 341). The cause of this phenomenon is called Electricity. We may make use of the electrical pendulum, (represented in Fig. 342), in order to ascertain whether a body will become electrical by friction. This apparatus consists of a small ball, made of the pith of the elder, and suspended to a fine linen thread. If we would test a body, we bring it towards the ball; if it be not attracted, it is either non-electric, or too slightly electric to produce any effect. By the aid of the electric pendulum, it may be shown, that all resins, amber, sul- phur, and glass, become strongly electric by friction; the precious stones, wood, and charcoal, seldom give the slightest indications Fig. 342. CONDUCTORS AND NON-CONDUCTORS. 369 of attraction; metals do not appear, at first sight, to admit of being made electric, for we do not perceive the least trace of attraction in this apparatus on forcibly rubbing a metal rod. All bodies thus fall under two great classes ; that is, such as become electric by friction, and such as do not thus acquire an electric condition. The former we term idioelectric, the latter anelectric bodies. This division is founded, however, upon an erroneous view, for it has been found that all bodies, even metals, can be made electric by friction, and, although we may be unable, in many bodies, to perceive any trace of electricity from friction, the cause depends upon other circumstances, of which we shall soon treat. Conductors and Non- Conductors. It was formerly supposed that the bodies, designated by the term anelectric, could not, by any means, be brought into an electric condition. In 1727, ex- periments were made, with a glass tube, open at both ends, on this subject, by Gray, an English natural philosopher. He wanted to see whether it would become electric, if closed up at both ends by a cork stopper. At that epoch, science was so little advanced, that experiments were made at random, there being neither hypo- thesis nor theory by which to conduct the course of investigation. To his great astonishment, Gray found that the stoppers them- selves had become electric, although cork belonged to the sub- stances reckoned anelectric. A metal wire, passed through the cork, became electric, independently of the length at which it was used ; having successively carried the electrical rod to the first, second, and third stories of his house, and let the metal wire descend to the ground. He rubbed the glass tube, while a friend brought light bodies to the lower end of the wire, on which they were instantly attracted by it. It follows from thence, that metals have the property of assuming, and imparting to other bodies, an electric condition. The same property is possessed, however, by all anelectric bodies ; and, hence, they have been termed conductors of electricity. Idioelectric bodies, on the other hand, are non-conductors; for when, by friction, we make one end of a glass tube electric, the other end exhibits no trace of attraction. We may easily demonstrate this fundamental truth by the aid of an electrifying machine, of which we may make use to deve- lop electricity, without knowing the principle of its construction. 370 CONDUCTORS AND NON-CONDUCTORS. The conductor of the machine is a metallic body, which is made electric. If we bring in contact with the conductor, when in an electrified condition, a metal wire, suspended by a silk thread, or, better still, some cylindrical metal body, standing on a glass pedestal, the metal will be electrified through its whole extent ; as soon, however, as it be connected with the earth, by means of any good conductor, all its electricity will instantly disappear. From this it follows that silk threads and glass rods are non- conductors of electricity insulators. A conductor of electricity can, therefore, only remain electric as long as it is insulated, that is, surrounded by perfect non-conductors. The air must be an insulator, since, if it were not so, electricity would be instantly withdrawn by the atmosphere from metals. Water and steam are good conductors, consequently, when the atmosphere is damp, the electricity will soon be lost, which, in a dry condition of the air, would have adhered to an insulated conductor for a long period of time. The human body is likewise a good conductor. If we stand on the ground, and lay hold of the conductor of an electrifying machine, all the electricity evolved from turning the machine will immediately escape ; but, if we stand upon a bad conductor, as a piece of resin, the whole body will become electric. This ex- plains the reason of a metallic rod not becoming electric by fric- tion when we hold it in the hand ; all the electricity obtained by the friction being immediately given off to the human body, and thence to the ground. The best insulators may become conductors if they be covered with condensed vapor. It is, therefore, of the greatest import- ance to the successful result of electrical experiments, that the glass feet, resin rods, &c., used for insulating a conductor, should be well dried by warmth and friction. Instead of dividing bodies into conductors and non-conductors, we ought, more correctly speaking, to term them good and bad conductors, since there do not exist any absolute non-conductors ; shell-lac, and more especially resin, silk, and glass are the worst conductors we have ; while, on the contrary, metals constitute the best conductors. Of the two kinds of Electricity. Let us take a simple electrical pendulum (see Fig. 342), whose nob is suspended to a silk thread. If we now bring a rubbed glass, or shell-lac rod to the pendulum, ELECTRICITY OF FLUIDS, ETC. 371 the pith ball will be strongly attracted, then touch the rod, and, after adhering to it for some minutes, will be repelled. This re- pulsion depends upon the electricity communicated to the ball by contact with the rod, for, on touching it with the hand, and then bringing it back to its natural condition, it will be again attracted, and repelled after a second Fig. 343. time being brought into con- tact. It follows that the repelled ball is really electric, from its being attracted by bodies in their natural condition, provided we make choice of conductors for the experiments. If we take two insulated pendulums, one of which has been made electric by contact with a glass rod rubbed with silk, and the other by a rod of shell-lac rubbed with fur or flannel, we shall perceive the following remarkable pheno- mena. The ball that has been repelled by the glass rod will be attracted by the shell-lac rod, while the one repelled by the shell- lac will be attracted by the glass. The electricity evolved from glass, consequently, is not identical with that evolved from resins, since the one attracts, and the other repels. These two kinds of electricity have received the names of vitre- ous and resinous electricity. The former is also termed positive, and the latter negative. The discovery of these two different kinds of electricity was made by Dufay in the year 1773. Of the Electric Fluids, and the Natural Condition of Bodies. Owing to the rapidity with which electricity distributes itself through conductors, it has been concluded that it must be a body endowed with remarkable powers of motion, and, from the laws of vitreous and resinous electricity, it has been further assumed that there must be two electric, as there are two magnetic, fluids. When these two fluids are united in one body, and when they mutually neutralize each other in that body, the body is in its na- tural condition. If, however, the two electricities are decomposed in a body, it will become electric, positively, if the vitreous elec- tricity, and negatively, if the resinous electricity predominates. There exists, however, an essential difference between the electric and magnetic fluids ; the latter being, as it were, enclosed in the 372 ELECTRICITY OF FLUIDS, ETC. magnetic particles, while the electric fluid can pass freely from one body to another. If + electricity be given off by friction in a body, electricity must be developed in an equal degree. We may show this by a simple experiment. If we rub together two discs of different substances, which are insulated by glass rods, they will exhibit no trace of electricity so long as they rest on each other; Flg ' 344 ' as soon, however, as they are separated, the one will be found to be positively electric, and the other nega- tively so, and in an equal degree. This experiment is best exemplified where one disc is of glass, and the other of some wood covered with leather, which has been rubbed over with amalgam. We may, also, take discs of any other substance, such as resin, metal, &c., covering them with different materials, to vary the experiment, as, for instance, with cloth, silk, paper, &c. Since a body in its natural condition contains both electricities in equal quantities, there is no reason to suppose that it is disposed to take up and retain either kind in particular ; it may, therefore, become positively or negatively electric, according to the sub- stance with which we rub it. Glass, for instance, becomes posi- tively electric when rubbed with wool or silk, and negatively so, when rubbed with cat-skin. In order, therefore, to designate the fluids distinctly, we must thus express ourselves. Positive or -f electricity is that kind of electricity assumed by glass, on the latter being rubbed with wool or silk ; negative or electricity, on the contrary, is that kind developed by resins rubbed with cat-skin, wool or silk. If we suppose a list of different bodies to be so drawn up, that each one, when rubbed with all those succeeding it, becomes positively a -f electric, we shall soon remark how the smallest change of circumstances alters the order of this series. A change of temperature, for instance, may oblige us to move the body upwards or downwards in the series. The same action is often produced by making the surface of a body rougher or smoother. The color, the arrangement of the molecules or fibres, or simply a more or less strongly applied pressure, may produce similar phenomena. A black silk ribbon, for instance, will be negatively electrified when rubbed with a white silk ribbon. Even on rubbing two pieces of the ribbon crosswise together, the COMMUNICATION OF ELECTRICITY. 373 one used for rubbing will become positively electrified, and the other negatively so. Again, on rubbing a polished glass disc upon a ground glass disc, they will likewise become oppositely electric, &c. Communication of Electricity . Free electricity may pass from one body to another, as well by immediate contact, as at great distances, the communication depending upon the capacity of the body for conducting electricity and the amount of its surface. On being brought into contact with an electrified body, bad conductors only take up electricity at the place of contact without its being transmitted over their whole extent. If, on the other hand, we touch an electrified insulator, it will lose its electricity only at the spot touched, the remainder of its surface continuing electric as before. This may be easily seen by means of a rubbed piece of sealing-wax, or a glass-rod. The case is very different with good conductors. When touched at one point by an electric body, the electricity will be diffused over the whole conductor, and if we bring an insulated electrified conductor into contact with the earth, it will immediately lose its electricity. Electricity may also pass from one body to another, without immediate contact, and here we remark the extraordinary pheno- menon of the electric spark. On bringing a metal rod, or one of the knuckles, near a rubbed glass or shell-lac rod, we see a brightly shining spark emitted, and hear a crackling noise. If the elec- trified body be an insulated metal of considerable surface, as the conductor of the electrifying machine, the sparks will be more vivid, passing, under some circumstances, to a distance of 12 inches ; their light will then be dazzlingly bright, and the noise accompanying them very loud. Otto von Guericke, the inventor of the air-pump, was the first who observed electric sparks. Subsequently Dufay proved to the astonishment of every one, that they might be drawn from the human body as from the conductor of a machine. To make this experiment, we must stand upon a piece of resin, or a stool with glass-legs (an insulated stool), and bring our body into contact with the conductor of the machine. On turning the machine we shall be conscious of a peculiar sensation upon the skin, especially the face, as though we were entangled in a web. The hair on the head will stand on end. If, now, the electrified human body be brought into contact with an insulated conductor, 32 374 COMMUNICATION OF ELECTRICITY. as another person, for instance, and the latter advance the knuckles, a spark will be emitted, which will be felt in proportion to the distance it has traversed. Electricity always distributes itself according to the amount of surfaces on passing from one insulated conductor to another; in order, therefore, to deprive an insulated conductor of all its elec- tricity, we must bring it into contact with another, having an infinitely larger area, as, for instance, with the ground, for it is thus brought in contact with the whole earth's surface, in which its electricity is wholly lost from being regularly distributed over so vast an extent. If we were to bring an insulated electrified metal ball into contact with another equally large, likewise insu- lated and non-electric, the former would lose exactly half its electricity. On bringing an insulated metal ball near the con- ductor of an electrifying machine, only faint sparks will be drawn from the machine by means of a non-insulated conductor. A taper that has been just extinguished may be relighted by an electric spark. In like manner, ether and alcohol may be influenced by the electric spark ; to effect this we must pour the fluid into a metallic vessel, and bring near to the surface of the fluid the electrified body from which the sparks are to be emitted. The electric pistol is represented in Fig. 345. It is a small Fig 345 metallic vessel secured by a cork stopper. A metal wire terminating in two small balls b and V penetrates into the vessel without being in contact with the wall. For the purpose of effect- ing this, the wire is fastened with sealing-wax into a glass tube t t f , and this cemented into an aperture of the lateral wall. The electric spark conducted by the wire passes from the ball b' to the opposite wall. If, now, the vessel be filled with an explosive gas, as a mixture of hydrogen and atmospheric air, the spark will produce such an effect by the explosion of the machine as to cause the stopper to be propelled with a loud report. ELECTRICITY BY INDUCTION. 375 CHAPTER II. Fig. 346. ELECTRICITY BY INDUCTION. WE have seen that each of the electric fluids repels the like fluid and attracts the opposite. This attraction and repulsion not only show themselves in the decomposed fluids, but on those still in combination, whence it happens that the combined electri- cities of a body in a natural condition are dis- turbed by the approximation of an electric body. Let a ring of metal be attached to an insulated hook, and have two metallic threads passing through it, at the end of which are two pith balls. On the approach of an elastic body r, the balls will start away from each other even when r is very far removed, and no spark is transmitted to them. This di- vergence increases the nearer we bring r. It is evidently not the effect of transmitted electricity, for the pendulums fall together the moment we remove r. The electricities which were combined in the metallic ring and the pendulums before the approximation of r, have been separated ; that kind of electricity which is like that of r,. is repelled towards the balls, whilst the opposite is attracted to the ring. If, therefore, the electric body r is a rubbed rod of resin, that is electric, the ring will become + electric, and the balls . We may demonstrate, by means of a test disc, that the two kinds of electricity are really distributed in the way indicated. A test disc is made of gold leaf, or gold paper, from 1 to 2 centimetres in diameter, (^ to inch) and fastened to a long rod of shell-lac, or thin glass rod covered with varnish. If we touch the ring with this iisc whilst the negatively electric body r is so near it :hat the pendulums diverge, the test disc will be charged with Fig. 347. 376 ELECTRICITY BY INDUCTION. the electricity of the ring, the nature of which we shall learn by bringing a simple electric pendulum near the disc to which elec- tricity has already been imparted. Supposing that the simple pendulum has been made + electric by contact with a glass rod, it will be repelled by the test disc, since the latter, as well as the ring, is + electric. This experiment may be conducted as follows. We must attach to each hook-like extremity of a metal rod, supported on an insulated glass stand, a couple of pendulums having conduct- ing threads made either of slender metallic wire or linen thread. Both these double pendulums will diverge on the approach of an electric body r, the balls of the one pair being charged with +, and the other with electricity. On removing the body r, the Fig. 348. pendulums will again approach each other, because the separated electricities then immediately combine. A body electrified by induction, acts on its part again, by induc- tion upon other bodies brought sufficiently near it, that is, within its sphere of activity, which may extend to a considerable dis- tance. A glance at Figs. 349 to 352, will suffice to show the arrangement that must be made, in order to demonstrate the truth of this by experiment ; m is the conductor of an electrifying ma- chine, c one insulated metallic cylinder, c' another, b a metallic ball, and b f a pith-ball. If, by means of a conducting medium, we bring an insulated conductor (electrified by induction) into contact with the ground, ELECTRICITY BY INDUCTION. 377 while the electric body still acts inductively by its approximation, all the repelled electricity will be carried off by the earth, and Fig. 349. Fig. 350. Fig. 351. Fig. 352. the insulated conductor will only remain charged with the elec- tricity attracted from the inductive body r. If we again destroy the communication with the earth, and remove r, the insulated conductor will be charged, throughout its whole extent, with the same electricity. The apparatus in Fig. 346, made in a somewhat different form, serves admirably as an electroscope. Care must be taken that the pendulums are secured, in a glass vessel, in order to hinder the injurious interference of external influences, as currents of air, &c., besides which, the conducting system must be carefully insulated. The pendulums may be formed of blades of straw, and balls made of the elder pith, suspended to metallic threads, or of metallic plates. Fig. 353 represents a gold leaf electrometer. A glass tube passed through the opening of the glass vessel, having a metal rod, covered with shell-lac varnish, fastened to it, and penetrating Fig. 353. Fig. 354. 378 ELECTRICITY BY INDUCTION. into the vessel, while the gold leaf pendulums are fastened to the lower extremity of this metallic rod ; a metal plate is screwed on the top. In order to be able to measure the divergence of the pendu- lums, a graduated arc is either introduced into the interior of the glass vessel ; or, instead of this, a glass box is used, as repre- sented in Fig. 354, on the side of which the graduated arc is attached. The experiment, shown in Fig. 346, may also be made by the above delineated electroscope. If we place above it an electric body, as a rubbed glass rod, for instance, the pendulums will diverge ; the nature of the electricity collected in the upper plate, may be ascertained by means of the test disc, it being the con- trary to that of the approximating body r, If we wish to examine into the nature of the electricity of any body, the electroscope must be charged beforehand with a kind of electricity with which we are acquainted, and this may be done by bringing a body r, whose electricity is known, near the appa- ratus, and touching the plate with the finger. By this means all the repelled electricity is carried off, there remaining only the portion attracted and accumulated upon the plate. It is to a cer- tain extent combined, that is to say, it cannot escape, being at- tracted by r y on which account the pendulums do not diverge ; immediately, however, on removing the finger and the body r+ Fi 355 the pendulums will diverge as the electricity which was combined with the plate by the body r, disperses itself freely over the whole insulated system, consequently also over the pendulums. The electricity with which the electroscope is in this manner charged must naturally be contrary to that of the body r\ thus, if we want a negative charge we may make use of a glass rod rubbed with silk, since this is + electric. If we bring an electric body to the charged electroscope, the divergence of the pendu- lums will either be increased or diminished in consequence. It will be increased if the electricity of the body to be examined, be the same as that imparted to the apparatus, ELECTRICITY BY INDUCTION. 379 for by its approximation, the electricities of the electroscope are more thoroughly decomposed than was the case before, and more electricity of the same kind as that already in the pendulums, is imparted to them, when their divergence must consequently in- crease. If the approximated body be of the contrary electricity to that imparted by the electroscope, the divergence diminishes as the electricity is withdrawn from the pendulum and drawn into the plate. Whatever be the electricity with which the apparatus is charged, there will still be undecomposed electricities in the ap- paratus, which will be decomposed by the approximated body: if the electricity in the latter be contrary to that present in the elec- troscope, the amount of electricity already developed* will be drawn into the plate, while the other will be urged into the pen- dulums, the divergency of which must therefore diminish. At a definite distance from the approximated body, the electricities will neutralize each other in the pendulums, which will then fall closely together. If the body to be tested be brought still nearer, the pendulums will again diverge, but with electricity of a kind contrary to that which made them previously diverge. The divergence of the pendulums likewise diminishes on bring- Fig. 356. Fig. 357. Fig. 358. Fig. 359. ing a non-conductor near the charged electroscope. This follows as the necessary consequence of the laws of electric induction. On uniting two similar electroscopes by an insulated conductor, and bringing an electric body r near one of them, the pendulums in both jars will diverge, the one from +, and the other from electricity. On removing the connecting conductor (we must, of 380 THE ELECTROPHORUS. course, hold it by the insulated handle) the pendulums will not meet again, even after the removal of the body r effecting the induction, owing to the separated electricities having no way by which they can pass back to each other. We may know that the electricities in both apparatuses are of different natures, by bring- ing the same electric body first to the one, and then to the other electroscope, when we shall see them diverge in the one case, and collapse in the other. The above-described phenomena of attraction can also be ex- plained by the laws of electric induction. If a body in a natural condition be brought near one that is electric, its electricities will be decomposed. This will also be the case with the cork ball of the simple electric pendulum. If it be suspended by a silk thread, the repelled electricity cannot escape from the ball, but will be urged to the reverse side of the ball, whilst the attracted electri- city will be accumulated in the front. As the attracted electricity is nearer to the body from which the action proceeds, the attrac- tion will be stronger than the repulsion ; the force urging the ball towards the electric body will be equal to the difference of these two opposite forces; a very small removal of the electric body will, therefore, be followed by attraction. The action will be far stronger where the ball is suspended to a conducting thread, as in that case the repelled electricity can escape, and the attraction will consequently not be weakened. A ball of shell-lac is not attracted by the approximation of an electric body, as the approximated body is only capable, with difficulty, of causing induction. This phenomenon resembles what maybe seen in the case of a magnet, which easily occasions a magnetic induction in a piece of soft iron, but can only effect the same in a piece of steel with extreme difficulty. The Electrophorus is one of the most important electrical ap- paratuses, and may, in many cases, replace the electrifying ma- chine. It consists of a cake of resin, which, as seen in Fig. 360, is fused in a plate of metal, or a cake of resin simply laid Fig. 360. upon a somewhat larger metal plate. It is very important that the surface of the cake of resin should be as smooth as possible. On this cake, the surface of which has been made negatively elec- tric by striking it with a fox-tail or cat's-skin, we place a metal cover pro- THE ELECTRIFYING MACHINE. 381 vided with an insulated handle m. The Fig. 361. electricity of the cake of resin acts inductively upon the two electricities hitherto combined in the cover, the -f electricity is attracted, the electri- city repelled ; the former will, there- fore, accumulate in the lower part of the cover, and the latter in its upper part. On bringing the knuckle of the finger near the cover, a spark will be elicited, and, on touching the cover with the finger, all the electricity will escape, -f electricity alone re- maining, which, however, is combined with the electricity of the cake of resin, as long as the cover is on ; but, if this be re- moved, the 4- electricity will be liberated, and we may draw a spark of -f electricity from the cover. If the cake of resin be laid directly upon a metal plate, there is less fear of the cake cracking by the change of temperature, as may easily be the case, owing to the unequal expansion of the metal and resin in melted cakes. The best substance for an electrophorus, is shell-lac mixed with Venice turpentine. Zinc may be used as the material for constructing the metallic plate on which the resin cake is laid. The cover is generally of brass, and has its edge rounded off. Covers of glass, wood, or pasteboard answer the purpose, however, when coated with tin- foil ; but care must be taken to have the under surface lying on the cake of resin as smooth as possible. In the place of an insulated glass handle, the cover may be fastened with three silk cords. The Electrifying Machine consists of a rubbing body, a rubber, and an insulated conductor. The rubbing body is generally a horse-hair cushion. The rub- bing surface, a piece of leather covered with amalgam. The body rubbed is a glass disc or cylinder. The insulated conductor is generally a system of hollow con- ductors, made of brass plate, spherically rounded at the extremi- ties, and supported by glass legs, varnished with shell-lac. Many different forms have been given to the electrifying ma- chine; the one most in use is represented in Fig. 362. The dia- meter of the glass plate a varies from 20 to 60 inches. An axis passes through an opening in its centre, and supports the winch b. The pillars d bear the plate, and likewise the couple of pairs of cushions e and e f , which rub the plate from the edge to about J 382 THE ELECTRIFYING MACHINE. or J of its diameter. The conductor fgf is insulated by the columns A, and terminates in two arms i, which pass round the plate across its horizontal diameter. Fig. 362. Fig. 364. Figs. 363 and 364 exhibit more plainly the arrangement of the cushions, and the manner in which they are secured. If we turn the glass disc round, by means of the winch, it will become positively electric by the friction against the leather cushion covered with amalgam. After turning the disc one-quar- ter round, one spot on the disc lying between the cushions al- ways comes to the arms i. The + electricity of the glass acts here decomposingly upon the conductor; the electricity is THE ELECTRIFYING MACHINE. 383 attracted, and flows over the glass, and then brings it back to its former condition, that is, neutralizing more or less entirely its + electricity. This latter electricity remains upon the conductor. In order to prevent the electricity of the glass from being wasted in the air, on its passage from the rubber to the arm i, the disc is protected on both sides by pieces of oil-silk. It is necessary to rub the glass legs and the disc with warm woolen cloths, or with heated dry blotting-paper, before using the apparatus, in order that it may work efficiently. The electricity of the rubber passes to the ground, and its escape is necessary, since, if it were to remain upon the cushion, it would acquire such a degree of tension as partially to flow over the glass plate, and partially neutralize the -f electricity. The electricities that are liberated by friction must immediately be carried off at the spot where they are set free, otherwise we should be unable to develop electricity again at the same place. Glass cylinders are used as well as the plates in the construction of electrifying machines. Fig. 365 represents a cylinder-machine, Fig. 365. which, as usual, is so arranged that positive and negative elec- tricity may be engendered at will ; a is the glass cylinder revolving upon a horizontal axis 6, and rubbed throughout its whole length by a single cushion e. This cushion is connected with a con- ductor r. The conductor v is diametrically opposite to the cushion 384 THE STEAM ELECTRIFYING MACHINE. e, and is provided with points on the side turned towards the cylinder. The upper half of the cylinder is protected by a piece of oil silk fastened to the rubber e, so that the glass rubbed at e may not lose its electricity on its passage to the conductor v. The latter is of course charged with + electricity. If we wish for a powerful charge of -f- electricity on v, we must put the conductor r in connection with the ground. On the other hand, we must take care to enable the -f electricity to pass freely from the con- ductor v, if we want to have a strong charge of electricity on the conductor r. The Steam Electrifying Machine. Many years ago, the dis- covery was accidentally made, in England, that a boiler, from which steam was forcibly propelled through a small aperture, was strongly electric ; by pursuing this discovery, means were found for converting a steam boiler into an electrifying machine far sur- passing, in its action, every known apparatus of the kind. Fig. 366 represents a machine of this description of medium size. The boiler, which is 18 inches in diameter, and 3 feet in length, rests upon four glass legs. It is heated internally in a similar manner as the boilers used in steamboats. Fig. 367 is a section of the boiler. On the top of the boiler there is a cap, to which a short brass tube, closeable, by means of a cock, is attached ; the conducting pipes may be screwed on the short tube, and will presently be described. Before the cap there is a safety valve, whose weight is mova- ble, and may so far project that the steam must exert a pressure of 90 Ibs. on the square inch, before it can raise the valve. On the reverse side of the boiler there is a glass tube con- nected above and below with the boiler, so that we may, by this tube, see, as in locomotives, the height at which the water stands. Fig. 368 represents the apparatus with its conducting aper- tures delineated, as seen from above. The cast iron tube b c (Fig. 366), about 8 inches in length, and 2 inches in diameter, is screwed on at a. From this tube the steam escapes through 6 horizontal tubes d d f , which pass through a box of brass-plate filled with cold water, by which means, a portion of the escaping steam is condensed, and the action considerably increased. At an opening o in the upper cover of the box F, a brass tube THE STEAM ELECTRIFYING MACHINE. 385 is put on, which passes at n (Fig. 366) into the chimney, and gives a passage to the steam formed in the box F. Fig. 366. Fig. 367. Fig. 369. Fig. 369 gives a section of the conducting pipes d r represented in Fig. 368, at about half their actual size. At the end of the tube, a piece of brass M N is screwed on, having a wooden plug a b c d, which forms the end of the escape aperture. This longitudinally bored wooden cylinder is secured to its place by a short brass cylinder r screwed into the brass work M N. A brass plate is so placed before the opening of the bored cylinder r, that the steam must pass along the winding course, designated by the arrow, before it can escape by the opening. If the apparatus, in Fig. 368, be screwed on the boiler, and the steam have the necessary force of tension, the separating 33 386 THE STEAM ELECTRIFYING MACHINE. cock will be opened by turning the handle t, Fig. 366, a quarter round, and the steam escaping, with force, from the six openings, the boiler will become electric. The escaping steam has the opposite electricity to that contained in the boiler ; in order to heighten the action of the apparatus, it is essential to let the steam escape as fast as possible, and this is best effected by placing, in the current of steam, a row of metallic points fastened to a brass rod communicating with the ground. This rod, or staff, stands on a glass pedestal, by which it may be insulated to prove that the steam has really the opposite kind of electricity to that of the boiler. By means of this hydro-electrifying machine, a battery of 36 square feet, in area, may be perfectly charged in the space of 30 seconds. The source of this strong development of electricity is not owing to the formation of gas, as we might, at first, be inclined to believe ; but entirely to the friction against the sides of the tube of the violently escaping steam that is mixed with particles of water. That such is really the case, is proved by the escape of the electricity every moment the safety-valve is opened, although the formation of steam continues, in the meantime, uninterrupted. For the generation of electricity, it is essential that the already condensed particles of water should be carried away with the escaping steam through the apertures, an object which is effected by the condensation apparatus JF, seen in Fig. 368. If the escape pipes be of sufficient length, we may dispense with a special cool- ing apparatus. When the opening for the steam is formed by a wooden tube, as delineated, the boiler will be in a state of electricity, and the steam in one of 4- electricity ; the same is the case when metal or glass is used for the purpose ; and, if an ivory tube be used, the boiler will scarcely manifest a trace of a charge. On applying a little oil of turpentine to the mouth of the tube, the boiler will be positively, and the steam negatively electric. OF ELECTRIC FORCES. 387 CHAPTER III. OF ELECTRIC FORCES. Diminution of Electrical Power with the Increase of Distance. The law by which electrical attractions and repulsions diminish in proportion as the distance increases, may be shown by the os- cillations of an electric pendulum. We must let a small shell-lac needle, horizontally suspended by a silk thread, and supporting at one end a disc of electrified gold leaf, oscillate by the influence of an electrified insulated ball. If the ball and the disc be charged with the same electricity, the disc will form the end of the elec- trified pendulum turned away from the ball ; but if the electricities of the disc and the ball be different, the former will be turned towards the latter. We may, in like manner, judge of the accele- rating force exercised on the electric pendulum by its oscillations. From these data it may be seen that electrical attractions and repulsions stand in an inverse relation to the squares of distance. Distribution of Electricity on the Surfaces of Conducting Bodies. As long as a body remains in a natural condition, that is, as long as the two electric fluids are not combined, they are, probably, uniformly distributed through the whole mass of the body. As soon, however, as one fluid becomes separated from the other, and a conductor is charged with free electricity, the individual elements of these freed electricities will act repulsively upon each other, retreating as far apart as possible, until checked by some impe- diment. A perfectly good conducting body cannot oppose any resistance within itself to this dispersion ; the electricity, there- fore, distributes itself over its surface, and would be still further dispersed if the body were in a space easily penetrated by the elec- itricity. Electricity always distributes itself over the surface of a conductor, on which it is retained by the atmosphere, which en- velops it as if it were a non-conducting layer. The following experiment will show, in the simplest manner, that electricity only distributes itself over the surface, and not through the interior of bodies. A ball, 7 or 8 inches in diameter, and having a hollow 8 or 10 388 DISTRIBUTION OF ELECTRICITY ON THE lines in breadth, and 1 inch in depth, must be insulated and charged with electricity ; if, now, we touch this ball in any part, with a test disc, it will become charged with electricity, while, on touching the bottom of the hollow, with the test disc, it will not be removed from its natural condition. Let us now consider the manner in which electricity distributes itself over the surface of bodies. If we electrify an insulated body, the law of symmetry requires that the electricity should distribute itself uniformly over the whole surface, forming everywhere a layer of equal density. We may convince ourselves by experiment that such is the case. If, for instance, we touch the electrified ball at any spot with the test disc, the latter will immediately form, as it were, an element of the spherical surface, as large a quantity of electricity distri- buting itself over its surface as there was upon the portion 01 the sphere covered by the disc ; the strength of the electric charge in the disc may be determined after its removal from the sphere, by bringing it into contact with the plate of an electroscope. The divergency of the pieces of gold leaf will be the same, at whatever part of the ball we attach the disc. If the insulated conductor to be electrified be not spherical, no equal distribution of the electricity will take place, that is to say, the electrical layer distributed over the body will not be every- where equally dense. If, by the aid of a test disc, we test the density of the electricity at different parts of a cylinder, with rounded ends, (Fig. 370,) we shall find the density of the electri- Fi 370 city, greater at the extremities than in the mid- dle. The disc will be much more strongly charged, on holding it to the end of the cylin- der, in such a manner that its edge shall not touch the top of it, but that its plane shall lie in the line of prolongation of the axis of the cylinder. Similar results are obtained by examining the electrical condition of a disc, for instance, the cover of an electrophorus. We may easily understand that a distribution of electricity must occur on the sur- face of bodies possessing unequal expansion in different directions, for, in consequence of the mutual repulsion of the separate parti- cles of the electric fluid, these particles will retire as far as possible from the middle of the body, accumulating in its remotest projections. SURFACES OF CONDUCTING BODIES. The more a body departs from the spherical form, the less equally is electricity distributed over its surface, and the more does it collect at the points lying most remote from the middle, and that, in proportion to the want of density in those parts. It follows, therefore, that if a point be brought near an insulated conductor, the electricity will have an extraordinary density at this pointed end. But the denser the electricity is at any point, the sooner will it be able to overcome the resistance of the air, which strives to keep it upon the body. Hence it happens, that electricity flows so readily from sharply pointed bodies. We might adduce a number of experiments by which this power of pointed bodies is manifested, but we will limit ourselves to a few illustrations. 1. On putting a point to the end of the conductor of an elec- trifying machine, it will be found impossible to charge it in such a manner as to draw sparks from it. All the electricity engen- dered by the turning of the machine being immediately discharged by the point. 2. In the same manner, on bringing a point that is in connec- tion with the ground within a few inches of the conductor of the machine, it will be equally impossible to charge the conductor. The electricity of the latter decomposing the combined electricities of the point, and repelling the like kind, while it will attract the contrary, and this contrary electricity will accumulate with such brce at the point as to pass over to the conductor and neutralize the electricity of the latter. On the. above mentioned property of pointed bodies rests the construction of lightning conductors. Angles and sharp edges to conducting bodies act similarly to joints. It is, therefore, essential, carefully to avoid all angular brms in the construction of any apparatus destined to retain elec- tricity. On bringing an insulated electric conductor near another con- ductor, the distribution of the electricity on the surfaces will experience considerable modifications. If we bring an electric insulated sphere near another body of the same kind, likewise insulated and charged with the same electricity, there will no longer be a uniform distribution of electricity upon the surface. As the electricity of the one sphere repels that of the other, the density of the electricity will be the most inconsiderable at those 33* 390 OF COMBINED ELECTRICITY. Fig. 371. Fig. 372. points of the spheres turned towards each other, and greatest at the most remotely opposite points. Figs. 371 and 372, represent two balls. At a and b the density of the electricity is at the minimum, at c and d it is at the maximum. The nearer we bring the two balls, the more will the density diminish at a and b, and increase at c and a. If we bring these spheres into contact, the density of the electricity will be null at the point of contact. If the two spheres had been charged with opposite electricities, we should have found the greatest density at a and 6, and the smallest at c and d. The accumulation of electricity increases at a and b on bringing the spheres near to- gether, until at last a spark is emitted. A non-electric conductor, on being brought near an electrified insulated conductor, will act similarly to a body charged with the opposite electricity, as it becomes electric by induction or approxi- mation to the conductor. CHAPTER IV. OF COMBINED ELECTRICITY. WE have already seen that if two insulated conductors charged with opposite electricities be separated by a layer of air, the elec- tricity of the one will attract that of the other, in such a manner that we may alternately put either body in connection with the ground without its electricity being entirely carried off. In Figs. 371 and 372, for instance, the ball to the left is charged with +, and. that to the right with electricity, and we alternately touch either with the finger without the charge being lost. The elec- tricity of the one sphere is attracted by the opposite electricity of the other sphere, and is thus prevented from escaping, being com- OF COMBINED ELECTRICITY. 391 bined. The nearer we bring these two kinds of electricity to each other, the more strongly will they be mutually attracted, and the more perfect will be their combination; if, however, the two conductors be separated only by a layer of air, the combination will not be perfect, as we cannot bring them very near each other without the layer of air being broken, and a spark emitted. To make the combination as perfect as possible, the two conductors charged with opposite electricities must in the place of air be separated by some other insulator capable of opposing a greater resistance to the passage of electricity, and for this purpose glass or resin answers best. The Franklin plate is especially well adapted to facilitate the examination of the properties of combined electricity. Fig. 373 represents a glass plate, the sides of which are about 1 foot in length. The middle of Fig ^ 373 ' the glass on either side is covered with tin foil, leaving a free margin all round of about a hand's breadth. We may varnish over the uncovered parts of the glass, in order the better to insulate them. If we charge the front part, covered with the tin foil, with -f, and the reverse side with electricity, the opposite electricities will be separated from each other merely by the thickness of the glass disc ; this they are, however, unable to penetrate, and thus the combination will be tolerably well effected. To charge the two-coated sides of the Franklin plate with op- posite electricities, it is unnecessary to bring each into connec- tion with the source of electricity. If we bring one side, (the front one,) into communication with the conductor of the electri- fying machine, a portion of the + electricity will pass off from the conductor to the coated surface. The electricity of the front surface acts inductively upon the combined electricities of the back surface ; and as soon as we place it in communication with the ground, the + electricity will pass into the ground, while the - electricity will be induced to the reverse surface. But the electricity of the reverse side acts repulsively upon the -f electri- city of the front side, thus enabling electricity to pass again from the conductor to the front coated surface, which again, by its re- 392 OF COMBINED ELECTRICITY. pulsive power, increases the electricity of the reverse side. We may in this manner easily charge one coated surface with -f , and the other with electricity. However small the distance separating the two surfaces, the mutual combination is not perfect. In order to have the elec- tricity perfectly combined on the one side, it is necessary that there should be an excess of electricity on the other, that is, that free electricity must be present. On touching the one coated surface of a charged Franklin plate with the finger, while the other side, (the front for instance,) is no longer in connection with the conductor, we can only bring off a portion of electricity, while a strong charge of electricity perfectly combined, remains upon the reverse surface. In order, however, to have this electricity perfectly combined, it is indispensably necessary that there should be an excess of + electricity on the opposite side. We may easily convince ourselves that such is the case. If after all the non- combined electricity of the reverse side has been carried off, we touch the front coated surface, a faint spark will be emitted on the approximation of the finger, which proves that free electricity is present. If now we remove all the free + electricity from the front side, there will again be free electricity on the opposite side, and we may draw a faint spark from the reverse coated sur- face, &c. The excess of electricity which must be present on the one surface, in order perfectly to combine the opposite electricity on the other side, may be made apparent to the eye. We must secure with wax, a light electric pendu- lum on each side of the disc in the manner re- presented in Fig. 374, which shows a diagonal section of the disc. On the side on which there is free electricity, the pendulum will be repelled, while, on the other side it will remain hanging vertically, and in contact with the coated surface. If we touch the pendulum on the one side where there is free electricity, the pendulum will fall, while the one on the opposite side will rise. We may, therefore, by alternately touching one or other of the sides, make either pendulum rise. This phenomenon may be easily explained. If there be an excess of + electricity on the one side, it will act Fig. 374. OF COMBINED ELECTRICITY. 393 attractively upon the electricity on the other surface, as well as upon the little electricity in the ball of the pendulum. The electricity certainly repels the electricity in the ball, but the force with which the excess of -f electricity attracts the negative ball is greater than the force of repulsion. On carrying off the excess of -f electricity, the liberated electricity distributes itself partially over the ball which is now repelled, there being no excess of + electricity present on the other side to hold it back. The .apparatus will, by degrees, become wholly discharged if we continue alternately to touch the two surfaces with the finger, and thus remove all the free electricity on the one side. If we touch both surfaces at once, or, by any other means, put them into connection with each other, the discharge will take place all at once, while the accumulated opposite electricities of the two surfaces will pass, in this manner, from one to the other. The discharging rod, represented in Fig. 375, is commonly used for this purpose. It consists of two curved brass rods b c and b' c, which are united at c by a hinge. Each arm of the dis- charging rod terminates in a small brass ball b and &', and is also provided with an insulated handle m and m'. We must touch one surface with one of the balls, and on approximating the other to the op- posite, a spark of vivid light will be emitted, at a certain distance, with loud explosion. The Leyden jar is, in principle, nothing but a modification of Franklin's plate, and consists of a glass vessel, covered externally with tin foil to within a few inches of the rim ; internally, the vessel is simi- larly coated, or filled with some con- ducting substance, as iron filings or small seed. The inner coating is connected with a brass rod passing through the stopper or cover of the vessel, and ending in a knob. Figs. 376 and 377 represent two forms of the Leyden jar. The part of the glass that is not covered must be varnished. To charge the jar, the external coating must Fig. 376. 394 THE LEYDEN JAR. be brought into connection with the ground, and the knob with the conductor of the machine. We may, however, reversely, put the inner coating into connection with the ground, and con- nect the external one with the conductor of the machine. Leyden jars often discharge themselves when either a spark is emitted from the external coating to the metal rod, or the glass is broken. In the latter case, the jar becomes, of course, unfit for further use. When we use several conducting bodies, to discharge a jar, the electricity will immediately pass over to the best con- ductor. If we press a metal wire, with one hand, to the external coating, we may, with impunity, hold the opposite end of the wire to the knob, with the other hand, the electric shock passing through the wire, and not the body ; to effect this, the wire must not, however, be very thin. In order to obtain a very strong charge, it is necessary to use very large jars, either separate or connected in one electric bat- tery. Fig. 378 represents an apparatus of this kind. All the external coatings of the jars are in connection with each other, as well as the inner coatings. When the electric shock passes from a Leyden jar through the human body, it produces a sensation which it would be difficult to de- scribe, an involuntary con- vulsion of the nerves. The best manner of trying the experiment upon oneself, is to lay one hand upon the external coating, and, with the other, grasp the knob. In a weak dis- charge, the shock is only perceptible in the fore part of the arm, if it be stronger, we then feel it in the upper arm, producing an even, sharp pain in the breast, and very strong shocks may prove dangerous. Powerful batteries are not necessary if we want to kill smaller animals, as birds, hares, &c., by an electric shock; the larger batteries are capable of destroying the larger animals. Anatomical examinations of the bodies of the animals, killed by an electric shock, have shown that there is no injury inflicted on the organs; the violent contortions exhibited, however, in the THE LEYDEN JAR. 395 bodies, where the shock has not been sufficiently strong to pro- duce death, manifest the degree to which the nervous system has been affected. If several persons form a chain by holding each other's hands, all will simultaneously feel the shock, on the one first in the ring, touching the external coating of the jar, and the last the knob. We may ignite combustible fluids much more securely by aid of a Leyden jar than by a spark direct from the conductor of the machine. Even pulverized Colophony, scattered over cotton wool, and gunpowder may be ignited by the sparks of a discharge of a Leyden jar. Henley's general discharging rod, represented in Fig. 379, is Fig. 379. very convenient in many experiments which may be made with the Leyden jars and the electric battery. The one arm is in con- nection with the external coating by means of the chain c, while, to the other arm, is secured another chain airs of plates is fixed to a wooden frame, so that they may all be lipped simultaneously into, or taken out of the liquid. Water is 35* 414 THE TROUGH APPARATUS. the liquid generally used, to which T Vth sulphuric acid, and ^th nitric acid, is added. The number of pairs of plates, and their surface required, depend upon the purposes to which the voltaic apparatus is applied. Many phenomena may be produced with a battery of many pairs of small size ; others, again, require a single pair only, but of considerable dimensions, and with perfect metallic contact. Fig. 398. Fig. 399. I I 1 1 I II I i i 101! Fig. 400. Fig. 401. Fig. 402. The simple circuit shown in Figs. 401 and 402, is used for such experiments as require a large quantity of electricity in motion, but of a small degree of tension. C is a vessel formed of two cylinders of copper sheeting of different dia- meters, the one placed within the other, and so arranged that the space intervening between the two may be filled by the zinc cylinder z 9 and the acidulated water. A copper wire ending in a cup containing mercury, is soldered to the zinc cylinder. A similar mercury cup is at- tached to the copper vessel. In placing the zinc cylinder within the copper vessel, care must be taken that the zinc does not come in contact with the copper. This is most easily prevented by means of pieces of cork. If we wish to complete the circuit, we must connect the mercury cups by a metallic wire. This apparatus has this advantage, that it enables the zinc to be very conveniently cleaned. HARE'S CALORIMOTOR. 415 Hare's Calorimotor, represented in Figs. 403 and 404, is used where we have to act upon a large surface of metal plates. Fi s- 403 - Fig- 404. On a wooden cylinder 6, about 3 inches in diameter, and from a foot to a foot and a half in height, there are two plates, one of zinc and the other of copper, rolled up in the same manner, and separated by cloth strips /. We thus ob- tain a pair of plates of 50 to 60 square feet in area. The name Calorimotor is applied to this apparatus from its special property of making metal wires red hot, and even fusing them. [The apparatus, as devised by Dr. Hare, differs in form from the above, as may be seen in Fig. 405. A a are cubical boxes, Fig. 405. one containing acidulated, and the other pure water ; b b is a wooden frame containing zinc and copper plates, alternating with each other, and from i to J an inch apart ; T T t t are masses of tin cast over the protruding edges of the sheets which are to communicate with each other. The small figure represents a horizontal section of the series of plates, showing the mode in which 416 BECQUEREL'S CONSTANT BATTERY. the junction between the sheets and the tin masses is effected. Between z z, only the zinc is in contact with the tin, whilst be- tween c c, the copper alone is connected with it. At the back of the frame, ten sheets of copper between c c, and ten sheets of zinc between z z, also communicate by a common mass of tin, ex- tending the whole length of the frame between T T\ but, in front, as shown in the larger figure, there is an interstice between the mass of tin connecting the ten copper sheets, and that con- necting the ten zinc sheets : ff screw forceps on each side of the interstice to hold the wire, which is to undergo ignition. The plates are separated by a wooden partition p p. The swivel 8 permits the frame to be swung round after removal from the acid in Jly and to be lowered into the pure water in a, for the purpose of washing off the adhering acid.] In all the circuits we have hitherto described, whether simple or compound, the action is very energetic immediately after im- mersion into the acid fluid, but it very rapidly diminishes. This variation in the current always occasions great disturbance in experiments made to compare the force of different currents. The constant batteries which have lately come into use, are, how- ever, free from this inconvenience. We must here limit ourselves to a description of the most important constant circuits, reserving for a subsequent occasion an exposition of the theory as well as the causes that contribute to the rapid diminution of the force of the current in ordinary circuits. As inventor of the constant circuit, BecquereVs name deserves mention. Fig. 406 represents an element of BecquereVs constant circuit ; it consists of a hollow cylin- Fig. 406. , - ,,. , .. der a made of thin copper sheeting, loaded with some sand 6, and closed on all sides. The bottom c is even, the top d conical, having over it a rim e perforated with numerous holes. The whole cylinder is surrounded by a bladder g, fastened to the rim e above the holes f. We now pour a solution of sulphate of copper on the cone d, and this running through the holes f, fills the space between the bladder and the cylinder a; a few crystals of sulphate of copper, (blue vitriol,) are laid upon the BECQUEREL'S CONSTANT BATTERY. 417 cone d, being gradually dissolved by the fluid flowing over them. The bladder is enclosed in a hollow cylinder of zinc A, slit length- wise, so that it may be widened or contracted at will. This zinc cylinder, as well as the bladder containing the copper cylinder, and the blue vitriol solution, are immersed in a vessel i, made either of glass or porcelain, which contains dilute sulphuric acid, or a solution of sulphate of zinc, or of muriate of soda. Two strong copper wires p and n, one of which is soldered to the zinc cylinder, and the other to the copper, form the two poles of the element. If we establish a metallic connection between these two poles, the electric current will begin to circulate. Daniel's constant battery is only a modification of BecquereVs invention. [It consists, Fig. 407, of a copper cell or vessel, forming the negative metal. A rod of amalgamated zinc is placed within a tube of porous earthenware. Attached to each metal is a binding screw, to form connections. To put this cell in action, place the parts, as shown in the figure, fill the porous tube with a mixture of one part of sul- phuric acid, and ten parts of water ; and the copper cell with a saturated solution of sulphate of copper. The perforated metal shelf is to support additional sul- phate to keep up the strength of the solution.] In the Bunsen battery, the place of the copper is supplied by carbon, which is still more negatively electric, and is used here in the form of hollow cylinders. A hollow cylinder of this kind, open at the bottom, 5 inches in height, and 2J inches in diameter, having its sides about 3 lines in thickness, is placed in a glass vessel, as seen in Fig. 408, somewhat con- tracted towards the top, so as to have no great interstice between the carbon and the glass, the cylinder standing conse- quently quite fast in the glass. We now place in the hollow of the carbon cylinder, a hollow cylinder of porous clay, closed at the bottom, and having, at the height of about 4 inches, such a diameter as to make it fit into the cavity of the carbon cylinder, and to leave a very small space between the clay and the carbon. The clay cavity is filled with dilute sulphuric acid, but the glass 418 BECQUEREL'S CONSTANT BATTERY. contains so much concentrated nitric acid, that when the clay cylinder is put in, almost the whole free space of the glass is filled to the narrow neck of the vessel with the last named fluid. The upper end of the carbon cylinder projects beyond the glass, and is slightly conical, so that a likewise slightly conical ring of zinc a can be fastened to it. This ring supports, by means of a zinc brace 6, a hollow zinc cylinder c about 3J inches in height, and 1J inch in diameter. This cylinder c is suspended in the clay cavity of the next glass in the dilute sulphuric acid. Fig. 409 clearly exhibits the manner in which one pair of zinc plates is connected with the next, the diagrams showing the out- lines of four pairs. The Flg * 409> carbon cylinders are distin- guished by different horizontal bands. Within each carbon cylinder, we see two white rings in the figure ; the outer one represents the clay cy- linder seen from above, the inner one, the zinc cylinder. The zinc cylinder of the first glass is connected by a strip with the zinc ring encircling the charcoal cylinder of the second glass. In like manner, a zinc strip connects the zinc cylinder of the second glass with the zinc ring of the third, and a third strip joins the third zinc cylinder to the fourth zinc ring. The ring placed upon the first carbon cylinder ends in a zinc strip, serving as a positive pole ; the zinc strip 7i, with which the zinc cylinder terminates in the fourth glass, is the negative pole of the circuit. In the same manner, we may construct circuits of any number of pairs. In each separate pair, the -f current passes from the zinc ring enclosing the carbon, through the strip, to the zinc cylinder of the next glass, from the latter, through the dilute sulphuric acid, the pores of the clay cavity, and the nitric acid to the next piece of carbon, &c. The carbon used for the cylinders, is prepared in a peculiar manner from coal and coke ; but we cannot enter here into an exposition of the process. PHYSIOLOGICAL ACTION OF GALVANIC PILES. 419 Grove's battery is very similar in its construction to Bunsen's, the difference between them being principally that, in the former, platinum is used instead of carbon. CHAPTER II. ACTIONS OF THE GALVANIC CURRENT. Physiological Actions of Galvanic Piles. The convulsions of the nerves produced by the electricity of the voltaic piles, are not less violent than those occasioned by common electric batteries ; their intensity depending upon the number of pairs of plates, that is, upon the amount of tension. To conduct the charge of the piles through the human body, it is necessary to moisten the hands, as, for instance, with salt water, the epidermis being a very bad conductor. On touching both poles of a pile of 20 to 30 pairs of plates with dry fingers, we do not experience the slightest shock, but the charge is perceptible the instant we wet the hands. The charge of a pile of 80 to 100 pairs of plates is very marked. We feel a shock at the moment in which we close the circuit with the fingers; as long as it remains closed, the electric current circulates through the body without producing any very marked action upon the feelings, and it is only with very powerful piles of many pairs of plates that one is conscious of a burning tingling sensation at the places where the current enters the body. A second shock is felt, however, at the moment in which the current is re-opened ; but this, termed the separation shock,is much weaker than the closing shock. Even a simple current will make a lightning-like appearance flash before the eyes. We may make the experiment in various ways ; thus, for instance, we may bring a silver plate towards the pupil of the eye, or towards the eye-lid, which must be previously well moistened, and then touch the plate with a piece of zinc held in the moistened hand, or retained in the mouth. On conducting the current of a pile through the eyes, the appearance of light will be stronger. If, also, we lay a piece of zinc above, and a piece of silver under 420 GENERATION OF LIGHT AND HEAT. the tongue, and then bring the upper extremities of both metals in contact, we shall perceive a peculiarly bitter taste. Generation of Light and Heat by Galvanic Currents. Galvanic currents, like the electricity of friction, produce heat and light. If we conduct a galvanic current through a metal wire, this will be heated ; the connecting wire must, however, be very short and thin, to yield a powerful action. The intensity of the heat will depend upon the size, and not on the number of the metal plates. To make metallic wires red hot, it is only necessary to use a sim- ple current of large surface, as represented in Fig. 410. A Bun- sen's battery is also well adapted for this experiment. The larger Fig. 410. the act i n g surface of the galvanic apparatus, the greater may be the thickness of the wires that are to be made red hot and melted. Iron and steel wire attain a white heat, melt, and burn with the emission of vivid sparks. Platinum wires become vividly glowing, and melt away, if they are made short and thin enough for the circuit used in the experiment. Thin gold-leaf volatilizes, and, as one cannot use it for touching the poles, without its being converted into vapor at the place of contact, the current is constantly interrupted and again closed, by which means we see emitted a number of small, shining sparks of a greenish color. Silver tissue exhibits the same phenomena. If we fasten to each of the poles of a galvanic circuit, pointed pieces of carbon (of the kind and size used in the carbon cylin- ders of Rumen's battery), we shall, as soon as these points come into contact, perceive an uncommonly glittering light. This bright light can be seen by a Burners battery of only four elements ; a small, brightly luminous star appearing where the points of the charcoal come into contact with each other. By increasing the number of the elements, the splendor of the appearance consider- ably increases ; and thus, in a circuit consisting of from 30 to 50 elements, we may obtain a light far exceeding in brightness Drum- mond's hydro-oxygen light. By the application of this number of pairs -of plates, we may remove the points of the pieces of carbon tolerably far from each other, if only the current passes, and we may thus obtain a splendid bow of light, formed by the glowing particles of the charcoal which pass from one pole to the other. CHEMICAL ACTIONS OF THE VOLTAIC PILE. 421 Chemical Actions of the Voltaic Pile. The first, and most im- portant chemical action of the pile, was discovered by Carlisle and Nicholson, at the beginning of the present century, (30th of April, 1800.) These two natural philosophers had hastily built up a pile of coins, zinc plates, and damp pieces of pasteboard, in order to repeat some of the experiments of Volta. After a few trials, the smell of hydrogen became obvious, and Nicholson was led by this to the happy idea of suffering the current to pass through a tube filled with water, into which fluid he plunged both poles, holding them at some distance apart. The hydrogen gas soon rose to the negative pole in small globules, whilst the zinc wire, connected with the positive pole, became oxidized. If, how- ever, a platinum, or silver wire was used in the place of the zinc, it did not oxidize ; but the oxygen likewise rose in bubbles to the surface. This water was at length directly decomposed into its elements. Cavendish certainly had already shown that oxygen and hydrogen combine to form water ; but, notwithstanding all efforts made for the purpose, no one had yet succeeded in accomplishing the direct decomposition of water. A suitable apparatus for the decomposition of water is represented in Fig. 411. It consists of a glass, in the bottom of which two platinum wires f andjf' are inserted, without being suffered to touch each other. Two glass bells, o and A, are filled with water, and set inverted in the glass, so that one may cover each of the wires. As soon as the wires f and f are brought into contact with the poles of the circuit, bubbles of gas are developed in large quantities. Pure oxygen gas always rises in the bell at the -f pole, and hydrogen gas at the other. It will, of course, be understood that the water in the bell must not be separated from that in the vessel, so that the current may pass through the fluid from one wire to the other. The development of gas will increase in quantity as the dis- tance between the polar wires /and f is diminished, and accord- ing to the amount of surface of the metal standing in contact with the water. In many apparatus, therefore, serving for the decomposition of water, the wires have been replaced by platinum plates. Distilled and perfectly pure water is, however, but slowly de- composed in this manner; but as soon as we pour a few drops of 36 422 CHEMICAL ACTIONS OF THE VOLTAIC PILE. Fig. 412. any acid, or dissolve a few grains of salt in the water, by which the conducting power of the fluid is considerably heightened, a very strong action begins, affording, in a short time, a large quantity of gas. We will subsequently consider how the quan- tity of the gas developed, depends upon the force of the current. The apparatus, shown in Fig. 412, may be used where we do not care to have the two kinds of gas separated, as it enables us to decom- pose a larger quantity of water, owing to the greater vicinity of two large polar plates of platinum. The explo- sive gas escapes through a curved tube, and, on immersing the opening of the latter under water, we may col- lect the gas, or make the escaping bubbles detonate. The quantity of oxygen liberated at the -f pole, and collected in the tube o, (Fig. 411), has only half the volume of the hydrogen which is liberated at the other pole, and rises in the tube h. The gases are, therefore, evolved exactly in the same proportion as they combine with water. Water, as is well known, consists of 1 equivalent of oxygen, + 1 equivalent of hydrogen. But one equivalent of hydrogen occupies, other things being the same, twice as large a space as one equivalent of oxygen. The gases evolved from the pile will, therefore, when combined together, again yield water. Grotthuss has given the following explanation of this remark- able phenomenon, which is now generally admitted by natural philosophers to be correct. When hydrogen gas is combined with oxygen, to form water, the atoms of the oxygen become ne- gatively electric, in the intimate connection established between the smaller particles, while the atoms of the hydrogen are posi- tively electric; but, owing to the uniform distribution of the par- ticles of both substances, the combination does not, of course, exhibit any liberated electricity. If, now, water be placed be- tween the poles of a galvanic circuit, the -f pole will act in such a manner, upon the most contiguous particles of water, that the constituent will be attracted, and turned to the -f pole, whilst *'lg. 413. CHEMICAL ACTIONS OF THE VOLTAIC PILE. 423 the repelled atom of water, of the first molecule of water, will be turned away from the -f pole. The water-particle 1, Fig. 413, will act upon the particle 2, in such a manner as to turn its elements to the same side ; in a m Flg ' 413 ' similar way, 2 will act upon 3, &c. It therefore follows, that all the molecules of water between the two poles, will turn their atoms of oxygen to the -f pole, and their atoms of hydrogen to the pole, some- what as shown in Fig. 413, where the circle represents particles of water, the black half the atom of hydrogen, and the white half the atom of oxygen. If, now, the attraction exercised by the 4- pole upon the atom of oxygen of the water-particle 1, be strong enough, it will tear it violently from the atom of hydrogen ; this latter will again combine with the oxygen of the water-parti- cle 2 ; the hydrogen of 2, again with the oxygen of 3, &c. In this manner, a constant decomposition and recombination of the water will go on along the whole line between the poles, but it is only at the poles that its constituents can be liberated. A decomposition of water occurs in the cells of the galvanic circuit, exactly in the same manner as between the poles. Oxides are decomposed by the galvanic circle in the same manner as water. Oxygen appears at the + pole, the radical at the pole. The following experiment will answer for metallic oxides that are reducible : if we strew a little dry pulverized oxide upon a platinum plate, brought in connection with the -H pole of the pile, and touch the powder with the wire, we shall soon see small metallic globules appear at the extremities of the wire. Oxides less easy of being reduced must be somewhat moistened, especially if they are in a pulverized state. The water will certainly also be partially decomposed, but this will only serve to increase the capacity for conducting electricity. After a time we shall see, when the pile is strong enough, small metallic globules, appearing at the pole. A new epoch in science began with the year 1807, when Davy, by means of a galvanic pile, made the discovery that alkalies could be decomposed, which had, until then, been regarded as simple bodies. Alkalies and earths were thus ranged in the class of oxides, and chemistry enriched by the acquisition of two new metallic bodies, potassium and sodium. A very strong battery is necessary to decompose potash. If we make the experiment in 424 CHEMICAL ACTIONS OF THE VOLTAIC PILE. the manner above indicated, we shall see numerous globules of metal appear at the negative pole, and again vanish, with the emission of sparks. This is potassium, liberated in the decom- position of potash. Its affinity to oxygen is, however, so great, that on being brought into contact with the air, it immediately oxidizes ; on being brought into contact with water, it abstracts the oxygen, and inflames the hydrogen gas, and has the appear- ance of fire. Potassium must, therefore, not be kept in a fluid containing oxygen. Petroleum, or naphtha, composed of carbon and hydrogen, is generally used for this purpose. Seebeck has proposed a means by which the potassium evolved by means of a galvanic pile, may be collected with more certainty. A hollow is made in the piece of caustic potash we wish to decom- pose, and mercury poured into it. The potash is then laid upon a piece of platinum in connection with the + pole of the pile, while the wire plunges into the mercury. The decomposition immediately begins, the oxygen is liberated in the platinum, while the potassium, combining with the mercury, forms a tolerably consistent amalgam. We may then separate the mercury, by distillation in an atmosphere of petroleum vapor, and thus obtain the potassium in a pure condition. Salts can also be decomposed by means of the galvanic current, the acid appearing at the + , and the earth, or base, at the pole. The decomposition of salts may be made perceptible in the follow- ing manner. We fill a V-formed curved tube (Fig. 414) with a saline solution, which is colored violet by tincture of litmus. If now we plunge the 4- polar wire into the fluid on the one side, and the wire on the other side, the fluid will be red at the +, and blue at the pole. On changing the poles, the original violet hue will be only restored by degrees, red appearing where the wire was blue before the inversion of the poles, and vice-versa. If we pour a saline solution into two contiguous vessels, connected by a moist asbestus cloth, or by an A-shaped syphon, filled with the fluid, and then plunge the -f polar wire into the one vessel, and the wire into the other, the decomposition will go on in the same manner ; and after a time, the acid will be in the vessel into which the -f wire has been im- mersed, and the base in the other. Even if we pour the earthy CHEMICAL ACTIONS OF THE VOLTAIC PILE. 425 solution into the vessel JL containing the + polar wire, and the acid into the other B, the acid will, after a time, be in A, and the base in B. This experiment has been modified in various ways. A saline solution is not always decomposed into the acid and base by the galvanic current, there appearing in the decomposi- tion, frequently, only one or other of these bodies. A solution of sulphate of copper, for instance, is so decomposed that the copper separates at the pole, whilst the oxygen of the oxide of copper no longer remains in its former combination on the other side. This decomposition of sulphate of copper is beautifully exhibited in the constant circuit of Becquerel and Daniel, already described. When the circuit is closed, the -f current passes from the zinc through the dilute sulphuric acid, then through the solution of sulphate of copper to the copper. If the zinc become + electric in contact with the copper, and the latter , the zinc is, of course, the +, and the copper the pole, the + current passes, there- fore, through the zinc, and the current through the copper into the fluid. On the one side of the partition water is decomposed, the oxygen passes over to the zinc, forming oxide of zinc, which, dissolving in the acid, forms sulphate of zinc. The hydrogen gas goes to the partition, where it forms, as it were, the + pole for the current passing into the other fluid. The oxide of copper is decomposed by this current, the oxygen of the oxide passes to the + pole, consequently, to the wall of partition, where it com- bines with the liberated hydrogen to form water, whilst the copper at the pole, that is, at the copper plate, is separated in the metallic form. A highly interesting application has been made of this metallic precipitate of copper, and is known under the name of galvano- plastics (electrotype) ; it is only necessary to give a definite form to the elements of a combination of this kind, to obtain im- pressions of this form in metallic copper. It is necessary to modify somewhat the form of the Becquerel circuit before applying it for this purpose. The apparatus repre- sented in Fig. 415, is especially well adapted for the multiplication of coins, medals, &c. ; a b is a glass vessel open at the top, about 6-8 inches in diameter. Within this hangs a second narrower glass vessel c d, likewise opening at the top, but closed at the 36* 426 CHEMICAL ACTIONS OF THE VOLTAIC PILE. bottom by having a bladder tied to it. Somewhat above the mid- Fig. 415 . die, a wire is tightly bound round the inner vessel, which it lifts up in such a manner, that the bladder is raised from 1,5 to 2 inches above the bot- tom, the wire branching out in three arms, which are attached to the rim of the outer vessel. The inner vessel is filled with very dilute sulphuric acid, while the space intervening between the inner and outer cylin- der is filled with a solution of sulphate of copper. Two pieces of wood laid cross-ways sup- port in the sulphuric acid a zinc block, to which a copper wire is soldered, connecting the zinc block with the mercury-cup q. A second copper wire passes from this cup to the form lying in the solution of sulphate of copper, which, of course, must be made of a substance more electro-negative than zinc. Such a form may be procured by taking an impression of a coin with Rose's fusible metal, and still more easily by means of wax or stearine. These two substances must be fused together with finely pulverized graphite, and the liquid then poured on the metal, which must be protected by a rim of paper, when a very beautiful form is obtained. This matrix, however, is not a conductor, and only becomes so by covering the surface, which is to receive the copper, with a thin delicate layer of fine copper bronze. This coating, which may be laid on with a fine brush, does not in any way take from the purity and sharpness of the outlines. The matrix must be plunged into the solution with its conducting surface turned up- ward. The copper wire requires only to be in contact with the fine graphite layer. The portion of the copper wire plunged in the solution of sul- phate of copper must be covered with shell-lac, or sealing-wax, to prevent metallic copper from being deposited upon this wire, which- deposition must be prevented except where it is attached to the matrix. The current circulating through the apparatus is very weak ; the copper deposits itself slowly upon the copper surface, and subsequently upon the copper wire; it is, therefore, necessary CHEMICAL ACTIONS OF THE VOLTAIC PILE. 427 from time to time to place the wire at a different part of the mould. The layer of copper will be thick enough, and may be removed in one or more days, according to the strength of the current. The copper deposit is most regular with a weak current, on which account the fluid, in which the zinc block is plunged, should be only slightly acid. The solution of sulphate of copper becomes lighter in color in proportion to the copper deposited from it. It is necessary occasionally to renew the solution as it becomes exhausted. It is often better to place the solution of sulphate of copper with the mould in the inner vessel, and the acid with the zinc block in the outer vessel. [A very neat decomposition cell consists of a box a foot deep, a foot long, and a few inches wide. Two parallel wires are ex- tended along the top, one connected with the negative, and the other with the positive metal of the battery. On the former are hung the moulds, and on the latter, a sheet of copper. Fig. 416 represents one of these cells connected with a Smee's battery. Fig. 416. This latter consists of platinized silver and amalgamated zinc. There is no diaphragm, and the exciting liquid is acid and water. The silver plate to be connected with the copper in the decom- position cell, and the zinc with the moulds. A full account of the various processes employed in electrotype will be found in a little work on Electrotype Manipulations, by C. V. Walker. (Carey and Hart.)] Many important applications of galvano-plasticshave been made within the last few years; by this means impressions of woodcuts have been taken, which retain all the purity and sharpness of the original outlines, and thus, as many fac-similes as we like may 428 CHEMICAL ACTIONS OF THE VOLTAIC PILE. be taken of the original, without any difference being perceptible between the first and last impressions. The woodcuts of the original German edition of this work, from which those in our present translation are copied, were impressed by copper type of this description. A graved copper plate will not bear many im- pressions being taken of it, without manifesting a decided dete- rioration in the latter impressions. Hence, the value of the proof- impression, and hence, the reason that steel engraving is so much valued, for a steel plate will bear a much larger number of im- pressions being taken of it. Steel, however, offers decided dis- advantages with reference to art, for owing to the hardness of its texture it opposes great difficulties to the artist, who cannot pos- sibly complete as perfect a work on steel as on copper. Now, however, a means has been devised of multiplying copper plates, even when of a large size, by the galvano-plastic process, so that the impressions of the copies, of which we may have an unlimited number, are quite equal to the original plates. Kobell, of Munich, has proposed a method by which pictures, drawn in bistre or Indian ink, may be multiplied by galvano plastically. A copper plate silvered over is used for painting on, and the color prepared for the purpose, is an ochre or coke rubbed up in a solution of wax and oil of turpentine, adding a little Dam- mara varnish. This color is laid on the plate in such a way, that the brightest lights remain free, the paint being laid on thicker in proportion to the depth of shadow required. As soon as the picture is finished, a wash of finely pulverized graphite is laid on with a fine brush, and the plate is put into the galvano-plastic appara- tus. By degrees, the copper is precipitated upon the painted plate, forming a second copper plate, on which all the lights ap- pear smooth, and the shadows are deeply impressed ; this plate will now yield, if treated like a graved copper plate, impressions similar to an Indian ink drawing. Thayer, of Vienna, has brought this method to great perfection, and there is reason to expect that it will prove of still greater practical importance to art. In the same manner as copper is precipitated at the negative pole of the circuit, by a galvanic process from a solution of sul- phate of copper, other metals, as gold, silver, platinum, &c., are deposited at the negative pole from suitable solutions, and we may thus gild and silver other metals, &c. It would lead us CHEMICAL ACTIONS OF THE VOLTAIC PILE. 429 beyond our proper limits were we to enlarge further upon this subject. An interesting illustration of metallic precipitations is presented by the NobilVs colored rings. If we pour a few drops of a solu- tion of acetate of lead upon a silver plate, and then touch the silver in the middle of the fluid with a small piece of zinc, several concentric colored rings will be formed around the places of contact. These rings appear still more beautiful on putting the fluid between the poles of a pile composed of many plates, flatten- ing the one pole, and pointing the other, and then turning the latter in such a manner to the former, that the electric current passes through the fluid from the flattened to the pointed pole, or vice versa. Nobili obtained similar phenomena of colors with other fluids. Chlorides, iodides, and bromides of metals are simply decom- posed by the electric current, the metal being deposited at the negative, and the chlorine, iodine, and bromine at the positive pole. The weakest current is capable of decomposing iodide of potassium. On exposing aqueous solutions to the action of the electric cur- rent, the result of the decomposition will often be modified by the presence of the water. To avoid this, Faraday has reduced many bodies to a fluid state by fusion, and thus exposed them to the action of the current. He thus decomposes chloride of lead, chlo- ride of silver, &c., laying them upon a glass plate, and fusing them over a spirit lamp, and then immersing both polar wires into the fluid mass. If polar wires of silver were plunged in fluid chloride of silver, the silver would be deposited at the pole, which had attached itself to the wire, whilst the other silver wire would be dissolved by the liberated chlorine. We have hitherto only spoken of decompositions produced by the galvanic current, but this current also favors to chemical combinations. If we bring any easily oxidizable metal, as zinc, for instance, near the -f polar wire, the metal will very easily combine with the oxygen separated from the water ; zinc only dissolves slowly in diluted sulphuric acid, if it be quite chemically pure ; on touching it with a piece of silver, a marked development of gas instantly begins to take place at the silver, while the zinc combines with the oxygen to form oxide, which is dissolved by the acid. 430 CHEMICAL ACTIONS OF THE VOLTAIC PILE. If the polar wires of a galvanic battery be made of zinc, and then immersed in acidulated water, the decomposition of the water will go on precisely as if platinum or copper wires were used. The hydrogen gas will be separated at the wire of the negative pole, which will not be affected by the acid, as would otherwise be the case if it were not made negatively electric by its connection with the pile, and thus protected from oxidation ; the wire of the polatine pole, on the contrary, will be so much the more rapidly acted upon. A metal, affected by an acid, or any other fluid, can be pro- tected from oxidation by being brought into connection with a metal positively electrified, so as to form the pole of a simple circuit. Whilst the current arising from the contact of two metals plunged in the same fluid increases the affinity of one of these for one element of the fluid, the power of the other metal to un- dergo the same changes is proportionally diminished. Thus, when a zinc and a copper plate, come into contact in a dilute acid, the zinc will oxidize more rapidly, and the copper less than would otherwise be the case. Davy^s experiments, on the pre- servation of the coppering of ships, affords a beautiful illustration of this principle. A copper plate, when immersed in sea water, is exposed to a rapid oxidation ; but, if the copper be brought into contact with zinc or iron, these metals will be dissolved, and the copper thus protected. Davy has ascertained that a piece of zinc of the size of the head of a small nail is sufficient to protect 40 to 50 square inches of copper. It has unfortunately been shown, however, that this excellent mode of preserving copper cannot be practically made use of, as copper must be acted upon to a certain extent, in order to save it from being injured by the adhesion of sea-weed and marine animals. The same principle has been applied by Von Althaus to prevent the rusting of the iron pans used in evaporating brine. Here, however, the protecting zinc could not be applied to the pans themselves, as the sulphate of zinc would distribute itself through the brine, he, therefore, separated the corners of the pans by a board, and filled these spaces with zinc, whose bottoms were formed with iron plates. Thus the zinc is in metallic connection with the iron, and the fluid passes in sufficient quantity through THE ELECTRO-CHEMICAL THEORY. 431 the wood to the zinc to complete the circuit, while the sulphate of zinc engendered cannot destroy the purity of the solution of salt. By this means, evaporation was effected at a lower temperature, and a considerable saving made in the expenditure of fuel. The Electro- Chemical Theory. The hitherto described phe- nomena exhibit remarkable relations between chemical and elec- trical forces. It had already been vaguely conjectured, that electrical forces were concerned in chemical phenomena ; this view was, however, only confirmed when the decomposition of water was effected by the voltaic battery ; that is to say, it was reserved for Davy and Berzelius to develop these views ; and they established the electro-chemical theory, according to which, we must seek for the fundamental cause of chemical combinations in electric attraction. Although it may not be fully proved, that chemical affinity and electrical attraction are perfectly identical, it must be confessed, that this theory combines many facts into one connecting bond in a manner that cannot be refuted by ex- perience. As zinc and copper, when brought into contact with each other become oppositely electric, so, also, according to the electro- chemical theory, the atoms of every two elements become oppo- sitely electric when brought into contact with each other; in short, all elements are, according to the signification already given at page 406, members of the series of tension. The extremes of this perfectly complete series are oxygen and potas- sium, the former being the , and the latter the + extremity. The following is the complete series of tension. Oxygen Bromine Sulphur Iodine Selenium Fluorine Tellurium Phosphorus Nitrogen Arsenic Chlorine Carbon Chromium Cerium Molybdenum Lanthenium Borax Yttrium Vanadium Cobalt Tungsten Nickel Antimony Iron 432 THE ELECTRO-CHEMICAL THEORY. Tantalium Cadmium Titanium Zinc Silicium Hydrogen Osmium Manganese Gold Zirconium Iridium Aluminum Rhodium Thorine Platinum Beryllium Palladium Magnesium Mercury Calcium Silver Strontium Copper Barium Uranium Lithium Bismuth Sodium Lead Potassium + This series contains all the simple substances, and to each its place is assigned, although there is still much uncertainty in this respect, and the position of most bodies, in the series of tension, is only approximatively, but not accurately, determined. This position has only been ascertained by direct experiment for a very few bodies ; the place of the majority having been conjec- tured from their chemical relation. According to the electro-chemical theory, the atoms of the ele- ments are not electrical in themselves, but become so on being brought into contact with others, whence it happens that the same body may at one time be +, and at another electric. Thus, for instance, sulphur in combination with oxygen is the electro-positive, and in conjunction with hydrogen the electro- negative, element. We have seen, that two heterogeneous metal plates, brought into contact with each other, become oppositely electric; but, that the greatest part of the electricity developed, remains com- bined on the surface of contact; the same is the case with chemi- cal combinations. If, for instance, a particle of oxygen and one of hydrogen come into contact, the former will become , and the latter + electric, both electricities will attract each other, and combine almost perfectly, owing to their close approximation. If, however, there is a little free + electricity on the one particle, and electricity on the other, the chemical combination cannot THE ELECTROLYTIC LAW. 433 give any evidence of free electricity, owing to the -f and par- ticles being uniformly distributed; thus, whenever we lay our hands on the body, an equal number of + and electric parti- cles will be touched. In the first place, the simple substances combine to form binary compounds. The compound bodies, as the oxygen, sulphur, and chlorine combinations, exhibit, among themselves, a relation simi- lar to that of simple substances; these binary combinations of the simple elements, oxides, sulphurets, and chlorides, &c., which are characterized by negatively electric properties, and, at the same time, capable of entering into combinations of a higher order, are termed acids; while those constituting the part of the positively electric constituents, are called salifiable bases. The character of an acid is generally the more strongly ex- pressed in proportion to the contiguity of its elements to the negative end of the scale of tension ; hence, sulphuric acid is the strongest of all acids. Oxygen forms acids in connection with the bodies standing at the head of the above series, and bases with the elements at the positive end; thus, potassium is the strongest of all bases. When the same body combines in several different proportions with oxygen, the combination will be so much the more negatively electric, because it will assume more of the acid, and less of the properties of a base, in proportion as the electro-negative element, the oxygen, predominates. Thus, 1 equivalent of manganese combined with 1 equivalent of oxygen, forms oxide of manganese, which possesses the properties of a base, whilst 1 equivalent of manganese -f 3 equivalents oxygen, forms manganic acid. The electro-chemical theory does not, in its present limits, embrace an explanation of all chemical phenomena; but the classification of bodies, founded upon it, agrees sufficiently with their relations, so as to give a clear insight into chemical laws. The Electrolytic Law. No electric current, or comparatively only a very weak one, can pass through a fluid without its passage being attended by chemical decomposition. Such a decomposi- tion as this occurs in every cell of every galvanic apparatus, as long as the circuit remains complete, and Faraday has shown that the quantity of the electric current is proportional to the decom- position taking place in each individual cell. It cannot be denied, that an intimate relation exists between 37 434 THE ELECTROLYTIC LAW. the passage of the electric current, through fluids, and their de- composition ; and, it may even be asserted, that the passage of the electricity is effected by chemical decomposition. The positive current passes in every cell, from the zinc, through the fluid, to the copper; but the particles of the hydrogen pass in the same direction ; they are the conductors of the -f electricity, which is conveyed by them to the copper plate. Indeed, we have seen, that, in accordance with the principles of the electro-chemical theory, the elements are held firmly together in each atom of water, because oxygen and hydrogen, brought into contact, be- come oppositely electric, and because these opposite electricities of the elements of water mutually combine with each other. When a particle of hydrogen is separated from its oxygen, all its combined electricity will be liberated ; it will be, however, imme- diately recombined when the hydrogen, on the other hand, com- bines with another particle of oxygen, and thus each atom of hydrogen will carry off its combined -f electricity, whilst, at the same time, its positive electricity will be liberated at the pole with the hydrogen. Whilst the ordinary zinc of commerce is rapidly dissolved when plunged into dilute sulphuric acid, chemically pure zinc, or amal- gamated zinc, will remain unaffected in the same fluid. If we construct a galvanic circuit with chemically pure, or amalga- mated zinc plates, no decomposition can possibly occur in such a circuit while open. But the moment it is closed, a decomposition of water begins in every cell ; there is, however, no more water decomposed, nor zinc dissolved, than is necessary to conduct the circulating current ; the quantity of the dissolved zinc must, there- fore, stand in a definite relation to this current. Faraday made use of the current of such a circuit for the decomposition of water, and ascertained definitively the amount of explosive gas evolved in a given time. It was thus found that, for each equal portion of hydrogen gas liberated between the polar wires, or, rather, the plates of the poles, 32,3 equal portions of zinc were dissolved in each cell. But now the weights of the chemical equivalents of hydrogen and zinc are to each other as 12,48 to 403,23, or as 1 to 32,3. For every equivalent of hydrogen, therefore, evolved in the decomposing cells, 1 equivalent of zinc must be dissolved in each cell of the circuit. If the same current be conducted through 4 decomposing cells, THEORY OF CONSTANT CIRCUITS. 435 of which the first contains water, the second chloride of silver, the third chloride of lead, the fourth chloride of tin, all in a fluid condition, the quantities of hydrogen gas, silver, lead, and tin, which are precipitated at the four poles, are, to each other, as 1 : 108 : 103,6 : 57,9, whilst, at the + poles, oxygen and chlorine are separated in the proportions of 8 : 35,4. Similar facts have been demonstrated for many other composite bodies. It follows, from these facts, that the chemical equivalents repre- sent those relative weights of the substances which assume an equally strong electric polarity in connection with one and the same element. Theory of Constant Circuits. The common voltaic circuit, in which only one fluid is used, gives, as we have already seen, an uncommonly strong current at the first moment ; this, however, soon abates in intensity, whilst, in the Becquerel circuits, Daniel's, Groves', and Bunsen's apparatus, the current continues with un- abated force. Now that we have learnt to understand the chemi- cal phenomena in the circuit, we may be able to explain why the current remains constant in the one kind of apparatus, and loses rapidly its intensity in the other. A zinc and a copper plate, united by a copper wire at the top, are plunged into a vessel (Fig. 417) filled with a solution of sul- phate of zinc. At first, a tolerably strong current will be engendered, which, how- ever, will soon abate, and, finally, en- tirely cease. The reason of this cessation will be soon understood, on considering the process of the decomposition ; the inc ^ oxide of zinc of the solution is soon decomposed, the oxygen attaches itself to the zinc plate in order to form a new oxide, whilst, on the other side, metallic zinc is precipitated on the copper plate ; after a time, the copper plate becomes wholly covered over with zinc, when the current, of course, ceases. The copper is now no longer in connection with the fluid, but there is zinc on both sides of the copper, and of the fluid; the copper becomes negatively excited where it is soldered to the zinc plate, but this excitement does not occasion any current, since the newly formed zinc coat- ing gives rise to a totally opposite one. 436 THEORY OF CONSTANT CIRCUITS. If we take dilute sulphuric acid, instead of the solution of oxide of zinc, the water of the fluid, between the zinc and copper plate, will be decomposed ; in the place of the zinc, which is precipi- tated on the copper plate, as in the former case, the hydrogen will now be liberated; the copper plate will be covered with a coating of hydrogen, which will not, however, come into such intimate connection with the copper as in the former case, and cannot, therefore, so completely prevent the fluid from coming into con- tact with the copper plate as in the other. A total cessation of the current is, therefore, not possible here ; but the separation of hydrogen (which, according to Buff's experiments on the scale of tension, stands below zinc), occasions a diminution of the intensity of the current, in the same way as, in the other case, the deposition of zinc had done. If the reason of the diminution of the current in ordinary cir- cuits be rightly understood, it will be easy to find a method of avoiding this' occurrence ; it being only necessary to devise some arrangement by which the separation of hydrogen on the copper and platinum plates may be prevented, so that these plates may always remain in contact with the fluid in the same manner. In BecquerePs and Daniel's circuit, metallic copper is deposited on the copper plates instead of hydrogen, and thus a pure copper surface is always left in contact with the fluid. In Groves' battery, the platinum is surrounded by a layer of nitric acid, which like- wise circulates round the charcoal in Bunsen's apparatus ; this acid prevents the separation of the hydrogen on the platinum or the charcoal, for, at the moment of their origin, the deposited particles of hydrogen are again oxidized, and nitrous acid formed. This seems to be the most suitable place to say a few words con- cerning the various theories that have been advanced in explana- tion of the electrical phenomena of galvanic batteries, as they have formed the subject of the most animated discussions between different scientific men. The oldest of these is the theory of contact, established by Volta, according to which, the contact of different metals is the only source of the electricity of the pile. Volta had devoted especial attention to the study of the actions of tension in bat- teries, and these are explained more satisfactorily, according to his theory, than to that of any other. He doubtlessly disregarded THEORY OF CONSTANT CIRCUITS. 437 chemical phenomena, from being wholly ignorant of, or but slightly acquainted with them, and hence it arises that he did not devote sufficient attention to the part played by the fluids in the circuit, considering them merely as conductors, and not as elec- tromotors. When the chemical actions of the battery were better known and more accurately observed, the voltaic theory of contact was not satisfactory, and it became necessary either to corroborate and enlarge upon it, in order to admit of its embracing the newly discovered facts, or to set it wholly aside, and to form an entirely new hypothesis. Both methods have been adopted, and that by distinguished natural philosophers. The opponents of the theory of contact, among whom Faraday must be specially noticed, consider the chemical action exerted by the fluid upon the metal, as the source of the electric current of the circuit. Faraday was likewise induced, by his theoretical views, to in- troduce a new nomenclature, calling the poles "Electrodes," or the courses pursued by the electric current in entering the decom- posing fluid, the positive pole " Anode," and the negative pole " Cathode." The constituents of the electrolyte (the decomposed body) are, according to his nomenclature, Ions, the Cathion being the element separated at the cathode, and the Jlnion that which is found at the anode. It will not surprise us that so much misconception and differ- ence of opinion should exist with respect to the source of the electricity in the circuit, when we consider how little is known to us of the actual nature of electricity. What do we know con- cerning the generation of electricity by friction, beyond the simple fact? The reason of the difference of opinion that existed regard- ing galvanism, evidently arose from Volta?s disregard of the influence exercised by chemistry. This deficiency, or, rather, the partiality of this view, could not long escape observation; but while many learned men were striving to point out the importance of this influence, they fell into the opposite extreme of ascribing every effect to chemistry, and neglected those well proved facts which constituted the basis of the theory of contact. Some even suffered themselves to be so far led astray as to question the correctness of Voltcts fundamental experiments, or explained 37* 438 MAGNETIC ACTIONS OF THE GALVANIC CURRENTS. them by the hypothesis that the precious metals underwent oxi- dation. The adherents of both theories were most zealously active in advancing proofs of the correctness of their own opinions, and to these efforts we are principally indebted for the advance that has been made in the science of galvanism. Fechner, above all, deserves praise for having established, beyond doubt, the cor- rectness of Volta's fundamental experiments, and thus justified the views concerning the excitement of electricity in various metals. Faraday, on his side, has shown that galvanic currents may be produced without the contact of heterogeneous metals ; that the chemical decomposition of the fluid of the pile is propor- tional to the quantity of the electrical current ; and that, conse- quently, this decomposition stands in the closest connection with the formation of the current in the hydro-electric circuit. As a theory of galvanism should, if possible, embrace all the phenomena of the circuit, we can scarcely look for truth in the extreme views of either party. It seems, therefore, most suitable to the present stage of science to adopt some modified theory of contact as given above, since by this means we shall be best able to consider from one common point of view the different phe- nomena exhibited in the circuit. Magnetic Actions of the Galvanic Current. It had long been known, that, under certain circumstances, powerful electric charges could affect the magnetic needle; it had, for instance, been observed, that the needle of the compass lost the property of directing the course of the ship, if the latter had been struck by lightning. Many natural philosophers attempted to produce similar phenomena by the discharge of Leyden jars, and, indeed, some succeeded in altering the magnetic condition of very small needles, either by suffering the spark to pass very near the needle, or the whole force of the discharge to pass immediately through it. But all these experiments yielded no regular results, and people remained satisfied with the view that the electric shock acted upon the magnetic needle as the stroke of a hammer. Subsequent ex- periments were made in galvanic electricity which yielded no better fruit; finally, in the year 1820, Oersted, professor at the University of Copenhagen, discovered a means of causing elec- tricity to act certainly and constantly upon a magnet. He thus opened to the scientific men of all countries a new and extended MAGNETIC ACTIONS OF THE GALVANIC CURRENTS. 439 field of investigation, and never before, perhaps, had science been enriched in a short time with the acquisition of so many new truths. Electricity must be in motion to act upon magnetism when at rest, and in a state of great tension, it does not affect the magnet, as does a continuous electric current. In fact, on bringing a freely suspended magnetic needle to the terminating wire of a pile while the electric current is passing, the needle will deviate. This was the first experiment made by Oersted, and it is singular that a similar observation had not long since been accidentally made in the many experiments tried with the pile. The principal experiment on the action of the galvanic current upon the needle may be made in the following manner: a some- what thick copper wire must be bent into a square, the sides of which must be from 8 to 10 inches in length ; we must now plunge the two extremities of the wire a b andfg, Fig. 418, into the mercury cup of a galvanic battery of large surface, (as, for instance, into the cup of the apparatus seen in Figs. 401 and 402), or we must connect them with the poles of the Bunsen apparatus, securing them in such a ^__ manner that the planes of the square may coin- cide with the planes of the magnetic meridian. If we assume that the wire end a b is plunged into the .positively electric mercury cup, the cur- rent will circulate in the manner indicated by the arrows. It will ascend from b to c, but from c to d it will run in the direction of the magnetic me- ridian horizontally from south to north, thence will descend from d to e, and move again in a horizontal line from north to south along the portion of wire ef. On holding a magnetic needle exactly over the portion of wire c d, it would remain parallel with the wire c d, if no action of the current affected it ; but the current makes the needle deviate in such a manner that the south pole (that is, the one directed towards the north) lies to the east of the magnetic meridian. If we hold the needle under the portion of wire c d, the end of the needle turned to the north will be inclined towards the west. The exactly opposite action is observed in the portion of wire ef, in which the current moves in a direction parallel, but oppo- 440 MAGNETIC ACTIONS OF THE GALVANIC CURRENTS. site to that of the current in c d ; when the needle is held exactly over ef, a deviation to the west, and when held below it, a de- viation to the east, will be observed. At first great difficulty was experienced in knowing how to express in a few words the relations between the direction of the current and of that of the deviation ; this difficulty has, however, been very ingeniously removed by Ampere, who has given the following rule for ascertaining at all times the direction of the deviation. Suppose a little figure of a man to be so inserted into the wire that the + current shall enter at the feet and pass out at the head ; if, then, the face of the figure be turned to the needle, the south pole of the latter (the north end) will always be inclined towards the left side. The figure lies horizontally on the piece of wire c d, the head turned to the north, and the feet to the south. If the needle be held over the wire, the figure must lie on its back in order to have the face turned towards the needle, and in this position its left side will be the east. If the needle be held below the wire, the figure must be turned with its face downwards, when the left side will be the west. In the piece of wire ef y the feet of the figure are turned to the north, and the head to the south ; if it be laid on its back, the left side will be the west, and, of course, vice versa, if we lay it on its face. If a horizontal current, moving in the direction of the magnetic meridian, were to act alone upon the needle, the latter would place itself at right angles to the magnetic meridian ; but, besides the current, terrestrial magnetism comes into play, and strives to bring the needle back again into the meridian. The needle will, therefore, assume a middle position under the influence of these two forces, making an angle with the magnetic meridian, which will approach more and more towards a right angle in proportion as the force of the current is comparatively greater than the force of the terrestrial magnetism. The vertically directed current in b c and in d e causes the needle likewise to deviate, and the direction of this deviation may also be found according to Ampere's rules. Let us suppose this figure standing vertically to be turned towards the north end ; this end must then incline to the left. Here we must not forget, THE MULTIPLICATOR. 441 however, that the figure must stand upon its feet for an ascending current, and on its head for a descending one. It follows, from Ampere's rule, that the same vertical current either attracts or repels the north end of the needle, according to the side of the wire on which this pole is placed. In Fig. 419, N S represents a horizontal needle seen from above ; JV" is the north end of the needle, w a vertical Fi wire, which naturally seems con- tracted to a point, as seen from above. If, now, a -f current pass from be- low upward through the wire, we must suppose the figure to be up- right ; but if this upright figure be turned with its face towards JV, and the pole JVin relation to this figure be turned to the left, as the arrow indicates, the needle will evidently be repelled by the wire. If, however, the needle is in the position JV*' S f , it will evidently be attracted by the wire. The Multiplicator, or the Galvanometer. Shortly after Oersted had made his important discovery, Schweigger constructed his multiplicator, the object of which is to multiply the electro- magnetic action of the current. This instrument is actually so sensitive, that it may serve to detect the weakest electric currents. All parts of the current traversing the elongated parallelogram p q r o n, Fig. 420, in the direction of the arrows, act in a similar way upon the needle a b, which rotates in a horizontal plane. If a be the south end, and b the north end, the current will show a tendency at all points to turn the needle in such a manner that b shall project beyond the plane of the figure, whilst a will retreat behind it. The lower portion of wire, therefore, supports the action of the upper in the same manner as does the current in the portions p q and r o. A second current of the same force, moving in the same direction round the needle, will produce as great an effect as the first, and thus it will be with a third, a fourth, &c. A wire, therefore, wound round a needle, in 100 convolutions, all of which are traversed by the same current, must produce an action of 100 times greater intensity than one of a single convolution ; the current must not, however, be propagated laterally from one winding to the other, but must 442 THE MULTIPLICATOR. Fig. 421. Fig. 422. traverse the wire throughout its whole length, being carried actually round the needle. To effect this, we take a copper wire, from 15 to 20 yards in length, and closely twined round with silk, which is then wound upon a wooden or metallic frame. The two extremities of the wires of the multiplicator must remain free, so that they may be brought into contact with the poles of the gal- vanic circuit. The needle is suspended by a silk untwisted thread, and the whole apparatus protected from currents of air by a glass bell. On making an experiment with this, we place the frame in such a manner that the planes of the circumvolutions shall coin- cide with the magnetic meridian, when the needle will likewise be in the plane of the circumvolutions while no current is passing ; but, as soon as this is established, the needle will deviate in pro- portion to the intensity of the current. Nobili has made a multiplicator infinitely more delicate than the one we have been considering, by making use of two needles with opposite poles, instead of one needle, as seen in Fig. 421, and still better in Fig. 422. In a system of needles of this kind, the directing force of the earth's mag- netism is very inconside- rable, it being only the difference of the forces with which the terrestrial magnetism strives to direct each needle. If both needles were absolutely equal, and possessed a perfectly equal amount of magnetism, the directing force exercised by the earth upon this system would be null. But one of the needles is suspended within, and the other over the coils of wire; both will, therefore, be turned towards the same side by the current. An apparatus of this kind is extremely delicate. To connect the wires in a secure manner, we must either pass both through a perfectly straight blade of straw, or secure them to a very thin wire, as seen in Fig. 422. The upper needle moves in a circle divided into 360 degrees. The line connecting and 180 is marked upon I Fig. 423. THE TANGENT COMPASS. 443 424. the magnetic meridian ; when there is no current passing through the convolutions, the needle points to 0. The deviation of the needle increases with the increasing force of the current ; this force is not, however, pro- portional to the angle of deviation. The direction of the deviation of the nee- dle determines the direction of the current. Fig. 423 represents a complete galvanometer, and 424 exhibits the frame, with the coils of the wire, as seen from above. The Tangent Compass. When we have to do with stronger currents, it is not necessary to use an astatic needle, or to wind the wire so many times round the needle ; we are, consequently, enabled to construct instruments in which the angle of deviation stands in a simple relation to the force of the current. The most simple and useful apparatus for measuring powerful currents is the so-called tangent compass, represented at Fig. 425. The current is conducted by a circularly formed vertical copper strip round the needle, which is in the middle of the circle, compared with whose diameter ; it is very small. The current is conducted through a hollow copper cylinder, from which it passes into the circular band, while the other end of the copper ring is in con- nection with a copper rod passing through the centre of the copper tube, without being in contact with it. Thus the cur- rent may rise through the hollow copper cylinder, and pass over to the copper ring, traversing its whole length, and returning again through the copper rod, which is insulated in the mid- dle of the cylinder. The apparatus is so placed, that the copper ring lies in the plane of the magnetic meridian, the needle naturally being, in this case, in the vertical plane of the ring, and pointing to the of the graduated division ; as soon, however, as a galvanic current passes through the cop- per ring, the needle is made to deviate, and the force of the Fig. 425. 444 FORCE OF THE GALVANIC CIRCUIT. current will be proportional to the trigonometrical tangent of the angle of deviation ; hence the name of the instrument. Force of the Galvanic Circuit. The agent which produces the phenomena of galvanism is nothing more than the electricity gene- rated in the electrifying machine, and in the electrophorus, only here the electricity is in motion, and there it is at rest ; the one presents us with phenomena of motion, the other those of pressure ; the one affording us an abundant, the other a comparatively poor supply of electricity. We may, perhaps, make the true relation of the matter clearer by an illustration. Thus, we may compare the electrifying machine to a well, which yields water but sparingly, but lies high on a hill. The water may be collected in a narrow conducting pipe continued into the valley, and closed below. The walls of this tube have naturally to sustain a great pressure, especially at the lower end, although the mass of water in the tube may be small. At the lower end of the tube there is an opening closed by a valve, which is pressed against the aperture by a spring or a weight. The more, however, the column of water rises in the tube, the stronger will be the pressure ; and when the external counter pres- sure no longer suffices to afford resistance, the valve will be opened, and the water will rush violently forth ; at the same time, however, the level of the water in the tube will rapidly sink; the external pressure will again acquire a preponderating force, and close the aperture. By degrees the tube will be refilled, and, after a time, the water will rise so high, that the valve will be again opened. In the electrifying machine, the conductor is the vessel, or conducting pipe, in which the electricity is accumulated. If we bring a conductor, as the knuckle of the finger, to the one end of the conductor, the greatest accumulation of electricity will take place ; the electricity will have a tendency to pass to the finger ; but the layer of air between the conductor and the hand, representing the weight which holds the valve down, will hinder its passage. It is only when the electricity on the conductor has accumulated to a certain amount, that the resistance is overcome, the layer of air broken through, and the conductor partly discharged. On bringing the finger still nearer to the conductor, the resistance opposed to the passage of the electricity is diminished, which again corresponds to the abatement of the pressure that keeps the valve of the conducting pipe closed. FORCE OF THE GALVANIC CIRCUIT. 445 If the opening at the lower end of the conducting tube were not shut by the valve, the water would flow out in the same pro- portion as that supplied by the spring, and the accumulation of the water, together with the pressure sustained by the walls, would cease. As, however, the spring yields only a small quantity of water, very little will flow from the aperture, and the water which was able to bear so great a pressure when accumulated in the tube, can scarcely produce any perceptible mechanical effect, when it is suffered to flow freely out. The case of the conductor of the machine being brought in conducting communication with the earth or the rubber, corre- sponds to the free discharge of water from a scantily supplied spring. All tension, or accumulation of electricity on the con- ductor ceases; the thinnest wire being then able to draw off all the electricity from the conductor; while the freely discharging electricity scarcely gives the slightest evidence of those powerful actions observed in galvanic apparatus. A galvanic apparatus is like a very copious spring having an inconsiderable fall, and whose water is freely discharged in wide channels. The whole mass of the water exercises but a trifling pressure on the walls ; but it is capable of producing mechanical effects, moving wheels, &c. If a large Leyden jar be discharged by a thin wire, the latter will, as we have already seen, become red hot, owing to the quan- tity of electricity passed through it. The action, however, is only momentary, as all the electricity accumulated in the jar by the continued turning of the machine passes in a moment through the thin wire. The case is totally different when we unite by a thin short wire both poles of a galvanic apparatus with large plates. The wire will become red hot even when it is far thicker than the wire heated by the discharge of the Leyden jar: but here the heating is not momentary, but continues as long as the current passes through the wire ; at every moment, therefore, the galvanic apparatus yields incomparably more electricity than can be accumulated in the Leyden jar, by a continued turning of the machine. Let us now proceed to examine the circumstances on which depends the quantity of electricity which can be engendered by a galvanic apparatus. When two metals are brought into contact, if only at a few 38 446 FORCE OF THE GALVANIC CIRCUIT. points, we at once obtain an abundant supply of electricity. We have already seen that we cannot form a galvanic apparatus with- out such bodies as belong to the series of tension. Galvanic cir- cuits are constructed of metals and fluids ; the latter, however, are not good conductors of electricity, and rank in this respect far below metals. The moist layers intervening between the metal plates of the voltaic pile are not able in a given time to give a passage to all the electricity which in the same period of time may possibly be engendered by the electromotor force of the pile. It will, of course, be understood that the quantity of the electricity which can circulate in such an apparatus, depends upon the diagonal section of the moist layers ; now as the diago- nal section of the moist conductor in the voltaic pile depends upon the size of the double plates, we may, by increasing the size of the latter, augment the quantity of the electricity. We shall subsequently learn by experimental proofs to test the cor- rectness of this view. With the increase of the plates in the voltaic pile, the surfaces of contact between the copper and zinc also increase ; that the increased quantity of the electric current is not occasioned by this circumstance is, however, proved by the fact that the appa- ratus delineated in Figs. 401, 402, and 404, which have a large diagonal fluid surface intervening between the copper and zinc, yield a considerable quantity of electricity, although the two metals are only brought into contact at a proportionally small sur- face, namely, where the copper wire is soldered to the zinc cylin- der or plate. Everything, therefore, which promotes the passage of electri- city through the fluid conductor effects an immediate increase of the quantity engendered. The shorter the course is, which the electricity must traverse in passing through the fluid, and, conse- quently, the thinner the fluid layer between the metal plates, the greater will be the quantity of electricity that can circulate in the apparatus. Thus, the greater the conducting power of the fluid, and the closer the metal plates approximate to each other in the fluid, the greater will be the electric quantity of the current. Let us now inquire into the influence exercised by the number of the double plates upon the galvanic current. If we suppose a moist disc or layer to be placed between a zinc and a copper plate, and the metals united by a copper wire, we shall have a OHM'S LAW. 447 closed simple galvanic circuit. The resistance to be opposed by the current in the moist conductor is incomparably greater than the resistance opposed by the wire to the circulation of the cur- rent ; the apparatus yielding far more electricity than the moist conductor can transmit. If we double the number of elements, connecting the uppermost copperplate by a copper wire with the lowest zinc plate, we shall have a circuit of two elements. The question here arises, as to whether, by this arrangement, a larger quantity of electricity can be made to circulate than in the above considered simple circuit? In the simple circuit, the quantity of the circulating electricity is limited by the resistance of the moist conductor; now, this resistance is doubled by the second moist layer; but then, on the other hand, the tension urging the passage of the electric current has become twice as great, and, consequently, an equal quantity of electricity will circulate in both cases. The increase of the num- ber of double plates does not tend to augment the quantity of the circulating electricity when the circuit is perfectly closed, since, in this case, it is quite immaterial whether we use one or many pairs of plates. In an imperfectly closed circuit, however, that j is, where a bad conductor has been made to complete the circuit, many plates must be made use of, as a greater degree of electric tension is necessary to force a passage, as it were, through the i bad conductor. The intensity of the galvanic current is propor- tional to the number of the double plates. Ohm's Law. The above indicated relations of the force of the current with reference to the elements of the circuit have been reduced by Ohm to strict mathematical formula. By means of i the law named after him, (of which we shall treat presently), a secure basis was first given to the investigations made on the force 3f the electric current. In order that an electric current may pass through a conductor, [t is indubitably necessary that the electricity should have an un- equal degree of tension at different parts of the conductor. If, (i jbr instance, we touch the conductor of an electrifying machine Ivith a wire, the electricity will be propelled through the latter, olely on account of the strong tension of the electricity, which .rives it through the wire to the conductor, there being a greater ccumulation of electricity at the end of the wire in contact with ie conductor than at the opposite end ; thus, on connecting to- I 448 OHM'S LAW. gether by means of a wire, two similar conductors equally stronglj charged with electricity, no current will be formed. When the Voltaic pile is insulated, the opposite electricities al the poles will be in a state of tension, and this condition cannot, possibly, entirely cease, on connecting the two poles by a conduc- tor, since no + electricity can flow from the + pole if there be noi here a greater accumulation of the same kind of electricity; certain tension, like a certain pressure, as it were, is necessary to occasion a motion, by which the resistances may be overcome in the conductor through which the current is to pass. The quantity of electricity passing through a conductor depend: essentially upon two circumstances; first, on the resistance to be overcome in the conductor; and next, on the tension or pressure urging the electricity through the conductor ; it will now be easily seen, that the quantity of electricity passing in a given time through some specified conductor, must stand in an inverse rela- tion to the resistance in the conductor, and in a direct relation t( the electric tension urging the current through the conductor The tension is here to a certain extent the accelerating force. The quantity of electricity passing through a conductor, tha V is, the force of the current, may be expressed by ,ifE desig- JL nate the electric tension engendered by the current, and L the resistance to be overcome in the conductor. Let us here consider the current of one simple closed voltaic element. Let e be the tension occasioned by the current, a, the resistance in the circuit itself, and / that in the wire closing the /> circuit; then the force of the current^ = If we had combined n such elements into a column, the electric tension, setting in motion the current, would be n e ; bu the resistance in the circuit being increased in an equal proper tion, as it has to be overcome not only in one element, but in j elements, the resistance in the conductor will be now n a,. li now, the arc, closing the circle, is the same as in the simple cir 77 P cuit, we have for the force of the current p l = - -,. 7171 -f / If I were very small, in comparison with x, the above give: P 71 ( value of p would be nearly -, but the value of p 1 would be OHM'S LAW. 449 consequently, also, = ?; if, therefore, the resistance in the arc, closing the circuit, be small in comparison with the resistance of one single element, the increase of the elements will afford no advantage. On the other hand, an increase of the elements will occasion an increase in the force of the current, if / be very large ; that is, if there be a considerable resistance to be overcome in the arc closing the circuit. We will now consider the influence exercised on a simple cir- cuit, by an increase of its surface. The force of the current, for a single element, was designated above as p = - '- ; if, now, ^ -p If the surface of the voltaic elements be increased n times, without altering anything else, the only result will be to make the resist- ance in the circuit itself n times smaller, owing to the diagonal section of the fluid, through which the current must pass, becom- ing n times greater; instead, therefore, of the resistance si, we shall now have -, and, consequently, the force of the current p n ill now be, >r, what is the same thing, If I, that is to say, the resistance in the arc closing the circuit, rere null, the force of the current would be proportional to the iperficies of the electric element ; and this is very nearly the ise when I is extremely small; an increase of surface produces, lerefore, an increase in the force of the current, if the resistance the closing arc be small in proportion to the resistance in the Ircuit itself. The values for the resistances in the circuit itself, and in the sing arc, must, as we shall presently see, be referred to the |me unit. I These laws are fully confirmed by experiment. I In order to show that the force of the current stands in an rerse relation to the length of the closing arc, we have merely I complete the circuit of a galvanic element (for instance, one of 38* 450 OHM'S LAW. BecquerePs elements) by a tangential compass, and then insert, according to the series, pieces of wire of different length, noting each time the corresponding deviation. A series of experiments of this kind gave the following results : Length of the copper wires inserted. Deviation observed. Tangents of the angles of deviation. metre. 62 00' 1,880 5 " 16 ft. 4 in. 40 20 0,849 10 " 32 " 9 " 28 30 0,543 40 " 45 " " 9 45 0,172 70 " 77 " 3 " 6 00 0,105 100 " 110 " 1 " 4 15 0,074 We observe, here, no regularity in the decrease of the intensity of the current on lengthening the inserted wire ; but, when we consider that this wire is not the only resistance to the current, and that in the electromotor apparatus itself, and in the different parts of the compass through which the current passes, a resist- ance has to be overcome, which we will designate as the resistance of the element, it will be evident that this last named resistance may be estimated as equal to the resistance of a copper wire of the same thickness as the one inserted, and of the unknown length x ; the following, therefore, are actually the corresponding lengths of the circuit, and of the angles of deviation. Length of the chain. Deviation observed. Tangents of the angle of deviation. X 62 00' 1,880 x + 5, 16 ft. 4 in. 40 20 0,849 x + 10, 32 " 9 " 28 30 0,543 x + 40, 45 " " 9 45 0,172 x + 70, 77 3 " 6 00 0,105 x + 100, 110 1 4 15 0,074 If, now, the force of the hydro-electric currents is actually in- versely as the length of the circuit, the numbers of the first column must be inversely as the numbers of the last, and, consequently, x : x + 5 = 0,849 : 1,880, whence it follows that x = 4,11. If, in the same manner, we compare the first observation with all OHM'S LAW. 451 those succeeding it, we shall always obtain the same value fora:; and, indeed, the values thus computed for x are very nearly equal to each other : we find, for instance, besides the value already computed, 4,06 (13,28 ft.), 4,03 (13,15 ft), 4,14 (13,58 ft.), and 4,09 (13,45 ft.), metres. The mean of which is 4,08 (13,36 ft.). The resistance of the element is, therefore, equal to the resist- ance of a copper wire, 4,08 metres (13,36 ft.) in length, and of the same thickness as the one inserted. If we make this length our standard, we may easily, by aid of the general law, that the force of the current is inversely as the length of the circuit, compute the deviations that will be obtained, and then compare them with those directly observed, as has been done in the follow- ing table. The com- The deviation Length of the circuit. puted devia- actually ob- Difference. tion. served. 4,08 metres, 13,36 ft. 62 00' 62 00' 9,08 " 29,79 " 40 18 40 20 + 2 14,08 " 46,19 " 28 41 28 30 11 44,08 " 144,62 9 56 9 45 11 74,08 " 243,05 " 5 57 6 00 -f 3 104,08 " 341,47 4 14 4 15 + 1 Such an accordance between the results of observation, and those derived from a general law, leaves no doubt as to the cor- rectness of that law. In order to show that, in a perfectly closed circuit, that is, where the resistance in the conductor is very inconsiderable, the number of the elements does not increase the force of the current in the closing arc, we must successively complete a circuit, composed of 1, 2, 3, or 4 elements, through the tangential compass, and then observe the corresponding deviation. A series of experiments of this kind, gave the following results : Number of elements. Deviation observed. 1 69 66,5 67,5 67 68 64 452 THE CONDUCTIBILITY OF METALS. We see here, that the force of the current remains almost en- tirely unchanged, not increasing with the addition of the elements. The reason of its not remaining wholly unchanged is, that the in- dividual elements are not perfectly equal. Where, however, there is a considerable resistance to be over- come, the force of the current is certainly increased with the number of the elements. Six elements, closed by the tangential compass, yielded a deviation of 39 after the insertion of a wire 40 yards in length. One element, closed in the tangential compass by the same wire, measuring 40 feet in length, only showed a deviation of 11. Capacity of Metals for conducting Electric Currents, or the Conductibility of Metals. In the experiments given, (at p. 450,) pieces of wire, varying in length, were inserted in the closing arc of the circuit, and the relation of the force of the current to the length of the closing wire was thus obtained. If, now, we insert into the closing arc, wires of equal length, but of unequal thickness, composed of the same metal, and still observe the corresponding deviations of the needle of the tangential compass, we shall ascertain from these experiments the relation that the force of the current bears to the thickness of the wires ; and here we find, that the force of the current is proportional to the trans- verse section of the wires; or, in other words, that two wires, com- posed of the same metal, will exercise an equal resistance, if their lengths are inversely as their transverse sections. In order to compare the conductibility of different metals, no method is simpler, or more certain, than to conduct the current of a sufficiently powerful element through a tangential compass, to insert wires of different metals in the closing arc, and to observe the corresponding deviations. The following are the numbers expressing the capacity of dif- ferent metals for conducting electric currents : Silver . . . .136 Gold .... 103 Copper . . . .100 Zinc .... 28 Platinum ... 22 Iron .... 17 Mercury .... 2,6. THE CONDUCTIBILITY OF METALS. 453 That is to say, a copper wire of 100 feet in length, offers as great a resistance to an electric current, as equally thick wires of silver, zinc, platinum, iron, &c., which are respectively 136, 28, 22, or 17 feet in length. The conducting power of fluids is very small in comparison to that of metals: thus, ex. gr., the conducting power of platinum is 2J million times as great as that of a solution of sulphate of copper ; while the conducting power of distilled water is only 0,0025 of the conducting power of a solution of sulphate of copper. 454 MAGNETIC ACTIONS OF THE CURRENTS. PART IV. ELECTRO -MAGNETISM. CHAPTER I. MAGNETIC ACTIONS OF THE CURRENT. WE have already remarked that the electric current is capable of making the magnetic needle deviate, and it now remains for us, without entering further into these magnetic actions, to pass to the consideration of the applications that have been made of the devia- tion of the magnetic needle, to ascertain the laws of the force of the current. The following chapter is devoted to the further con- sideration of the magnetic actions of the electric current. Magnetization by the Galvanic Current. The electric current acts not only on free magnetism, but is likewise capable of sepa- rating the still combined magnetic fluids. In order to show the action of the current on soft iron, we need only plunge the wire into iron filings, or strew them over it during the passage of the Fig 426 Fig 427 g a l yan i c current. The iron filings remain hang- U ing to the wire until the current is broken ; small steel needles may be converted into permanent magnets by means of the galvanic current; in order, however, to render the current very active, we must make it pass transversely round the needle, as is the case in the arrangement we are about to describe. A copper wire is wound spi- rally round a glass tube, in which a steel needle is placed (see Fig. 426). If now we let a current pass through the convolutions of the wire, the needle will become permanently magnetic, and it is only necessary that the current should pass through it for the space of a minute, to magnetize the needle as perfectly as possible. MAGNETIZATION BY THE GALVANIC CURRENTS. 455 We distinguish right-handed helices as seen in Fig. 426, from left-handed helices as seen in Fig. 427. In the former, the con- volutions run in the same manner as in a cork-screw, or in an ordinary screw. In right-handed helices the north pole (that is the south end) is at that end of the needle where the -f current enters it, while, in the left-handed helix, the north pole is at the extremity from whence the current passes out. In the figures, the north pole is designated as 6, and the south pole as a. We may make magnets of soft iron by means of the galvanic current, far surpassing all steel magnets in force. For this pur- pose, it is only necessary to encircle a strong horse-shoe of soft iron with thick copper wire, in the way represented in Fig. 428. The copper wire must be covered with silk, in order that the cur- rent may not pass laterally from one winding to another, (these windings lying close together,) or be trans- ferred to the iron, but traverse the wire in its whole length. The wire is twisted round the curved lines of a horse-shoe, passing round in the same direction, but somewhat inclined to the right; if, there- fore, the -f current enters at c, a north pole will be formed there, and a south pole at b. By means of a holder, we may sus- pend weights to a magnet of this kind. Thus, a magnet whose diameter is about 2 or 3 inches, and whose limbs are about 1 foot or 1,5 feet in length may sustain a weight of from 800 to lOOOlbs., provided the wire be thick, and the cur- rent passing through it be of sufficient strength. As electro-mo- tors for these electro-magnets, simple circuits of a large area are used, or Groves'' or Bunsens^ elements; for this purpose, however, all the zinc cylinders must be connected together, in the same manner as all the carbon cylinders or platinum plates. The mag- netism vanishes as the current ceases. As we can engender a temporarily powerful magnetism in soft iron by the galvanic current, we are also able to produce steel magnets of great force by the same means. An arrangement especially applicable to this purpose is the wire coil constructed by Elias, and represented in Fig. 429. A copper wire about 25 feet in length, and Jth of an inch in 456 GALVANIC CURRENT AS A MOVING FORCE. thickness, must be properly encircled with silk, and then wound into a coil, as seen in the figure. The height of the wire coil amounts to about 1 inch, and the diameter of the inner cavity to 1J inches. The two extremities of the wires are brought into connection with the poles of a powerful voltaic element when we want to magnetize a steel rod. Fig. 429. Whilst a strong current circulates through the wire coils, the steel staff or rod must be inserted into the coil, and moved back- ward and forward, and when the middle part is a second time in the coil, the circuit is opened, and the rod can then be taken out perfectly magnetized. It is best to put a piece of soft iron above and below the steel rod, and, if the rod to be magnetized be of a horse-shoe shape, it should be provided with a holder during the operation. Application of the Galvanic Current as a Moving Force. The powerful magnetic actions which the electric current is capable of producing, have led to the idea of applying them as a moving power. Fig. 430 shows an apparatus which is well adapted to exhibit the manner in which a continuous motion may be pro- duced by the magnetizing action of the galvanic current. Ji B is a piece of soft iron curved into the form of a horse-shoe, and fixed to a stand, being encircled by a copper wire in the man- ner indicated in the electro-magnet in Fig. 428. The one end of the wire goes to the brass column a, the other to 6, the poles of a .powerful galvanic element are attached at a and 6, and the iron A B is thus converted into a magnet. Within the horse-shoe JJ B, a similar smaller one C D, is in- troduced, which rotates about a vertical axis. This iron C D is likewise encircled by a copper wire in the manner indicated, the two ends of the wire being plunged into a wooden ring-shaped channel filled with mercury. This channel is divided into two GALVANIC CURRENT AS A MOVING FORCE. 457 parts by means of a wooden or ivory partition, the one part being in communication by means of a copper wire with the brass column c, and the other with the brass column d. (The two poles of a simple circuit are attached at c and d. (The two partitions must now be filled with mercury to such a height that the level may project beyond the partition walls, although not so Fig. 430. as to pass from one space to the other, which may easily happen, owing to the mercury forming a convex drop, as it were, in each division. The two ends of the electro-magnet C D penetrate sufficiently far into the vessel so as to dip into the mercury on either side of the partition wall, but in such a manner as to admit of their passing freely over it during the rotation of the electro- magnet C D. In the position of the electro-magnet C D repre- sented in Fig. 430, supposing the + pole of a powerful galvanic element to be connected at c, and its pole at d, the + current will pass from c to the left division of the channel, from whence it will go through the copper wire round the moving horse-shoe from D to C, then from C into the right division of the channel, 39 458 GALVANIC CURRENT AS A MOVING FORCE. and from thence to d. In this position, the pole C will be at- tracted by A y and D by B, by which a rotatory motion of the electro-magnet C D will be induced. But now when C reaches A^ and D reaches B, the two ends of the wire of the inner elec- tro-magnet will pass over the partition wall : the current that makes C D magnetic, will be interrupted for a moment ; as soon, however, as the ends of the wires have passed from one division into the other, the current will go in an opposite direction through the copper wire encircling C D, the pole C will then be repelled by A, and D by B, whilst C and B and D and A will attract each other, thus the rotation of the inner electro-magnet will be con- tinued until C comes to B, and D to A, and by another inversion of the poles of the inner electro-magnet, the rotation of the latter will be continued in an opposite direction. A notched wheel is secured to the rotatory axis of the inner electro-magnet, and connected with a second wheel of larger dia- meter. Around the axis of the latter a string is wound, which passes over a pulley, and supports a hanging weight that is lifted by the rotation of the inner electro-magnet. This apparatus is merely an improvement upon Ritchie's rota- tion apparatus, in which a steel magnet supplies the place of the external electro-magnet, whilst the rotating iron has the form of a straight rod surrounded by a wire, the extremities of which are immersed in a channel filled with mercury, as in our apparatus, the rotation being maintained by the inversion of the poles suc- ceeding every semi-revolution. The attempts made by Jacobi in Petersburg, and Wagner in Frankfort, to apply the galvanic current practically as a moving power, have not hitherto afforded the desired results. Another practical application of the magnetization of soft iron, by galvanic currents, has been made use of in the Electric Tele- graph, the arrangement of which is essentially as follows. If the two extremities of a wire, encircling a U-shaped piece of soft iron, be made so long as to pass many miles, to some distant place, at which there is a galvanic circuit, we may, by alternately closing and opening this circuit with the wire ends, communicate mag- netism to, or remove it from, the distant iron ; and, thus, we may, consequently, cause the electro-magnet alternately to attract, and again to repel an armature, the motion of which is by means of a tooth of the wheel conveyed to the hand of a disc, round the GALVANIC CURRENT AS A MOVING FORCE. 459 margin of which the letters of the alphabet are marked. If the hand be properly placed, it will move to Jl on the first closing of the circuit, to B on the succeeding opening, and to C on a second closing, and so forth. We may, thus, bring the hand to any number of letters, after the corresponding number of openings and closings of the circuit, and, consequently, designate words and sentences, no less than single letters. [Since the above was written, by Professor Miiller, the electro- magnetic telegraph has been greatly improved, and has become of vast importance, in this country, as a mode of transmitting intelligence, from one place to another, with the utmost speed and certainty. It may, therefore, be of interest to give a slight sketch of the history of this invention, before describing the in- struments now in most general use. This has been derived from various sources, the principal of which are, " The American Electro-Magnetic Telegraph," by Vail; the "Manual of Mag- netism," by Davis; and the article, "Telegraph," in the Ency- clopedia Americana, vol. xiii. 575. The first electric telegraph appears to have been devised by Lesage, at Geneva, in 1774. It consisted of twenty-four pro- perly insulated wires, each terminating, at one end, in a pith ball electroscope; when the other end of any one of these wires was put in communication with the prime conductor of an electrical machine, the ball became repelled, and a corresponding letter was indicated. Numerous other telegraphs, of a similar character, were proposed, from time to time, by Lomond, in 1787; by Rei- zen, in 1794; and by Salva and Belancourt, in 1798, and a very ingenious one by Ronalds, in 1816. In all these, the common electrical machine being used, no important results were obtained from the very nature of the instruments employed, and the tend- ency of the electricity itself to be dissipated during its passage. In 1800, the discoveries of Volta opened a new field, and in 1809, Simmering first suggested a galvanic telegraph, founded on the property of the current to decompose water; his plan, however, vvas not made public until 1811, a year previous to which Dr. voxe, of Philadelphia, passed signals along a wire, of a mile in ength, and proposed a telegraph, founded on the instantaneous mssage of the current, and its property of producing chemical hanges upon prepared paper. His plan was published, in 1816, n Thompson's Annals of Philosophy. 460 GALVANIC CURRENT AS A MOVING FORCE. It was not, however, until after the discovery by Oersted, in 1820, of the action of a galvanic current on a magnet, that any truly practical results were obtained, the first of which were founded on the proposal of Ampere to employ the electro-mag- netic current to transmit intelligence, by observing the deflection it caused in the needle, instead of its action upon water. The instrument, founded on this idea, had the disadvantage of requir- ing a wire for each signal, as well as one to return the current to the battery. After this, numerous other plans were devised, among which, the most important are those of Wheatstone, in England, in 1840; of Schilling, in Russia, in 1832; of Gauss and Weber, in Gottingen, in 1833 ; and by Steinheil, in Munich, about 1837. It would be impossible to notice these, and many others of the kind, and we must, therefore, refer to the authorities above quoted for their history and mode of operation. The electro-magnetic telegraph now in use in this country, is claimed to have been suggested, in 1832, by Dr. C. T. Jackson and Professor Morse, but was not patented by the latter until 1837 ; and finally matured and put in operation, between Balti- more and Washington, in 1844. This form is exceedingly effi- cient and simple, and was the first devised that recorded the mes- sage sent by it ; thus dispensing with the uncertain attention of an assistant. The signals in this are not made by indicating the letters of the alphabet, but arbitrary signs, composed of variously arranged dots and lines. Its operation is as follows : the electrical current is generated by any constant battery, (Groves' is usually preferred,) passes from the transmitting to the receiving station by means of a con- necting wire, which, at the latter place, is coiled, in the usual manner, around the legs of a U-shaped bar of soft iron ; this bar is, of course, rendered magnetic during the action of the current. The keeper of the magnet is placed upon one end of a lever, the other end of which is armed with one or more points, which, when the keeper is suddenly drawn downwards, by the magnetic action, strike upwards into a groove, or grooves, in a steel roller situated above them. Under this roller passes a slip of paper, which, being unrolled, by machinery, from a cylinder, during the action of the acting agent, receives a mark from the points attached to the keeper. The circuit is completed, or broken, by means of a metallic spring or key, connected with one pole of the GALVANIC CURRENT AS A MOVING FORCE. 461 battery, which may be pressed down by the finger, upon a metal stud connected with the other pole. When pressed down, the circuit is complete ; when the pressure is removed, the spring, rising by its elasticity, the circuit is broken. The wires, between the stations, are stretched upon poles; but great inconvenience has arisen from their breaking, and from the effects of atmospheric electricity ; and it will, probably, become necessary to resort to the plan proposed by Mr. Bain, or to some analogous mode of insu- lating them under ground. Fig. 431 represents the recording part of the telegraph. It Fig. 431. consists, as has been stated, of an electro-magnet, armature, and .ever ; one end of which marks the strip of paper, by means of a alunt point, when the instrument is in action. Fig. 432 shows the telegraph with the clock-work usually em- ployed. The electro-magnet Jl and the lever are the same as in Fig. 432. 462 GALVANIC CURRENT AS A MOVING FORCE. Fig. 433. the simpler instrument, but connected with them is an apparatus moved by clock-work, designed to carry the paper as it is un- wound from a cylinder S, by the rollers, between which it passes and receives the registering mark. The primary movement of the lever is to set the clock-work in action, and a break and fric- tion wheel are sometimes added, so as to stop it after a cessation of the transmission of signals. A bell B is connected with the lever,, to apprize the attendant of the instant of the commence- ment of the operation. Fig. 433 is a representation of the instrument usually em- ployed to complete or break the circuit, by which the sys- tem of lines and dots, repre- senting the different letters and numbers, are produced at the other end of the telegraph. The signs employed by Professor Morse, are as follows : P-- 2 q 3 r _ -- 4 s 5 t 6 u 7 v 8 w 9 y -- -- z &c. - These characters, being formed by various combinations of dots, or of long and short lines, are, of course, capable of being indefinitely changed, as may, from time to time, be arranged by the conductors of the telegraph. In sending a message, a short space is used between each letter of a word, longer ones between the words, and still longer between sentences. INFLUENCE OF TERRESTRIAL MAGNETISM. 463 Instead of a galvanic series, a magneto-electric machine may be employed for working the telegraph, and the whole apparatus is susceptible of a variety of modifications to increase its efficiency and certainty, many of which will be found described and figured in Davis's Manual. Contrivances have, also, been applied to it, which enables the machine to print the message in the usual let- ters of this character are modifications of Bain, in London, and House, in this country ; but they are, of course, somewhat com- plicated, and it has been thought best to notice the apparatus in one of its most simple forms.] Direction of Currents by the influence of Terrestrial Magnetism. Since the current exercises an influence on magnets, we cannot doubt that a like action is conversely transferred by magnets to the current, and that they are able to direct it in different ways. Amongst all these converse phenomena, the most interesting is that exercised by terrestrial magnetism on currents, and attempts had frequently been made to establish moving currents, which, when left to themselves, might exhibit all the phenomena of the needle ; these experiments, however, all failed, owing to the ne- cessary mobility not being given to the currents. At length all these difficulties were overcome by an ingenious contrivance of Jlmpere, which admits of being applied to all currents. Fig. 434 represents two vertical brass columns secured to a wooden stand, and having at the top two horizontal arms, terminating in the mercury cups x and y y in which the central point of one is placed vertically below the other. Where the horizontal arms appear to be in contact, they are separated by insulating substances ; when, therefore, the feet of the co- lumns are brought in connec- tion with both poles of the circuit, one of the electric fluids will reach the cup x, and the other the cup y. One of these cups may be named the positive, and the other the negative. A copper wire, curved in the manner shown in Figs 435 and 436, is suspended to the cups x and y. The wire ends are sepa- rated by an insulating substance where they appear to be in con- Fig. 434. 464 INFLUENCE OF TERRESTRIAL MAGNETISM. tact ; they are curved at the top, and provided with steel points, which are plunged into the cups x and y (Fig. 434). The one point penetrates to the bottom of the cup, and rests upon a small glass plate, while the other point is only just immersed in the mercury. By this suspension the wire becomes very moveable. Fig. 435. Fig. 436. On suffering a current to pass, the wire, after making several oscillations, will place itself in a definite position, to which it will invariably return if removed from it. If we turn the current, bringing the column, which was pre- viously in connection with the + pole of the circuit, into contact with the pole, and vice versa, the wire will describe half a revolution round its vertical axis of rotation before it will recover its equilibrium. In both positions of equilibrium, the circle stands in such a manner that its plane makes a right angle with that of the magnetic meridian. Stable equilibrium will be established when the positive current passes from east to west in the lower half of the circle. Very weak currents are even directed by terrestrial magnetism, and on this principle rests the construction of the apparatus in Fig. 437. In a piece of cork, swimming in acidu- lated water, we secure a piece of zinc and a piece of copper, which reach into the fluid, and are con- nected at the top by a circular copper wire. When placed upon the water, a current will be found w r hich passes from the zinc in the water to the copper, and then through the wire, following the direction indi- cated by the arrows. This current is sufficiently strong to be directed by terrestrial magnetism, and will, therefore, so much the more be directed, attracted, and repelled, by a magnet. As a closed circular current, revolving round a vertical axis, Fig. 437. ACTION OF GALVANIC CURRENTS ON EACH OTHER. 465 places itself at right angles with the magnetic meridian, it follows that a combination of parallel circles, which are traversed in the same direction, must range themselves in like manner. Thus, the wire helix, seen in Fig. 438, when suspended by Ampere's stand, and when traversed by a current, must place itself in such a manner that its Flg * 438 ' axis shall be in the line of the direction of the needle of decimation. It not only follows from this, that the needle of declination may be thus imi- tated by a wire helix, but also that the south pole, that is, the one directed to the north, is the one on the right side of which lies the ascend- ing current, if we look at it from its present side. If we look at the wire from a, we have the ascending current to the right, and the descending one to the left ; but if we consider the wire helix in the direction of b, we shall have the ascending current to our left ; a, consequently, is the south pole, and must turn to the north. In like manner, we may say that, if a needle of declina- tion be placed in a position of equilibrium, the lower current will go from east to west. The board, to which the different windings of the wire helix (Fig. 438) are secured, is made of a non-conducting substance. If we bring a magnetic bar to the helices we have been con- sidering, we may observe phenomena perfectly similar to those exhibited on bringing a magnetic bar near a needle of declination. In fact all the apparatus hitherto described will, as we may con- jecture, be affected by magnetic bars. Reciprocal Action of Galvanic Currents on each other. Two parallel currents always exercise an action on each other, which is more or less energetic according to their distance, intensity and length. If we consider the direction of the motion produced, we shall find it to be subjected to the following simple law; two pa- rallel currents attract each other if they move in the same direction, but repel each other if their directions be opposite. The above statement may be proved by the following appa- ratus ; a b c d ef is a rectangular figure formed of copper wire, and suspended in the mercury cups x and y. The current as- cends through the column *, traverses the wire figure in the direc- tion of the arrows, and descends into the column v. The current 466 ACTION OF GALVANIC CURRENTS ON EACH OTHER. in the column t, follows the same direction as that in the piece of wire d e ; the same is the case with respect to the current in b c and v. If we remove the rectangular figure from the position represented in Fig. 439, it will always return to the same, owing to d e being attracted by t, and b c by v. If we put the wire figure in Fig. 439 in the place of that sus- Fig. 439. Fig. 440. pended in Fig. 440, the current in the wire will have an opposite direction from that in the succeeding column, and we shall ob- serve a repulsion ; parallel opposite currents, therefore, repel each other. We call such currents as are not parallel, cross currents, whe- ther they lie in the same plane, and their directions intersect each other, or whether they are in different planes, and do not intersect each other. In the first case, the crossing point is the point in which they intersect each other ; in the second, it is a point of the shortest distance of both currents. Two cross currents always strive to range themselves parallel to each other, in order to move in the same direction; or in other words : attraction takes place between the parts of a current and those which approach the cross- ing point, and then again, between those going from the crossing point. Repulsion occurs between a current moving towards the crossing point, and another moving away from the same point. If, for instance, a b and c d (Fig. 441) are two currents, whose crossing point is r, attraction will take place between the parts a r and c r, in which the current passes towards the crossing point, and between the parts r b and r d, in which it goes from the crossing point. Repulsion takes place between a r and r d, and further between c r and r b. AMPERE'S THEORY OF MAGNETISM. 467 The apparatus of which a diagonal section is represented in Fig. 442, and an outline in Fig. 443, serve to prove this proposi- Fig. 441. Fig. 443. tion. Two semi-circular channels, divided by insulated partition walls a and 6, are inserted in a plate of wood. In the middle point rises a spike, to which is attached an easily moving copper needle c d, the extremities of which are of iron and dip into the mercury of the channel. Somewhat below this needle there is another, ef, the extremities of which are likewise dipped into the mercury, and may be moved by the hand. The current which enters at x passes into the one channel, and then through the two needles into the other, and passes out at y. The repulsion is exhibited on placing the needles in the posi- tion indicated by Fig. 443, and the attraction on bringing them into such a position, that the angle e r d may be less than a right angle. Ampere's Theory of Magnetism. The principle of this theory consists in considering each molecule of a magnet surrounded as it were by a current, always circulating about it and returning upon its own course, which may for the sake of simplicity be re- garded as circular. We must, therefore, according to this theory, regard every section at right angles to the axis of the magnet to be somewhat similar to what we have attempted to delineate in Fig. 444. Instead of taking into account all the elementary cur- rents of each diagonal section, we may suppose the latter to be Fig. 444. Fig. 445. 468 AMPERE'S THEORY OF MAGNETISM. Fig. 446. encircled by one single current, which is, as it were, the resultant of all the elementary currents of the diagonal section, and con- sequently we may regard a magnetic bar as a system of parallelly closed currents, somewhat in the manner shown in Fig. 445. What we have said here of a magnetic rod applies equally to a magnetic needle, and, in short, to every magnet, let its form be what it may. Let us suppose a wire helix extending from m, Fig. 446, to either side, and traversed by the current in the direction of the arrows; if further we assume this to be cut through at m, and the two parts separated, it follows from our definition that there will be a south pole at a and a north pole at 6, for on turning to the pole at a, we shall have the ascending current to our right, while on turning to the pole at 6, we here have it to our left. If we cut a wire helix at right angles to its axis, two contrary poles will be formed, exactly as on breaking a magnet. Further, it is clear that the contrary poles a and b attract each other, for on looking only at the end circle, we see that the cur- rents are directed parallelly and similarly, and the same is the case with respect to all the other circles. The best way to give an illustration of the attraction and re- pulsion of the poles in different positions of the magnets with respect to each other, is by drawing arrows upon wooden or pasteboard cylinders from 1 to 1,5 foot in length, and from 2 to 3 inches in diameter, as seen in Fig. 445, which represents the direction of the currents ; further, we may, in like manner, mark on both cylinders the similar poles, designating the north pole as +, for instance, and the south pole as . By the help of two such models we may easily show how similar poles always repel, and contrary poles attract each other, and in whatever manner we bring them near one another. According to this hypothesis, the magnetism of the earth also depends upon such currents, moving in the crust of the earth parallel with the magnetic equator. ROTATION OF MOVABLE CURRENTS AND MAGNETS. 469 Fig. 447. Fig. 448. Rotation of Movable Currents and Magnets. Let abed, Fig. 447, be the horizontal section of a magnet standing in a vertical position, and a vertical current appearing foreshortened at the point s, and which we will assume to be ascending, and which is capable of rotating round the vertical axis of the magnet; it will then be evident from the above developed principles, that the portion a b of the mag- netic current will repel the current s, while it will be attracted by b c, the current s must consequently ro- tate in the direction of the current in the magnet. If the current s were descending, the rotatory direction would be reversed ; in like manner, of course, the inversion of the magnetic poles will occasion the rotation to assume an inverse direction. A rotation of this kind may be effected by means of the ap- paratus seen in 448. To a vertical staff/ is attached a movable horizontal staff a, in such a manner that it may be moved to any height we please, by means of a screw. This horizontal staff is provided with a brass ring, to which is attached a circular wooden channel for holding mercury. In the brass ring there is a cork disc, through the middle of which passes a vertical magnetic bar, having at the top a joint with a steel cup screwed on it. This cup has a fine point in its centre, sup- porting a copper band b, which is curved at either side, in such a manner that its lower ends, with their platinum points, dip into the mercury. In the middle of the copper band is a mercury cup p. On the one polar wire of the chain being immersed in the cup jp, and the other in the channel, the current passes through the two arms of the copper band, which then begins to rotate. The action of the magnet on the current in the one arm of the band is sustained by the action which the magnet produces on the current in the other arm. 40 470 PHENOMENA OF INDUCTION. We may similarly produce the rotation of a movable magnet round a fixed current, and the rotation of a moving current round a fixed magnet ; and the apparatus serving for this purpose have been constructed in a variety of ways. CHAPTER II. PHENOMENA OF INDUCTION. AN electric current is able to engender like electric currents in another contiguous conductor at the moment of its origin or its cessation, and also by mere approximation or distance. These phenomena were discovered by Faraday in the year 1838, and deserve the greatest attention, both owing to their theoretical importance, and to the numerous facts that can be derived from this principle. These new currents produced in conductors by the distributing action of other currents, are termed Induction currents. They might also be called temporary currents, as they last but a moment. If we were to name them according to their origin, as has been done in the case of the thermo-electric and the hydro-electric currents, we might give them the appellation of magneto-electric, or electro-electric, since they are either engen- dered by magnetism or electricity. We will, however, once for all, abide by the term Induction currents, which has also been adopted by the majority of natural philosophers. Action of an Electric Current on a Conducting Circuit within itself. Two copper wires covered with silk thread are wound upon a reel of wood or metal in the way exhibited in Fig. 449. The one wire runs beside the other without there being any com- munication between them ; if, therefore, we close a galvanic circuit with one wire, while we place its two ends a and b in con- nection with its poles, the current will circulate through that wire without passing into the other. In this other wire, however, a cur- ACTION OF AN ELECTRIC CURRENT, ETC. 471 rent in an opposite direction is produced by the inductive action of this current, provided the ends c and d of this second wire are in connection ; which may be effected by means of a multiplicator, on bringing c into communication with the end of one of the wires of the latter, and d with the end of the other wire. At the moment in which we close the galvanic circuit with the first wire, the deviation of the needle of the multiplicator indicates a current in the adjoining wire ; supposing the positive current to pass in the main wire from a to 6, the multiplicator manifests that there is a current in the contiguous wire traversing it in a direction from d to c. This current in the adjoining wire is not, however, lasting, for the needle of the multiplicator returns immediately to zero on the graduated line ; as soon as the principal current is interrupted, the needle of the galvanometer turns in the opposite direction, it, therefore, indicates a current passing through the neighboring wire in the direction from c to d, consequently, in the same direc- tion in which the interrupted current had moved. An electric current may, therefore, induce currents in a conti- guous wire both at the moment of its origin and of its cessation. The current induced by the closing of the circuit has the opposite direction to the one induced by the interruption of the circuit, and is in the same direction as the principal current. In the above adduced experiments, the current in the principal wire induced a current in the other wire both at the moment of its origin and of its cessation; we might, therefore, conjecture that these actions were produced by some modifications accom- panying the beginning and ending of the current. To remove all doubt on the subject, Faraday has proved by experiment, that exactly the same results are obtained on bringing a conducting wire that is traversed by a current, consequently, the wire from which the inducing action proceeds nearer to, or further from the wire in which we wish to induce a current. If, therefore, we say that the action of a current on a closed conductor begins, we either understand thereby that the inducing current itself begins, or that it is already on its course, and brought near to the closed conductor. In these two cases the actions are precisely similar. If we say that the action of a current on a closed conductor stops, it means, that the inducing current itself either ceases, or is removed from the closed conductor. 472 ACTION OF THE WINDINGS ON EACH OTHER. Currents of induction produce all the actions of ordinary cur- rents, as, for instance, shocks and sparks. On bringing the ends of the wires c d close together, we see a spark pass over, if the circuit be closed by the ends a and b of the inducing wire. If we seize the wire end c in one hand, and d in the other, (the hands must be somewhat moistened for making the experiment), we shall feel, on the opening and closing of the principal current a shock, the violence of which will depend upon the length of the coiled wire. Very violent actions may be produced on the nerves by the above described double spiral apparatus, for if the encircling wire be of considerable length, the intensity of the inductive currents will be incomparably stronger than those of the current yielded by the galvanic circuit commonly used. A simple galvanic cir- cuit, or even a battery of 4, 6, or even 12 pairs gives no shocks by itself, but if we close a circuit of a few or only one pair, with the ends of the inducing wire, we shall obtain a powerful shock at this wire. An induction spiral changes, therefore, in some degree the electric quantity of a current yielded by one or more pairs of large superficies into a current of great intensity; an apparatus of this kind affords, therefore, an excellent means of producing physiological effects, if care be taken alternately to close and open the circuit in rapid succession. Many very ingenious con- trivances have been proposed for effecting this purpose. Action of the Windings on each other. If we close a simple circuit by a short wire, we shall obtain only a faint spark on again opening it, and no shock ; but if we use a very long wire instead of the short one, we shall see a much stronger spark on opening the circuit, and if we hold one end of the wire in one hand, and the other in the opposite hand, we shall perceive a shock at the moment of opening the circuit. These actions are very much strengthened by winding the wire as closely Fig. 450.^ ag p OSS ibi e> ant [ nere ^ i s? O f course, neces- sary to cover the wire with silk, in order to prevent the current passing laterally from one winding to another. This action of long spiral wires may be well shown by means of a simple spiral, Fig. 450, it being only necessary to plunge the wire ends m and n INDUCTION OF ELECTRIC CURRENTS BY MAGNETS. 473 into the mercury cups forming the poles of a galvanic circuit, and on withdrawing the ends of the wires we shall see a brighter spark and feel the shock. On suffering these shocks to pass in rapid succession through the body, violent actions on the nerves may be induced. As to what relates to the explanation of these phenomena, we shall easily comprehend that they must stand in a very close re- lation to the induction phenomena before described. Faraday ascribes these effects to an inductive action reciprocally exercised on each other by the convolutions of one and the same spiral, and calls this current of induction an extra-current. It arises at the moment of the opening and closing of the circuit. Induction of Electric Currents by Magnets. A metal wire, en- circled with silk, must be wound over a wooden or metal rod, the inner opening of which is sufficiently large to admit of the inser- tion of a magnet. The two ends m and n of the wire must be put r.?;o communication with the two ends of the multiplicator wire of a galvanometer, sufficiently far removed to prevent the magnet from causing the needle of the instrument to deviate. At the moment in which the magnet is inserted into the helix, we shall observe a deviation of the galvanome- ter needle, which, however, will soon return to the point of the graduated division, moving away again, in an opposite direction, on withdrawing the magnet from the helix. The direction of the current, indicated by the galvanome^r, on the approximation of the magnet, is opposite to that of the cur- rents, which, according to Ampere's theory, circulate about the magnet; the current, induced in the wire, on the removal of the magnet, has the same direction as these currents. By this experiment, an action is produced on the closed wire coils, on the approximation or removal of the magnet ; but this magnetic action may begin and cease in a different manner; it [may, for instance, begin at the moment in which the magnetic i fluids in the iron are decomposed, and cease when it returns to the non-magnetic condition. This may be shown in the following manner. 40* 474 INDUCTION OF ELECTRIC CURRENTS BY MAGNETS. In Fig. 452 a & is a strong horse-shoe magnet, m c n a piece of soft iron, likewise bent in the form of a horse-shoe, and having its limbs enclosed by the coils of one long wire, covered with silk. The direction of the coils, on both limbs, must be such that, on the current passing through the wire, the two limbs may form opposite poles. The two ends of the wire are connected together at a sufficient distance from the iron and the magnet, and a simple magnetic needle, above or below which the wire is conducted, is at once made to deviate by the induced current. If we rapidly bring the magnet a b to the limbs m n, the needle will indicate the pre- sence of a current having an opposite direction to that which, according to Jlmpere's theory, circulates round the iron that has now been converted into a magnet. On the removal of the mag- net a b, the induced current takes the same direction as the one now ceasing in the soft iron. We may easily show that this current, induced in the wire, is not the direct action of the magnetic poles of the approximated magnet; for this current attains such intensity, that, if even the two ends of the wire are not in perfect contact, but at some little distance from each other, a vivid spark will pass over, as well when the magnet is rapidly approximated, as when it is removed. This electric spark is evidently produced by magnetic actions. On taking one end of the wire in each hand, we experience, on the approximation and removal of the magnet, a shock, which, provided the magnet be sufficiently powerful, will be like the shock of a small Leyden jar. Currents may even be induced by terrestrial magnetism. If we hold a rod of soft iron, encircled by a wire helix, in the direc- tion of the needle of inclination, and then suddenly invert it, so that its upper part shall incline downward, and vice versa, a cur- rent will be induced in the wire helix. If the inner horse-shoe of the apparatus, seen in Fig. 430, rotate under the circumstances indicated in the experiment ad- duced, currents must be induced in the windings of the wire, on the approximation of the limbs of the inner horse-shoe towards MAGNETO-ELECTRIC MACHINES OF ROTATION. 475 those of the external iron, these currents will be, according to the above developed principles, opposite to those occasioned by the rotation; the currents, induced by rotation, must necessarily weaken the force with which the limbs of the two horse-shoes attract and repel each other; and thus, these currents of induc- tion cause the mechanical effect, produced by such apparatus of rotation, to be much less considerable than one might be led to expect, judging from the force of magnetism that may be imparted to a piece of soft iron by a galvanic current. Magneto -Electric Machines of Rotation. If we suppose the ends of the inductive-spirals, which are at the poles of the core of a horse-shoe formed of a piece of soft iron, (as have been consi- dered at page 474,) to be in connection with each other, and then, that this soft iron revolves rapidly about a vertical axis, so that the pole m, which is immediately above a, after half a revo- lution, stands above 6, there will then be a current induced in the convolutions of the wire, m recedes from a, and n from b ; this current will now continue with varying strength, but with unvary- ing direction during half a revolution, that is, while m turns from a to 6, and n from b to a ; as soon, however, as the second rota- tion begins, the direction of the current will change, and will again change after the completion of a whole rotation ; if, there- fore, the soft iron rotate rapidly with its wire convolutions, the latter will be constantly traversed by alternating currents passing into each other every time the poles of the soft iron stand over the poles of the magnet. That the direction of the currents actually changes in the way indicated, is easily seen from the rules given concerning the direction of the induced currents, for, as a and b are opposite poles, the removal of a must induce a current in the same direction as an approximation towards the pole b. In order to be able conveniently to make experiments on the currents induced by magnets, machines have been constructed according to the above indicated principles, which bear the name of magneto-electric machines of rotation. Fig. 453 represents one of these. The inductive spirals, A and B, are wound round two cylinders of soft iron, secured to the two ends of a horizontal iron plate, the centre of which is on a vertical iron axis, as may be seen in Fig. 454. The manner in which the rotation of this 476 MAGNETO-ELECTRIC MACHINES OF ROTATION. Fig. 453. Fig. 454. vertical iron axis is effected, is made apparent in Fig. 453, and needs no further explanation. During the rotation the two iron cores pass under the poles of several powerful horse-shoe magnets, laid hori- zontally over each other, and each iron core of the horse-shoe is thus alternately converted into a north and a south pole. The convolutions around both iron cores are, of course, formed only by one very long piece of wire. The one end is fastened by means of a screw to an iron ring g, protected by some insulating substance, solid wood or iron, from contact with the iron axis of rotation, as seen in Fig. 455. The opposite end of the wire is, in like manner, screwed upon the iron plate which supports two cores ; it is, consequently, in contact with the whole iron axis of rotation. On this iron axis an iron cylinder h is immediately secured, which we will at once consider. As the iron ring g is in com- MAGNETO-ELECTRIC MACHINES OF ROTATION. 477 munication with one end of the wire, and the iron Fig. 455. cylinder h with the other, we may regard g and h as the ends themselves ; the inductive spiral will be closed on bringing g and h into connecting commu- nication with each other ; on this being done, the current of in- duction will circulate in the wire coils, and the whole system be made to rotate. For the sake of simplifying the matter, we will designate the whole rotating system by the name of Inductor. We have still to consider the iron cylinder A, which consists of three divisions lying over one another, and of which only the middle one has a perfectly unbroken circumference. At the upper parts are two channel-like depressions diametrically opposite to each other, while, at the lower end of h, a part is cut away, which takes off about half the circumference, as may be clearly seen in our Figure. On either side of the axis of rotation is a small brass column with several apertures, in which metallic springs may be inserted, and the circuit be thus closed in various ways. Our Figure represents the machine as it must be arranged, in order to produce powerful physiological actions. In the upper- most aperture of the column to the right, a spring is screwed on which constantly presses upon the iron ring g during the rotation of the inductor ; but the steel spring in the next aperture closes upon the upper part of the iron cylinder A, and in this manner the circuit is closed ; while, as often as the end of the steel wire passes over one of the channel-like depressions, the connection is interrupted. This interruption occurs exactly when the poles of the inductors have been removed from over the magnetic poles. There exists, however, another connection between the iron ring _ and the cylinder A, into which the human body may be brought. A brass spring, constantly pressing upon the middle part of the cylinder A, is screwed into the left side of the brass pillar ; by which means the small brass pillar to the left is connected with h, as g is with the pillar to the right. A metallic conductor L is in connecting contact with the pillar to the left, and the conductor R with the pillar to the right; as often, therefore, as the current there is interrupted by the sliding of the steel spring over the depres- sions, the shock of disjunction will pass through the body, for it is only then that the electric current (which hitherto has passed directly from h through the steel spring to the right hand pillar) 478 MAGNETO-ELECTRIC MACHINES OF ROTATION. Fig. 456. now passes by a circuitous course, first to the left pillar, from this to the conductor L, through the human body to R, and then finally to the pillar at the right. On turning the machine rapidly, the shocks of disjunction will succeed each other so violently that it will scarcely be possible to endure the effect. If we wish to weaken the intensity of the shocks, it is only necessary to turn the machine more slowly, or to connect both poles of the inducing magnets, by means of an armature of soft iron. THERMO-ELECTRIC CURRENTS, ETC. 479 PART V. THERMO-ELECTRIC CURRENTS AND ANIMAL ELECTRICITY.* IF two metallic bars be so soldered together that they compose a closed circuit of any form we choose to give them, a more or less intense current will be produced as often as the temperature varies at the two places of junction, the current continuing as long as this difference of temperature is maintained. This may be shown for a special case with the apparatus in Fig. 457. s s' is a piece of bismuth, s c s' a band of copper sol- dered on the ends of the bismuth bars ; a b is a Fi 457 magnetic needle, movable freely on a point. If the two places of junction have the same tempera- 'ture as the surrounding air, the apparatus must be so placed that the plane s c s r may coincide with the plane of the magnetic meridian, and that, consequently, the needle may stand parallel with the axis and the longer sides of the bismuth bar. As soon, now, as one of the joining-places, s, for instance, is heated, the needle will experience a more or less strongly marked deviation; but if this spot s be cooled below the temperature of the surrounding air, we shall observe a deviation in the opposite direction. These deviations of the needle, first to the one side and then to the other, evidently indicate the presence of an electric current, traversing the apparatus in a definite direction, if the spot s be warmer than s f ; but in an opposite one if s be cooler than s f . All metals do not yield the same marked results as bismuth and copper ; and in such cases we must use a system of two needles, as seen in Fig. 458, instead of one. The upper band s c s 1 has * Professor T. Thomson's "Heat and Electricity," 8vo. 2d edition, London, 1840. 480 THERMO-ELECTRIC CURRENTS, ETC. Fig. 458. Fig. 459. fa Fig. 460. an opening in the middle, to admit of the passage of the con- necting piece between the two needles, while the point, however, on which* the system of the two needles plays, passes to the upper needle. It is not essential to have an especial apparatus (as seen in Fig. 458) for making the fundamental experiments on thermo-electric currents, since we may use any delicately suspended compass needle destined for this purpose, somewhat like that delineated in Fig. 459. Here we have an elongated parallelogram, Fig. 460, as the thermo-electric element, composed of bismuth and antimony. In our figure the lightly shaded half designates the former, and the darkly shaded half the latter constituent. The two metals are soldered together at s and s f . In order to make this experiment, we must carefully warm, over a small spirit lamp, the one sol- dered junction, and then hold one of the longer sides of the figure over the magnetic needle, which must then be in its usual position. We must re- mark here, that Fig. 460 is deli- neated on a somewhat smaller scale than 459 ; since the parallelogram of bismuth and antimony ought to be so large, that each of its longer sides may be at least of equal length with the magnetic needle. Simple thermo-electric circuits are often made in the manner represented in Fig. 461 ; a b is a small bar of antimony or bis- muth, at both sides of which a copper wire a e d b is soldered. To make this experiment, we must warm the one sol- dered joining either at a or b, and hold the piece of wire e d over the needle. The investigations that have been made as to the mutual relation of different metals, with respect to the excitement of thermo-electric currents, have shown that the metals Fig. 461. THERMO-ELECTRIC PILES. 481 admit of being ranged in one series, which has this property, that, on forming a circuit of every two metals, and heating the place of contact of the two, the + current at this spot will pass from the metal standing immediately below it to the one above. Antimony Tin Arsenic Silver Iron Manganese Zinc Cobalt Gold Palladium Copper Platinum Brass Nickel Rhodium Mercury Lead Bismuth Thus, in the apparatus, Fig. 457, the current will pass in the direction from s over c to s f , and then back to s on heating the soldered part at s. At this point s, therefore, the next body standing higher, viz., copper, is positive with respect to the lower one, bismuth. In the parallelogram, Fig. 460, the positive cur- rent circulates in the direction of the arrow, if the spot at s is warmer. Thermo-electric Piles. As in the case of Volta's piles, so we may also here combine many thermo-electric elements to form thermo-electric piles, capable of giving a current if the soldered parts 1, 3, 5, &c., be warmed, while the intervening points re- main cold. Thermo-electric piles of this kind may serve, in connection with multiplicators, to make the slightest difference of tempera- ture manifest. Amongst all those constructed for this purpose, the apparatus proposed by Mobile is undeniably the most ingenious, and the most sensitive. Fig. 462 represents an apparatus of this kind. It is composed of from 25 to 30 very fine needles of bismuth and antimony, which are about 4 or 5 centi- metres in length. They are so soldered Fig ' 463 ' together, see Fig. 463, that all the even soldered joinings are on one side, and the odd joinings on the other. The whole forms a small, compact, solid bundle, owing to the insulating substances with which the intervals between the several rods are filled ; for 41 482 ANIMAL ELECTRICITY. they must, of course, not be in contact, excepting at the soldered joinings. One of the two half elements in which the circuit ter- minates is in connection with the peg x 9 and the other, with the peg y, x and y form in this manner the two poles of the pile, and are brought into communication with the ends of the multipli- cator wire. If the soldered points on the one side experience the slightest elevation of temperature, the multiplicator needle will at once deviate from the magnetic meridian. Animal Electricity. It has been long known that there are fishes capable of imparting electric shocks; among which, the most remarkable, are the torpedo and the electric eel. The former is met with in the Mediterranean and in the Atlantic Ocean, and the latter only in the inland pools of South America. When the torpedo is out of water, we experience a shock on touching any part of its skin, either with the finger or the whole hand. We may, in like manner, receive a shock on touching the fish with a good conductor, as that of a metal rod several feet in length. The shock is prevented by every bad conductor, and we may, conse- quently, seize the animal with impu- nity by means of a glass or resin hook. The back of the animal is positively, and the abdomen negatively electric ; the electric current passing through a conducting wire, and connecting the back and abdomen, produces all the actions of electric currents, although only in a modified form. The organ in which the electricity is developed has, in the different electric fishes, essentially the same texture and appearance, although its form, size and arrangement differ. We will now at- tempt to give an idea of the organ of the torpedo the fish which has been most accurately examined. Fig. 464 represents a torpedo seen from above, opened at the side to show Fig. 464. ANIMAL ELECTRICITY. 483 the electric organ. This passes anteriorly close to the fore part of the head, its upper surface touching the skin of the back by means of a fibrous membrane, and the lower surface touching that of the abdomen ; its external surface rests upon the muscle of the lateral fin, and the inner one at the principal muscle of the head and the anterior part of the trunk. Seen from above or below, the electric organ exhibits polygonal, or roundish divisions (Fig. 465) ; but, from a lateral point of view, it exhibits parallel stripes or bands, as seen in Fig. 466. Fig. 465. Fig. 466. The whole organ consists of a number of polygonal, or round- ish columns, the axis of which runs in a direction from the abdo- men to the back. The marginal edge of each column forms a somewhat thick tendinous mem- brane, appearing to answer the same purpose as the glass plates between which the galvanic pile is built up. Each column con- sists of a number of fine tenias, which are either plane, or curved, and are separated by very adhesive mucous layers ; thus these columns afford a striking resemblance in their construction to a galvanic pile. There are generally found to be from 400 to 500 such columns or piles on either side of a torpedo. In the electric eel (Fig. 467), the electric organ is situated in its Fig. 467. tail. In this animal the anus lies so far forward, that the tail of the gymnotus is nearly 4J times as long as the body and head combined ; and here the electric organ extends almost the whole length of the tail on either side of and under it, so that the electric apparatus of the animal has a very great extension, owing to which the electric eel is able to impart shocks of extreme violence. In the gymnotus, the columns forming the electric organ do not lie vertically, as in the torpedo, but extend in the direction of the tail ; so that the discs of which they are composed stand vertically. 484 ANIMAL ELECTRICITY. Hence it comes, that, in the electric eel, the positive current goes in the direction of the head towards the tail; consequently, not like the torpedo, where the current passes from the back to the abdomen. Electric currents, not occasioned by especial electric organs, have been observed in the animal organism. Nobili has found, that, on touching with the one wire end of a multiplicator the head of a living or dead frog, and its feet with the other wire, a current will pass from the head to the feet. In like manner, a current may be observed on making an incision into the muscle of any animal, and connecting the exterior surface of the muscle with the cut surface by means of the multiplicator. OF HEAT. 485 SECTION VII OF HEAT.* CHAPTER I. EXPANSION. OUR capacity of feeling enables us to discriminate between the different conditions which we term hot, warm, cold, &c., in various bodies. If a body that we call cold become warm, and hot, it will increase in volume, or be expanded. The unknown cause producing this expansion of bodies, and which, at the same time, occasions the different above-mentioned impressions on our capability of feeling, is termed heat. Heat not only effects an expansion in bodies, but is likewise able to alter their aggregate conditions, fusing solid, and evapo- rizing fluid bodies. We will now proceed to the consideration of the laws of these phenomena. The Thermometer. Since all bodies are expanded by heat, and as the volume of a body depends upon the degree of heat it possesses, the expansion of a body may serve to measure the degree of its heat; and this degree of heat we term tem- perature, and the instrument used to define it, a ther- lg '^ mometer. Fig. 468 represents a mercurial thermometer; the bulb is filled with mercury; this fluid rises in the tube to a definite height, dependent on the temperature. If the bulb be warmed, the volume of the mercury will be in- creased, and it will rise in the tube, and we say the tem- perature has increased. If the bulb be cooled, the volume of the mercury will again diminish, and the fluid will sink in the tube, and we say that the temperature has fallen. * See Professor Thompson's "Heat and Electricity," 2d edition, 8vo. 1840. 41* 486 THE THERMOMETER. At equal degrees of temperature, the top of the mercury will always occupy the same place in the tube ; thus, on comparing a larger or a smaller thermometer with the first, both will rise and fall together, but the actual amount of the rising and falling may be very different. If, for instance, the two bulbs are equal, but the tube of the one 10 times larger in its bore than that of the other, the mercury will, at an equal degree of temperature, rise 10 times higher in the narrower tube. A thermometer of this kind can only serve to show whether a certain degree of temperature be present, or whether it be higher or lower, according as the top of the mercury stands higher or lower in the tube. Such an instrument might be of some use to science ; but it is only by their graduation that thermometers can be rendered practically useful : thus enabling us to express the temperatures, to compare them, and thus ascertain the laws of heat. It will of course be understood that only such glass tubes must be applied to thermometers as are perfectly cylindrical; and whether they are so, is known by observing if a globule of mer- cary suffered to pass up and down one of these tubes occupy an equal length in all parts of the tube. After a tube has been blown out into a bulb, it must be filled . 469 with mercury ; for this purpose the bulb is warmed, in order that the air contained within it may be expanded, and then the open end of the tube is rapidly plunged into the mercury (Fig. 469). On the bulb cooling, the mercury ascends into the tube. It is sufficient here, if only a few drops reach the bulb. If we now again invert the instrument, and heat the ball a second time till the fluid begins to boil, the vapor of the mercury will soon fill the whole space, driving the air entirely out ; and when the open end of the tube is again quickly plunged into the mercury, we may be sure of the bulb becoming entirely filled. Before the thermometer is closed, it must be regulated ; that is to say, as much mercury must be added or taken away, as is necessary to make the amount correspond to the medium tern- THE THERMOMETER. 487 Fig. 470. Fig. 471. perature, for which the thermometer is intended; it must then be hermetically closed. The graduation of thermometers consists in marking two fixed points on the tube, and then dividing the intervening space into equal parts. For these points, the boiling and freezing points of water are generally taken. To determine the latter, the thermo- meter ball and the tube, as far as it is filled by the mercury, are plunged into a vessel filled with finely pounded ice, (Fig. 470.) If the temperature of the surrounding air be higher than the freezing point, the ice will melt, and the whole mass will assume the fixed temperature of the freezing point. The thermometer will also soon acquire this tempera- ture, and from that moment it will remain perfectly stationary, when we have only to mark, with accuracy, the point of the tube where the top of the column of mercury stands. This ppint is first designated by a line of ink, and subsequently marked by a diamond. In order to determine the boiling point, we take a vessel with a long neck, (Fig. 471,) and heat distilled water within it to the boiling point ; after the boiling has gone on some time, all parts of the vessel will be equally heated, and the vapor will escape at the lateral openings ; the thermometer is then surrounded on all sides by vapor, the temperature of which will be the same as that of the upper layer of water. The mercury will soon rise to a point at which it will remain standing, and which it will not exceed. This point is designated as 100 C. (212 F.) If at this moment the height of the barometer be not exactly 760 mm (30 inches), a correction must be made, the amount of which will be given when we treat more fully of boiling. In the centigrade thermometers the interval between the two fixed points is divided into 100 parts, and the thermometer scale thus made. * All thermometers constructed in this manner are comparable instruments ; that is to say, they exhibit an equal number of de- grees at equal temperatures. Mercurial thermometers may be constructed, which go to the 600th F. degree ; but beyond this it is not expedient to raise them, 488 THE THERMOMETER. for fear of approaching too nearly to the boiling point of mercury, which is 644 F. Below zero, the graduations of mercurial ther- mometers may go correctly as far as 30 F. or 32 F.; but beyond this we should approach too nearly to 39 F., the freezing point of mercury. As we approximate to the tempera- tures in which bodies change their aggregate condition, their ex- pansion is no longer regular. All thermometers are not graduated according to the centigrade scale. In Germany and France Reaumur's thermometers are much used, which are divided into 80, although for scientific investiga- tions the centigrade division of Celsius is almost exclusively applied to thermometers. It is, however, easy to reduce Celsius' scale to that of Reaumur, and vice versa; for as 100 C. = 80 R., 1 C. = 0,8 R., and 1 R. == 1,25 C. Consequently x C. = x, 0,8 R., and n R. = n . 2,25 C. We may thus express the same thing in words : In order to change Reaumur's scale to that of Celsius, we multiply the number of the Reaumur scale by 1,25, or by fths. If, on the other hand, we want to change Celsius' degrees into the Reaumur scale, we multiply the given number of the degrees by 0,8, or, what is the same, by |ths. In England Fahrenheit's scale is exclusively made use of, the of which does not correspond with those of the two above-men- tioned scales. The null point, or of Fahrenheit's thermometer, agrees with the graduated line 17|ths of Celsius. Its melting point for ice is 32, and the boiling point of water at 212 ; so that the interval between the two is divided into 180 degrees. According, therefore, to their absolute value, 180 F. = 100 C. ; consequently 1 F. = fths C., and 1 C. = f ths F. It is necessary, however, before we attempt to reduce the de- grees of one of these thermometers to the scales of the others, to take in-to account that their zero points do not coincide. On changing Fahrenheit's scale into that of the Celsian thermometer, we must subtract 32 from the given fundamental number, and multiply the remainder by f : thus we have x F. = (x 32) C. On changing the Celsius or centigrade scale into that of Fahrenheit, we multiply it by f , and add 32 to the product ; con- sequently y C. = (y . | + 32) F. In order to facilitate a comparison of the different scales, we give the following table. EXPANSION OF SOLID BODIES. 489 Celsius. Reaumur. Fahrenheit. 20 16 4 10 8 + 14 32 + 10 + 8 50 20 16 68 30 24 86 40 32 104 50 40 122 60 48 140 70 56 158 80 64 176 90 72 194 100 80 212 Expansion of Solid Bodies. As the expansion of solid bodies by heat is inconsiderable, means must be devised for making it more apparent to the eye. This is most simply effected in the following way. A rod b V (Fig. 472) made of the body to be examined, is sup- ported at one ex- Fig. 472. tremity against a firm ^<^^ & obstacle //', whilst its other extremity rests against the shorter arm of an angular lever, I c I', that can rotate round the fixed point c. If, now, the end / of the shorter arm be pushed onward by the ex- pansion of the rod b b' y the other end V will traverse a much wider space; and we may in this manner make even the slightest pro- longation of the rod b b f perceptible, provided the length c I' be very large in proportion to c I. By aid of apparatus, the construction of which essentially rests upon the above-mentioned principles, the expansion of many bo- dies has been ascertained. The following list will give a few of the most important of these. For an elevation of temperature from 32 to 212 F., we have these expansions: 490 EXPANSION OF SOLID BODIES. Platinum . . . about 0,00086 or TT V T Glass on the average . " 0,00087 " jrW Steel (hard) . . . " 0,00124 " T Iron 0,00122 " T }r Copper 0,00171 7 1 T Tin . ..." 0,00217 " T fr Lead " 0,00285 3 | T Zinc . . . . < 0,00294 " *J T A steel rod, therefore, which, at 32 F., has a length of 807 lines, will have a length of 808 lines at 212 F. ; a zinc rod of only 340 lines in length will expand 1 line at an increase of tem- perature from 32 to 212 F. Amongst all the above given bodies, platinum expands the least, and zinc the most. Almost all solid bodies expand equally between 32 and 212 F., that is, their expansion is proportional to the elevation of tem- perature. At an increase of temperature from 32 to 50 F., copper expands 0,000171 ; at an elevation of temperature from 32 to 34 F., it expands 0,0000171 of its length at 32. The number expressing the extent of length from 32, which a body expands at an elevation of temperature from 32 to 212, is termed the coefficient of the expansion of length. The above table gives the coefficients for platinum, glass, steel, &c. Cubic expansion is the increase in the volume of a body pro- duced by an elevation of temperature. Here, too, the volume of the body at 32 is taken as the starting point, and, by the coeffi- cience of expansion, we here understand the number giving the quantity which expresses by how much of its original volume at 32 a body, on heating it to 212, expands. If we say, that the coefficient of the expansion of mercury is 0,018, it means that mercury expands at an elevation of temperature of 212 about 1 8 of its volume at 32. If we know the coefficients of ex- pansion, and the volume of a body at 32, we may reckon its volume at any degree of temperature, provided that the expansion of the body be regular up to this degree of temperature. In liquid and gaseous bodies, the expansion can be determined directly by experiments, whilst, in solid bodies, it must be esti- mated from the linear expansion observed. THE CO-EFFICIENT OF EXPANSION OF SOLID BODIES. 491 The coefficient of expansion of solid bodies is three times as great as the coefficient for the linear expansion of the bodies. We may convince ourselves of this by the following reasoning. Let / be the side of a cube at 32, then Z 3 is its volume, which we will designate by v\ if the cube be heated to the 212, each side becomes I (I -f r); consequently the contents of the cube are: v' = I 3 (1 + r) 3 = I 3 (1 + 3 r + 3 r 2 + r 3 ). But as r is a very small quantity, we may disregard its higher powers, when the value of v f will, consequently, be reduced to v' = I 3 (1 + 3 r) = v (1 + 3 r). The volume v is, consequently, increased about 3 r v ; and the coefficient of expansion for the volume is, consequently, 3 r. We will endeavor to make this more apparent by a geometrical figure. Let a b c be a cube formed of a solid body at 32 (Fig. 473). If this cube were only expanded upwards, at an elevation of tem- perature of 212, its volume would increase as much as the quadratic plate a d c b, whose solid contents are v r, if v be the volume of the original die, and r the linear coefficient of expan- sion. If the cube only expanded towards the left side, it would be increased by an equally large plate c g bfj and, finally, a third plate bihc, whose contents are likewise r v, would be the result of the expansion of the body anteriorly. The cubic contents of these three plates together are 3 r v. To complete the estimation of the in- crease by heat of the cube, we ought to add the contents of the corners, which are filled up at the places where every two of the above-mentioned plates meet together at the edges; but the amount of this is so inconsiderable, that it may be dis- regarded, since the size of the linear expansion d a is very small in comparison with the lengths of the sides of the original cube, and we may thus, without serious error, assume 3 r v to be the whole increase of the volume. The coefficient for the expansion of length in glass, for instance, is 0,00087, at an elevation of temperature from 32 to 212; con- sequently a mass of glass will expand about 0,00251 of its volume ; the same is the case with the contents of a glass vessel. If a glass 492 EXPANSION OF FLUIDS. vessel, at a temperature of 32, contains exactly 1000 cubic cen- timetres, its contents will at 212 have increased to 1002,51 cubic centimetres. Expansion of Fluids. The apparatus in Fig. 474 may be used to determine the expansion of various fluid bodies. The neck of a glass vessel of corresponding size is so much contracted at one spot, that the part above may be, in some degree, considered as a funnel. The narrowest part of the neck a is marked in some way. The globe is now filled with the fluid to be examined, so that it reaches above a, within the funnel, and the whole is cooled down to 32, while the appa- ratus is entirely surrounded with melting snow, or ice. When the fluid is cooled to 32, all the fluid standing above the mark must be removed. If we weigh the filled globe, abstracting from the weight found, that of the glass vessel, we shall obtain the weight of the fluid, rising in the globe, at 32. As soon as the globe is warmed, the fluid will expand, ascending above the mark a on the funnel. When we have warmed it to a certain degree of temperature, as 212, we must remove all the fluid standing above a, and weigh it a second time. After this, it will be easy to cal- culate the apparent expansion. The expansion thus determined is, as we have already remarked, only the apparent one ; the true expansion of fluids being only found on adding the increase, by heat, of the contents of the glass vessel to the apparent expansion. At an elevation of temperature from 32 to 212, the expansion of the volume at 32, is as follows: Mercury . . . about 0,018 Water ... " 0,045 Spirits of wine . . " 0,100 Oil .... " 0,100 nearly. [Mr. Dalton has given somewhat different estimates as the results of his experiments on these bodies. Mercury .... 0,0200 Water .... 0,0466 Alcohol . . . . 0,1100 Fixed oils . . . 0,0800 Oil of turpentine . . 0,0700 ] EXPANSION OF GASES. 493 As we see, the expansion by heat is very considerable in the case of spirits of wine and oil, a circumstance that ought to be attended to in commerce. Most fluids do not expand regularly between 32 and 212. This is best seen by constructing thermometers of different fluids, and comparing them with one of mercury. If, for instance, we heat a water thermometer, which has long been exposed to a tem- perature of 32, it will not immediately rise, but will first sink, and only begin to rise when the temperature has been raised to 42. If we take into account the expansion of the glass, it will be found that water has a maximum density at about 40, that is, at 40 water is denser than at any other temperature. Water of 40 will expand whether we heat or cool it. Spirits of wine do not expand regularly, on which account, a spirit thermometer does not, at all temperatures, correspond with one of mercury. Expansion of Gases. Gases expand by heat far more than solid and fluid bodies, and their coefficients of expansion are the same for all temperatures ; further, gases always expand in pro- portion to the elevation of temperature. At an elevation from 32 to 212, the expansion of gases amounts to 0,365 of their volume at 32. Different methods have been used to ascertain the coefficients of expansion for gases, amongst which, however, the following is the most simple. A glass bulb is blown at the one end of a thin glass tube, as seen in Fig. 475, while the other end is drawn to a fine point. On immersing the bulb in boiling F . 4?5 water, in such a manner, of course, that the point shall project tolerably far beyond the fluid, the air within it will soon be heated to 212, and, in consequence of this, will partially escape from the ball. The point must now be closed over a spirit lamp, and the bulb suffered to cool gradually; when it has become quite cold, we must then invert it, put the point into the mer- cury, and break it off; the mercury will now naturally force its way into the ball, because the air within has been rarefied by the previous heating. 42 494 CHANGE OF THE STATE OF AGGREGATION. If we cool the ball to 32, by means of melted snow laid upon it, the mercury, forcing its way in, will exactly fill the space in which the air, remaining in the bulb, has expanded at an eleva- tion of temperature from 32 to 212. If we determine, by weight, the quantity of mercury that has entered, we shall obtain the weight of the amount of mercury which the whole bulb is capable of containing ; and thus, consequently, we may calculate the coefficients of expansion of air. CHAPTER II. CHANGE OF THE STATE OF AGGREGATION. Fusion. We may easily see that fusion, that is, the transition of a body from the solid to the fluid condition, must be a pheno- menon of heat, and that no other power in nature, but this, is capable of producing a similar effect. We may break ice and reduce it to powder, and we may expend every mechanical power upon it; but yet it will not be converted into water until acted upon by heat. The same is the case with lead, wax, &c. Whether a body be solid or fluid, depends, therefore, entirely and solely on its temperature. At any other distance from the sun, than the one occupied by it, the earth would present a very dif- ferent aspect ; at a greater approximation to that luminary, most metals would be in a constant state of fusion, while, at a greater distance from it, the sea would be a solid mass; there would be no running water, and, probably, no fluid, on the circulation of which the phenomena of animal and vegetable life depend. As heat penetrates and expands all bodies, the question natu- rally arises, whether all solid bodies are fusible ? In this respect great differences present themselves amongst bodies ; some are easily fusible, and pass into a fluid condition at even a low tem- perature, as, for instance, ice, phosphorus, sulphur, wax, fat, &c.j others, again, require high temperatures to reduce them to fusion, as tin, lead, &c. ; finally, there are bodies which only melt at very FUSION. 495 high temperatures, as gold, iron, platinum. No success has, as yet, attended the attempts made to fuse charcoal, although many natural philosophers maintain that they have observed traces of fusion at the edges of the diamonds submitted to experiment. Judging from analogy, we must conclude that there are no abso- lutely infusible bodies, and that all would melt if exposed to a sufficiently high degree of temperature. Organic bodies undergo, for the most part, a chemical decom- position by the action of heat before they are reduced to a state of fusion. On a body passing from the solid to the fluid condition, we ob- serve two remarkable phenomena. In the first place , it remains solid up to a certain fixed temperature, which is always the same for the same body, and at which alone fusion begins ; and secondly ', the temperature does not change during fusion, let the amount 01 heat imparted be what it may. Heat is, therefore, absorbed during fusion, and incorporates with the body without producing any further action on the feelings or on the thermometer. The invariability of the fusion point and the absorption of latent heat are two essential conditions of fusion. The following table gives the point of fusion for different sub- stances. Wrought English iron 1600 degrees C. 2912 degrees F. Soft French iron 1500 " 2732 i The least fusible steel 1400 " 2552 [The most easily fusible steel 1300 " 2372 !:Gray cast-iron, second smelt- ing 1200 " 2192 Easily fusible gray cast-iron 1050 " 1922 " Hold 1250 " 2302 " Silver 1000 " 1832 iironze 900 " 1652 untimony 432 " 809 " :inc 360 " 680 ture we please between 32 and 212. The temperature of this water, which may be deter- mined by properly applied thermometers, is, at the same time, that of the two barometers, and of the steam in the one. In order to obtain the degree of elasticity of the steam corresponding to each degree of temperature, we have only to determine in what relations the depression of the steam barometer stands to the height of the column of mercury in the perfect barometer. The following method may be adopted for measuring the force of tension of steam above 212. A wider vessel is fixed into a tolerably long glass tube, Fig. 480, somewhat in the same manner as the cistern of a barometer; the longer and shorter tubes are both open 504 ESTIMATE OF THE FORCE OF TENSION. at the top. On pouring in mercury, it will, of course, rise equally high in both tubes. The fluid to be tested is then poured upon the mercury in the wider tube, and after being kept up to the boiling point for some time after all the air has been expelled, the tube is sealed. If we put the vessel into a fluid, the temperature of which is above the boiling point of the enclosed fluid, vapor will be formed, which presses upon the mercury (in the vessel), causing it to rise in the long tube. The difference of the mercury level in the vessel and the tube, indicates how much the power of ten- sion of the vapor exceeds the amount of the pressure of the atmo- sphere. The apparatus is fastened to a graduated stem, both for the purpose of being able to measure the height to which the column of mercury is raised, and also to protect the tube from being struck or broken. If the tube be long enough, we may, by means of this apparatus, measure the tension of steam at 3 or 4 atmo- spheres. In order to be able to measure higher tensions, we need only fuse together the ascending tube, so that a definite quantity of air may be enclosed in it. When the steam in the vessel drives the mercury into the tube, the enclosed air becom^l compressed, and we may easily compute the force of tension of the steam by the difference in the height of the two surfaces of mercury. The following tables contain the maximum of the force of ten- sion of steam for different temperatures : Degrees. Force of tension of steam in millimetres, 0.039 inch. Pressure upon 1 square centimetre, 0.393 inch sq., in kilogrammes, 1 5,444 grs. 32 F. 5 0,007 10 50 " 9 0,013 20 68 " 17 0,023 30 86 " 30 0,042 40 104 " 53 0,072 50 122 " 89 0,126 60 140 " 145 0,196 70 158 " 229 0,311 80 176 " 352 0,478 90 194 " 525 0,714 100 212 " 760 1,033 OF THE VAPOR OF WATER. 505 Force of tension in atmospheres. Corresponding tempe- ratures. Pressure upon 1 square centimetre, '393 inch sq., expressed in kilogrammes, 15,444 grs. 1 100 212 F. 1,03 2 121 249 2,07 4 145 293 4,83 6 160 320 " 6,20 8 172 341 8,26 10 182 359 " 10,33 15 200 392 15,49 20 215 419 " 20,66 25 226 438 " 25,82 30 236 456 " 30,99 We see from these tables, that at the temperature of the boiling point, the force of tension of steam equipoises the pressure of the atmosphere. This is universally true : the force of tension of the vapor formed from any boiling liquid is always equal to the pres- sure on the surface of the liquid ; for if it were less, the vapor could not remain in the interior of the liquid in the form of bub- bles, and if it were more considerable the vapor must have been previously formed. The vapors of all liquids have an equal force of tension at the boiling point. Dalton was of opinion that the force of tension must be equal at an equal number of degrees above or below the boiling point; it would only be necessary, therefore, according to this law, to have a table for the force of tension of saturated steam, and to know the boiling point of a liquid, in order to ascertain the force of tension of the vapor at any temperature. The boiling point of alcohol, for instance, is 172 F., the force of tension of the vapor of alcohol at 235, that is, 63 above the boiling point, must be equal to the force of ten- sion of steam at 275, which is 2280 mm (89.76 in.) or 3 atmo- spheres. According to this law, the force of tension of the saturated vapor of alcohol at 32 would be equal to 19 mra (-748 in.), because this is the force of tension of steam at a temperature 172 F. below the boiling point of water. From the experiments of many natural philosophers it is evident, however, that this law is not correct. The force of tension of vapor increases, as we see, in a far more rapid ratio than the temperature; that is to say, a definite eleva- 43 506 OF THE VAPOR OF WATER. tion of temperature produces a far greater increase of the force of tension at high than at low degrees of temperature. Thus, while an elevation of temperature from 212 to 249 (that is, about 37) increases the force of tension of steam about 1 atmosphere; it will increase at an elevation from 438 to 456 (that is, at only 18 more) about 5 atmospheres, consequently between 438 and 456, an elevation of temperature of only 3f would suffice to raise the force of tension of steam to about 1 atmosphere. There are two reasons for the increase of the force of tension at an increasing temperature. Let us suppose some enclosed space to be filled by steam at 212, that is, with a vapor whose force of tension equals 1 atmosphere, and that there is no more water in this space, it being entirely precluded from ingress. If, now, the temperature of this space be raised to 249, the vapor will strive to expand, and since it will not be able to do so, its force of ten- sion will increase, although not much ; the vapor will then be no longer saturated, but quite in the condition of a gas. If, how- ever, there still remain any water in this space, then, in conse- quence of the increase of temperature, a new quantity of vapor will be formed of 1 atmosphere; if, then, the force of tension increases by 1 atmosphere, the vapor will become denser, when, in consequence of its greater density, it will exercise a greater pressure. 1 cubic inch of water yields: 1700 cubic inches of saturated steam at 212 897 " " " 249 207 " " " 359 There are liquids whose boiling points lie below the average temperature of the air, and such bodies can of course not become liquid under ordinary circumstances, being at the usual tempe- rature, and the usual pressure of the atmosphere, in a gaseous form, such gases must, therefore, be compressed and cooled, in order to become liquid. Thus, for instance, we find sulphurous acid at 14, and when rendered liquid under pressure in a glass tube, its vapors exert a pressure of about 5 atmospheres, even at 77. Cyanogen gas, ammonia, carbonic acid, &c., also admit of being condensed into liquids by compression and cooling. The vapor of liquid carbonic acid has at 32 a force of tension of 36, and at 86 a force of tension equal to 73 atmospheres. THE STEAM ENGINE. 507 The Steam Engine. Steam has, in more recent times, as we all know, been used as a moving force, and it is owing to the introduction of the steam engine that industry and general inter- course among men have made such rapid advances. Passing by the older forms of this machine, we will at once enter upon the consideration of Watts' steam engine. The cylinder JJ is made air-tight below as well as above, so that the atmospheric air cannot pass on either side upon the piston C. The steam which is conducted from the boiler through the tube Z of the engine, enters the cylinder alternately at E and D. We shall presently enter fully into the manner in which this alternation is produced. In the position of the engine, as seen in our figure, the steam enters above at E. The steam in the lower part of the cylinder escapes at D, in order to reach the condenser T through the pipe H, and is there condensed ; the steam presses above upon the piston C, while below it there is a rarefied space ; the piston, therefore, is in the act of descending. Fig. 481. 508 THE STEAM ENGINE. The condensation of the steam in the cylinder on the one side of the piston takes place by the latter being brought into con- nection with the above-mentioned condenser; this is the space marked /, being connected either with the lower or the upper part of the cylinder. Cold water is constantly poured into the condenser, and a condensation of the steam thus effected ; but by this means, in accordance with the principles illustrated by Fig. 472 (page 502), the force of tension of the steam is diminished in that part of the cylinder which is connected with the condenser; the steam then passes from the cylinder into the condenser, to be there condensed. Many contrivances have been proposed for making the steam enter the cylinder alternately from above and below, whilst the steam escapes from the other side of the piston towards the con- denser. The simplest of these arrangements is the cross-cock. This is perforated, as seen in Fig. 482. The tube .K" leads to the boiler, C to the condenser, to the upper, and U to the lower part of the cylinder. If the cross-cock be placed in the position Fig. 482. Fig. 483. aS S6en In Fi S' 482 > the Steam will flow from the boiler into the upper part of the cylinder, whilst its under part is connected by the tubes U and C, with the con- denser. When the piston has penetrated far into the cylinder, the cross-cock is brought, by a half revolution, into the position seen in Fig. 483. Now the tubes K and U are connected, the steam, therefore, enters, escaping from the upper part of the cylinder through the tubes and C towards the condenser; now, therefore, there must be an upward directed motion of the piston. The cross-cock has not proved to be applicable to larger en- gines, owing to the impossibility of making the channels of the cock wide enough to admit of the passage of the requisite quantity of steam. The sliding valve is now most generally made use of, it is applied to the engine we have delineated, and is represented in Figs. 484 and 485, in its two extreme positions, being drawn on a large scale. The steam passes through the tube Z to a re- ceiver, from which the tubes D and E lead to the cylinder. This receiver is divided into two separate spaces by means of the slide THE STEAM ENGINE. 509 Fig. 484. Fig. 485. F. The middle portion m of the receiver is quite shut off from the upper part a', and the lower part a, whilst these two spaces are themselves connected by the cavity of the slide. The steam now flows from the boiler into the space m, the spaces a and a re- maining connected with the con- denser. If the sliding valve have the position of Fig. 484, the steam will flow from m through the com- munication E from above, into the cylinder ; while the steam passes under the piston, through that of D to a, and from thence to the condenser. If, however, the slid- ing valve lie in the position repre- sented in Fig. 485, the steam will flow from m through D from be- low into the cylinder, the steam above the piston will pass through E towards a f , and from thence through the sliding valve to a, and finally reach the condenser. The sliding valve has been re- presented in Fig. 486, as seen in .the direction of Z, in order that we may form to ourselves a per- fectly correct idea of its construc- tion. The manner in which the slide is drawn up and down the machine, will presently be further considered. The condenser T, Fig. 481, stands in a receiver partly filled with cold water, constantly flow- ing into the condenser from an opening not visible in our figure. The quantity of the water enter- ing may be increased or dimin- ished at will, by means of a cock. 43* Fig. 486. 510 THE STEAM ENGINE. The water is pumped out of the condenser by the pump K. As is well known, more or less air is always absorbed in all water ; this is liberated in the boiler, and passes, together with the steam, through the engine into the condenser. In the same manner, air will be disengaged from the cold water flowing into the condenser. The steam will become condensed, while the air will remain in a gaseous condition. This air would, by degrees, accumulate in the condenser, and thus prevent the creation of a vacuum on the one side of the piston, if it were not at the same time carried off by the pump K, which has, on that account, received the name of an air-pump. By means of this pump, the water is carried from the condenser into the receiver jR, from which it is almost entirely discharged by the tube S. The heat which was latent by the evaporation of the water in the boiler, is again liberated by the condensation of the steam in the condenser; this liberated heat raises the tempera- ture of the cold water thrown into the condenser; the water carried through the pump K towards R is therefore warm, on which ac- count it is more advantageous than cold water for feeding the boiler. The water required for the boiler passes through the tube Mto a pump, which carries it through the tube M f . This pump, as well as the air-pump, is put into motion by the engine itself; for in- stance, the pump rod L is attached to the beam, and is raised as the piston C descends, and is pressed down as the latter ascends. When the piston of the warm water pump, attached to the rod L, rises, the suction valve v opens, and, at the descent of the piston, the valve n. On the other side of the beam, exactly behind L, there is another pump rod, through which cold water is raised into the tube T f , and brought through U into the receiver containing the condenser. Let us now consider how the upward and downward motion of the piston C is transmitted. The piston rod moves, air and steam tight, through the stuffing- box in the middle of the upper cover of the cylinders ; being con- nected with the end of the beam by a system of movable rods, bearing the name of the parallelogram. The object of this con- trivance is merely to establish a perfectly vertical motion of the piston rod, which could not be effected if the rod, or handle, were fastened directly to the end of the balancer; since it would, in THE STEAM ENGINE. 51 1 that case, deviate alternately to the left and right, and, conse- quently, so much affect the stuffing-box, that the air-tightness would soon be destroyed. The one end of the working beam is alternately drawn up and down by the piston, while its other extremity has constantly an opposite motion: that is to say, when the piston Crises, the right arm of the beam goes down, and vice versa. The upward and downward motion of the beam is constantly changed into a cir- cular motion by the connecting rod P, and the crooked handle Q. The axis of this handle is the main axis of the machine which is to be set in motion, and around this axis moves the fly- wheel X. The motion of the piston Cis very irregular. As it comes to a state of rest at the upper and lower end of the cylinder, and then reverses its motion, it is evident that it cannot perform its course with uniform velocity. Its velocity is greatest when it passes the middle of the cylinder, and diminishes the more it approaches either end. On considering the motion of the handle, we shall find that, with uniform velocity of revolution, the motion in a ver- tical direction is still very changeable. The handle stands in a horizontal position when the piston C is in the middle of the cylinder, at which moment the motion of the handle is in a ver- tical direction ; this motion inclines, however, horizontally when the piston C attains its highest or lowest position. The vertical portion of the motion of the handle is perfectly similar to the motion of the piston ; in proportion as the motion of the handle becomes more horizontal, the velocity of the piston diminishes, without any diminution in the velocity of the revolving action of the handle. The diameter of the path traversed by the handle Q, is of course equal to the height of the cylinder, allowing for the thick- ness of the piston, provided that both arms of the beam are of equal length ; the length of the arm of the handle Q is, therefore, equal to half the length to which the piston can be raised. The fly-wheel X serves to maintain uniformity in the motion of the engine. Even if the pressure of the steam upon the piston were quite invariable, it could not equally contribute to the revo- lution of the handle in all its positions. Indeed, we may consider the pressure acting by means of the connecting rod P upon the handle, as divided into forces at right angles to each other, the 512 THE STEAM ENGINE. one acting in the direction of the handle itself, as pressure upon the axis does not contribute to produce revolution ; this is brought about entirely by the force acting tangentially to the curve of the handle. The amount of these forces varies at every moment. When the arm of the handle stands vertically, every pressure pro- ceeding from the piston acts solely and alone as pressure upon the axis of the curved handle. If the engine were to be brought to a stand-still in this position, the greatest pressure applied to the piston would be unable to set it in motion; the only reason, there- fore, that the engine does not remain absolutely motionless on coming into this position is, that the individual parts of the engine continue their motion by virtue of the inertia, in the same manner as a pendulum moves on by virtue of its inertia when arrived at its position of rest. When once the curved handle has passed its vertical position, that portion of the pressure transmitted by P, and which occasioned the revolution of the handle, is increased more and more, and attains its maximum when the arm of the handle is directed horizontally. The force, therefore, which turns the handle, varies constantly, becoming null twice during one complete revolution, both when the arm of the handle attains its highest and its lowest position ; and, in like manner, it twice attains a maximum. If we examine the motion produced by so variable a force, we shall easily see that it can only be alternately accelerated and retarded. If the circle represented in Fig. 487 exhibit the path described by the handle, we shall perceive that an acceleration of motion will take place from b to d, because here the moving force will act with the greatest energy. The motion accumulated, as it were, in the parts of the machine must, how- ever, diminish as the arm of the handle moves from d to /*, because the moving force has, in the mean time, become very weak, and even abso- lutely null, and thus a retardation is caused of motion by these hinderances ; on the way from f to h it is again accelerated, and again retarded from h to b. These alternations in the motion of the curved handle lie in the nature of things, and cannot be wholly avoided. The differences between the greatest and the least velocity become, however, smaller in proportion to the magnitude of the inert mass to be moved ; by means of a sufficiently large balance wheel, we may THE STEAM ENGINE. 513 render these differences in the velocity of revolution so inconside- rably small, as to exercise no further injurious influence. The force acting on the part from 6 to d, and more strongly from/ to h, cannot effect any marked increase of velocity, as it must move a very considerable inert mass; as, however, a considerable quantity of motion is accumulated in the balance wheel, the de- crease in the quantity of motion, as the handle passes from d to/, or from b to h, is not sufficiently great to occasion a perceptible diminution of velocity. The balance wheel thus equalizes the irregularity of motion inherent in the arrangement of the engine. The work which a steam engine may have to perform, be it of what kind it may, never opposes an absolutely uniform resistance to the moving force ; and this would occasion irregularity in the working of the whole engine, were it not otherwise rendered uniform by the balance-wheel. As the work to be performed by the engine, that is, the resistance to be overcome, increases or diminishes, the going of the engine will become quicker or slower. Momentary disturbances of this kind will be equalized by the balance wheel, while a universal diminution of the resistance and the load would be followed, pro- vided the afflux of steam remained the same, by a continually in- creasing acceleration in the motion of the engine. In order that the velocity may not exceed certain limits, a valve must be attached to the steam pipe, in order that the ingress of steam may be more or less retarded, according as the valve passes more and more from the horizontal position (that of perfect aperture), to the vertical (that of perfect closure). The turning of this valve must, however, be effected by the engine itself, and this is done by means of an apparatus termed the regulator. A somewhat tense string i passes round the rotating axis of the balance wheel over a vertical wheel o, Fig. 488, in such a man- ner that the wheel o is made to rotate by the revolution of the principal axis. A vertical conical wheel is fastened to the axis of the disc o, whose teeth work into a similar wheel placed horizon- tally, and which is thus made to rotate on its vertical axis. This axis is prolonged into a rod, to the upper end of which the coni- cal pendulum Fis attached. The pendulum V consists of two heavy balls so fastened to the upper end of the vertical rod that by its rapid rotation, the balls 514 THE STEAM ENGINE. Fig. 488. fly apart, owing to their centrifugal force. The rods to which the balls are attached, are connected by means of a nut h surrounding the vertical rod. The nut h is raised up as soon as the balls fly apart; and by this motion of h the angular lever r s a is turned round Jhe axis s, the rod a b drawn towards the right side, by which the angular lever b c d is turned round the axis c, and the rod e d thus finally drawn down ; but as e is the extreme point of a lever arm, the rotating axis of which is the axis round which the valve moves in the tube Z, the valve is closed by this point e being drawn down. The whole lever system of which we have been speaking here is only represented in outline in our Figure, it being placed on the front side of the engine, and, therefore, really not visible from the point of view in our sectional delinea- tion of the engine. The working of the cross-cock, or the raising and lowering of the sliding valve, in short, the motion of the apparatus which THE STEAM ENGINE. 515 serves to conduct the steam alternately to the upper and lower part of the cylinder must be effected by the engine itself. The instrument by which this motion is produced, is designated the governor. The most important external portion of the governor, is the eccentric disc, indicated in our Fig. 488 by the letter y. This is a circular metallic plate fastened to the axis of the fly-wheel, whose central point does not, however, correspond with the central point of revolution, as may be more plainly seen in Fig. 489. During Fig. 489. every revolution of the axis the central point of the eccentric disc describes a circle. A ring passes around the circumference of the eccentric disc, prolonged towards the one side into a rod, whose end fits at Tinto a lever arm revolving round a fixed axis F. The distance of the centre of the eccentric disc from T varies, as the lever arm F T passes, and returns to the position seen in Fig. 490, during each entire revolution of the main axis ; the Fig. 490. chord of the one described in this manner by the point T is, how- ever, evidently equal to the diameter of the circle described by the central point of the eccentric disc. The axis of jP passes through the whole width of the machine, 516 THE STEAM ENGINE. Fig. 491. as may be plainly seen in Fig. 491, where this axis is represented at its full length. To this axis are attached two perfectly equal and parallel lever arms N 9 on either side of the receiver, in which the sliding valve is enclosed. Fig. 489 exhi- bits only one of these in its true form, while both are seen fore- shortened in Fig. 491. To each of these lever arms a vertical bar M, directed upwards, is secured, being connected at the top by a horizontal transverse bar Q, supporting in its centre the bar R, to which the slid- ing valve is attached. This rod passes, air and steam-tight, through a stuffing-box into the receiver of the sliding valve. The motion of the lever JV* produces, by means of the rods M, an alternate raising and lowering of the transverse rod Q, by which the sliding valve is also raised up and down. Let us now consider the influence exercised by the removal of the condenser. If the steam act on the one side of the piston with a force of tension of one atmosphere, while the part of the cylinder lying on the other side is in connection with the air, and not with the condenser, the pressure of the steam on the one side of the piston will be equal to the pressure of the atmospheric air on the other side, and, consequently, there can be no motion. In order to produce this, it is necessary to raise the force of tension of the steam. Provided this have been made equal to the pres- sure of two atmospheres, the effect will be precisely the same as if there were a vacuum on the one side of the piston, while the steam pressed upon the other side with the force of tension of one atmosphere ; the half of the effective power of the steam being thus lost in overcoming the resistance of the air. If the moving steam had actually a force of tension equal to 3, 4, 5, &c., atmo- spheres, ^, J, or i, &c. of this power would be lost in overcoming the resistance of the air if there were no condenser. The greater, THE STEAM ENGINE. 517 therefore, the force of tension of the steam acting in the engine, the less will be the loss of power in overcoming atmospheric resistance where there is no condenser. If, therefore, the steam that is to move the engine, has only a force of tension equal to one atmosphere, or but a little more, a condenser will be indis- pensably necessary; if, however, the force of tension of the effect- ive steam be greater, the engine may act without a condenser, the advantage of which will diminish in proportion to the increase in the force of tension of the moving steam. The resistance which has to be overcome in the moving of the condensing pump (air-pump), exhausts, however, also a portion of the power of the steam. Thus, at a certain amount of steam pressure, the advan- tages afforded by the condenser are again counteracted by the resistance of the air-pump ; and, consequently, in this case it is quite immaterial whether or not we use a condenser. In engines, worked by steam, of still stronger force of tension, the condenser is more disadvantageous than the contrary, and in such apparatus it is, therefore, wholly omitted. Such steam engines as are worked with a condenser are called low pressure engines, while those that have no condensers are termed high pressure engines. High pressure engines are more simple in their construction than those of low pressure, owing to the absence of a condenser and air-pump, and the former may be used of much smaller dimensions than the latter, and yet produce the same result; for the combined pressure of steam having a force of tension equal to 4 atmospheres acting upon a surface of 1 square foot, is as great as the combined pressure of steam with a force of tension equal to atmosphere acting upon a surface of 4 square feet. From these causes, high pressure engines are used wherever it is desirable to use an engine of considerable force in a small compass. [As the steam engine, invented by Oliver Evans, of Philadel- phia, in 1784, and patented by the State of Maryland in 1787, may be considered as the origin of all the high pressure engines now in use, however modified, the following description and repre- sentation of it, Fig. 492, as given by Prof. Johnson, (Scientific Class Book, 319,) are worthy of attention. A. Working cylinder, to which the steam, equal to several at- mospheres in pressure, is admitted by the pipe o, and the rotary valve v. 44 518 THE STEAM ENGINE. S. Smoke pipe arising from the inferior flue, after the latter leaves the head of the boiler. G. Fire grate, or furnace, from which the flame passes in the direction marked by the arrow. P. Force pump, which draws the water from the reservoir of hot water R, situated above it. This water is kept hot by the steam escaping from the cylinder A, after it has fulfilled its duty there. THE LOCOMOTIVE. 519 520 THE LOCOMOTIVE. p. Pump rod connected with the beam above. V. Safety valve connected with the boiler, and furnished with a graduated lever and weight, to regulate the pressure. /. Working beam connected to an upright support by rods k k, to oscillating triangle T", to pump rod p, piston rod /, and to shackle bar 6, which last gives motion to fly-wheel W. g is a toothed wheel, geared to another of the same diameter, which, being connected with the two equal bevel wheels at e, communicate motion to the rotary valve v. s is the escape pipe, by which the steam is conducted to the tank or reservoir jR.] One of the best known and most interesting high pressure en- gines is the Locomotive used on railroads. See Fig. 493. A is the furnace : the fuel is thrown upon the grate through the opening a, which may be closed by a door. There is no escape for the heated air from the furnace, excepting through a series of horizontal tubes, leading from Jl to D ; from D the heated air passes with the smoke out at the chimney. In Fig. 494 we see how these tubes lie above and beside each other. These tubes are carried through a space filled with water, besides which the fur- nace itself is enclosed on all sides by water. From the extraor- dinarily large surface with which the water is in this manner brought into contact, a considerable quantity of steam is formed at every moment. The steam is collected over the water in the space marked B and C ; and from C it is carried through the tube c to the cylinder. If the mouth of the tube c were situated very low down, a large quantity of water would, by the violent boiling, be mechanically carried into the tube c, and from thence into the cylinder. To prevent this, the steam chamber at C is elevated. The tube c soon branches ofFinto two tubes d and d f , as may be plainly seen in Fig. 496. In Fig. 495 there is only one of these tubes visible, viz. d. Each leads to a receiver i, from which the steam enters the cylinder F. On either side lies a cylinder, as seen in Fig. 496 ; Fig. 495 exhibits only one, viz., the front one of these cylinders. It is represented lengthwise here ; the surface of the' section does not, however, correspond with the whole of the remaining figure, but lies in front of it. The cylinders lie hori- zontally, and the piston, together with the piston rods, passes backwards and forwards in a horizontal position. Two passages run to either end of the cylinder from the receiver i, to which the THE LOCOMOTIVE. 521 44' 522 THE LOCOMOTIVE. steam is conducted by the tubes c and d. On the lower side of the receiver i, a slide moves backwards and forwards, and forms at the middle a box o which opens downwards. The position indi- cated in Fig. 493 shows both passages closed by means of this slide. If we suppose this to be so far moved to the left, that the passage to the left, instead of being closed, opens into the cavity o, that to the right will be brought into connection with the steam reservoir i ; in this position of the slide the steam will enter on the right side into the cylinder F, and, consequently, drive the piston to the left, whilst the steam will pass from the left side of the piston, through the passage to the left, into the box o, and from thence to the chimney through the tubes p and q. If, however, the slide were pushed to the fullest extreme towards the right, the steam would flow from i through the passage to the left into the cylinder, escaping on the other side to the right through the passage into the box. The piston rod is secured by so-called connecting rods, that is, it is prevented by this means from deviating from its course, and is thus only able to pass to and fro in the same straight line. To the piston rod is immediately attached the driving rod, which turns the crank n round its axis m. The middle wheels of the engine are also fastened to the axis m, so that by each movement of the piston, a complete revolution of the wheel is effected; thus, at every forward and backward movement of the piston, the engine is propelled a distance equal to the circumference of the middle wheels. To this axis m is likewise attached the eccentric disc, by which the slide in the receiver i is moved. As may be seen in our Figure, the x shaped extremity of the rod, fastened to the ring of the eccentric disc, grasps the upper part of the lever, whose ful- crum is at s. By the motion of this lever, the bars t fastened to it are moved to and fro, and with them the slide. By the raising of the lever JV, the X shaped extremity of the bar is pressed down, and a retrograde motion thus imparted to the locomotive ; but here we must end our description, as we are unable to pursue it in detail, .ff and L are safety valves; / is the steam whistle. [The locomotive engines constructed in this country differ some- what from the foregoing in their details, and, therefore, the repre- sentation of Fig. 497, one of Baldwin's excellent locomotives, has THE LOCOMOTIVE. 523 524 THE LOCOMOTIVE. been given for the purposes of comparison ; and it will be per- ceived that it is far more powerful and efficient than those figured and described by the author.] The effect which a steam engine is capable of producing, that is, the power of the machine, depends upon the quantity of water which in a given time can be converted into steam in the boiler; let us, therefore, examine into the action which a litre of water can produce when converted into steam. If we assume that the surface of the piston is 1 square decimetre (3.93 inches sq.), and the height of the cylinder (the height to which the piston can be raised) is 10 decimetres (1 yd. 3 inches), the contents of the cylinder will be 10 cubic decimetres, or 10 litres (610.28 cubic inches); in order, therefore, to drive the piston to the top, 10 litres of steam must pass from the boiler into the cylinder. If, now, the steam has a force of tension equal to 1 atmosphere, the pres- sure exercised upon every square centimetre (.393 inch sq.) of the surface of the piston is about 1 kilogramme (2J Ibs. tr.), and the combined pressure upon the whole piston, consequently, 100 kilogrammes (250 Ibs. tr.) ; if, therefore, there existed no impedi- ments to motion, we might load the piston with 100 kilogrammes (250 Ibs. tr.), and this weight would be lifted 10 decimetres (1 yd. 3 in.), if we conducted 10 litres (21.13 pts.) of steam at 212 into the cylinder. The effect, therefore, that can be produced by 10 litres (21.13 pts.) of steam at 212, is capable of raising 100 kilogrammes (250 Ibs. tr.) to the height of 10 decimetres (39.37 in.), or of raising 1000 kilogrammes (2500 Ibs. tr.) to a height of 1 decimetre (3.93 in.). A litre (2.11 pts.) of water yields, how- ever, 1700 litres (3587 pts.) of steam at 212; with 1 litre of water, therefore, when converted into steam, we may produce an effect capable of raising 170,000 kilogrammes (425,000 Ibs. tr.) to the height of 1 decimetre (3.93 in.). In order the better to calculate the power of an engine, it is usual to compare them with horse power. If we assume that one horse is able to raise 750 kilogrammes (1875 Ibs. tr.)to the height of 1 decimetre (3.93 in.) in one second of time, (the best obser- vations on the labor of horses, and the profitable application of their powers, yield a result equivalent to the above named,) we should say, that an engine, in which sufficient steam was formed every second to raise 750 kilogrammes (1875 Ibs.) to the height THE LOCOMOTIVE. 525 of 1 decimetre (3.93 in.), (or 534 Ibs. to the height of 1 foot,) was a one-horse power engine. But the steam obtained from 1 litre of water will be capable of raising 170,000 kilogrammes (425,000 Ibs.) to the height of 1 decimetre (3.93 in.); if, therefore, 1 litre (2.11 pts.) of water be converted into steam in the boiler in 17Q ' 000 /425,000\ 750 \ 1875 /' sequently in 226 seconds, the total effect which the steam in this engine can produce, is equal to one-horse power. A machine of this kind consumes, therefore, about 15 litres (31.70 pts.) of water in an hour. All the mechanical power of steam cannot, however, be reckoned as available. Much is lost owing to the piston not acting in an absolute vacuum, to the friction of the piston to be overcome, and the number of pumps that must be set in motion, &c. All these resistances diminish the available effect of the machine to almost the half of the calculated power. Great advantage has been obtained in the high-pressure engines by the application of the expansion of the steam in the cylinder, which is effected by cutting off the afflux of steam from the boiler into the cylinder, when the piston has traversed J or f , &c., of its course. That a greater effect can be produced with an equal expenditure of steam by the application of the principle of expansion, may be perceived by the following simple conside- rations. If, during the whole time in which the piston is rising, steam pours into the steam cylinder, (as is generally the case in ordi- nary engines,) having a power of tension which we will assume to be equal to 2 atmospheres, the whole cylinder, when the piston is quite raised, will be filled with steam having a power of ten- sion equal to 2 atmospheres; and during the time the piston is being raised, there will be a mechanical effect produced, which we will designate as E. If now we suffer steam of double the force of tension, that is, equal to 4 atmospheres, to enter the cylinder, the pressure against the piston will be twice as great, and the mechanical effect E will be produced when the piston is only half raised ; that is, when it reaches the middle of the cylinder. If, at this moment, the further afflux of steam to the cylinder be prevented, the piston will continue the rest of its course, whilst the pressure acting upon 526 THE LOCOMOTIVE. it will diminish by degrees to the half; and when it reaches the end of its course, the force of tension of the steam will still be equal to 2 atmospheres. Since, during the first half of the ascent of the piston, the mechanical effect E is already produced, then the whole effect which the steam produces during the second half of the piston's ascent while so expanding, that its tension diminishes from 4 to 2 atmospheres, may be considered as gain ; for the quantity of steam filling the cylinder at the close of the piston's motion, is precisely as large as if steam, having a force of tension of 2 atmospheres, had flowed in while the piston was completing its motion. The steam is generally cut off by means of a special expansion- slide. In ordinary machines, the steam flows from the boiler directly into the chamber, in which the sliding valves move, to admit of the entrance of the steam, first to the one and then to the other side of the piston ; we will call this chamber a. In expansion engines, there is usually, in front of this, another chamber, b ; in the plate between b and a there is an opening, through which the steam passes from b to a; this opening can be closed at the proper times by a second slide at b. The motion of this expansion-slide is effected by a properly placed eccentric disc in the same manner as the motion of the sliding valves. The conversion of fluids into gaseous bodies is commonly termed evaporation. Liquids can either be evaporated by boiling, when vapors are formed throughout the whole mass, or by exhalation, when the formation of vapor is limited to the surface of the liquid. On observing the boiling of a liquid, we generally see a more or less energetic motion pervading all the particles; but, if the liquid be boiled in a glass vessel, we may observe bubbles of steam formed at the warmer sides of the vessel and rise to the top. Although at first small, they soon increase in volume as they rise. The bubbles succeed each other most rapidly at the hottest parts of the side. In order that bubbles may be formed in the liquid, which exercises a pressure upon them from all sides, the steam expanding them must have a force of tension equal to the pressure surrounding them. The first condition of boiling is, therefore, that the temperature be sufficiently high to THE LOCOMOTIVE. 527 enable the force of tension of the steam to sustain the pressure acting from all sides upon the bubbles of steam. A second con- dition is, that sufficient heat be present to be absorbed as latent heat during the formation of steam. From the. first condition, it follows that the boiling point of a liquid varies with the pressure on it ; and, from the second, that the rapidity of boiling depends on the amount of heat which can be conveyed, in a given time, through the sides of the vessel to the liquid. At the level of the sea, and at the mean pressure of 30 inches, pure water boils at 212; on the summit of Mont Blanc, at an elevation of 4775 metres, (15,518 ft.,) where the pressure of the atmosphere amounts only to 417 mm , water boils at a temperature at which the force of tension of steam is 417 ram (16.41 in.) ; that is, at about 183. At still greater elevations, water would boil at lower temperatures. If we have a table of the force of tension of the vapor of a liquid, we may easily find the temperature of the boiling point at a given pressure ; for it is the same degree of temperature at which the force of tension of the saturated vapor is equal to that pressure. We may, conversely, bring a liquid at any given temperature to the boiling point, by sufficiently dimi- nishing the pressure. At a pressure of 30 mm , (1.18 in.,) for instance, the boiling tem- perature of water is 86, because, at this temperature, the force of tension of the saturated steam is 30 mm (1.18 in.). Under a pres- sure of 10 mm (.393 in.), water boils at 51, and under a pressure of 5 ram (.196 in.), at 32. The truth of these data may be shown by experiment. Water at 86 must be put in a glass vessel under the exhausted receiver of the air-pump: after a few strokes of the piston, the barometer gauge will show a pressure only of 30 mm (1.18 in.), and the boil- ing will then begin with the same energy as if the water stood in the open air over a hot fire. This boiling, however, will soon cease, because the receiver will be filled with steam, which will press upon the liquid; another stroke of the piston will soon remove this steam, and cause the boiling to recommence. It is not possible in our air-pumps to make water boil at 32, as no rarefaction of 5 mm (.196 in.) can be produced, owing to the con- tinual re-formation of steam on the surface of the water. 528 THE LOCOMOTIVE. In the apparatus seen in Fig. 498, we observe an analogous, but still more striking phenomenon. A balloon with a long neck a is half filled with water ; when, by the boiling of the liquid, all the air has been driven out, the neck is closed by a cork, and the balloon inverted, as seen in Fig. 498. When left to itself, we perceive no ebullition, but as soon as cold water is poured upon the part, the water begins to boil with energy. This is owing to the steam being condensed in the upper part of the balloon, and the pressure on the liquid being thus dimi- nished. The variations in the boiling point have been confirmed by direct experiments, made at elevated districts in the Alps, the Pyrenees, and other mountain ranges. Boiling water is, consequently, not equally hot at all places on the earth, and, therefore, not everywhere alike applicable to do- mestic purposes, and the preparation of food. At Quito, for instance, water boils at 194, and this temperature is too low for boiling many substances which require a temperature of 212. As the barometer constantly varies at one and the same place, it follows that the boiling point varies also. If we increase the pressure on fluids, we find that their ebulli- tion is retarded, and we may even prevent this entirely if we make the pressure sufficiently strong. This is the case with the apparatus known by the name of Papin's Digestor, see Fig. 499. By means of this, water may be heated to a very high temperature without boiling. The appara- tus consists of a cylindrical vessel of iron, or, still better, of brass or copper, the sides of which are capable of sustaining a very considerable degree of pressure. The opening is provided with a safety-valve, which can be closed and loaded, so that it shall require a pressure of from 40 to 50 atmospheres to raise it. Boiling is rendered im- possible, as the steam, which is above the liquid, is unable to escape, and, consequently, exercises a sufficiently strong pressure to prevent it. As soon as the valve is opened, the steam issues with great force; the temperature of the vessel falls, however, simultaneously, as all the heat which had been Fig. 499. THE LOCOMOTIVE. 529 combined is given off at once by the energetic formation of steam. This digester was invented in the middle of the 17th century by Papin, a learned man, residing at Marburg and Cassel. It served for a number of remarkable experiments, partly to prove the mechanical force of steam, and partly to show the solvent force of water when heated above 212. People learnt with astonishment, that as nutritious a substance might be drawn from bones as from the most juicy portions of the muscle. On causing water to boil in a vessel from which the steam can only escape through a proportionately small opening, we observe an elevation of the boiling point. All the steam that has been formed by the heat passing every moment into the liquid, can only escape through a small opening, if a greater rapidity of motion has been imparted by the greater force of tension of the steam. Not only the steam pressing upon the surface of a liquid mass, but likewise the weight of the column of liquid acts upon the par- ticles in the interior. If, for instance, we had a boiler filled to a height of 32 feet with water, a pressure of 2 atmospheres would act upon the bottom, and here, consequently, steam-bubbles would be formed at a temperature of 250. But as the temperature of the liquid mass on the surface cannot rise above 212, the liquid will constantly ascend from the bottom, owing to its less specific weight. As the pressure decreases with the ascent, steam-bubbles are formed ; but their temperature decreases, however, from 250 to 212. These bubbles, which are formed at the bottom of the vessel, increase in size as they rise, owing to the pressure acting upon them becoming continually less. These phenomena may be observed even in small vessels, in which the water only mounts to a few inches in depth. Before perfect ebullition has een established, bubbles of steam are formed at the bottom ; hich, however, are condensed on their ascending, owing to their ntering layers of water whose temperature is too low. Hence rises the peculiar sound which we perceive some minutes before erfect boiling has commenced. On making the experiment in glass bulb, we may observe how bubbles are formed at the ottora, how they ascend, and then disappear; and we then say le water sings. This singing is a sign that the water will soon e in a state of perfect ebullition. 45 530 EVAPORATIONLATENT HEAT OF VAPORS. Boiling is likewise retarded by substances which are dissolved in the water ; thus, a saturated solution of common salt brine boils at 227, a solution of saltpetre at 240, a saturated solution of acetate of potass at 336, of nitrate of ammonia at 356. Evaporation is the term applied to the formation of vapor on the free surface of a liquid ; whilst, as we have seen, ebullition consists in vapor being formed in the interior of the liquid mass. Water evaporates from the surface of rivers, lakes, and seas, and the surface of damp ground and plants. The vapor has here, evidently, too inconsiderable a force of tension to overcome the pressure of the atmospheric air. Daily observation shows us that vapor is formed at every degree of temperature, and that it dis- tributes itself through the air even at the weakest degree of ten- sion. It was formerly assumed that a chemical affinity existing between the molecules of the air and those of vapor was the cause of this phenomenon ; we have seen, however, that there is no need of having recourse here to chemical forces. The steam of water, be its force of tension ever so inconsiderable, mixes with the air the same as two gases mix. The only condition ne- cessary, therefore, for the evaporation of a liquid is, that the sur- rounding layers of air be not saturated with vapor; as, further, in the mixture of two gases, the molecules of the one form a me- chanical impediment to the distribution of those of the other, the air acts as a hinderance in evaporation to the rapid dispersion of the vapor. In a perfectly calm atmosphere, therefore, evaporation goes on very slowly, whilst it progresses rapidly in an agitated state of air; the liquid then comes continually into contact with new layers of air, that are not saturated with vapor. Hence it happens that water evaporates very quickly when a dry wind is in rapid motion. Latent Heat of Vapors. When a liquid evaporates, it must absorb heat ; this absorbed heat is as imperceptible to the feelings and the thermometer as the heat which becomes latent by fusion. That heat is latent in the formation of vapor, is proved by the temperature of the liquid remaining unchanged during ebulli- tion.' The temperature of boiling water remains at 212, how- ever much we may increase the fire; all the heat which is added to the boiling water serves only to convert water at 212 into steam at 212. LATENT HEAT OF VAPORS. 531 Fig. 500. The absorption of heat during the evaporation of liquids may easily be rendered perceptible to the feelings. On pouring but a few drops of an easily evaporable liquid, as spirits of wine, sul- phuric ether, &c., upon the hand, we experience a sensation of cold because the hand has been deprived of the heat drawn away for the evaporation of the liquid. If we surround the bulb of a thermometer with cotton wool, and then moisten the latter with sulphuric ether, the thermometer will fall several degrees. After having learnt to know the manner in which heat becomes latent in the formation of vapor, it remains to determine the amount of this heat ; that is, to ascertain how much heat is necessary to convert a definite quantity of a liquid into vapor. Fig. 500 represents a glass bulb a, in which water is kept boiling by means of a spirit lamp ; if, now, the vapor formed be conducted through a glass tube b into a cylindrical vessel c filled with cold water, the vapor here will be condensed, and conse- quently, the heat which was ab- sorbed at a, in the formation of vapor, will be again liberated at c; the cold water at c will be thus gradually jwarmed, and from the elevation of temperature thus produced, |we may determine the amount of the latent heat of vapors. If we assume that, after ebullition has been going on for some e in the vessel a, all the air has been wholly expelled, and the of a crooked tube be then plunged into the cold water of the linder c, all the bubbles of vapor will at once be condensed as ;y come into contact with the cold water. In proportion, how- er, as the water becomes warmer in c, the bubbles will likewise .e larger, until finally, even if the water at c be heated to ,e boiling point, the bubbles will rise uncondensed through the >le mass of liquid, and a state of ebullition be established at c. .t the moment in which ebullition begins at c, the experiment be interrupted by our removing the glass cylinder c. Provided now, that there had been 11 cubic inches of water at at the beginning of the experiment, the cylinder at the close the experiment would have contained 13 cubic inches of water 532 LATENT HEAT OF VAPORS. at 212, 2 cubic inches of water having been thus added. This additional water has now been evaporated in the vessel a, and again condensed in the cylinder c ; the latent heat, which was com- bined in a has become liberated in c, and has heated the 11 cubic inches of water from 32 to 212; the same amount of heat, therefore, which has been absorbed by the evaporation of 2 cubic inches of water, was sufficient to raise the temperature of the 11 cubic inches of water from 32 to 212. But now 2 are to 11 as 1 to 5,5, and we may therefore express the result of our experiment in the following manner : The amount of heat necessary to con- vert a definite quantity of water from 212 into steam at 212, suffices to raise the temperature of a mass of water 5| times greater, from 32 to 212. We have already stated, that, for the unit of heat, that quantity of heat is assumed, which is requisite to raise the temperature of 1 Ib. of water 1; to raise the temperature of 5J Ibs. of water to the same amount, 5,5 are therefore necessary, and 550 such units of heat to raise the temperature of this mass 212. The latent heat of 1 Ib. of steam is consequently equal to 550. The above given experiment is not calculated to determine the latent heat of steam, affording always more or less incorrect re- sults. It is, however, well adapted to show the connection of the matter. The reason of the special want of accuracy attend- ing the results of this experiment, is, that at the high temperature to which water must be raised in the cylinder c, a considerable loss of heat is experienced by all that surrounds it ; a not incon- siderable amount of steam is condensed in the tube, giving off to the air heat that is set free, and which comes to the cylinder c as water. We may, therefore, easily understand, that until the water in c is made to boil, more water will pass over from the vessel a than would be the case if these two sources of error were not present ; hence this experiment is of little value in giving the latent heat of steam. We cannot here enter more fully into the consideration of the more precise methods in use for ascertaining this amount. LATENT HEAT OF VAPORS. 533 In distillation, the vapors formed in any vessel by heat are con- ducted into a pipe surrounded by cold water, and the vapor is converted into a liquid state ; the temperature of the cold water is, however, considerably raised in the heat liberated by the con- densation of the vapor. This may be easily shown by means of a small still, (Fig. 502,) in which the vapor is conducted from the glass bulb in which it is formed, into a straight tube, passing through a wider one, which contains the cold water. The cold Fig. 502. Fig. 503. water, which enters the condensing tube, flows forth from the other end heated. In distillations conducted on a large scale, the tube in which the vapor is condensed has the form of a helix, and is conducted through the vessel filled with the cold water, as seen in Fig. 503, in order that the vapor may remain as long as pos- sible in contact with the cold water, and that we may be quite sure that no vapor will escape from the open end of the tube in an uncondensed state. When an apparatus of this kind has been in operation for some time, we shall always find the upper layers of the water in the refrigerator very hot, owing to the heated water constantly rising to the surface. We might determine the value of the latent heat of vapors by any distillatory apparatus, if it were possible every time accu- rately to calculate the amount of vapor condensed in a given time, and the quantity of heat yielded by it to the cold water ; in order, therefore, accurately to determine the latent heat of vapors, it is only necessary to construct an apparatus in such a 45* 534 FREEZING OF WATER IN A VACUUM. manner as to enable us to obtain these amounts with exactitude. According to this principle, the latent heat of the vapors of dif- ferent liquids has been ascertained. Thus The latent heat of steam is . 540 " " vapor of alcohol . 214 " " sulphuric ether . 90 That is to say, in order to convert 1 Ib. of these liquids into vapor under the pressure of one atmosphere, 540, 214, or 90 times as much heat is combined as is necessary to raise the temperature 1 Ib. of water 1. The latent heat of vapors is not the same for all temperatures, being greater for low, and less for high temperatures. Production of Cold by Evaporation. If a liquid boil in the open air, it will retain a constant temperature, owing to its constantly receiving as much heat through the sides of the vessel as is ab- sorbed by the formation of vapor. But when ebullition goes on under the air-pump, the temperature continually falls, because the vapor withdraws from the fluid itself, and from the surrounding bodies, the latent heat necessary to its formation. The following experiments may be explained by the absorption of heat which takes place in rapid evaporation. Freezing of Water in a Vacuum. We place under the receiver of the air-pump a broad glass dish filled with sulphuric acid. A few inches above it is a thin flat metallic capsule, as seen in Fig. 504, containing a small quantity of water. This capsule is gene- rally suspended by three threads, or is made to rest upon three fine metallic feet, which stand upon the edge of the lower glass ves- sel. A few minutes after the air has been as much as possible exhausted, we see ice needles upon the capsule, and, after a time, the whole mass becomes solid. This remark- able experiment was first made by Leslie. The sulphuric acid absorbs the steam as soon as it is formed, and thus maintains a rapid evaporation. All bodies that absorb steam with energy produce the same action. The metallic capsule ought to be extremely thin, in order, likewise, to take part in the cool- ing, and must be insulated from the surrounding part by means FREEZING OF MERCURY. 535 of bad conductors, so that none of the external heat may be con- veyed to the water. In Wollastorfs Kryophorus water likewise freezes by its own evaporization. Two glass bulbs, Fig. 505, are connected by a tube. A little water is poured into each bulb, e and by its boiling, all the air is driven from the apparatus. When this is done, the aperture at e is fused by the blow-pipe, and the whole thus rendered air-tight. If, now, all the water be suffered to flow into one bulb, while the other is plunged into a freezing mixture, the condensation of the steam constantly going on in the other bulb will occasion so rapid an evaporation as to cause the water to freeze. Water may also easily be made to freeze by the evaporation of sulphuric ether. For this purpose a glass tube, 1 line in width, is enclosed in cotton wool moistened with sulphuric ether. The tube thus prepared is placed in any kind of glass vessel, and put under the receiver of the air-pump. On exhausting the air, the ether is so rapidly evaporated that the water freezes. Freezing of Mercury. We may carry cooling by evaporation down to the freezing point of mercury. To effect this we surround a thermometer bulb with a sponge, or other porous tissue, which must be moistened with sulphuret of carbon, or still better, with liquid sulphurous acid. Evaporation goes on so rapidly, and the amount of heat abstracted is so great, that the thermometer falls to 14 4, or even 22, and the mercury in the bulb freezes after the lapse of a few minutes. A liquid evaporates more rapidly, consequently generates a greater degree of cold during its evaporation, in proportion to the lowness of its boiling point ; on this account a greater degree of cold is produced by the evaporation of sulphuric ether than by water, more by sulphurous acid than by ether, and, finally, still more by liquid carbonic acid than by sulphurous acid. 536 SPECIFIC HEAT OF BODIES. CHAPTER III. SPECIFIC HEAT OF BODIES. Means of Comparing Quantities of Heat. We assume as a self-evident principle, that the same quantity of heat must always be required to produce the same effect. If, for instance, 1 Ib. of iron at 50 have, from any cause, been heated to the temperature of 51, the same quantity of heat must always be required, whether the source be the sun, or a fire ; or whether it reach the iron by contact or by radiation. In like manner, the same amount of heat will always be required to fuse 1 Ib. of ice at 32, and a definite quantity to evaporate 1 Ib. of water at 212. The quan- tities of heat must, however, also be proportional to the weight of the substances on which they act, in order to produce a definite effect; that is, to raise the temperature of 100 Ibs. of iron, from 50 to 51 ; and, in order to fuse 100 Ibs. of ice, or evaporate 100 Ibs. of water, a hundredfold greater amount of heat is neces- sary than is required to produce the same effect on 1 Ib. of these substances. A substance has a greater or less capacity for heat, according as a greater or less quantity of heat is required to produce a definite change of temperature, or an elevation of temperature of 1 ; this requisite quantity of heat is termed the specific heat of the substance. Two bodies have equal capacities of heat, if of equal weight ; they require the same quantity of heat to raise their temperature 1; on the contrary, the capacity of heat of a body is 2, 3, or 4 times greater than that of another, if it require a 2, 3, or 4 times greater quantity of heat. One and the same body may have a variable capacity for heat; as, for instance, is the case with platinum, which requires a greater amount of heat to be heated from 212 to 213, than to raise its temperature from 32 to 33. The capacity of water for heat is constant, on which account this liquid has been chosen as the unit. From these definitions it follows, that a body, whose weight is m, and whose capacity for heat is c, will, at an elevation or de- THE METHOD OF MIXTURES. 537 pression of temperature of , receive or lose an amount of heat, the product of which may be expressed by m c t. In order to determine the specific heat of bodies, three different methods have been pursued, viz., that of the fusion of ice, mix- tures, and cooling. According to the first method, the body whose specific heat is to be determined, is weighed, heated to a definite temperature, and placed in a vessel filled with pieces of ice. While it cools, a part of the ice is fused, and, from the quantity of water, we obtain the quantity of heat lost by the body, and hence, conse- quently, its specific heat. The cooling method is based upon the following principle. If a heated body be brought into a space in which it can only cool by radiation, it will, if other circumstances remain the same, cool slower in proportion to the amount of specific heat. The method of mixtures affords the most accurate results, and must, therefore, be somewhat more attentively considered. This method consists principally in this; a weighed quantity of the body to be examined is heated to a certain temperature, and then plunged into a vessel with water, the temperature of which has been raised by the cooling of the body; if we know the quantity of the cold water, we may ascertain the elevation of temperature sustained by it from the cooling of the immersed body, and thus the specific heat of the latter may be computed. If we assume that a platinum ball weighing 200 grms. (3088 grs.), warmed to 212, has been immersed in a mass of water of 105 grms. (1621 grs.), at 59, and has raised its temperature, by its own cooling, to 68, that is, has heated the water 9, it is clear, that the 200 grms. (3088 grs.) of platinum must be cooled down to 176, in order to heat 105 grms. (1621 grs.) of water 9. The same amount of heat that has been yielded by the platinum ball would, therefore, also have sufficed to raise the temperature of 525 grms. (8108 grs.) of water (1.8). If the platinum ball had only weighed 1 grm., (15.444 grs.,) the amount of heat given off by it, at a depression of temperature of 176, would be able to warm only * 9 (j\ or 2,625 grms. (grs.) of water (1.8), or 200 VoOoo/ 1 grm. (15.444 grs.) of water 2,625. Hence, it follows, that the same amount of heat that raises the temperature of 1 grm. (15.444 grs.) of platinum 176, can only raise an equal mass of 538 RESULTS OF EXPERIMENTS ON SPECIFIC HEATS. water 2,625; platinum thus requires only 2 ' 625 , that is, 0,0328 oU times less heat than an equal quantity of water, to experience an equal variation of temperature ; the specific heat of platinum is, consequently, 0,0328. If we designate the weight of the cooling water by m, and the elevation of temperature by t, (in the above-given example they were 105 grms. (1621 grs.) and 9), and the weight and depres- sion of temperature of the cooled body as m and t', (in our exam- ples they stood as 200 grms. (3088 grs.) of platinum and 176,) it follows from the above-given considerations, for a concrete case, that we have the following formula for the computation of the vn specific heat c of the cooled body : c = jj ; that is, expressed ftv L in words, we find the specific heat of the cooled body by dividing the product of the weight of the cooling water, and its variation of temperature by the product of the weight of the body and its depression of temperature. Results of the Experiments on Specific Heats. The determina- tion of specific heat has acquired much importance in chemistry from the labors of Dulong and Petit, who found that the product obtained on multiplying the specific heat of an element by its atomic weight, was always constant. Thus, for instance, they found the specific heat of iron to be equal to 0,1100, while the atomic weight of the metal was 339,2, and their product is 37,31. If we multiply the specific heat of copper 0,0949 with its atomic weight 395,7, we obtain the product 37,55, a value which agrees almost perfectly with what has been found for iron. In like manner, it was found that this product was almost exactly the same for all metallic elements; it, therefore, appears that the principle of the specific heat of metallic elements being inversely proportional to their atomic weight, is well-grounded. We have, thus, one means more of learning to know the atomic weight of a body, and to test the value of atomic weights found by other methods. The atomic weights of the elements were not, at the period when Dulong and Petit carried out their researches, as firmly established as at present ; choice had often to be made between many atomic weights for the same body, and Dulong and Petit naturally selected the one most in harmony with their own law. TRANSMISSION OF HEAT. 539 Subsequently to that time, atomic weights were more exactly determined in another way ; but this, instead of confirming the law of Dulong, seemed rather to yield results in direct opposition to those obtained by his method. The most recent investigations of Regnault, upon specific heat, have, however, established the correctness of this law beyond all doubt. CHAPTER IV. TRANSMISSION OF HEAT. Existence of Radiating Heat. Radiating heat penetrates cer- tain bodies in the same manner as light passes through trans- parent bodies ; the rays of the sun, for instance, impinge upon our earth after they have traversed the whole atmosphere, and heat the earth's surface, whilst the higher regions of the air remain cold ; the rays of heat consequently pass for the most part through the atmosphere without being absorbed by it. On approaching the fire of a hearth, we experience a burning heat, and yet the air between us and the fire is not heated to an equal degree, for on holding up a screen this heat instantaneously ceases, which could not possibly be the case if the whole mass of air surround- ing us had so high a temperature. Hot bodies can, therefore, emit heat in all directions, which passes through the air as the rays of light through transparent bodies; we, therefore, speak of radiating heat, and rays Fig. 506. of heat, in the same manner as rays of light. If two large spheri- cal, or parabolic concave mirrors of polished tin- plate (Fig. 506), be re- moved about 10 or 12 feet from each other, and so placed that the axes of both mirrors fall upon the same line, and if a piece of tinder 540 RUMFORD'S DIFFERENTIAL THERMOMETER. be placed in the focus of the one mirror, and an iron ball in a state of white heat, or a burning coal, whose combustion is quick- ened by a bellows, be laid in the opposite focus, the tinder will soon ignite, as if it had been brought into contact with a fire. This experiment proves that the glowing body radiates heat ; for it is evident that the tinder has not been ignited by the intervening layers of air having become by degrees so strongly heated. On removing the tinder from the focus, it will not be ignited, even on being brought much nearer to the glowing body. If we put a ball at 560 in the place of the glowing coal, and a common thermometer in the place of the tinder, the thermo- meter will rapidly rise ; consequently, this ball at 560 likewise radiates heat. If, instead of the hot ball at 560, we take a vessel full of boiling water, or filled with water at 190, 170, or 160, we may not, perhaps, observe any further elevation of temperature in the thermometer; this, however, does not prove that the walls of the vessel radiate no more heat at this temperature, but merely, that a common thermometer is not sensitive enough for this purpose. More sensitive instruments have, therefore, been made use of, as, for instance, an air thermometer, Rumford's or Leslie's Fig. 507. differential thermometer, or MellonVs thermo-multipli- cator. An air thermometer may be constructed for this pur- pose, somewhat in the manner represented in Fig. 507. A bulb of from 1 to 1^ inch in diameter is blown at the end of a tube, the bore of which is about 0.039 inch ; the tube is bent, as may be seen in the figure, and has in the middle a second bulb, and at its other extremity a funnel, in order to prevent the fluid standing between c and d from returning into the lower bulb, or running out at the top. When the dimensions of the instrument are known, we may easily compute almost the full degree of its sen- sitiveness ; it cannot, however, be graduated, owing to the fluid remaining exposed to the atmospheric pressure, and owing to the alternate entrance and escape of air from the lower bulb. Rumford's Differential Thermometer. Fig. 508 exhibits an apparatus consisting of two glass bulbs, a and 6, connected by a bent glass tube, whose horizontal part is from 15 to 18 inches in length. In this tube there is an index of alcohol, or sulphuric LESLIE'S DIFFERENTIAL THERMOMETER. 541 Fig. 508. Fig. 509. o o acid, pressed upon on each side by the air of the bulbs, and it will consequently only stand in a fixed position when the pressure on both sides is equal. The place occupied by the index when the temperature of both bulbs is per- fectly equal, is the zero of the division. If the one bulb be heated more than the other, the index will be driven towards the cooler bulb, and its removal from the zero will be proportional to the difference of temperature of the two bulbs. Leslie's Differential Thermometer. Fig. 509 is constructed in a similar way, with the exception of having somewhat smaller bulbs, and the vertical arms of the connecting tubes being longer, and nearer to each other. Mellon? s thermo-multiplicator consists of a thermo-electric pile, Fig. 509, such as has already been described at page 481, and of a very sensitive multiplicator. The pile is carefully blackened at both ends with soot, and placed, together with its casing, at p (Fig. 511) upon a stand ; the coverings a and b serve to keep the currents of air and the lateral radiations from the pile ; as the one b is conical, it also serves to concentrate the rays of heat from this side, if necessary. The copper wire forming the galvanometer, is 7 or 8 yards long, and is wound 40 times round a metal frame. The well chosen magnetized needles, after having been carefully compensated, are connected together, as seen in Fig. 512. This system is suspended by a cocoon thread, hanging in the centre of a glass bell c, Fig. 51 1. By turning the knob /, the cocoon thread may be somewhat raised or lowered, together with the needles. The apparatus must be placed upon a sufficiently strong table, and at a proper level, so that the thread hangs exactly in the middle of the graduated circle, and so directed that 46 / c \ f cf Fig. 510. 542 CAPACITY OF BO.DIES TO RADIATE HEAT. Fig. 511. Fig. 512. the needles point to the zero of the scale, when their plane coin- cides with the magnetic meridian. The easily expanding wire spirals, g and h, which are in connection with the two ends of the thermo-electric pile at x and y, and at ra and n, with the ends of the multiplica- tor wire, serve to restore the connection be- tween the thermo-electric pile, and the multiplicator. The smallest difference of temperature between both blackened ends of the column causes a deviation of the needle, which may be seen by the graduated scale. Capacity of Bodies to Radiate Heat. The capacity possessed by bodies of radiating heat is very dissimilar, and depends essen- tially upon the condition of the surface ; in general the surfaces of the less dense bodies radiate, other circumstances being the same, ABSORPTION OF RAYS OF HEAT. 543 more heat than the surfaces of bodies possessing a greater density. The irregularity in the capacity of radiation of different surfaces, has been illustrated by Leslie in the following manner : he brought the bulb of his differential thermometer into the focus of a con- cave mirror, and placed at some distance from the axis of a mir- ror, a hollow tin-plate cube, filled with hot water; the sides of the vessel being from 7 to 8 inches in length, and one lateral side being covered with soot, while the other was polished ; when the latter side was turned towards the mirror, the effect was much less considerable upon the differential thermometer than when the blackened side was turned towards it ; the surface rubbed with soot, consequently radiated far more heat than the polished metal- lic surface. This method is certainly quite capable of showing the differ- ence in capacity of radiation; but to give more exact compari- sons, however, MellonVs method is far more preferable ; he placed at a proper distance from the thermo-pile a hollow cube of tin plate, the side of which was from 2J to 3 inches long, and which was filled with hot water, kept at a constant temperature by means of a spirit lamp ; the lateral surfaces of this cube were differently prepared, one being covered with soot, another with white lead, the third with Indian ink, and the remaining one po- lished. The deviations of the needle were very unequal, as the one or the other side was turned towards the thermo-multiplicator, and from the deviations thus observed, was found without further difficulty, the relation in which the capacities of emission stand to each other for different fluids. In this manner the capacity of radiation has been determined for the following bodies : Lamp-black . . 100 Indian ink . . 85 White lead . . 100 Gum lac . Isinglass . . 91 Metallic surface . 12 Thus, if we designate the capacity for radiation in pine soot as 100, that of a polished surface will be equal to 12, conse- 12 quently, only of the former. 100 Absorption of Rays of Heat. Every body has the power of absorbing more or less the rays of heat, which impinge upon it coming from some other body; this is proved in the above-named experiments, for bodies are only heated in the focus of a concave 544 REFLECTION AND DIFFUSION OF HEAT. mirror, because they absorb the rays of heat concentrated upon them by the mirrors. That this power, however, appertains to all bodies, is proved by their assuming a temperature when exposed to the sun's rays, which is higher than the temperature of the air. The power of absorption is not equal for all bodies, which arises from their not having equal power of emission, for a sur- face which easily radiates heat must, conversely, also have the capacity for absorbing these rays. This inequality in the power of absorption may be shown by a simple experiment ; for instance, if we put a thermometer, whose bulb has been blackened, in the rays of the sun, it will rise much more rapidly than another, whose surface has not been blackened ; the blackened surface of the one thermometer bulb absorbs, therefore, evidently more rays of heat than the polished surface of the other. The rays of heat absorbed by a body are, therefore, the cause of its becoming heated ; and thus, in order to heat a body by radiation as much as possible, it is necessary to cover it with some coating, which strongly absorbs rays of heat ; for the same reason, thermoscopes, which serve to manifest, in a striking manner, the actions of the radiation of heat, the bulbs of differ- ential thermometers, and the two ends of the thermo-electric pile are coated over with soot, as this substance has a stronger capacity for absorption than any other with which we are acquainted. We have seen above that metallic surfaces possess only a very small power of emission, and hence it follows that they are only capable of absorbing rays of heat to a very small degree. Reflection and Diffusion of the Rays of Heat. Bodies have, in general, the capacity of reflecting a portion of the rays of heat impinging upon (hem in the same manner as they more or less regularly reflect rays of light. The mirrors, which were used in the above experiments, furnish us with a decisive proof of the re- flection of rays of heat, for they are not themselves heated in the experiment with the tinder. A simple mode of reasoning con- vinces us that most bodies must possess this capacity for reflection, and that, if we may so speak, it is complementary to the power of absorption, for the sum of the absorbed rays of heat must evi- dently be equal to the combined whole of the incident rays, pro- vided the body suffer no rays of heat to pass through it. When, therefore, the power of reflection is greater, the power of absorp- CAPACITY OF BODIES TO TRANSMIT RAYS OF HEAT. 545 tion is smaller, and conversely. A body that reflects no rays of heat must absorb all rays, as, indeed, is the case with such sur- faces as are carefully covered with soot ; polished metallic surfaces, on the other hand, which possess a great capacity of reflection, only absorb rays of heat to a very inconsiderable degree. Rays of heat are reflected precisely according to the same laws as rays of light, that is to say, the angle of reflection is equal to the angle of incidence ; this follows from the experiments with the concave mirrors, as the focal points for the rays of heat cor- respond with those of the rays of light. As rays of light are irregularly distributed in all directions on the surface of a perfectly polished body, rays of heat likewise undergo a diffusion on the surface of most bodies. We may con- vince ourselves of this by the following experiment. If we suffer the sunbeams to fall through an opening in the shutter of a dark room upon the opposite wall, the luminous spot, which is visible from all directions, owing to its distributing sunlight on every side, will also distribute rays of heat irregularly, that is, it will throw forth rays of heat in all directions, as if it were itself a source of heat. This diffusion of the rays of heat is rendered manifest on turning the thermo-electric pile towards the bright spot; we shall see the needle deviate at whatever part of the room we place the instrument ; and the action cannot, therefore, arise from a regular reflection, while it is evident, that it is not the consequence of a heating of the part of the wall on which the sun's rays have fallen, for the needle will return to the zero of the scale as soon as the aperture in the shutter is closed. Capacity of Bodies to transmit Rays of Heat. That solid bodies can transmit rays of heat in the same manner that transparent bodies transmit rays of light, has already been proved, by showing that we are able to ignite combustible bodies on holding them in the focus of a lens exposed to the rays of the sun. More accurate investigations could only be made by help of the thermo-electric pile, and Melloni has carried out a series of highly interesting ob- servations upon the transmission of the rays of heat through differ- ent bodies. Such bodies as retain rays of heat as transparent bodies retain rays of light, are termed by Melloni, athermanous; and those which are to rays of heat as transparent bodies are to rays of light, 46* 546 CAPACITY OF BODIES TO TRANSMIT RAYS OF HEAT. are called by him diathermanous. Air, consequently, is a diather- manous body ; ancl we shall soon see that many solid and fluid bodies are diathermanous, although in very unequal degrees. The experiments were made in the following manner. The source of heat, a small oil lamp, for instance, or a hollow cube of tin plate filled with hot water, and blackened on the out- side w r ith soot to radiate heat the better, was so placed as to pro- duce a deviation of the needle of 30; when the rays of heat were then received upon a plate of the body to be examined, and placed at r, Fig. 509, the needle receded sometimes more, some- times less, and it was thus observed that equally thick and equally transparent plates of different bodies did not transmit equal quan- tities of radiating heat. If, for instance, the free radiation of the source of heat cause a deviation of 30, the needle will recede to 28 if a plate of rock salt from 0.11 to 0.15 of an inch in thick- ness be placed at r, whilst an equally thick plate of quartz will Fig. 513. DISTRIBUTION OF HEAT BY CONDUCTORS. 547 cause the needle to recede to 15 or 16; mineral or rock salt, con- sequently, transmits rays of heat far better than rock crystal. Many less transparent bodies even transmit rays of heat better than those that are perfectly transparent. Whilst, for instance, a wholly transparent plate of alum reduces the deviation of the needle from 30 to 3 or 4, a far thicker plate of smoky-topaz brings the needle back to 14 or 15. Some bodies which are almost wholly opaque, as black glass and black mica, transmit rays of heat tolerably well. If we suffer the rays of heat that have passed through a glass plate to fall upon an alum plate, they will be wholly absorbed ; whilst, however, an alum plate will transmit almost all the rays of heat that had previously passed through a plate of citric acid. This phenomenon has the greatest analogy with the transmission of light through a colored medium; rays of light that have passed through green glass are, it is well known, easily transmit- ted through other green glasses, which are absorbed when suffered to fall upon red glass ; the differences between rays of heat are, therefore, quite analogous to the differences of color in light. Similar resemblances have been observed in relation to the capacity of emission and absorption of bodies. Rays of heat are refrangible, like rays of light, as may best be seen by means of a prism of rock salt. Phenomena of polariza- tion have also been shown in rays of heat. Distribution of Heat by Conductors. Heat may pass from one body to another, not only by radiation, but by immediate contact, and may then be transmitted through the whole mass; there is, however, a great inequality in different bodies in relation to the facility with which this is effected ; in many, heat is very easily transmitted, whilst in others it passes with much less facility from one particle to another. A match that is burning at one end may be held between the fingers at the other extremity without any elevation of temperature being even felt in the wood ; the high temperature of the burning end is not speedily transmitted to the rest of the mass of wood, because wood is a bad conductor of heat. An equally long metallic wire made glowing hot at one extremity cannot be grasped at the other end without burning the hand; heat, consequently, distributes itself from the glowing part to the whole of the rod, metal being a good conductor. 548 LIQUIDS AND GASES AS CONDUCTORS OF HEAT. We may make use of Ingenhousz's apparatus (Fig. 514) to show Fig 514 the inequality of the capacity of different bodies to transmit heat. Many rods made of the substances to be compared are in- serted into the lateral wall of a box of tin plate, the rods being all of equal diameter, and all covered with a layer of wax; on pouring boiling water or hot oil into the box, the heat will penetrate more or less into the rods and fuse the wax coating. If we assume that one rod is of copper, another of iron, a third of lead, a fourth of glass, and the last of wood, the wax coating of copper will be perfectly fused before the coatings over the other rods are much melted, showing that copper is the best conductor of these five bodies. The fusion of the wax is more rapid over the iron than the lead, and when all the wax has melted off the copper rod, fusion has only progressed to a very small extent upon the glass rod, while scarcely a trace of fusion is perceptible on the wooden rod ; which proves that wood is the worst conductor of heat among these five substances. Of all bodies, metals are the best conductors of heat ; and ashes, silk, hair, straw, wood, &c., and porous bodies especially, are the w r orst. In practical life we are constantly making numerous applica- tions of the good or bad capacity of different bodies for conducting heat. Thus, objects that we wish to protect from the cold, we surround with bad conductors of heat: twisting straw round trees and shrubs in winter to save them from the effect of the frost; on the same principle our clothes keep us warm, owing to their being made of bad conductors of heat. We can bring a liquid to a state of boiling much more rapidly in a copper vessel than in one made of porcelain, and having equally thick walls. Capacity of Liquids and Gases for conducting Heat. Heat is distributed through liquids principally by currents, which arise from the heated particles rising more rapidly to the surface, owing to their inconsiderable density. These currents may be made apparent by throwing shavings into water enclosed in a glass ves- sel, and then heating it slowly from below (Fig. 515), when we shall see the current rise in the middle, and be directed upwards, and turn downwards on either side. On heating a liquid from above, so that the hydrostatic equilibrium is not disturbed, the LIQUIDS AND GASES AS CONDUCTORS OF HEAT. 549 Fig. 515. heat can only be transmitted in the same manner through the mass of the liquid, as is the case with solid bodies ; that is to say, by the heat being conducted from one layer to the other. In such cases, heat is only slowly diffused through the mass of the liquid ; liquids, consequently, are bad conductors of heat. In order to convince one's self of the bad capacity of liquids for conducting heat, one need only plunge the bulb of a thermometer into cold water, and then pour hot oil upon the water. The up- permost layers of water will scarcely manifest any elevation of temperature. Despretz has determined the capacity of liquids for conducting heat, by heat- ing columns of water 1 metre (yard) in height and from 0,2 to 0,4 metres (6 to 12 inches) in diameter, by continually pouring hot water over them from above. This process was con- tinued for about 30 hours, until the temperature of the columns was settled and stable on all sides. From these experiments it follows that the capacity of water for conducting heat is about 96 times less than that of copper. The air and gases especially are likewise very bad conductors of heat ; but we are unable, owing to the radiation of heat, to ascertain their capacity for conducting heat, by means of the thermometer brought into the different layers of the mass of air to be examined. That gases generally, and the air in particular, are bad conductors of heat, is, however, proved by this : that bodies surrounded on all sides by layers of air, can only be cooled or heated very slowly, if only the intermixture of the layers of air be prevented. We thus see the utility of double windows and double doors in keeping a room warm. The bad capacity for conducting heat which we perceive in porous bodies, as straw, wool, &c., depends especially upon their innumerable interstices being filled with air. Bodies, which we say keep us warm, as, for instance, our clothes, straw, &c., are not warm in themselves, but owe the property they possess to their bad power of conduct- 550 GENERATION OF HEAT BY CHEMICAL COMBINATIONS. ing heat ; if we wrap any of these round ice, they will hinder its fusion, by protecting it from all external heat. CHAPTER V. Fig. 516. DIFFERENT SOURCES OF HEAT.* Generation of Heat by Chemical Combinations. Excepting the sun, chemical combinations furnish us with the most important sources of heat. Almost every chemical process is accompanied by a development of heat. The development of heat induced by combustion, that is, by a rapid combination of bodies with oxygen, is of the greatest im- portance. In order to determine the amount of heat developed in combus- tion, Rumford made use of the apparatus delineated in Fig. 516. The box JL is filled with water, through which passes a worm tube ; the entrance of this tube is formed by a funnel, below which are placed the bodies to be consumed. The experi- ment is easily made with oil and alcohol, which are poured into a little lamp, which must be weighed at the beginning and end of the experiment, in order to ascertain the quantity of the material consumed. The flame and the products of combustion pass through the tube, and heat the water of the apparatus. From the elevation of temperature experienced by the water, together with the whole apparatus, we may estimate * Thomson's "Heat and Electricity," 2d edition, 8vo., 1840. ANIMAL HEAT. 551 the amount of heat engendered by combustion; but here we must not disregard the heat carried off by the gaseous products of com- bustion from the tube. By experiments of this kind, the following results were obtained as to the amount of heat developed. By the combustion of 1 grm. The temperature of 1 kilogramme (15.444 grs.) of (2.679 Ib.) of water may be raised Hydrogen 65,32 Olefiant gas 20,96 Absolute alcohol .... 12,52 Charcoal 13,12 Wax 18,90 Rapeseed oil .... 16,75 Tallow 15,06 Animal Heat. The temperature of the heat of blood of all ani- mals is almost always different from that of the medium in which they live. The animals of the polar regions are always warmer than the ice on which they live ; but in the countries on the equator they are cooler than the glowing air which they inhale. Neither birds nor fish have the same temperature as the air or the water surrounding them ; the animal body must consequently have a peculiar heat, which it is constantly able to engender. The internal heat of the human body appears to be the same for all organs, and to be equal to that, to which a small thermo- meter rises, when we place the bulb under the tongue, and close the mouth, until it has ceased to rise ; this temperature is about 98 F. Age, climate, health, and disease, can but slightly affect it. The blood heat is greater in birds than in any other animals, amounting, on an average, to 107.6; the blood heat of the mam- malia is very nearly equal to that of man. In birds and the mammalia, the blood heat is independent of the temperature sur- rounding it ; but, in other species of animals, as the amphibia, fishes, &c., the temperature of the body varies but little from the surrounding medium. What, then, is the source of animal heat? The air which we inhale becomes changed in the same manner as the air that has served in the combustion of bodies; the oxygen being converted into carbonic acid, and a regular process of combustion being 552 DEVELOPMENT OF HEAT BY MECHANICAL MEANS. thus carried on in the lungs. Since Lavoisier made this disco- very, the source of animal heat has ceased to be a mystery. Car- bon is brought into the body with the food, and is then combined in the lungs with the oxygen of the inhaled air. By the oxidation of carbon in the animal body, the same amount of heat must, how- ever, necessarily be engendered as if the carbon had been con- verted, by rapid combustion, into carbonic acid. In a cold medium, men and animals constantly lose more heat than in a warmer atmosphere ; as, however, the blood heat in the mammalia and in birds is independent of the temperature of the air, it is evident that more heat must be engendered in the body if a greater quantity be withdrawn every moment from it, and more, consequently, when the body is in a colder air, than when it gives forth but little heat in a warmer medium. In order, how- ever, to be able to engender more heat in the same periods of time, more carbon must be introduced into the body, by the oxi- dation of which substance heat is developed : in the same manner as we must consume more fuel in a stove during cold weather than during a less intense degree of cold, in order to maintain a constant and fixed temperature in the apartment. Thus, too, we may understand why the inhabitants of northern countries require to partake of more food, and especially of the kind containing a greater amount of carbon, than is necessary for those who live in hotter zones. Development of Heat by Mechanical Means. We have already stated that heat is liberated by the compression of air ; and when this is rapidly effected, a very considerable elevation of tempera- ture may be brought about, on which depends the pneumatic tinder-box. Fluids that do not admit of strong compression, show but an inconsiderable elevation of temperature. Solid bodies are often very much heated by compression, as we may observe in the case of hammering metals and striking coins. It has not yet been determined with certainty, whether the elevation of the tem- perature of solid bodies, by compression, must likewise be ascribed to the circumstance, that their heat is smaller with a greater de- gree of density, and that, consequently, a part of the heat, which is maintained in them, as specific heat, escapes in a perceptible form on their being compressed. The considerable elevations of temperature occasioned by fric- tion are generally known. The iron tire of a wheel often becomes THEORETICAL VIEWS CONCERNING HEAT. 553 so heated that it will hiss on coming into contact with water ; dry wood may be ignited by friction, and an iron nail may be brought into a state of white heat on being held against a moving grind- stone of 7J feet in diameter. At the present time, we are unable to afford a satisfactory explanation of these phenomena. Theoretical Views concerning Heat* We have become ac- quainted with the most important laws of the phenomena of heat, without having entered upon the question of what heat really is.f In this respect, therefore, the theory of heat has been treated pre- cisely in the same manner as the first part of the theory of light, where the empirical laws of reflection and refraction were deve- loped, without anything further being said of the nature of light. We are, however, still deficient in a theory from which the phe- nomena of heat may be derived (as the phenomena of light from the wave theory), not only qualitatively, but also quantitatively. We generally imagine that heat is an imponderable substance, penetrating bodies: and this idea answers very well for many phenomena ; as, for instance, the combination of heat, and the capacity for conducting heat, affording us a good representation of these phenomena, the expressions being based upon this view. If, however, the phenomena of the capacity for conducting heat, of latent heat, and of diffusion of heat, accord tolerably well with the idea of a substance of heat, it is, on the other hand, very im- probable that there are such substances, and more likely that imponderables will all vanish from physics, as has already been the case with respect to light. In the theory of heat, the most important step made, is, probably, that which corresponds to the introduction of the theory of vibration in the case of light. There are some phenomena which cannot be reconciled with the views of heat being a substance; for instance, radiation and the generation of heat by friction. The laws of the radiation of heat are so similar to those of the radiation of light, that we are tempted to ascribe the former like- wise to a vibration of ether. If, however, radiating heat were :ransmitted by the vibrations of ether, perceptible heat must like- wise be occasioned by the vibrations of the material parts of )odies. * Graham's "Elements of Chemistry," 2d edition, 8vo. 1847. t Thomson's "Heat and Electricity," 2d edition, 8vo. 1840. 47 554 THEORETICAL VIEWS CONCERNING HEAT. That the phenomena of heat actually arise from such vibrations, is very probable, although we are not able, even in a satisfactory degree, to explain all phenomena of heat on this hypothesis ; and we are still unable to dispense with the idea of a substance of heat in our representations and descriptions. In order to explain the phenomena of heat by vibrations, we must assume, that the temperature of bodies increases with the amplitude of the oscillations ; and by such means we may also explain expansion by heat. The number of the vibrations is increased on the transition from the solid to the fluid, and from the latter to the gaseous condition. An increase in the number of the vibrations is, with an equal amount of motion, alone possible when the amplitude is less ; and thus we may explain the combination of heat. METEOROLOGY. 555 SECTION VIII. METEOROLOGY.* CHAPTER I. DISTRIBUTION OF HEAT ON THE EARTH'S SURFACE. THE heating of the earth's surface, and of the atmosphere, by which alone the vegetable and animal world can thrive, is alone owing to the rays of the sun, which must thus be regarded as the source of all life, upon our planet. Where the mid-day sun stands vertically above the heads of the inhabitants, and its rays strike the earth's surface at a right angle, a luxuriant vegetation is developed, if a second condition of its existence, namely, mois- ture, be not wanting ; but where the solar rays constantly fall too obliquely to produce any marked effect, nature is chained in eternal ice, and all animal and vegetable life ceases. In order to take a general survey of the distribution of heat on the earth's surface, we must, in the first place, investigate the consequences produced by the diurnal and annual motion of the earth. In consequence of the annual motion of the earth, the sun continually alters its apparent position in the heavens; the path which it traverses, during the year, passes through twelve con- stellations, called the signs of the zodiac. If we suppose the vault of heaven to be one large concave sphere, the path of the sun will describe a large circle upon it, > The want of space prevents this important subject being treated as fully here as it deserves. The reader is, therefore, referred to the excellent translation of KAEMTZ'S Complete Course of Meteorology, with Notes by C. V. Walker, illustrated with 15 plates. London, 1845. 556 DISTRIBUTION OF HEAT ON THE EARTH'S SURFACE. generally known by the name of the elliptic. This line does not coincide with the celestial equator, intersecting it at an angle of 23 28'. Twice in the year, namely, on the 21st of March, and on the 21st of September, the sun passes the celestial equator. From March till September it is on the north, and from September to March on the south, hemisphere; on the 21st of June it reaches its most northern, and on the 21st of December its most southern, point ; being, on the first-named day, at 23 28' north, and the last-named, at 23 28' south, of the celestial equator. The direction of our earth's axis coincides with the axis of the heavens, the plane of the terrestrial equator, with that of the celestial equator ; if, therefore, the sun stand directly upon the celestial equator, its rays strike the earth's surface at every place upon the terrestrial equator perpendicularly at mid-day, whilst they only glance over the two terrestrial poles, striking the parts contiguous to them very obliquely. If we suppose two circles to be drawn upon the earth's surface parallel with the equator, one 23 28' north, and the other equally far south of it, the former will be the tropic of Cancer, and the latter the tropic of Capricorn. All places lying upon these tropics receive once in the year the sun's rays perpendicularly, this being on the 21st of June for the tropic of Cancer, and the 21st of December for the tropic of Capricorn. The whole terrestrial zone lying between those two tropics is termed the hot zone, because the rays of the sun falling but very little obliquely, are able here to produce the most powerful effect. Heat is tolerably equally distributed throughout the whole year on the equator, because the sun's rays strike the earth rectangu- larly twice annually, while they do not fall very obliquely at any time intervening between these periods. The more we approach the tropics, the more marked are the differences of temperature at different periods of the year. In the tropics, the solar rays only fall once in the year perpendicularly on the .earth's surface, and once they make an angle of 47 with the direction of the plumb line, falling, consequently, with very considerable obliquity ; the temperatures of the hottest and coldest season, separated by a period of half a year, differ very consider- ably from each other. DISTRIBUTION OF HEAT ON THE EARTH'S SURFACE. 557 On either side of the hot zone, extending from the tropics to the polar zones, (the polar zones are those which have 24 hours exactly for their longest day, and lie exactly 66 32' north and south of the equator,) are the northern and southern temperate zones ; the four seasons of the year are most strongly characterized in these zones ; in general, heat diminishes with the distance from the equator. Around the poles, extending to the polar tropics, are the north- ern and southern frigid zones. In consequence of the rotation of the earth upon its axis, the sun appears to participate in the apparent motion of all the pla- nets ; and another result of this diurnal motion, is evidently the alternation between day and night. It is only during the former period that the solar rays warm the earth's surface, which, after sunset, radiates heat towards the heavens, without the loss of heat being compensated for; during the night, therefore, the surface of the earth must be cooled. Under the equator the day and night are equal throughout the year, each day and night lasting 12 hours; as soon, however, as we remove from the equator, the length of the day varies with the season of the year, the variation becoming more striking as we approach nearer to the poles. The following table contains the length of the longest day for different geographical latitudes : Polar elevation. Length of the longest day. .... 12 hours. 16 44' . . . . 13 30 48' . . . . 14 " 49 22' . . . .16 " 63 23' . . . .20 " 66 32' . . . .24 " 67 23' . . . . 1 month. 73 39' . . . .3 months. 90 .... 6 u At the equator, therefore, the variation in the day's length can- not exercise any influence upon the course of the heat in the dif- ferent seasons of the year. As the inequality in the length of the days is not very considerable even under the tropics, the variation in the length of the day between the tropics cannot very much 47* 558 DISTRIBUTION OF HEAT ON THE EARTH'S SURFACE. increase or diminish the differences of temperature between the hot and cold seasons of the year ; this is the case, to a very con- siderable degree, in high latitudes. In summer, when the sun's rays fall less obliquely, the sun remains longer above the horizon in high latitudes; this longer period compensates for what is lost in intensity by the solar rays, and it thus happens that it may be very hot during the summer even at places which are far removed from the equator, (at St. Petersburgh, for instance, the thermometer sometimes rises in a hot summer to 86 ;) in the winter, on the other hand, when the more obliquely falling solar rays have only little power of acting, the day is very short, and the night, during which period the earth radiates its heat, extremely long ; in consequence of which, the temperature must fall very low at this season. The difference between the temperature of summer and winter will, therefore, generally be greater the further we remove from the equator. At Bogota, which is 4 35' N. of the equator, the difference of temperature between the hottest and coldest month amounts only to 3; in Mexico (19 25' N. lat.) this difference is 14, at Paris (48 50' N. lat.) 48, and for St. Petersburgh (59 56' N. lat. 57. From the above indicated considerations, it follows, therefore : 1. That heat must diminish from the equator towards the poles. 2. That, in the vicinity of the equator, heat is distributed tole- rably equally over the whole year; that, consequently, the charac- ter of our seasons ceases there to be recognizable. 3. That the seasons always differ more in proportion as we go further from the equator, and that, at the same time, the difference between the summer and winter temperature becomes always more considerable. 4. That, even in the neighborhood of the polar circles, the summer may be very hot. This we find fully confirmed by experience, notwithstanding which, such a consideration can only teach us roughly to know the distribution of heat upon the earth, it being impossible, from the geographical latitude of a place, to draw any conclusion, even remotely certain, as to its climatic relations. If the whole earth's surface were covered by water, or if it were OBSERVATION OF THE THERMOMETER. 559 all formed of solid plane land, possessing everywhere the same character, and having an equal capacity at all places for absorb- ing and again radiating heat, the temperature of a place would depend only on its geographical latitude, and, consequently, all places having the same latitude would have a like climate. Now, however, the action that may be produced by the solar rays is modified by manifold causes, the climate of one district depending not only upon the direction of the solar rays, but also upon the circumstances under which they act, such as the conformation of the land and the sea, the direction and height of the mountain range, the direction of the prevailing wind, &c. Hence it follows that places of the same geographical latitude have frequently a very different climate, and we may thus easily see that theoretical considerations do not suffice as data, from whence to draw conclu- sions regarding climatic relations ; the true distribution of heat over the earth's surface can only be satisfactorily ascertained by means of observations conducted for a protracted term of years. Humboldt was the first who entered here with success upon the course of induction, the sole and only path that leads to truth in all physical sciences. On his voyages and travels in both hemi- spheres, he collected, with unwearied zeal, facts which, by his excellent mode of combining them, have first laid the foundation of scientific meteorology. Observation of the Thermometer. In order to be able to ob- serve accurately the temperature of the air at different places, we must place a good thermometer in the open air, upon the north side of a building, and 3 or 4 decimetres removed from the wall, so that it may not receive the sun's rays ; we must, likewise, be careful that there is no white wall in the neighborhood, from which rays of heat may be reflected towards the thermometer. If the thermometer should be moistened by rain, we must carefully dry the bulb five minutes before we use it, for the suspended drops of water would, by their evaporation, lower the temperature of the mercury in the bulb. It is often of the greatest importance to meteorology to learn the highest and lowest temperature that may have prevailed during any interval, without it being absolutely necessary to observe the exact moment in which this maximum or minimum occurs. This may be effected by the thermometrograph, represented in Fig. 560 OBSERVATION OF THE THERMOMETER. 517, which consists of two thermometers, the tubes of which are placed horizontally, and of which one is a mercurial, and the Fig. 517. other a spirit thermometer. In the tube of the former lies a steel pin, which is pushed through the column of mercury when the mercury in the bulb expands ; when, however, the thermometer is re-cooled, the mercurial column recedes, while the steel pin remains in the position to which it was pushed at the highest stand of the thermometer ; such a thermometer, consequently, yields the maximum of the temperature that may have prevailed within a certain period. Within the tube of the spirit thermometer, is a very fine glass rod, somewhat thicker at its extremities, as may be plainly seen in Fig. 517; this glass rod lies within the column of spirits, and on the spirit cooling in the bulb, and the fluid retreating in the tube to the first knob of this rod, the latter will be carried away with the retreating fluid column, when any further sinking of the temperature occurs, owing to the adhesion between the spirit and the glass; if, however, the fluid in the bulb be again warmed, it will, on the rising of the thermometer, pass by the rod without carrying it with it; this index, which must be made of some darkly stained glass, in order to be made more apparent, remains, conse- quently, lying in the place corresponding to the minimum of the temperature which prevailed within a certain period of time. When the bulb of the one thermometer lies on the right side, that of the other is on the left, and on inclining the whole apparatus, and striking it gently, the steel rod will fall by its weight on to the column of mercury, and the glass rod to the very end of the column of spirit. If we leave the apparatus thus arranged, the steel rod will be pushed on by every ascent of the temperature, DIURNAL VARIATIONS OF TEMPERATURE. 561 while the glass rod will be drawn back at every depression of the temperature. This instrument is especially calculated to give the maximum and minimum of the diurnal temperature. On setting it in the proper manner every evening, we may, the following evening, see what has been the highest, and what the lowest temperature dur- ing the last 24 hours. Diurnal Variations of Temperature. In order to be able accu- rately to follow all the variations of heat in the atmosphere during the 24 hours, we must observe a thermometer at very short inter- vals, as, for instance, from one hour to another. If such obser- vations are to be pursued for any length of time, it is evident that they cannot be conducted by one single individual, but that many must combine for the same purpose ; in every case it is very la- borious to institute a series of observations of this kind. From such series of observations it has been shown that the minimum of temperature occurs shortly before sunrise, and the maximum a few hours after 12 at noon, somewhat later in sum- mer, and somewhat earlier in winter. This course may be easily explained. Before noon, whilst the sun is constantly rising higher, the earth's surface receives more heat than it radiates ; its temperature and that of the atmosphere must, therefore, increase ; this continues somewhat beyond noon ; but as the sun sinks lower, and its rays become less effective, the heated earth radiates more heat than can be supplied by the solar rays; this cooling naturally continues after sunset, until the morning-dawn announces the return of the sun. The diurnal variations in the thermometer do not always follow this normal course, which may frequently be disturbed by foreign influences, as, for instance, changes of weather, &c. ; in order, therefore, to ascertain with exactitude the law of diurnal varia- tions of heat, we must deduce the mean normal course from a combination of as many numerous observations as can possibly be instituted. By taking the mean of every 24 hours' observations, we obtain the mean temperature of the day. As it is uncommonly wearisome and laborious to pursue for any length of time these hourly observations of the thermometer, it is of the greatest importance to meteorology to devise methods by 562 MEAN TEMPERATURE OF THE MONTHS. which the mean diurnal temperature may be ascertained without making these hourly observations. Twice in the day the ther- mometer must indicate the mean diurnal temperature ; it, there- fore, seems the simplest to calculate the hours in which such is the case, and then limit our observations of the thermometer to those periods of the day ; such a course may, however, easily lead us into errors, since the thermometer varies most suddenly exactly at this time, and we should thus commit a very considera- ble mistake in our calculations, if our observations were made either a little too early or too late. A far more correct result is obtained by observing the thermometer at several similar hours, for instance, at 4 and 10 A.M., and at 4 and 10 P.M. ; this method is, as Brewster has shown, correct to T Vth of a degree ; we like- wise obtain a very useful result by making our observations at 7 A.M. at noon, and at 10 P.M., and then taking the mean of these three periods. The mean of the highest and lowest degree of the thermometer during the 24 hours varies so inconsiderably from the actual mean temperature derived from hourly observations, that we may more easily compute the mean diurnal temperature by aid of the ther- mometrograph described at page 560. Mean Temperature of the Months, and of the Year. When we know the mean temperature of all the days of a month, we have only to divide the sum of the mean diurnal temperatures by the number of days, in order to obtain the mean temperature of the month. On taking the arithmetical mean from the mean temperature found for the 12 months of the year, we obtain the mean tempera- ture of the year. In order to determine, with exactness, the mean temperature of a place, we must take the mean of the mean temperatures obtained from a large series of calculations. In general, the mean annual temperatures do not vary much, so that we obtain the mean tem- perature of a place with tolerable accuracy, even when we only know it for a few years. For Paris, the mean temperatures of the years intervening between 1803 and 1816, were as follows : 51 50,8 49,6 52 51,1 49,4 MEAN TEMPERATURE OF THE YEAR. 563 49,2 51 51 53,3 51 49,2 51,3 49,6 The highest of these mean annual temperatures varies only about 4,1 from the lowest. On taking the mean of these 14 numbers, we obtain as a mean temperature for Paris 50,6, whilst the amount derived from a series of 30 annual mean temperatures is 51,4. In order to find the true mean temperature of a month, we must know the mean temperature of this month for a series of years, and take the mean of these. The greatest heat generally occurs in our latitudes some time after the summer solstice, and the greatest cold some time after the winter solstice. July is, on an average, the hottest, and January the coldest month. If the period of the highest and lowest temperature is not exactly the same for all places of the same hemisphere, the difference is only occasioned by local influences. We may, on an average, consider the 26th of July as the hottest, and the 14th of January as the coldest day of the year for the temperate zone of the northern hemisphere. It has been proved from numerous observations on temperature, that the mean annual temperature generally occurs on the 24th of April, and the 21st of October in the northern temperate zone ; the annual course of the heat in these parts is therefore as follows. The temperature rises from the middle of January at first slowly, more rapidly in April and May, and again more slowly until the middle of July, from which period it diminishes but slowly in August, more rapidly in September and October, finally reaching its minimum again in the middle of January. This admits of an easy explanation. When the sun, after the winter solstice, again ascends, this ascent goes on so slowly, and the days increase so little, that as yet no more powerful effect from the sun's rays is possible. On this account, the minimum of the yearly temperature occurs after the winter solstice ; a rise of temperature first takes place when the sun has returned somewhat farther north. About the time of the equinoxes, the sun's progress in the heavens to- 564 MEAN TEMPERATURE OF THE YEAR. wards the north is quickest: the increase of temperature for this reason is at this time the most perceptible. When the sun has attained its highest position, the earth has not yet become so warmed that the heat which the ground loses by radiation is equal to the quantity of heat, which it receives from the sun's rays; the balance would only be restored after the sun had remained a longer time at its northern solstice. But now the sun goes back after its summer solstice, very slowly at first. The effect of the sun's rays is for some time quite as powerful as at the moment of the solstice ; the temperature, therefore, will still rise after the longest day, and indeed even to the middle of July, and then again fall. These considerations lead to the divi- sion of the year into four seasons. The astronomical division, when the seasons are limited by the equinoxes and solstices, is the most suitable to meteorology. It would be better were we to divide the year in such a manner, that the hottest month (July) should fall in the middle of summer, and the coldest month (January) in the middle of winter. Ac- cording to this, winter would include the months of December, January, and February; spring, March, April, and May; summer, June, July, and August; and autumn, September, October, and November. According to this signification, we must understand the seasons given in the following table, which contains the mean annual temperature, mean temperature of individual years, and the hottest and coldest months for a large number of places scat- tered over different parts of the earth's surface. The numbers of this table are only mean numbers, from which the true temperature inclines sometimes towards one side, some- times towards the other, and thus, too, the mean temperatures of the hottest and coldest months by no means indicate the limits between which the thermometer may fluctuate at one and the same spot. It thus happens, that even in districts enjoying a warm climate and a mild winter, an extraordinary degree of cold is often felt; thus, for instance, in the year 1507 the harbor of Mar- seilles was frozen over its whole extent, for which a cold of at least 0,4 was requisite; in the year 1658, Charles X., with his whole army and their heavy artillery, crossed the little Belt. In 1709 the Gulf of Venice, and the harbors of Marseilles, Genoa, and Cette were frozen over; and in 1789 the thermometer fell at MEAN TEMPERATURE OF FORTY-THREE PLACES. 565 "If i "in i|i i i i 1 1 i 1 1 1 1 i 1 1 i :|t|||i|||t|| O.O.IO.O.C9 3D, O OS O> ^ ||| l|l 1 1 l||l 1 1 1 1 1 1 1 1 1 1 1 I 1 1 | | | .||||||||| |||| K}}&3^3*wa-3* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 gg^^^ r-l I s - l>- * r-KO O iH n< O5 CO Ci * T*< ^ QD OJ r-( OS p.- J ll.l.i.'^ < *L<. e ^S > , ,, .> ,.W., , r-ICi.HT-ICOOI-Ojr i OO*aOJeOOl^iNaoaOCO^' 'O'*lOlOiOOOiOiOOOiOCOCOtCQOt>.ticOQ9 1 + Tj-QOOiOS 0 03 CO * 00 TJI * <# " " """ " j t^ TH W GO i-l es ^o'|-?|'S55 ' Brag's l-g'l: Sal' '2lo-32S.S S l llillllslll I Ililll|illlililiilli111l1i 566 MEAN TEMPERATURE AT DIFFERENT PLACES. Marseilles to 16. The following table gives the highest and lowest degrees of temperature observed at different places. Minimum. Maximum. Difference. Surinam .... 70,3 90,1 19,8 Pondicherry . . . .71 112,3 41,3 Esna (Egypt) . . . 117,3 Cairo .... 48,3 104,2 55,9 Rome .... 22,1 100,4 78,3 Paris . . . 9,3 101,1 110,4 Prague . . . 17,5 95,9 113,4 Moscow . . . 38 89,6 127,6 Fort Reliance (North America) 70 Considerable deviations from the normal annual course of heat do not occur locally, but are scattered over wide districts; thus, for instance, the winter of 1821 and 1822 was very mild in Europe, but in the December of the latter year a severe cold prevailed over the whole of Western Europe. A similar very considerable deviation never has, however, been spread over an entire hemi- sphere. The northern hemisphere is generally divided in a northern to a southern direction into two halves, upon which op- posite deviations from the normal temperature may be observed; these deviations are greatest in the middle of the two halves, while a more average temperature is perceived where they ap- proach each other. Thus, in February, 1828, it was very cold in Kasan and Irkutzk, unusually mild in North America, whilst Europe remained unaffected between these two opposite deviations. In December, 1829, this maximum of cold inclined towards Berlin, while it also continued to be very marked at Kasan; in North America, however, the weather was unusually mild ; but in December, 1831, the excessive cold was limited to America. Generally speaking, these deviations from the average range of heat are observed to be similar in Europe and Asia, and opposite in America. Frequently, although not so remarkable, the boundary line of opposite deviations runs from east to west. A deviation from the mean temperature often continues for a long time in the same direction. Thus, from June, 1815, to the December of 1816, there prevailed in Europe an unusually low degree of temperature, which occasioned the failures in the crops ISOTHERMAL LINES. 567 in 1816 ; 1822 was a remarkable year for the vines, the unusual heat continuing then from November, 1821, to November, 1822. From this it follows, that the opinion so prevalent of a cold winter succeeding a hot summer, and a warm winter a cold sum- mer, is altogether erroneous, since the contrary often occurs, as may be seen from the examples above given ; thus, too, the hot summer of 1834 succeeded a very mild winter. These deviations from the mean range of heat are more marked in winter than in summer. From all this it appears highly probable that the same quantity of heat is always distributed over the earth's surface, although unequally. A cold winter is the consequence of a long preva- lence of north-east winds, and a cold summer is induced by the continuance of south-west winds; these alternating exclusively prevalent currents of air being, as Dove has shown, the controlling agents in the relations of weather. If a hot summer is to succeed a cold winter, the north-east wind must prevail throughout the whole year ; while, on the other hand, the wind must blow chiefly from the south-west for the same space of time to bring a cold summer after a mild winter. Isothermal Lines. A table of the kind given at page 565, con- tains many of the elements, from which we may calculate the distribution of heat over the earth's surface. At all events, we may see from such a table that all places lying under the same degree. of latitude have not the same mean temperature. Thus, for instance, the mean annual heat at the North Cape is 32,1 ; whilst Nain, on the coast of Labrador, has a mean annual tem- perature of 25, although Labrador is 14 south of the North Cape. Humboldt was the first to give us a clear view of the distribution of heat over the earth, making use, for this purpose, of his isothermal lines, by which he connected together all such places in the same hemisphere having equal mean annual tempe- ratures. If we suppose, for instance, a traveler starting from Paris to make a journey round the earth in such a manner as to visit all places of the northern hemispheres which have the same mean annual heat as Paris, that is, 51,4, the course he will thus pursue will be a line of equal mean annual heat, consequently an isother- mal line; this line, instead of corresponding with the degree of 568 ISOTHERMAL LINES. latitude of Paris, will be irregular and curved, passing through places having a very different latitude from Paris. Fig. 518 represents the earth's surface in Mercator's propor- tions, with the isothermal lines at every 5 degrees. At the ter- restrial equator, the mean temperature of the sea-coast is 81,5, although somewhat less upon the western coast of America and Africa ; in the interior of these two continents, especially in that of Africa, the mean temperature is higher than on the sea-shore ; the mean temperature of the equator in the latter continent is above 84. An examination of the chart in Fig. 518, will spare us a fur- ther description of the course of the isothermal lines. We observe how considerable their curves become in the northern hemisphere the further we remove from the equator; the isothermal line of 32, for instance, ascends from the southern end of the coast of Labrador across Iceland towards the North Cape, in order to de- cline again considerably in the interior of Asia. Where the isothermal lines incline the farthest towards the south, they describe a concave ; and where they ascend the highest towards the north, a convex vertex. The southern turning points of the isothermal lines lie in the east of North America and in the interior of Asia, while the northern turning points lie on the western coasts of Europe and America. The relations of temperature of the southern hemisphere are not nearly so perfectly known to us as those of the northern hemi- sphere; we may, however, consider it as established, that the southern is colder than the northern hemisphere, although the difference may, perhaps, be less considerable than we are gene- rally disposed to assume it. The circumstance that has probably contributed to the opinion that the southern is so much colder than the northern hemisphere, is, that the relations of temperature of the southern part of America have been compared with those of like northern latitudes in Europe, where the isothermal lines ascend so very considerably to the north; the matter is very different when we compare districts of South America with those lying equally far from the equator on the east side of North America. That the southern hemisphere is somewhat colder than the northern, arises probably from the fact, that in the former, water, and in the latter, land, predominates. The continent is much more ISOTHERMAL LINES. .069 48' 570 ISOTHERMAL AND ISOCHIMENAL LINES. heated by the absorption of the sun's rays than the sea, which reflects a great portion of them. Isothermal and Isochimenal Lines. We have thus stated that all places lying on the same parallel circle have not the same climate; here, however, the question arises, whether all places on the same isothermal lines, consequently such as have the same mean annual heat, have likewise otherwise equal climatic rela- tions. We need only look at the table, page 565, in order to convince ourselves that such is not the case. Thus, for instance, Edinburgh and Tubingen have the same mean annual temperature of 47,6; at the former place, however, the mean temperature of winter is 38,6, at the latter 32,2 F.; Tubingen, consequently, has a far colder winter than Edinburgh. But then, again, the mean summer temperature of Tubingen is 62,7 F., while it is only 58,4 F. for Edinburgh. With a like mean annual tempe- rature, Edinburgh has, therefore, a milder winter and a colder summer than Tubingen. In order to know the relations of heat of a country, it is not sufficient to be acquainted with its mean annual temperature; we must also know how heat is distributed during the different seasons of the year. This distribution may be shown upon an isothermal chart, by setting down, according to Humboldfs idea, the mean summer and winter temperature against the different places upon one and the same isothermal line, which could not be done on our isothermal chart, owing to its small size ; we shall thus see, that in the immediate vicinity of the convex summit of the isothermal lines, the differences between the mean summer and winter temperature are the least; the same reasons, consequently, which cause the isothermal lines upon the western coast of Europe and America to rise so far to the northward, make the difference between the summer and winter temperature less considerable. A very good idea of the distribution of heat in winter and summer may be obtained by means of a chart, in which all places having the same mean winter temperature are connected together by curved lines, as are also all the places that have the same mean summer temperature. The lines of like mean winter temperature are termed isochimenal, and those of like mean summer tempe- rature, isothermal. Fig. 519 represents a small chart of Europe with the isothermal and isochimenal lines drawn at every 5 degrees. ISOTHERMAL AND ISOCHIMENAL LINES. 571 Fig. 519. flOC 20 C. +4 F. The curves, whose corresponding temperatures are on the right the chart, are the isockimenal, and the other the isothermal . We may easily see from this chart, that the western coasts the southern part of Norway, Denmark, a portion of Bohemia Hungary, Transylvania, Bessarabia, and the southern extre- mity of the peninsula of the Crimea, have the same mean winter temperature of 0- (32 F.). Bohemia, however, has the same immer heat as the districts lying at the mouth of the Garonne, in the Crimea the summer is far hotter. Dublin has the ame mean winter temperature, viz., 5 (41 F.) as Nantes, Upper Italy, and Constantinople, with the same summer heat as Dron- theim and Finland. The isothermal line of 20 (68 F.) passes from the mouth of the Garonne, nearly over Strasburg and Wurzburg to Bohemia, the Ukraine, the country of the Don Cossacks, somewhat to the north of the Caspian Sea ; how different, however, is the mean winter temperature at different places upon this line ! On the western coasts of France it is 5= '41- F.), in Bohemia (32 F.), in the Ukraine 5 C (23 F.), and somewhat to the north of the Caspian Sea even 10 (14 F.). 572 THE CLIMATE ON LAND AND AT SEA. The Climate on Land and at Sea. The consideration of the last map, and the table at page 565, leads us to the important differ- ence between the climate at sea and on the land, or, as we may also express it, between the continental and littoral climate. The differences between the summer and winter temperature increase with the distance from the sea ; on the sea-side the summers are cool and the winters mild, whilst in the interior we have hot sum- mers and cold winters. These differences appear very marked, on comparing the relations of temperature of the western shores of Europe with those of northern Asia. In order to be able easily to mark the relation of the mean annual temperature to the dis- tribution of heat, we have given examples derived from the table, page 565, the mean annual temperature first, the mean summer temperature above, and the mean winter temperature below a horizontal line : Littoral climate. Continental climate. N OTth Cape . -OiM Mh*. . ,0^(3^1) ***. .- 0, M05COW ._3,a The influence that such climatic differences must exercise upon vegetation is evident. Thus, in many parts of Siberia, at Jakuzk, for instance, where the mean annual temperature is - - 9,70 (14,7 F.), while the mean winter temperature is 38,9 (38,1), wheat and rye are raised upon a soil which remains constantly frozen at the depth of 3 feet; while in Iceland, where the mean temperature of the year is very much higher, and the winter's cold but inconsiderable, it is impossible to raise any of the cereals, as the low summer temperature does not suffer them to ripen. In the north-east of Ireland, where there is scarcely any ice or frost in the winter, at the same latitude as Konigsberg, the myrtle thrives as well as in Portugal; on the coast of Devonshire, the Camellia Japonica and the Fuchsia Coccinea live through the winter in the open air ; the winter is not colder in Plymouth than in Florence and Montpellier; the vine will not thrive in England, however, for, although it can endure a tolerably strong degree of cold, it requires a hot summer to make the fruit ripen and yield a drinkable wine. CAUSES OF CURVATURE OF THE ISOTHERMAL LINES. 573 These differences are owing to the more easy absorption and radiation of heat, which becomes heated and again cooled more rapidly than the sea, which, by the continent, is everywhere of a uniform nature, and from its transparency, and the considera- ble amount of specific heat of water, is neither so rapidly heated, nor so speedily deprived of the heat it has once acquired. The temperature of the surface of the sea is, on that account, far more uniform ; the diurnal as well as the annual alternations are incom- parably less than in the middle of large continents, whence arises the above-mentioned difference between the climate on the land and at sea ; it is, likewise, augmented by the sky, which is mostly overcast on the shores of countries lying towards the north, and tempers the heating influence of the solar rays in summer, and checks the excessive cooling of the earth in winter by radiation of heat. Causes of the Curvature of the Isothermal Lines. The most important causes that contribute to the curvature of the isother- mal lines so much to the north on the western shores of Europe and America, are essentially as follows: In the northern temperate zone, south-west and north-east winds prevail. The former come from the equatorial districts, and partially bear the heat of the tropics towards colder regions ; this warming influence of the south-west winds is, however, most marked in those districts which are the most exposed to south-western currents of air, and thus we see why it is that the western shores of great continents become warmer than the eastern coasts, and that the isothermal lines in Europe, which is actually only a peninsular prolongation of the Asiatic continent, and on the western shores of North America, ascend further to the north than in the interior of Asia, and on the eastern shores of North America. A second cause, to which Europe owes its relatively warm cli- mate, is this, that, in the equatorial region, it is bounded towards the south, not by a sea, but by an extensive continent, Africa, whose vast extent of desert and sand render it extremely hot when exposed to the vertical solar rays. A warm current of air rises continually from the glowing hot sandy wastes, to descend again in Europe. Finally, the current known by the name of the Gulf Stream, contributes considerably to make the European climate milder. 574 CAUSES OF CURVATURE OF THE ISOTHERMAL LINES. The origin of this current is to be sought for in the Gulf of Mexico, where the water is at a temperature of 87 F. Issuing from the Gulf, between Cuba and Florida, the stream at first skirts the American shores, and then, as it comes into higher latitudes, turns with decreasing temperature eastward towards Europe. Although the Gulf Stream does not actually reach the shores of Europe, it nevertheless distributes its heated waters, under the influence of the prevailing south-west winds, to the European waters, as is proved by our finding, on the western shores of Ire- land and on the coast of Norway, the fruits of trees that grow in the hot zone of America; the west and south winds remain, there- fore, long in contact with a sea-water, whose temperature between 45 and 50 degrees of latitude does not, even in January, sink below from 51 to 48 F. Northern Europe is thus separated by the influence of the Gulf Stream from the circle of polar ice, by means of a sea free from ice ; even at the coldest season of the year the limits of polar ice do not reach the European shores. Whilst all circumstances thus combine to raise the temperature in Europe, many causes contribute in Northern Asia to lower the isothermal lines very considerably. In the south of Asia there are no extensive districts of land between the tropics, but merely a few peninsulas comprised within this zone ; the sea, however, does not become so much heated as the African deserts, partly because the water absorbs rays of heat to an incomparably smaller extent, and partly, also, because a great quantity of heat goes off in the latent state, owing to the constant evaporation of water from the surface of the sea. The warm currents of air, which, rising from the basin of the Indian Ocean, would convey the heat of the tropics to the interior and north of Asia, are impeded in their course by the huge mountain ranges in the south of Asia, whilst the land, which gradually flattens towards the north, is left exposed to the north and north-east winds. While Europe does not stretch far northward, Asia penetrates a considerable way into the Arctic Sea, which, deprived of all those heating influences by which the temperature of the European seas is raised, is almost always covered with ice. In every direction the northern shores of Asia penetrate the wintry limits of the polar ice, the summer boundary of which is only removed for a short time, and at a few places from the coasts; that this circumstance, however, must considerably lower the temperature, will be easily understood TEMPERATURE OF THE GROUND. 575 when we consider how much heat becomes latent by the fusion of such masses of ice. The considerable depression of the isothermal lines in the in- terior, and upon the eastern shores of North America, depends in part upon the south-west winds, which, not being sea, but land- winds, are therefore unable any longer to diffuse the milder influ- ence that they exert upon the western shores. Whilst the European shores are washed by warmer waters, cold sea-currents come from the north and south towards the eastern shores of North America. Such a current coming from Spitzbergen, passes be- tween Iceland and Greenland, and then combines with the currents that come from Hudson's Bay and Baffin's Bay, passes down the coast of Labrador, past Newfoundland, and empties itself finally in the Gulf Stream at 44 N. lat. This arctic cur- rent bears the cold of the polar regions, partly by the low tem- perature of the water, but chiefly by floating icebergs, into the southern districts, and thus becomes a main cause of the con- siderable depression of the isothermal lines on the eastern coasts of America. Temperature of the Ground. We have hitherto only spoken of the temperature of the air, and not of that of the upper layers of the ground, which vary considerably from the temperature of the air, according to the nature of the surface. Where the soil is barren, deprived of vegetable growths, stony or sandy, it becomes far hotter by the absorption of rays of heat than one that is covered with plants; for instance, a piece of meadow-land be- comes much cooler by nocturnal radiation than the air, whose temperature is made more uniform by the effect of continued currents. In the deserts of Africa, the heat of the sand often amounts to from 122 to 140 F. A soil covered with vegetable growths remains cooler, owing to the solar rays not striking it directly ; the plants themselves combine, to a certain degree, a large amount of heat, whilst a quantity of water is evaporated by vegetation ; but they cool so considerably in their great capacity of emission of heat by radiation, as we shall see when we come to speak of the formation of dew, that the temperature of the grass often falls from 10 to 15 below that of the air. In the interior of woods and forests the air is constantly cool, owing to the thick leafy covering acting in the same cooling manner as the 576 TEMPERATURE OF THE GROUND. covering of grass, and because the cooled air is precipitated upon the tops of the trees. The heat on the uppermost surface of the ground can only penetrate to the interior by degrees, owing to its imperfect capa- city for conducting heat ; the deeper layers of the soil lose their heat less rapidly than the upper ones, and thus at some little depth the variations of temperature are less marked than on the surface itself. In Germany these variations of temperature dis- appear at a depth of 6 decimetres, (about 190 feet,) and at a greater depth the annual variations even vanish ; so that a tem- perature prevails here differing but little from the mean tempera- ture of the place. Although all the heat upon the earth's surface comes from the sun alone, the earth has also its own peculiar heat, as may be proved by the increase of temperature observed at great depths. If the heat augment towards the centre of the earth in the same proportion as our observations indicate, at the depth of 3200 metres, there would be a temperature equal to that of boiling water, while at the centre of the earth all bodies would be in a state of fusion. That upon the surface of our planet we perceive nothing of this intense heat of its interior may be explained by the bad capacity for conducting heat possessed by the cooled earth's crust, which surrounds this glowing nucleus. Springs that yield the most copious supply of water vary but little in their temperature at the different seasons ; in our hemi- sphere they attain their highest temperature in September, and their lowest in March ; the difference between the two amounting generally to only 1 or 2. Springs which arise from a great depth have a far higher tem- perature, as is the case with salt and other mineral springs. The water of many of these salt springs has almost the temperature of the boiling point. Decrease of Temperature in the Upper Regions of the Mr. The heating of the air arises from two causes : in the first place it absorbs a part of the rays of heat coming from the sun ; but as the air absorbs rays of heat to a much more inconsiderable degree than the earth's surface, the air is likewise much less heated by the absorption of rays of heat than the ground ; thus the atmo- sphere receives the greatest portion of its heat from below. If the air were not an elastic fluid, the density of the atmosphere TEMPERATURE OF THE GROUND. 577 would remain the same for all elevations; the strata of air warmed upon the surface would ascend to the limits of the atmosphere, and the uppermost strata of the air surrounding our earth would likewise be the warmest. But as the warm strata of air expand in their ascent, heat is absorbed by this expansion, and their tem- perature lowered : from which it follows that the higher strata are the coldest. We may easily convince ourselves that such a depression of temperature actually occurs in the higher regions of the air, when we ascend into these regions by means of a balloon, or to the summit of some high mountain. In the Alps, an elevation of 585 feet corresponds, on an average, to a depression of temperature of 1. As a consequence of the decrease of temperature with an increase of altitude, the summits of high mountains are always covered with snow. The limits of perpetual snow naturally lie higher in proportion as we approach the torrid zone. The height of the snow-line is as follows : The coast of Norway . 720 metres 2340 feet Iceland ... 936 " 3042 " The Alps . . . 2708 8801 " Mount Etna . . . 2905 9441 The Himalayas . . 4500 " 14625 Mexico . . . 4500 Quito .... 4800 15600 [These estimates are lower than those given by other authors. It is generally stated that the snow limit on the Himalayas is 17,000 feet, and in Mexico 14,700 to 15,030 feet.] 49 578 ON THE PRESSURE OF THE ATMOSPHERE AND WINDS. CHAPTER II. ON THE PRESSURE OF THE ATMOSPHERE AND WINDS. WE have already seen that the pressure of the air is measured by the barometer. We, however, observe constant variations in this instrument, indicative of an alternate decrease and increase in the pressure of the atmosphere. These variations of the thermometer are either periodical or accidental. Periodical variations are very marked in their character in the tropics; for instance, the thermometer falls from 10 A.M. to 4 P.M., then rises until 11 P.M. ; falls again till 4 A.M., and again rises until 10 A. M. The barometer thus indicates two daily maxima, at 10 A. M. and at 11 P. M., and two minima, at 4 A. M. and at 4 P. M. The amount of these diurnal variations is about 2 mm (0,0787 inch). An annual period of the fluctuations of the barometer is also very strongly marked within the tropics. Thus, north of the equator the barometer falls from January till July, and then rises again from July to January. In July the barometer stands, on an average, from 2 to 4 millimetres (0,0787 to 0,1574 in.) lower than in January. In higher latitudes, the accidental fluctuations of the barometer are so considerable as to make one lose sight of the trifling periodic variations presented in these regions. In order to decide whether there are not also a periodical rise and fall in the acci- dental oscillations of the barometer, it is necessary to compare the mean numbers of a large series of barometric observations made 'at regularly settled hours of the day. If we observe the barometer for the term of a month at several fixed hours of the day, and take the mean of all the observations, it will suffice to prove the existence of a diurnal period of the fluctuations of the barometer even for our own region. Observations of this kind have proved that these periodical CAUSES OF OSCILLATIONS IN THE BAROMETER. 579 oscillations occur even in our latitude, the barometer standing at 9 A.M., on an average, 0,7 millimetres (0,027 in.) higher than at 2 P.M.; the mean height of the barometer is also somewhat less in summer than in winter. Causes of the Oscillations in the Barometer. The cause of all these oscillations is to be sought for in the unequal and constantly varying distribution of heat over the earth's surface. As the distribution of heat constantly varies, the equilibrium is likewise disturbed at every moment, and currents of air arise which strive to restore the balance ; the air is thus in constant motion, some- times more heated, and then lighter, and at other times more cooled, and consequently denser. As it contains sometimes more, some- times less vapor, the pressure of the columns of air will also be exposed to continual changes, indicated by the barometer. That actual changes of temperature are really the causes of the oscillations of the barometer, is proved by their being most incon- siderable in the tropics, where the temperature varies so little ; in higher latitudes, on the contrary, where the variations of tem- perature are always more considerable, the amplitude of the acci- dental oscillations of the barometer is likewise very great: even in summer, when the temperature is generally less changeable, the oscillations of the barometer are less than in winter. Although we may generally show that the unequal and con- stantly varying temperature of the air must be followed by con- stant ch-anges in the amount of the atmospheric pressure, we are, however, still far from being able, satisfactorily, to explain these phenomena. If the air is much heated at any spot, it expands; the column of air rises above the mass of air, and rests upon the colder parts surrounding it; the ascended air, consequently, flows off laterally from above, the pressure of the air must decrease at the warmer places, and the barometer sinks ; in the colder parts, however, the barometer ascends, because the laterally diffused air, in the upper regions of the heated places, is distributed over the atmosphere of the cooler parts. We hence see why, in our districts, the barometer stands, on an average, lowest with a south-west and highest with a north-east wind : the former winds bring us warm, and the latter cold, air. Whenever there is a warm current of air, the atmosphere must have a greater height than where the cold wind prevails, if the 580 CAUSES OF OSCILLATIONS IN THE BAROMETER. pressure of the whole column of air is to be equal at both places; and if such were actually the case, the air of the warm current would flow off from above, consequently the barometer would fall when exposed to the warm, and rise when exposed to the cold. In Europe, south-west winds, generally, are the ones which bring rain, because, coming from warmer seas, they are satu- rated with vapor, which, gradually condensing, falls as rain when the wind reaches colder districts. In this condensation of vapor, we have another reason why the barometer falls with the south- west winds. As long, for instance, as the vapor of water, as a gas, forms a constituent of the atmosphere, it contributes to the atmospheric pressure, and thus a portion of the column of mer- cury in the barometer is sustained by the vapor, and the baro- meter falls when the vapor is separated by condensation from the atmosphere. As the south-west winds, which occasion a sinking of the baro- meter in our latitudes, bring a damp air and rainy weather, whilst the north-east winds, which- dry the air and clear the sky, cause the barometer to rise, we may say, that, in general, a high state of the barometer indicates fine weather, whilst its depressed condi- tion forebodes the contrary. This is, however, only, as we have before remarked, an average rule, for the sky is often cloudy with a north-east wind, and clear with one coming from the south- west; the statement is in so far true as that the barometer stands high or low according to which of these two winds prevails, the remark in the latter case being nearly true on an average. We are unable to account for such anomalies, from our insufficient knowledge of the manifold elements which affect the condition of equilibrium of the atmosphere. That a high state of the barometer generally indicates clear weather, and a fall of the mercury in the barometer tube the contrary, is only true for those places where the w r arm winds are those which bring the rain. At the mouth of the river La Plata, for instance, the cold south-east winds coming from the sea, and which cause the barometer to rise, are winds which bring rain, while the warm north-west winds, that make the barometer fall, are dry land-winds, and bring clear weather. To the cause that rain is here conveyed, by cold winds, is to be ascribed the small quantity of rain in these regions ; whilst, at the same latitude, on ORIGIN OF THE WINDS. 581 Fig. 520. the western coast of South America, much rain falls, although here, too, the warm north-west wind comes from the sea. Origin of the Winds. If in winter we partially open the door of a heated apartment communi- cating with a cold space, and hold a burning taper to the upper part of the crevice (as seen in Fig. 520), the outward direction of the flame will indicate the presence of a cur- rent of air passing from the heated apartment into the cooler atmo- sphere. As we move the taper downward, the flame will con- stantly become more and more up- right ; until at about the middle of the height it will remain perfectly still, being no longer affected by currents of air. On moving it downward, however, the flame will be driven inward. We thus see that the heated air flows out at the top of the room, whilst the cold air enters near the floor. As here the unequal warming of the two spaces gives rise to currents of air on a small scale, so does the unequal and ever- changing warming of the earth's surface give rise to those currents of air which we call winds. Here, too, we may see the air ascend in the more heated regions, and flow off towards the colder parts, whilst, below, the air flows from the colder to the wanner regions. We have a simple illustration of this in those land and sea- winds, which we so frequently observe on the sea-shore, especially of islands. A few hours after sunrise a land-wind sets in from the sea, owing to the land being more strongly heated than the sea by the sun's rays ; the air rises over the land, and flows to- wards the sea, while, from below, the air is borne from the water towards the shore. This sea-wind is at first but light, and only perceptible on the coast ; by degrees, however, it increases, and then it may be felt out at sea at a considerable distance from land ; between 2 and 3 P. M. it is strongest, afterwards dying away, until, at sunset, a calm sets in. The land and sea are now cooled by the radiation of heat towards the sky, the former, however, more rapidly than the latter, and the air then flows 49* 582 TRADE-WINDS AND MONSOONS. towards the sea from the lower regions of the land, whilst an oppositely directed current is perceptible in the upper regions of the air. A rapid condensation of atmospheric vapor is also to be reckoned amongst the causes which give rise to violent storms. When we consider what an enormous mass of water falls to the ground during a sharp shower of rain in the course of a few minutes, and what an enormous volume this water must have comprised when suspended in the air in the form of vapor, it appears evident that a considerable rarefaction of the air must be occasioned by this sudden condensation of vapor, and that it must rush with violence into the rarefied space, the more so, as owing to the condensation of the vapor, the temperature of the air is raised by the liberated heat, and a strong rising current thus engendered. We often observe the clouds pass in a direction different from the one indicated by the weather-cock, and that the higher clouds move in an opposite direction to those below them, whence it is evident that, at different elevations, currents of air move in con- trary directions. Trade-winds and Monsoons. When Columbus, on his voyage of discovery towards America, saw that his ship was driven on by a continual east wind, his companions became filled with terror, as they feared they should never be able to return to Europe. This wind of the tropics, which constantly blows from the east to the west, and so greatly excited the wonder of the first navi- gators of the 15th century, is the trade-wind. Seamen avail them- selves of this wind to sail from Europe to America, by steering southward from Madeira to the vicinity of the tropic, where they are then carried westward by the trade-wind. This course is so certain, and attended with so little labor, that the Spanish sailors gave the name of Ladies' Gulf (el Golfo de las Damas) to this portion of the Atlantic Ocean. This wind also blows in the South Sea, and the Spanish navigators let their ships be propelled by it in a straight line from Acapulco to Manilla. In the Atlantic Ocean the trade- winds extend from 28 to 30 lat.; but in the great ocean (the Pacific) only to 25 N. lat. In the northern half of the torrid zone, the trade-wind blows in a north-east direction, and becomes more decidedly east as it ap- proaches the equator. The limits of the trade-wind are less well defined in the southern hemisphere, where it has a south-east TRADE-WINDS AND MONSOONS. 583 direction, and inclines more towards due east the more it ap- proaches the equator. These winds blow round the whole globe ; but, as a general rule, they do not become perceptible within fifty German miles from the land. Where the north-east trade-wind meets the south-east trade-wind of the southern hemisphere, the two merge into a purely eastern wind ; which, however, is not perceptible, because the horizontal motion of the air (which has been heated by the intensity of the sun's rays, and thus made to ascend), is neutralized by this ver- tical motion. There would be almost a perfect calm in these regions if the violent storms accompanying the torrents of rain, which occur almost daily with thunder and lightning, were not to disturb the calm of the atmosphere, and prevent the blowing of soft regular winds. This zone, which separates the trade-winds of both hemispheres, is the region of calms. The little map, seen in Fig. 521, serves to indicate the regions Fig. 521. in which the trade-winds prevail. The middle of the region of calms, extending about 6 in width, does not coincide with the equator, as we might be led to expect, but lies to the north of it. During our summer months, the zone of these calms is broader, and its northern boundary is further removed from the equator, whilst its southern line is but little changed. The cause why the region of calms lies in the northern hemi- sphere, may be sought for in the configuration of the continent. The trade winds may be easily explained. The air that has been strongly heated in "the equatorial regions ascends, and rising 584 TRADE-WINDS AND MONSOONS. over the colder masses of air on either side, flows upwards towards the poles, whilst below, it flows from the poles towards the equator. If the earth did not rotate on its axis, the trade- wind in the northern hemisphere would blow directly from north to south, while in the southern hemisphere its direction would be opposite. The earth, however, rotates from west to east, and the atmosphere surrounding it partakes of this rotatory motion. The nearer a place upon the earth's surface is to the poles, the slower will it move during its twenty-four hours' revolution, be- cause the space it describes diminishes as it recedes from the equator. The rotatory velocity of the mass of air over the earth, is, consequently, less near the poles than it is at the equator; if, then, a mass of air comes from higher latitudes to the equator, it will pass over districts with a less velocity of rotation than that with which these move from west to east ; in relation to the places rotating below it, it will, therefore, have a motion from east to west. This motion combines with the motion towards the equator to produce a north-east in the northern, and a south-east wind in the southern, hemisphere. The air which rises in the equatorial regions flows off on either side towards the direction of the poles. The course of the upper trade-wind is naturally directly opposite to that of the lower one, being south-west in the northern, and north-west in the southern, hemisphere. We may prove by facts, that there is actually a trade-wind in the upper regions of the air; thus, for instance, on the 25th of February, 1835, at an eruption of the volcano of Cosiguina, in the State of Guatimala, the ashes were ejected to the elevation of the upper trade-wind, and were carried by it in a south-west direc- tion, and precipitated on the island of Jamaica, although the north trade-wind was blowing in the regions below. At a greater distance from the equator, however, the upper trade-wind inclines more and more towards the earth's surface. At the summit of the Peak of Teneriflfe, west winds almost always prevail, whilst the lower trade-wind blows at the level of the sea. In the Indian Ocean, the regularity of the trade-winds is dis- turbed by the configuration of the land surrounding this sea for instance, by the Asiatic continent. In the southern part of the Indian Ocean, between New Holland and Madagascar, the south- east trade-wind prevails throughout the year, while a constant WINDS IN HIGHER LATITUDES. 585 south-west wind blows in the northern part of this ocean during six months of the year, and a constant north-east wind during the remaining period of the year. These regularly alternating winds are called monsoons. The south-west wind blows from April till October, while the north-east wind prevails during the other months. As during the winter the Asiatic continent is cooled, while a greater heat is engendered in the southern regions, a north-east trade-wind must naturally pass from the colder parts of Asia to hotter regions. At this time, too, the north-east trade-wind is separated from the south-west trade-wind, in the Indian Ocean, by the region of calms. During the summer months, the passage of the south-east trade- wind between New Holland and Madagascar, is not disturbed, whilst, in the northern parts of the Indian Ocean, the wind that had blown during the winter from the north-east, is now changed into a south-west wind, owing to the Asiatic continent becoming so strongly heated, and a current of air being thus conveyed towards the north, which, by the rotation of the earth, is converted into a south- w r est wind. Winds in Higher Latitudes. The upper trade-wind, which brings the air from the equatorial regions, falls more and more, as has been already mentioned, and, finally, reaches the earth as a south-west wind ; when beyond the region of the trade- winds, the two currents of air that pass from the poles to the equator, and back from the equator to the poles, no longer blow over, but even with each other endeavoring to replace one another; thus, on the south-west or the north-east wind predominating from time to time, we see, on the transition of the wind from one direction to another, the currents of air moving in all points of the weather- cock. Although the south-west and north-east winds predominate also in higher latitudes, we find no regularly periodic alternation in their occurrence, as is the case with the monsoons in the Indian Ocean. The following table indicates the frequency of the winds in different countries; giving the number of average times that each wind blows during every one thousand days. 586 LAWS OF THE CHANGE OF WIND. Countries. N. N.E. E. S.E. S. S.W. W. N.W. England 82 Ill 99 81 Ill 225 171 120 France . 126 140 84 76 117 192 155 110 Germany 84 98 119 87 97 185 198 131 Denmark 65 98 100 129 92 198 161 156 Sweden . 102 104 80 110 128 210 159 106 Prussia . 99 191 81 130 98 143 166 192 N. America 96 116 49 108 123 197 101 210 Laws of the Change of Wind. Although the changes in the direction of the wind appear, on a superficial view, to be wholly devoid of rule in our regions, attentive observers have long since made the remark that winds generally succeed each other in the following order : S. SW. W. JYW. JV. WE. E. SE. S. This alternation in the winds may be the most regularly observed during the winter. The changes of the barometer and thermometer, which are connected with these changes of wind, have been well described by Dove, in the following words. " When the south-west wind, constantly increasing in force, at length predominates, it raises the temperature above the freezing point; and the snow is consequently converted into rain, whilst the barometer falls to the lowest mark. The wind then veers round to the west, and the dense flakes of snow indicate the accession of a colder wind no less than the rapid rise of the barometer, the motion of the weather-cock, and the thermometer. A north wind clears the heavens, and a north-east wind effects a maximum of cold, and of the barometer. This, however, is gradually lowered, and the occurrence of fine cirri indicates by the direction from which they come, the advent of a more southern wind, which is soon felt by the barometer, although the weather- cock may not have experienced any change, and may still be pointing due east. The southern wind, however, continues to drive the eastern current downward, and on a decided falling of the mercury, the weather-cock points south-east, when the heavens again become gradually overcast, and with the increase of heat, the snow that had fallen with a south-east and south wind, is again converted into rain by the south-west wind. The same then begins again, the change from the east to the west course being generally characterized by the occurrence of a short interval of fine weather." The shifting of wind does not always admit of being as regu- LAWS OF THE CHANGE OF WIND. 587 larly traced as is indicated above, there being often a recurrence of the wind to its old quarter ; this, however, is far more fre- quently observed in the west than the eastern points of the com- pass. A perfect change of the wind in an opposite direction, as from south to east, north or west, is very rarely observed in Europe. The explanation of this law is obtained by the generalization of the explanation concerning the trade-winds. If the air from any cause be driven from the poles towards the equator, it will pass from places having but an inconsiderable rotatory velocity, to such as possess a greater degree of speed ; and its motion will thus acquire an eastern direction, as we have seen in the case of the trade-wind. On the northern hemisphere the winds which arise in the north pass therefore, in their gradual progress, through the north-east to the east. If an east wind thus arise, it will, if the same causes continue in operation which have driven the air towards the equator, act retardingly upon the polar current ; the air will acquire the same speed of rotation as the place over which it passes ; and if the tendency to return to the equator still continue, the wind will shift back to the north, when the same series of phenomena will be repeated. If, however, after the polar current has predominated for a time, and the direction of the wind has become eastern, currents set in from the equator, the east wind will pass from south-east to the south. If the air move from south to north, it will reach places having an inconsiderable velocity of rotation with the greatest velocity of rotation of the polar regions nearest the equator ; hastening, as it were, in advance of the earth's surface which rotates from west to east, until the southern direction of the wind is gradually changed to the south-west, and finally made quite western. By the constant tendency of the air to pass towards the poles, the wind is made to veer back again to the south, exactly in the same manner as the east wind veers to the north ; if, how- ever, the equatorial current be displaced by a current from the poles, the west wind will veer from north-west round to the north. In the southern hemisphere, the wind must necessarily veer about in an opposite direction. Where the trade-winds blow in the tropics, there is no com- plete rotation on the earth's surface ; the direction of the trade- 588 STORMS. wind is, therefore, only inclined more towards the east in its motion. In the region of the monsoon, there is only one complete rota- tion in the course of the whole year. We therefore see that the relations of the winds in the tropics correspond to the simplest case of the law of rotation. Storms. Storms are the result of a considerable disturbance in the equilibrium of the atmosphere, depending very probably upon a rapid condensation of vapor, as has already been surmised. More recent investigations have shown that storms may, for the most part, be regarded as great whirlwinds in motion. Storms rage with much more violence in the tropics than in higher latitudes ; the devastations occasioned by these hurricanes, known in America by the name of Tornadoes, are truly frightful. Thus, for instance, in the hurricane that devastated Guadaloupe on the 25th of July, solidly-built houses were torn up ; cannons were hurled from the top of the parapets of the batteries on which they were planted ; a plank of about 3 feet in length, 8 inches in breadth, and 10 lines in thickness, was propelled with such force through the air that it perforated the stem of a palm tree, about 17 inches in diameter, through and through. We often see how, in calm weather, sand and dust are carried by the wind with a whirling motion through the air. On the ap- proach of a storm, we may also notice larger whirlwinds of this Fig. 522. ATMOSPHERIC MOISTURE. 589 kind carrying sand, dust, leaves, and straw, &c., with them in their course. Hurricanes are nothing more than these whirlwinds on a large scale, and are generally caused by the struggle of two winds moving in opposite directions in the upper regions of the air. They usually form a double cone, the upper part of which, whose vertex inclined downwards, consists of a mass of clouds; while the lower cone, the point of which is directed upward, when formed over the sea, lakes and rivers, is composed of water or of sand, and other bodies found on land. These hurricanes are capable of uprooting trees, unroofing houses, and hurling beams to a distance of many hundred paces, &c. Water hurricanes are known as water spouts ; they often raise water to the height of many hundred feet. CHAPTER III. OF ATMOSPHERIC MOISTURE. Distribution of Vapor in the Mr. If, on a hot summer's day, we place a bowl filled with cold water in the open air, we observe that the quantity of the water rapidly diminishes, that is, it eva- porates, which means that it is converted into vapor, and then diffused through the air. The vapor of water is, like every other colorless transparent gas, invisible to our eyes, the water appear- ing to have entirely disappeared by evaporation. The water diffused through the air only becomes visible when, on returning to its fluid condition, it forms a mist, cloud, dew, or hoar-frost. In order, therefore, to convince ourselves of the ex- istence of vapor of water in the air, we must condense it by some means or another. We may immediately obtain the quantity of vapor contained i a definite volume of air, on sucking the air through a tube filled with hygrometric substances. We make use of an aspirator for the purpose of effecting a regular passage of the air through the absorption tube. The aspirator is a vessel filled with water, and 50 590 DISTRIBUTION OF VAPOR IN THE AIR. closed, excepting at two apertures ; from the one of which water constantly pours out through a tube, while the other is connected with the absorption tube in such a manner, that an amount of dry air equal to the discharged water may enter the vessel. The amount of vapor contained in a quantity of air sucked through the absorption tube, may be ascertained by weighing the tube before and after the experiment. This method of determining the quantity of water contained in the air entering the aspirator, to which various forms, more or less applicable, have been given, is somewhat uncertain, and does not yield the amount of water contained in the air at a definite moment, but merely the mean average of its quantity during the whole period of the experiment; on this account, smaller and more easily transportable apparatuses have been constructed, which are known by the name of hygrometers. It is well known that many organic bodies have the property of absorbing vapor, and thus increasing proportion ably in extent. Amongst others, we may mention hair, whalebone, &c., as hygrometric bodies, and these have, therefore, been employed in the construction of hygrometers. The best instrument of the kind is the Hair-hygrometer invented by Saussure, and which is represented in Fig. 523. The hair is fastened at its upper end to a little tongue a ; the other extremity passes over along one of the two grooves of a pulley ; while in the other groove a silk thread goes round the pulley, sup- porting a little weight f, by means of which the hair is kept at a constant tension. To the axis of the pulley, an index d is attached, which passes over the graduated arc s h, as the pulley is turned by the elonga- tion or shortening of the hair. When the instrument is in a damp atmosphere, the hair absorbs a considerable amount of vapor, and is thus made longer, while in a dry air it becomes shorter, so that the index is of course turned alternately to the one or to the other side. The instrument is graduated in the following manner. In the first place, it is placed under a receiver, the air within having been dried by chloride of calcium or by sulphuric acid. The DANIEL'S HYGROMETER. 591 point of the scale at which the index stops, under these circum- stances, is the point of greatest dryness, and is marked with 0. The instrument is then placed under a receiver, whose walls are moistened with distilled water, which is likewise poured upon the ground, on which the receiver is placed. The space below it soon becomes saturated with vapor, and the index then passes to the other end of the scale. The point at which it now stands, is the point of greatest moisture, and is marked 100. The space intervening between these two points must then be divided into 100 equal parts, which are termed degrees of moisture. The relation of these degrees to the quantity of water in the air, must, in the case of every instrument of the kind, be ascertained by means of experiments, into which we cannot enter more fully at present. DanieVs Hygrometer is represented in Fig. 524; it consists of a curved tube terminating in two bulbs ; Fi 524 the one a is either gilt, or covered with a thin metallic coating of platinum, while the other is wrapped in a piece of fine linen. The bulb a is half filled with ether, and contains a little thermometer, the graduated part of which penetrates into the tube t. The apparatus is per- fectly air-tight. If ether be dropped upon the ball b, it will cool it by its evaporation ; in the interior the vapor of the ether will be condensed, and an evaporation in the bulb a thus occasioned, since, to a certain degree, the ether dis- tils over from the warmer ball a, to the cooler one b. By the formation of vapor in the ball a, heat will be likewise absorbed, and the bulb become covered with a delicate dew. The origin of this dew admits of an easy explanation. We have seen above, that in a vacuum, the force of tension of steam cannot exceed certain limits, and that the maximum of the tension increases with the temperature. For a temperature of 68 (154 F.), for instance, the maximum of the force of tension of steam is 17,3 millimetres (.633 in.), and the corresponding density of the steam 0,00001718 ; in a vacuum of 1 cubic metre (27.0.3 cubic ft.), 592 DANIEL'S HYGROMETER. therefore, at a temperature of at most 78 (172 F,) 17,18 grms. (264.93 grs.) of water may be contained in the form of vapor. We have, however, further seen, that exactly as much steam may be contained in a space filled with air as in an equally large vacuum, and that, in this case, the force of tension of the air, and the force of tension of the steam diffused through it, correspond. At a temperature of 78 (172 F,), 17,18 grms. (264.93 grs.) of water may, therefore, be contained as vapor in 1 cubic metre of air (27.0.3 cubic ft.). We say the air is saturated with vapor, when the steam diffused through it has reached the maximum of the force of tension and density corresponding with its temperature. If we bring a colder body into an atmosphere saturated with moisture, it will cool the strata of air most contiguous ; a portion of the vapor contained will be condensed, and precipitated upon the cold body in the form of fine drops. In this manner the moisture which covers the window panes of an inhabited heated apartment is formed, if the temperature of the external air be low enough sufficiently to cool the panes of glass. The air is not always saturated with moisture, that is to say, it does not alw r ays contain as much vapor as from its temperature it might take up. If, for instance, we assume that every cubic metre of air contains only 13,63 grms. (210.49 grs.) of steam at a temperature of 78 (172 F.), the air will not be saturated, since at this temperature, each cubic metre of air is capable of containing 17,18 grms. (264.93 grs.) of vapor. The temperature at which the condensation of steam begins, that is, the temperature at which the air is exactly saturated with vapor, is called the dew point. DanieVs Hygrometer is intended for the observation of this dew point ; thus, as soon as the bulb a is cooled to the temperature of the dew point, this bulb begins to be covered with moisture, and the temperature of the dew point may be immediately ascertained from the thermometer which dips into the bulb a. If we now make use of a table giving the maximum quantity of vapor of water in a space of 1 cubic metre (27.0.3 cubic ft.) for each degree of temperature, we may likewise find, by means of such a table, what is the quantity of vapor of water in the air cor- responding to the dew point observed. AUGUST'S PSYCHROMETER. 593 August's Psychrometer is represented in Fig. 525 ; it consists of two thermometers fastened to one and the same stand : the bulb of the one is surrounded by fine linen, whilst that of the other remains free; on moistening with water the covering of the one bulb, the water will evaporate, and the more rapidly in proportion as the air is far removed from its point of saturation. The evaporation of the water is, however, accompanied by an absorption of heat, in consequence of which the covered thermometer falls. If the air be perfectly saturated with moisture, no water will be able to evaporate ; both temperatures, therefore, will stand equally high : if, however, the air be not thoroughly saturated with vapor, the co- vered thermometer will fall lower in proportion as the air is further removed from the point of satura- tion. We may judge of the condition of moisture of the air by the difference of temperature of the two thermometers. Diurnal and Annual Variation in the Quantity of Water contained in the Air. As more vapor may be diffused through the air at a high temperature, and as with an increasing heat the water eva- porates more and more from the surface of large masses of water and from the moist ground, it may well be supposed that the quantity of water contained in the air will diminish and increase in the course of the day. It has been ascertained by experiments with the above-described instruments, that, in general, the quantity of vapor in the air is increased as the temperature rises with the ascent of the sun ; this, however, only lasts till 9 o'clock, when an ascending cur- rent of air, occasioned by the strong heating of the surface of the ground, carries the vapor on high, so that the water contained in the lower strata of air diminishes, although the formation of vapor continues with the increase of the heat; this diminution continues till towards 4 o'clock; now the quantity of water of the lower strata of air again increases, because the upwardly directed current of air ceases to carry away the vapor formed ; this increase lasts, however, only until towards 9 o'clock, because the decreas- ing temperature of the air puts a limit to the further formation of vapor. 594 QUANTITY OF WATER CONTAINED IN THE AIR. In winter, when the action of the sun is less intense, the state of the case is different ; in January, we observe only one maximum of the contents of water in the air, at about 2 o'clock, and only one minimum at the time of sunrise. We say " the air is dry" when water evaporates rapidly, and when moistened objects become quickly dry owing to this rapid evaporation; and, on the other hand, we say " the air is damp" when moistened objects dry only slowly, or not at all, in the air, when the least decrease of temperature occasions a precipitation of moisture, and when somewhat colder objects become covered with moisture. We, therefore, call the air dry when it is far from being at its point of saturation, and moist when the dew point approaches very nearly to the degree of the temperature of the air; in thus judging of the dryness or the dampness of the air, we do not, therefore, express any opinion of the absolute quantity of water contained in the air. If on a hot summer's day at a temperature of 77, every cubic metre (27.0.3 cubic ft.) of air con- tains 13 grms. (200.76 grs.) of vapor, we say the air is very dry ; for at such a temperature the atmosphere can contain 22,5 grms. (339.76 grs.) of vapor for every cubic metre of air, other- wise the air must be cooled to 59, in order to be saturated by the same quantity of aqueous vapors. If, on the contrary, in winter, at a temperature of 35,6, the air contains only 6 grms. (92.66 grs.) of vapor, it is very damp, since the atmosphere is nearly perfectly saturated with vapor corresponding to that temperature, and the least decrease of temperature is followed by a precipita- tion of moisture. In this sense we may say, that, at the time of sunrise, the air is the dampest, although the absolute quantity of water is less then than at any other time of the day. Towards 3 o'clock p. M. in summer, the air is dryest. The absolute quantity of water contained in the air is, like the mean temperature of the air, at a minimum in January; it increases until July, when it reaches its maximum ; then, however, it again decreases until the end of the year. Although the quantity of water contained in the air is greater in summer than in winter, we say that the air is dryer in summer, because, on an average, it is further removed from the point of saturation during that season. MOISTURE OF THE AIR IN VARIOUS DISTRICTS. 595 Moisture of the Mr in various Districts. The formation of vapor is especially dependent upon two conditions, namely, upon the temperature, and upon the pressure of water. With an un- limited supply of water, vapor will be formed in proportion to the height of the temperature ; but with equal degrees of temperature, more vapor will be formed in districts which abound in water than in those which do not. Hence it follows, that the absolute quantity of water in the air, other circumstances being the same, decreases from the equator to the poles, and that the air is dryer in the interior of large continents, that is, it is there further removed from the point of saturation than on the sea or on the sea-shore. The clearness of the sky in continental countries, is a proof that the dryness of the air increases with the distance from the sea. Dew. It has already been stated, at page 591 , that fine dew is formed upon the polished bulb of DanieVs hygrometer, as the lat- ter is cooled. We may explain the formation of dew on a large scale in a similar manner. When in summer, after sunset, the sky remains clear, and the air calm ; the different objects on the earth's surface become more and more cooled by nocturnal radiation towards the sky ; their temperature falls from 7 to 23, or 25 even below the tempera- ture of the air; cold bodies also lower the temperature of the strata of air immediately surrounding them ; and when these are cooled down to the dew point, a portion of the vapor contained in them is precipitated upon cold bodies in the form of fine drops. As all bodies have not an equal capacity of radiating heat, some cool more perfectly than others, whence it follows, that many bodies may be densely covered with dew, whilst others will remain almost wholly dry. Grass and leaves, especially, cool rapidly by nocturnal radiation, partly because they possess a very strong capacity for radiation, and partly, also, because they stand exposed to the air, and can thus receive but little heat from the ground ; they are thus more thickly covered with dew than stones and the bare ground. When the sky is overcast by clouds, the formation of dew is prevented, owing to nocturnal radiation being impeded. Even when a somewhat brisk wind blows, no dew is formed, because warm air is constantly brought into contact with solid bodies, 596 MISTS AND CLOUDS. which are thus continually warmed, and allow of air passing over them before they can be cooled to the dew point. Hoar-frost is nothing but frozen dew. When the body, on which the condensed vapor is precipitated, is cooled below 32, vapor can no longer be deposited in a fluid form, but will appear as icicles. Mist and Clouds. When steam rises from a vessel of boiling water, and diffuses itself through a cooler atmosphere, it is imme- diately condensed, and there arises a mist in the air, which floats about in the form of a quantity of small hollow vesicles. This is also frequently called vapor, although it is no longer such, at least in the physical sense of the word, being a condensed aqueous gas. When the condensation of vapor does not occur by contact with cold solid bodies, but goes on in the air, mists arise, which are similar to those we see formed over boiling water. Mists generally arise when the water of lakes and rivers, or the damp ground, is warmer than the air which is saturated with moisture. The vapors formed in consequence of the higher tem- perature of the water, or the damp ground, are immediately re- condensed, when they diffuse themselves through the cooler air, already saturated with vapor. No mists are formed at an equal difference of temperature between the water and air, provided the air is dry, so that all the vapors rising from the surface diffuse themselves through it without saturating it. After what has just been said of the formation of mist, it will easily be understood that mists are especially formed in autumn over rivers and lakes, and damp meadows. In England, mists are very frequent, from the land being washed by a warm sea ; in like manner, the warm waters of the Gulf Stream, which flows as far as Newfoundland, are the cause of the thick fogs met with there. We often observe mists and fogs occur under totally different circumstances ; thus we find thick mists over rivers, whilst the air is warmer than the water or the ice. In this case, the warm air is saturated with moisture, and on its mixing with the layers of air, which have acquired a lower temperature from being in con- tact with the cold water or ice, a condensation of the vapor is necessarily brought about. The mists which rise over rivers and lakes in summer after a MISTS AND CLOUDS. 597 storm of rain, originate in a similar manner. Although the air is warmer than the surface of the water, it is saturated with mois- ture, and as soon as it is distributed over a place in which the freshness of the water is perceptible, the vapor becomes condensed by cooling. Mists are not, however, formed only over rivers and lakes, but over the middle of the continent, as soon as the warmer, damper masses of air are mixed with the colder, and their temperature thus lowered below the dew point. Clouds are nothing more than mists, which hover in the higher regions of the air, as mists are nothing more than clouds resting upon the surface of the ground. We often see the summits of mountains enveloped in clouds, whilst persons upon these eleva- tions are in the midst of mist. At first sight, it appears incomprehensible how clouds can float in the air, since they consist only of vesicles, which are evidently heavier than the surrounding air. Since the weight of these small vesicles of water is very small in comparison with their surfaces, the air must, in this case, oppose a considerable resist- ance ; they can only sink very slowly, as the soap bubble, which has a great resemblance to these vesicles of vapor, sinks but slowly in a calm atmosphere. These vesicles of vapor must, however, sink, although but slowly, and we might thus suppose that, in calm weather, the clouds would, at length, fall to the ground. The vesicles of vapor, however, which sink in calm weather, cannot reach the ground, owing to their soon reaching warmer strata of air that are not saturated with vapor, and where they again dissolve into vapor, and are lost to view ; whilst, however, the vesicles of vapor dissolve below, new ones are formed at the upper limits, and thus the cloud appears to float immovably in the air. We have just considered vesicles of vapor in a perfectly calm atmosphere, but when the air is agitated, they must follow the direction of the current of air ; a wind moving on in a horizontal direction, will also carry the clouds with it in the same direction, and an ascending current of air will lift them up, as soon as its velocity becomes greater than the velocity with which these vesi- cles would fall to the ground in a calm air. We may also observe how soap bubbles are carried away by the wind, and borne over 598 MISTS AND CLOUDS. the houses. Thus, too, the rising of the mist is explained by the ascending currents of air. The appearance of the clouds varies very much, according as they float higher or lower, are more or less dense, and are differ- ently illuminated, &c. Howard has distinguished clouds under the following heads : 1. The feathery cloud-cirrus consists of very delicate, more or less streaked, open or feathery filaments, which first appear in the sky after fine weather. In our figure 526, we may observe these in the right hand corner towards the bottom where the two birds are hovering. In dry weather, feathery clouds are more streaked, and in damp weather more confused. 2. The dense cloud, cumulus, represented in our figure exactly below the feathery cloud, forms large hemispherical masses which Fig. 526. appear to rest upon a horizontal basis ; these clouds are of most frequent occurrence in summer, often group themselves pictur- esquely together in large masses, and then, when lighted up by the sun, present the appearance of mountains of snow. STRATIFIED CLOUDS. 599 3. Stratified clouds, stratus, are horizontal streaks of clouds ; in our figure they are represented below the cumulus, and appear in extraordinary brilliancy of color at sunset. The main forms merge into a variety of others, which Howard has designated by the names of cirro-cumulus, cumulo- stratus, and nimbus. The feathery accumulated cloud, the cirro-cumulus, is the tran- sition of the feathery to the dense cloud ; they are those small, white, round clouds familiarly known as fleecy. When the feathery clouds are not scattered individually, but combined in streaks of considerable extension, they form feathery strata of clouds, cirro-stratus, which offer the appearance of expanded strata when they are near the horizon ; the cirro-stratus often cover the whole sky as with a veil. When these clouds become denser, they pass over into the streaked accumulated clouds, which often cover the whole horizon with a bluish-black tone of color, and finally pass over into the actual rainy cloud (nimbus) depicted at the left in our figure. When we consider how very various the clouds may be in form as well as in color, we shall easily understand how difficult it often is to decide whether the appearance of a cloud approaches more to one or other type. The feathery clouds are the highest of all kinds of clouds, since they present the same appearance when seen from high hills as from the valleys below. Kdmtz* determined their height at Halle to be about 20,000 feet. It is highly probable that the cirrus does not consist of vesicles of mist, but of flakes of snow. The denser clouds are usually formed when the vapors are raised up by the ascending currents of air, and then condensed by the lower temperature. Hence, it follows, that clouds often form towards noon, when the sun has ascended in the clear sky ; and towards evening the sky again clears, owing to the sinking of the clouds as the rising current ceases; the clouds again dissolve on reaching deeper, warmer regions, if the air be not saturated with vapor. As, however, the south-west wind brings more and more vapors with it when the air is saturated with vapor, the sinking clouds cannot be re-dissolved, but become denser and darker, whilst a stratum of feathery clouds often floats above the * See Complete Course of Meteorology," page 365. 600 QUANTITY OF RAIN. lower clouds. The lower masses of cloud- cumulus then pass more and more into the cumulo-stratus, and rain maybe expected. When by continued condensation of vapor, the separate vesicles of vapor become larger and heavier, when further, the separate globules approach each other and merge together, they form actual drops of water, which fall as rain. At a certain height the rain-drops are still very small ; they increase in size, however, as they fall, owing to the vapor of the strata of air becoming con- densed on which account they fall. Quantity of Rain. The quantity of rain which falls at anyone spot on the earth in the course of the year is a very important element of meteorology. The instruments made use of for this purpose are termed Rain gauges, Ombrometers or Udometers. Fig. 527 represents the usual rain gauge ; it consists of a tin Fi 527 cylinder b, which is from 5 to 6 inches in diameter, and on which a second cylinder a, with a funnel-like bottom, is placed. In the centre of this funnel there is an aper- ture; through which all the water, falling into the cylinder a, which is open at the top, flows into the receiver b. The receiver 6 is in connection, by means of a curved tube c, with a glass tube d, by means of which we may every time ascertain how high the water stands in b. Provided that the bores of a and b be equal, or, at any rate, not perceptibly dif- ferent, the height of the layer of water in b indicates the height to which the ground would be covered in a certain time, if the water were not imbibed, or evaporated. The annual quantity of rain is about as follows : at Lisbon . . .25 Paris inches. Dover . . .44 " London . .23 " Paris . . .21 " Ratisbon . .21 Bergen . . .83 " Stockholm . .19 " Petersburgh . .17 " Genoa . . .44 " Rome 29 QUANTITY OF RAIN. 601 The quantity of rain that falls, is not, however, uniformly dis- tributed throughout the year ; in this respect, Europe admits of being divided into three provinces. In England, on the western coasts of France, in the Nether- lands, and in Norway, autumnal rains predominate. In Germany, in the West-Rhenish provinces, Denmark and Sweden, rains are most prevalent in summer. Rains scarcely ever fall during summer in the south-east of France, in Italy, the south of Portugal, or in that part of Europe which is most contiguous to Africa. In Europe, the number of rainy days during the year generally decreases from south to north. On the average through the year there are about as follows : in southern Europe . . 120 rainy days. " central " . . 146 " " northern " . . 180 " That the quantity of rain does not alone depend upon the number of rainy days, is evident, since it matters not how many days, but how much it rains ; although the number of rainy days increases in northern districts, the intensity of the rain generally diminishes, and thus we see why in St. Petersburgh, for instance, the number of rainy days is in general greater, although the quan- tity of rain that falls is less. The quantity of rain, as well as the number of rainy days, decreases with the increased distance from the sea ; thus, for instance, there are about as follows : iii St. Petersburgh . . 168 " Casan .... 90 " Jakutzk .... 60 rainy days in the course of the year. As under equal circumstances rain in warmer districts is more intense than in colder, it is also more intense in the warmer than in the colder season of the year. There are, on an average, 3 rainy days in Germany in the winter, and 42 in the summer; the number of the rainy days in summer is, therefore, scarcely more considerable than in winter; and yet, the quantity of rain in summer is about double as great as in winter. In the summer months there often falls more rain in a single storm than during many weeks. 51 602 RAIN BETWEEN THE TROPICS. Rain between the Tropics. Where the trade-winds blow with the greatest regularity, the sky is for the most part clear, and it seldom rains; that is, when the sun stands above the other hemisphere. On continents, however, the regularity of the trade- winds is disturbed by the intensity of the ascending current of air as soon as the sun approaches the zenith ; about this time a violent rain sets in, which lasts many months, whilst, during the remainder of the year, the sky is uniformly clear, and the air dry. Humboldt has described the phenomena of the rainy season in the northern part of South America. From December till February the air is dry, and the sky clear. In March the air becomes more humid, the sky less pure ; the trade- winds then blow less strongly, and the air is often quite calm. By the end of March, the storms set in ; they begin in the afternoon, when the heat is greatest, and are accompanied by violent torrents of rain. Towards the end of April, the actual rainy season begins, the sky is overcast with a uniform gray tint, and it rains daily from 9 A.M. till 4 P.M.; at night the sky is mostly clear. The rain is the most violent when the sun is in the zenith. The time during the day in which it rains, then becomes gradually shorter, and towards the end of the rainy season, it rains only in the afternoon. The length of time of the rainy season is not the same for different districts, but lasts, generally speaking, from 3 to 5 months. In the East Indies, where the regularity of the trade-winds is disturbed by local influences, and where the monsoons take their place, we also find irregularities in the quantities of rain. On the steep western coasts of India, the rainy season corresponds with our winter, occurring at the time when the south-west monsoons prevail, and, being laden with humidity, strike the high mountains. Whilst it rains upon the coasts of Malabar, the sky is clear in the eastern shores of Coromandel ; here the rainy season comes in with the north-east trade-wind, that is, exactly at the time when the dry season prevails upon the western coasts. In the region of calms, periodical rains do not prevail; but vio- lent torrents of rain are of almost daily occurrence. The ascend- ing current of air carries a mass of vapor on high, which again SNOW AND HAIL. 603 condenses in the colder regions. The sun almost always rises with a clear sky, but towards noon a few clouds are formed, which become denser and denser, until, at length, an immense quantity of rain falls, amid violent gusts of wind and electrical discharges. Towards evening the clouds disperse, and the sun sinks in a clear sky. The annual quantity of rain that falls in the tropics is, in general, very great ; it amounts in Bombay, for instance, to 73,5, in Candi to 68,9, in Sierra Leone to 80,9, at Rio Janeiro to 55,6, at St. Domingo to 100,9, at the Havana to 85,7, and in Grenada to 105 Paris inches. If we now consider that rain is generally limited to a few months, and that it only rains during a few hours of the day, it is evident that the rain must be very violent. At Bombay there fell, in one day, 6 inches of rain, at Cayenne 10 inches in 10 hours. The drops are very large, and fall with such rapidity, that they give rise to a sensation of pain if they strike against the skin. Snow and Hail. Even at the present time, we know very little regarding the formation of snow. It is probable that the clouds in which the flakes of snow are first formed, consist, not of vesicles of vapor, but of minute crystals of ice, which, by the continuous condensation of vapor, become larger, and then form flakes of snow, which continue to increase in size while falling through the lower strata of air. When these lower regions are too warm, the flakes of snow melt before reaching the ground, so that it rains below while it snows above. The regular form assumed by flakes of snow, in the state which they can be best observed, namely, when they are placed on a dark body cooled below 32, was first described by Kepler. Scoresby had an opportunity, in the polar regions, of making a number of interesting observa- Fig. 528. 604 SNOW AND HAIL. lions on the forms of the flakes. His work contains nearly 100 different plates, of which some of the most interesting have been collected in Fig. 528. A mere superficial glance at these figures shows that all their forms are essentially referable to a regular hexagonal star, from whence it follows that snow-flakes belong to the hexagonal sys- tem of crystals (the crystal-system of rock crystals). Sleet, which we usually observe in March and April, is formed in the same manner as snow. The granules of sleet are formed of tolerably firm spherical icicles. Hail is one of the most fearful scourges to the agriculturist, and one of the most mysterious phenomena to the meteorologist. The ordinary size of hail-stones is that of a hazel-nut; they are very frequently smaller ; but these, being less dangerous, are not particularly regarded. They are often, however, much larger, and destroy everything they strike. Trustworthy philosophers have observed hail-stones which weighed 12 to 13 ounces. The form of hail-stones is liable to great variation ; most com- monly they are rounded, but sometimes flattened and angular. In their centre there is usually an opaque nucleus, resembling a granule of sleet: this nucleus is surrounded by a transparent mass of ice, in which we may often observe separate concentric layers ; sometimes alternating layers of transparent and opaque ice may be seen ; and, finally, even hail-stones with a striated structure have been observed. Pouillet found that the temperature of hail-stones varied from 31 to 25. Hail generally precedes a thunder-storm. It never, or at any rate, but very rarely, follows rain ; at least, when the latter has continued some time. A hail-storm generally lasts only a few minutes, very seldom so long as a quarter of an hour. The quantity of ice which escapes, from the clouds in so short a time is enormous ; the earth being often covered by it to the depth of several inches. Hail falls more frequently by day than by night. The clouds which bring it seem to have a considerable extension and depth, for they generally occasion great darkness. It is believed that they have been seen of a peculiar grayish red tint, and that great SNOW AND HAIL. 605 masses of clouds were suspended from their lower confines, and their edges variously indented. Hail-clouds seem generally to float very low. The inhabitants of mountainous districts often see clouds below them, which cover the valleys with hail ; it cannot, however, be determined with accuracy whether hail-clouds always descend so low. A peculiar rustling noise is heard a few seconds before the beginning of a hail-storm; and, finally, hail is always accom- panied by electrical phenomena. As to what concerns the explanation of hail, this presents two difficulties : namely, as to whence the great cold comes, which causes the water to freeze ; and next, how it is possible that the hail-stones, after having once become large enough to fall by their own weight, can yet remain long enough in the air to increase to so considerable a size. With regard to the first question, Volta thought that the solar rays were almost wholly absorbed at the upper confines of the dense clouds, which would necessarily occasion a rapid evapora- tion, especially when the air above the clouds was very dry; this evaporation would, according to him, cause so much heat to be absorbed, that the water in the lower strata of air would freeze. If, however, the evaporation of the water in the upper stratum of air were occasioned by the heat of the solar rays, it is not so clear why so much heat should be withdrawn from the lower layers of clouds by means of this evaporation. With reference to the second question Volta proposed a very ingenious theory, which has attained great celebrity. He assumes that two layers of clouds, heavily charged with opposite kinds of electricity^ hover above one another. If, now, the very small hail- stones fall upon the lower clouds, they will penetrate to a certain depth, and thus become surrounded by a new layer of ice ; they will, however, also become charged with the electricity of the lower cloud, and be repelled by it, while they will be attracted by the other ; they will, therefore, again rise, in spite of their gravity, to the upper cloud, where the same process will be re- peated ; thus they will move for a time backwards and forwards between the two clouds, until at last they will fall, when they become heavy enough, and when the clouds have lost their elec- tricity. 51* (506 COLOR OF THE SKY. It may be objected to this view, that it is scarcely conceivable that electricity is able, without any sudden action, that is, with- out any explosive discharge, to raise such large masses of ice ; and that if the electric charge of the two clouds were really so powerful, the electricity must instantaneously pass from one to the other; especially since the hail-stones must establish a con- nection between them. CHAPTER IV. OPTICAL PHENOMENA OF THE ATMOSPHERE. Color of the Sky. The clear sky appears to us to be blue, and this blue is sometimes brighter and whiter, and sometimes darker, according to the state of the atmosphere ; on high mountains the sky appears dark blue, or almost black. This is readily explained : if the air were perfectly transparenf, if its individual particles reflected, or rather scattered no light, the sun, moon and stars would shine out forth from a black ground ; but, as it actually is, the particles of air reflect the light, and thus it happens that during the day the whole sky appears bright, because the particles of air illuminated by the sun scatter the light in all directions. This illumination of the atmosphere by the sun's rays is the cause of our not seeing the stars during the day. The particles of air reflect mostly blue light, and hence it is that the dark vault of heaven is invested with a blue tint. The higher we rise in the atmosphere, so much the thinner is the blue envelop, and conse- quently so much the darker does the heaven above us appear ; thus the darkest blue is always in the zenith, while towards the hori- zon there is more of a whitish tint. The pure blue of the sky is especially decolorized by the con- densed vapor floating in the air, by fine mists, which often invest the sky as with a delicate veil, without being sufficiently dense to appear as clouds. The phenomena of the evening and morning red are explained by saying that the air permits of the passage of the red and yel- low rays in preference, but that it reflects the blue rays. The COLOR OF THE SKY. 607 sun's rays in the evening and morning have to traverse a con- siderable space through the atmosphere, hence the red coloring of the transmitted rays, which is particularly brilliant when clouds are illuminated by them. This opinion cannot be altogether correct, because the blue tint of the sky is not the complementary color of the evening red. The evening red depends probably on the vapor of water con- tained in the air. When a column of steam rises from the safety-valve of a steam- engine, as, for instance, of a locomotive, the sun seen through the steam appears of a deep orange red ; some feet above the safety-valve, at which the steam is escaping, its color by trans- mitted light has the deep orange tint already described ; at a greater distance, where the vapor is more perfectly condensed, the phenomenon entirely disappears. Even a moderately thick cloud of vapor is perfectly impenetrable to the sun's rays ; it throws a shadow like a solid body ; and when its thickness is small, it is then indeed transparent, but colorless throughout. The orange color of vapor appears, therefore, to pertain to a peculiar state of condensation. In a perfectly gaseous state, aqueous vapor is quite transparent and colorless ; in any transitive state, it is trans- parent and of a dingy red ; but when it is perfectly condensed into vesicles of mist, a thin layer is transparent and colorless, while a thick layer is perfectly opaque. Aqueous vapor, being a pure, colorless, elastic fluid, gives to the air most of its transparency, particularly as is observed when the sky clears after a severe rain. In the transition stage, it ad- mits of the passage of the yellow and red rays, and in this con- dition gives rise to the appearance of the evening red. This theory will also explain why it is that the evening red is far more brilliant than the morning red; that the evening red and the morning gray are signs of fine weather. Immediately after the maximum diurnal temperature has been attained, and before sunset, the surface of the earth and strata of air at different heights begin to lose heat by radiation. Before, however, this has led to the entire condensation of the aqueous vapor, it passes through that transition stage which causes the evening red. In the morn- ing the case is different. The vapors which, in the reversion of the process, would probably have given rise to the red, do not rise till they have been exposed sufficiently long to the sun's action; 608 THE RAINBOW. but then the time of the sun's rising is over, and the sun stands high in the heavens. The fiery appearance of the morning sky depends on the presence of such an excess of moisture, that by its condensation in the higher regions, actual clouds are formed, notwithstanding the tendency of the rising sun to disperse them ; the morning red is, therefore, to be considered as the forerunner of speedy rain. When the sun has disappeared in the western horizon, instead of there being immediate darkness, we have the twilight, which lasts, under different circumstances, for a longer or shorter time. The twilight is produced by the sun's continuing to shine on the atmosphere of the western sky, and on the aqueous particles sus- pended in it, for some time after it has disappeared from our view, and on these illuminated particles of air and water con- tinuing to transmit to us a light which becomes gradually fainter and fainter. In Germany, and countries of the same latitude, the twilight lasts till the sun is about 18 beltfw the horizon. The prolonged duration of twilight in higher latitudes is dependent on the circumstance that the sun's orbit is there very strongly in- clined towards the horizon, and that, consequently, it takes a very considerable time for the sun to sink 18 below it. The nearer we approach to the equator, so much the less oblique is the sun's orbit towards the horizon, until under the equator the two are at right angles ; in hot countries the twilight is, therefore, of shorter duration. In Italy it is shorter than in Germany, in Chili it lasts only a quarter of an hour, and in Cumana only a few minutes. This extremely short twilight is not solely to be referred to the direction of the sun's orbit with respect to the horizon; we must also take into consideration the extraordinary purity of the sky in those countries, for in our regions the delicate mists which float high in the air, and during the day, veil the sky, materially assist in reflecting the light, and so prolonging the twilight. The Rainbow. Every one knows that we see a rainbow when we have the sun behind us, and face a showery cloud. The rainbow forms the' base of a cone, whose vertex is the eye, and whose axis coincides with the straight line passing through the sun and the eye. Under the above conditions the rainbow appears in the mist of waterfalls and fountains. In order to explain the formation of the rainbow, we must follow the course of the sun's rays through a drop of rain. THE RAINBOW. 609 Fig. 529. If a ray SA (Fig. 529) strikes a rain-drop, it is refracted, and it is easy to calculate or to con- struct the direction of the re- fracted ray Ji B. The refracted ray Jl B is reflected at .B, by the posterior wall of the drop to C, and then after a second refraction emerges in the direc- tion C 0. The emergent ray C forms with the incident ray an angle S JV* 0. But many other rays fall on the drop parallel with SA\ and if we calculate or construct for each of them their path through the drop, as we have done in the figure for a second ray, it will be found that the emergent rays are not parallel to one another. While, therefore, a parallel pencil of light falls on the drop, a pencil of light strongly divergent emerges from it. It is easy to understand, that by this divergence of the rays emerging from the drop, the strength of the impression of the light which they produce is very much weakened, especially when the drops occur at only a slight distance from the eye. Of all the rays which enter the eye from a drop after two refractions and one reflection, those only can make that perceptible impression of light for which the divergence is a minimum, or, in other words, only those which emerge very nearly parallel. From more accurate examination, it follows that a considerable number of parallel incident rays fall or leave the drop nearly in the same direction, having suffered a deviation of very nearly 42 30'; and of all the rays emerging from the drop, these alone can produce a sensible impression of light. Let us suppose a straight line o p (Fig. 530) to be drawn through the sun and the eye of the observer, and a vertical plane to be carried through it. If through o we draw the straight line o v, so that the angle p o v = 42 30', then the rain-drops in this direction will send effective rays to the eye after an internal re- flection. The eye, however, does not receive effective rays from this direction alone, but, as may easily be conceived, likewise from all the drops of rain which lie on the surface of the cone, which arises from the revolution of the line o v about the axis op. 610 THE RAINBOW. the eye will, therefore, see a circle of light, the central point of which lies upon the straight line drawn through the eye, and whose radius appears under an angle of 42 30'. Fig. 530. In the direction mentioned we observe a circle, which appears as a red ring, about 30' in breadth, in consequence of the sun not being a mere point, but a disc, whose apparent diameter is 30'. But as the effective violet rays emerge in a direction mak- ing an angle of 40 30' with the incident rays, the eye per- ceives a violet ring about 30' broad, whose radius amounts to only 40 30'. Between these external arcs we observe the other prismatic colors, and thus the rainbow forms, as it were, a spec- trum extended into a circular arc. The whole breadth of the rainbow averages 2, since the radius of the red bow is 2 greater than that of the violet. The extension of the colored arc obviously depends on the sun's altitude above the horizon. When the sun is fast going down, the rainbow appears in the east, the centre of the bow then lying exactly in the horizon, since the line drawn through the sun and the eye is then a horizontal line ; when the observer stands on a plane, the rainbow then forms an exact semicircle; he can, however, see more than a semicircle, if he stand on an isolated mountain-top of small breadth. At sun-rise the rainbow appears in the west. In proportion to the height of the sun, so THE RAINBOW. 61 1 much the lower is the centre of the colored bow below the hori- zon, and, consequently, so much the smaller is the portion of the bow visible to the eye. If the sun's elevation above the hori- zon is 42 30', no rainbow is any longer visible to an observer standing on a plane at the level of the sea, since then its summit coincides with the horizon, and the whole arc falls below it. From the masts of ships we often observe rainbows forming a perfect circle. Such circular rainbows are also often observed in waterfalls and fountains. Besides the rainbow already described, we also usually observe a second and larger one, concentric with the first, but having the order of the colors reversed, in the exterior rainbow the red being the inner, and the violet the exterior color. The external rainbow is much the paler of the two, and has the colors much less strongly developed. Formerly it was erroneously believed that the second rainbow was a mere image of the first. The formation of the outer bow depends on exactly the same princi- ples as that of the inner bow, and is produced by the sun's rays, which have undergone a second refraction and a second internal reflection in the rain-drops. In Fig. 531 is represented the course which a ray of light pursues in the rain-drop in order to be a second time reflected. S A is lg ' the incident ray, which is refracted in the direction Jl jB, then reflected at B and C, and, finally, refracted at D in the direction D 0. In this case the incident and the emergent rays intersect, forming with one another an angle d, whose magni- tude varies according as the inci- dent ray impinges on the drop at another place, therefore under another angle of incidence. In this case the effective emergent red rays form an angle of 50, and the effective emergent violet rays an angle of 53J with the incident rays ; the eye, therefore, perceives a series of con- centric colored rings, the innermost of which is red, and has a radius of 50, whilst the outermost one, the violet, has a radius of 53. The outer rainbow is the paler because it is formed by rays 612 HALOS AND PARHELIA. which have undergone a second internal reflection, and (as is well known) after every reflection light becomes weaker. We should be able to see a third, and even a fourth rainbow, formed by rays which had undergone three or four internal reflections, if the light of these rays were not too faint. Halos and Parhelia. When the sky is invested with light clouds, we often observe colored rings close round the sun and moon. These rings are frequently imperfect, and mere portions. The fact that lunar halos are more frequently observed than solar halos, is dependent on the circumstance that the sun's light is too dazzling; the latter are, however, seen on observing the sun's image in still water, or in a mirror blackened at the back. These halos present the greatest similarity to the glory ob- servable round the flame of a taper on looking at it through a glass plate on which lycopodium seed has been strewed; in fact, both these phenomena depend on the phenomena of interference ; the vesicles of vapor may replace the minute particles of seed in the latter case. Fig. 532. Sometimes we also notice two larger colored circles around the sun and moon ; these must not be mistaken for halos. The radius of the smaller of these luminous rings appears under an IGNIS FATUUS. 613 angle of 22 or 23, whilst that of the greater under an angle of 46 or 47. The red in them is inverted inward ; the inner edge is the sharper, the outer is more undefined and less decidedly colored. The two circles rarely appear simultaneously. Fig. 532 exhibits the phenomenon as we have most commonly the opportunity of observing it ; the smaller ring has a radius of 22 or 23 ; it is intersected by a horizontal streak of light, which often extends to the sun itself. The streak is brightest at the points where it intersects the ring of light ; these bright spots, which we observe on both sides of the sun on the outer circum- ference of the ring, are the parhelia; sometimes one such parhe- lion appears vertically above the sun at the summit of the ring ; but at this point, also, there is often seen an arc of contact, as shown in Fig. 532. Moreover, we often observe parhelia without rings, or rings without parhelia. These rings and parhelia never appear in a perfectly unclouded sky, but only when it is overcast. The appearance of these rings has been explained by assuming that light is refracted by the crystals of ice suspended in the atmo- sphere. If the icicles are six-sided prisms, the two non-parallel and non-joining sides always form with one another an angle of 60; the icicles form, therefore, regular, equilateral, triangular prisms, in which the minimum of deviation is about 23. Rays, which have undergone in the icicles the minimum of deviation, are analogous to the active rays in the rainbow, since many rays emerge very nearly in the same direction. This hypothesis, there- fore, explains at the same time the formation of the ring, its size, and the order in which the colors take place. The ring of 46 is explained by the assumption that the axis of the prisms stands obliquely, in such a manner that the right angle which the lateral surfaces of the prism make with the base is the refracting angle of the prism. For a prism of ice, whose refracting angle is 90, the minimum of deviation is, in point of fact, 46. The light streaks accompanying the parhelia are explained by the reflection of the sun's rays from the vertical surfaces of the crystals of ice. The streak is brightest where it cuts the ring of 23, since here two causes co-operate to affect the stronger illu- mination. Ignis Fatuus, or the Will-o> -the- Wisp, is the name usually given to certain flames seen in marshy lands, moors, churchyards, 614 FALLING STARS, FIRE-BALLS, AND AEROLITES. &c., in fact, wherever putrefaction and decomposition are going on ; they usually appear a little above the ground, exhibit a flick- ering and unsteady motion, and soon again vanish. Although we are usually in the habit of treating these lights as thoroughly understood phenomena, there is yet great uncertainty regarding them, since they have not been sufficiently explained, and what is considered as matter of fact not at all times to be received, owing to the circumstance that most persons who have seen them were not in a state to make accurate observations, and to explain in an unprejudiced manner what they saw. Volta held the opinion that these lights were caused by marsh gas (light carburetted hydrogen) inflamed by an electric spark. But from whence could the spark arise ? Others are of opinion that they are caused by phosphuretted hydrogen, which inflames as soon as it comes into contact with atmospheric air ; but then there would be a momentary flash accompanied by a puff of smoke, and not a prolonged feeble light, such as is observed. The most probable view is, that they are caused by hydrogen gas containing phosphorus, which does not, properly speaking, burn as a flame, but is only faintly pbosphorescent. Falling Stars, Fire-balls, and Meteoric Stones. The appearance presented by falling stars is so generally known as to require no detailed description. It has been ascertained by corresponding observations that the height of falling stars averages 34 or 35 (German) miles, and that they move with a velocity varying from 4 to 8 (German) miles in a second. A very remarkable phenomenon connected with falling stars, is the periodically recurring showers, which have been observed from the 12th to the 14th of November, and on the 10th of August (the Feast of St. Lawrence) ; these periodic showers of stars of the latter date are noticed in an ancient English church calendar, and are termed the fiery tears of the Saint. One of the most considerable of these showers of stars was observed in North America on the 12th and 13th of November, 1833; they appeared to fall almost in contact, like flakes of snow in a snow-storm, and it was calculated, that in the course of nine hours no less than 240,000 fell. Fire-balls appear to have the same origin, and to be of the same nature as the falling stars just described, and to differ from FALLING STARS, FIRE-BALLS, AND AEROLITES. 615 them merely in size. Fire-balls have been seen amongst the great falling stars. Fire-balls explode with a great noise, and stony masses then fall from them, known as meteoric stones, or aerolites. Even during the day-time such meteoric stones have been seen to fall, with a loud report, from small gray clouds. Meteoric stones, just fallen, are still hot, and in consequence of the velocity of their fall, penetrate the earth to a greater or less degree. About the era of the last century, there was a strong tendency to regard the falling of stony masses from the atmosphere as fabulous ; but since that period various cases have occurred, which have been observed by several persons, and have been attested to by men, in whom confidence must be placed. We may especially mention the meteoric stone that fell at Aigle, in the department of Orne, on the 26th of April, 1803, examined by Biot, and that on the 22d of May, 1808, and that at Stauners, in Moravia. On the 13th of November, 1835, (at the period, therefore, of the fall- ing stars,) a house in the department of Ain was set on fire by an aerolite. Meteoric stones have a peculiar physiognomy, by which they may be distinguished from all terrestrial fossils ; but notwith- standing this, they differ so much individually, that Chladni, who devoted much attention to these subjects, regarded it as difficult to assign to them a general character. One of their most marked characteristics is, however, their containing a certain amount of native iron, and a bituminous, glistening, sometimes raised ex- ternal crust, which is scarcely ever absent. A further descrip- tion would involve us too deeply in mineralogical details. Stony masses have been found at various spots on the earth's surface, perfectly distinct in geological character from the moun- lin range in the vicinity, but presenting the greatest similarity to mes known to be of meteoric origin. Hence such masses are considered to be aerolites. The mass of meteoric stones is often very great; they have ?en found weighing from a few pounds up to 400 cwt. It can hardly be longer doubted that falling stars, fire-balls, md meteoric stones, are of cosmical origin, or that they are most >robably masses which, like the planets, revolve round the sun, 1 id, being drawn within the sphere of the earth's attraction, 616 DISCOVERY OF ATMOSPHERIC ELECTRICITY. fall. The fire and light accompanying them, are most easily accounted for by the assumption that these minute spheres are surrounded with an atmosphere of inflammable gas, which in- flames on entering into the oxygenized atmosphere of our earth. If we assume that, besides the innumerable individual masses of this kind revolving round the sun, whole swarms of them form a ring round that body, and further, that the plane of this ring cuts the earth's orbit at a definite point, we have an explanation of showers of the periodic falling stars. CHAPTER V. ON ATMOSPHERIC ELECTRICITY. Original Discovery of Jltmo spheric Electricity. Otto von Gue- rike, the distinguished inventor of the air-pump, was the first who observed an electric appearance of light. About the same time, Wall noticed a vivid spark, and heard a strong rustling sound, on rubbing a large cylinder of resin, and it is a remarkable thing that the first sparks drawn by the human hand were compared to lightning. These sparks, and these cracks seemed, says Wall, to a certain degree, to represent thunder and lightning. The analogy was surprising ; in order, however, to test its truth, and to detect, in so minute an appearance, the causes and laws of one of the grandest phenomena of nature, it was requisite that there should be a more direct proof. Whilst in Europe men occasionally asserted that lightning was actually an electric phe- nomenon, its experimental proof was established in America. Franklin, after making many electrical discoveries, especially on the Leyden jar, and on the influence of points, arrived at the happy idea of searching for electricity even in thunder clouds; he concluded that metallic points, placed on lofty buildings, would draw off the electricity from the clouds. He waited with im- patience for the completion of a steeple then being constructed in Philadelphia ; but at length, weary of waiting, he had recourse to another plan, which gave him even more certain results. Since ELECTRICITY DURING A THUNDER STORM. 617 all that was requisite was to raise a body a sufficient height in the air, he conceived that a kite, a child's toy, would answer his pur- pose as well as the highest steeple. He availed himself of the first thunder-storm, in order to try his experiment ; accompanied by a single person, his own son, since he was afraid of ridicule if his attempt failed, he set off into the open country, and began to fly his kite. A cloud of great promise passed over them with- out producing the least action. Another passed over, but he could draw no sparks, nor could he see any signs of electricity. At length the fibres of the string began to separate from one an- other, and he heard a rustling noise. Encouraged by these signs, Franklin applied his finger close to the end of the string, and then observed the emission of a spark, which was quickly followed by many others. Franklin performed his experiment in June, 1752 ; it was uni- versally repeated with the same results. De Romas, at Nerac, influenced by the first idea of Franklin, had likewise thought of making use of a kite instead of elevated points. Without having received any account of the results arrived at by Franklin, he obtained in June, 1753, very powerful evidences of electricity, owing to his ingenious contrivance of laying a fine metal wire the whole length of the string. In the year 1757, De Romas repeated his experiments, and obtained sparks of surprising size. " Let the reader only imagine," says he, "streaks of fire from 9 to 10 feet in length, and 1 inch in breadth, accompanied by a cracking, which was louder, or as loud, as a pistol shot. In less than an hour I obtained at least thirty such sparks, not to count the thou- sands which were 7 feet long, or less." Notwithstanding the measures of precaution taken by this skilful experimentalizer, he was struck down by the violence of the charge. These experiments prove most completely that lightning is only an electric spark. Electricity during a Thunder-storm. On examining the elec- trical condition of the clouds which gradually pass over the kite, we perceive that they are sometimes charged with positive or ne- gative electricity, and sometimes in a natural condition. Although we know nothing of the distribution of electricity in the clouds, the attraction and repulsion of the unequally, or equally electrified clouds, is doubtlessly the cause of the extraordinary motions ob- 52* 618 ELECTRICITY DURING A THUNDER-STORM. served in the heavens during a thunder-storm. During this gene- ral agitation of the atmosphere, we see lightning flash through the sky, and hear the thunder roll. These phenomena we are now about to consider more attentively. We often see lightning break from the clouds, and flash far across the sky. On observing this phenomenon below our feet, from high mountains, we are able to form a more correct idea of its extent, and all observers agree in stating that, under similar circumstances, they have observed flashes of lightning of at least a German mile in length ; we also know that several flashes proceed from the same cloud ; finally, it is known that lightning generally describes a zigzag line ; this form is common to lightning, and to the electric spark. The vesicles of vapor which form clouds are not such perfect conductors as metals ; and although we do not know the laws of equilibrium, and the distribution of electricity in imperfect con- ductors, it is still evident that they do not perfectly discharge themselves at once, and that they can be brought back to their natural condition by a few sparks; this explains the reason why the same cloud emits several flashes. The length of the lightning appears also to be a consequence of the imperfect power of conduction in clouds, and the mobility of the particles of which they consist. We may obtain sparks of 1 metre in length, through dry air, from the conductor of the best kind of electrical machines ; the sparks, however, are still longer when carried off over woollen or silk substances that have been scattered over with dust ; in the same manner we should also obtain longer sparks through a mist, if it did not too much dimin- ish the tension of the electricity. In order to explain the length of the lightning we must assume that, on the course which it takes, the particles of vapor are already electrified by induction, and that finally, when the lightning appears, the disturbed equilibrium is restored from one layer to another, and that, to a certain extent, sparks only pass from one particle to another, while the electric fluid does not traverse the whole course intervening between the remotely separated clouds. Thunder is not more difficult to explain than the noise of a small electrical spark, and arises from the vibrations of the powerfully agitated air. We see the light along the whole course of the lightning, and the report arises simultaneously upon the EFFECTS OF LIGHTNING UPON THE EARTH. 619 whole extent of the line; as, however, sound is more slowly propagated than light, traversing only 1125 feet in one second, we see the lightning before we hear the thunder; an observer, standing near one end of the course of the lightning, will not at once hear the sound arising simultaneously at all points. If we assume that the lightning is 4500 yards distant, and the observer stands in the prolongation of its course, the sound will reach him from the most remote extremity of the lightning, only 12 seconds later than from the part lying nearest to him. As, consequently, sound reaches the ear of the observer only by degrees from dif- ferent parts of the flash, he does not hear an instantaneous noise, but a more or less prolonged rolling of the thunder, increased in intensity by the echo of the clouds, and the duration of this sound depends upon the length of the lightning, and the position of the observer with regard to its course. Not only during thunder-storms, but even during a clear state of the atmosphere, we may, by aid of a good electroscope, show the existence of an electrical tension in the atmosphere. With regard to the origin of atmospheric electricity, we actually know nothing, although a very great deal has been written on this subject. Some are of opinion that the electricity of thunder- clouds originates in a rapid condensation of the atmospheric aqueous vapor, and, therefore, that electricity is a consequence of the rapid formation of dense clouds. Effects of Lightning upon the Earth. If we suppose that a thunder-cloud hovers from 2 to 6 thousand yards above the sea, or over a large lake, and if we assume it to be charged with positive electricity, it will act inductively, the -f electricity in the water will be repelled, and the accumulated upon the surface of the water ; this accumulation may be sufficiently great to occasion a marked elevation of the water, being able to form a large wave, a water mountain, as it were, which will continue as long as the electrical condition lasts; this latter, however, may terminate in three different ways. 1. When the electricity of the cloud is gradually dissipated without any discharge taking place, the naturally electrical con- dition of the water will thus by degrees be restored. 2. When a flash passes between the thunder-clouds, or a flash takes place between the cloud and some remote places on the earth, conse- quently, when the cloud is suddenly discharged, the electricity 620 EFFECTS OF LIGHTNING UPON THE EARTH. accumulated on the surface of the mountain of water, quickly flows off, and is replaced by its opposite kind, and equilibrium is in this manner at once restored. 3. When the thunder-cloud is near enough, and sufficiently strongly charged with electricity, the lightning passes over. This direct stroke generally occasions a more considerable swelling up of the water than the back- stroke. Such a shock cannot take place without producing a mechanical action upon the ponderable elements. We will now consider the actions of thunder- clouds upon land. A gradual separation and reunion of the electricity produces no visible actions; it appears, however, that such disturbances of the electrical equilibrium may be felt by organic beings, and have been experienced by persons affected with nervous diseases. The back-stroke is always less violent than the direct shock; and there is no evidence extant of its having occasioned ignition, although there is no lack of examples showing that men and animals have been struck dead by it ; in these cases the bodies have no limbs broken, and present no trace of wounds or marks of burns. The direct stroke produces the most fearful actions; on the lightning striking, it marks the spot where it struck the ground by one or more holes of various depths. Everything that is raised above the surface is, therefore, pecu- liarly exposed to the stroke of the lightning ; hence, it happens that animals are struck down in the middle of a plain : other cir- cumstances being the same, one is, however, safer upon a non- conducting than on a good conducting surface. Trees are good conductors, owing to the sap circulating in them ; when a thunder-cloud passes over, a strong accumulation of electricity takes place in the trees, and on this account we say with justice that trees attract the lightning: we ought never, therefore, to seek protection during a thunder-storm under trees, especially under such as stand alone, or even under bushes stand- ing exposed on a plain. Buildings are, generally speaking, constructed of metal, stone, and wood. The action of thunder- clouds on these substances varies with the difference of their nature. When the lightning strikes, it especially attacks the better conductors, whether they are free or surrounded by worse MECHANICAL ACTIONS OF LIGHTNING. 621 conductors; the distributing force of the atmospheric electricity acts as well upon the nail driven into the wall, as upon the weather-cock projecting in the air. The mechanical actions of lightning are usually very violent. When lightning strikes a room, the furniture is thrown down and broken, and metallic substances are torn out and hurled far away. Trees are cleft and split asunder by lightning ; we are usually able to trace a deep furrow, many centimetres in breadth, which runs from top to bottom, the peeled bark and the torn splinters may be found thrown far off, and we often observe at the bottom of the tree an aperture through which the electrical fluid passed into the ground. The physical actions of lightning show a more or less conside- rable elevation of temperature. When lightning strikes a straw shed, dry wood, or green trees, a carbonization, or even ignition takes place ; in trees there is seldom any trace of the former. Metals are strongly heated, melted, or volatilized by the lightning. Repeated strokes on high mountains produce evident traces of fusion. Lightning-conductors consist of a pointed metallic rod, project- ing into the air, and of a good conductor connecting the rod with the ground. The following conditions must be fulfilled where these instruments effect the purposes for which they are designed: 1. The rod must terminate in a very fine point. 2.. The connection with the ground must be perfect. 3. No interruption must occur from the point to the lower part of the conducting rod. 4. All parts of the apparatus must have the same dimensions. When a thunder cloud hovers over the lightning-conductor, the combined electricities of the rod and the conducting medium will be decomposed, the electricity will be repelled, which is the same as the one contained in the cloud, and diffuse itself freely in the earth, whilst the opposite electricity will be attracted to- wards the point, whence it can flow freely into the air, and thus an accumulation of electricity in the lightning-conductor will be rendered impossible. Whilst the conductor is thus inactivity, and the opposite electricities pass through it in an opposite direc- tion, we may, without danger, approach and even touch it, since no discharge is to be feared when there is no electrical tension. If we assume that one of the three first named conditions is 622 LIGHTNING-CONDUCTORS. Fig. 533. Fig. 534. Fig. 535. not fulfilled, that the point is blunt, the medium conducting into the ground imperfect or interrupted, it is evident that an accumu- lation of electricity in the lightning-conductor will not only be possible, but even unavoidable ; it will then form a charged con- ductor, in which an immense mass of electricity will be accumu- lated, from whence we may draw stronger or weaker sparks. If only the point be blunt, the lightning may strike, but it will follow the conducting medium without destroying the building. If the conducting medium be interrupted, or the connection with the ground imperfect, the lightning may likewise strike ; it will, however, distribute itself laterally to other conductors, and occasion the same disturbances that would occur if there were no lightning-conductor. Yet more : a lightning-conductor having this deficiency is very dangerous even where the lightning does not strike ; for when at any part of the conducting medium, the electricity is sufficiently accumu- lated, a spark may strike sideways, and crush or set fire to any objects. We may illustrate this by the following melancholy incident. Richmann, Pro- fessor of Physics at St. Petersburg, was suddenly struck dead by the emis- sion of a spark, which escaped from the lightning conductor attached to his house, the connecting medium of which he had interrupted, in order to examine the electricity of the clouds. Sokolow, engraver to the Academy, saw the spark strike Richmann on the forehead. After having stated what conditions must be fulfilled, in order to make a lightning-conductor efficient, and what dangers may ensue from the neglect of these precautions, there still remains something to be said of the practical arrangement of this apparatus. Gay- Lussac, under the auspices of the Academy of Sciences, has, at the sug- gestion of the Minister of the Interior, drawn up instructions rela- LIGHTNING-CONDUCTORS. 623 live to this subject, which leave nothing more to be desired, but from which we can only extract the most essential. The rod of the lightning-conductor is about 9 yards in length ; it is composed of three pieces, namely, an iron rod of 8^ yards in length, a brass rod of 18 inches, and a platinum needle of 2 inches long; taken together they form a cone sloping upward in a regular line. See Fig. 533. The platinum needle is soldered to the brass rod with silver, and the place of junction surrounded by a covering of copper, as may be more clearly seen in Fig. 534. The brass rod is screwed into the iron rod, and thence secured by means of transverse pins. The iron rod is often composed of two pieces in order to facili- tate its transport ; one of these fastens into the other by means of a long conical projection, 7 inches in length, which is then secured by a transverse pin. In Fig. 538 we see three different ways in which the rod may be fastened to buildings. Under the rod, about 3 inches from the roof a plate V b' (see Fig. 536) is screwed, in order to carry off the water 2 inches above this plate, the rod must be cylindri- cally and perfectly well turned, in order that a large screw / V Figs. 535 and 536 may be placed round it, in order to attach the conducting rod. The conductor is a quadrangular iron rod, the side of which measures from J to \ an inch, and which is fastened to the ring 1 1 by means of screws. Fig. 536. Fig. 537. Fig. 538. 624 LIGHTNING-CONDUCTORS. The conducting rod is carried over the roof and down the build- ing into the ground. Everything depends upon bringing the conducting rod in as good a connection with the ground as pos- sible. If there happen to be any well in the neighborhood, which does not become dry, or if a hole can be bored to the depth at which water is constantly to be found, it is sufficient as a means of conducting the rod, if we divide it into several arms. In order to increase the points of contact, the rod is conducted through windings to the well, or the bore-hole, which must then be filled with charcoal. This affords the double advantage of protecting the iron the better from rust, and placing it in connection with so good a conductor as the charcoal. If there be no w r ater in the neighbor- hood, the rod must at least be connected with some damp spot by means of a long canal filled with charcoal. To effect a still greater degree of security, we may branch the conducting rod off into several lateral canals. A rope twisted round with copper wire, as seen in Fig. 537, is often used in the place of a conducting rod. As we may easily see that the lightning cannot enter a con- ductor, constructed according to these principles, it will also as readily be understood that it cannot strike within some distance of the lightning-conductor. The electricity which pours copiously from the point, will be attracted by the thunder cloud, and when it has reached it, it neutralizes a part of the original electricity of this cloud. If, therefore, a thunder cloud be near enough to the lightning- conductor to act inductively on it, its electrical force will also be weakened by the efflux of the opposite electricity from the point. The nearer the cloud approaches, the more strongly will its inductive force act, but the more also will it be neutralized by the efflux of the opposite electricity. The efficiency of the lightning-conductor depends, however, likewise on other conditions. If other objects near it project be- yond it, the electricity of the clouds may act more strongly upon them than upon it, and a discharge thus take place ; the same is the case when there are any considerable masses of metal, iron rods, or a metallic roofing in the vicinity of the lightning-con- ductor. In the latter case, we must bring the metallic masses into LIGHTNING-CONDUCTORS. 625 as good a connection with the lightning-conductor as is possible, in order that the attracted electricity may flow unhindered through the point. It is, consequently, dangerous to insulate metallic roofs from the conductors, as some practical philosophers have proposed doing. Fortunately, the means used to effect such an insulation are not sufficient for the purpose, and they have thus produced only useless results. Experience shows us, that a lightning-conductor applied with all the necessary precaution, and of the dimensions indicated, is able to protect a circle having a radius of about 20 yards. 53 INDEX. Aberration, spherical, 264. Absolute strength, 73. Absorption of gases, by liquids, 147. of rays of heat, 543. Accelerated and retarded motion, 150. Achromatic prisms, 292. Achromatic telescopes, 292. Achromatism of the eyes, 304. Acid, table of diluted sulphuric, 107. , nitric, 107. , 433. Acoustics, 207. Action of the windings on each other, 472. of an electric current on a conduct- ing circuit within itself, 471. Adhesion, 77. between solid and liquid bodies, 108. Aggregate conditions, 31. Air, of the, 116. , decrease of temperature in the up- per regions of the, 576. , distribution of vapor in the, 589. is dry, the, 594. pressure of, 119. is damp, 594. purnp, the, 132. , combustible, 116. , fixed, 116. waves, formation of regular, in co- vered pipes, 227. , electric light in the, and in other gases under the pressure of the atmo- sphere, 398. , electric light in rarefied, 399. bad conductor of heat, 549. , diurnal and annual variation in the quantity of water contained in the, 593. in various districts, moisture of the, 595. Alcoholmeter, the, 102. of Gay-Lussac, 104. Althans of Sayn, 191, 430. Amount of atmospheric pressure, table of, 124. Ampere's experiments, 440. theory of magnetism, 467. Amplitude, 164. of the diurnal variations, 361. Angle of deviation, the, 69. of reflection, 260. of refraction, 270. Animal electricity, 479, 482. heat, 551. Anode, pole, 437. Archimedean principle, the, 90, 95. Areometer, the, 96. of Brissen, and G. G. Schmidt, 101. of Beaume, 105. of Cartier and Meisner, 105. of Gay-Lussac, 101. , the graduated, 98. , the per centage, 102. Armatures, magnetic, 351. Atmospheric electricity, original discovery of, 616. Atmosphere, 116. , transmission of sound through the, 217. ', electric light in the air, and in other gases under the pressure of the, 398. , of the pressure of the, and of the winds, 578. Atmospheric pressure, measurement of, 120. amount of, 124. moisture of, 589. Atomic weights, the, 431. Atoms, different nature of, 30. Attraction between solid and liquid bodies, 145. Atwood's falling machine, 152. August's psychrometer, 593. Auditory nerve, 251. Axes, secondary, 281. B. Balance, the, 67. , sensibility of the, 70. , hydrostatic, 95. 628 INDEX. Baldwin's locomotive, 522. Ball r Hero's, 141. Bars, magnetization of, 353. Barometer, the, 121. , height of the, 121. , construction of the, 121. , of the syphon, 122. , measurement of heights by the, 130. , Cavendish's double, 400. , causes of the oscillations in the, 579. Barometric gauge, 136. Battery, Wollaston's voltaic, 413. , the constant, 416. , Grove's, Bunsen's, 417, 419. , Daniell's, 417. , Smee's, 427. Beam must be as light as possible, the, 70. Beaume's areometer, 105. Becquerel's constant-circuit, 416, 425. Bellies, 232. Bellows, 201. Bi-convex glass lens, 274. Blowers, 199. Body, of hard and soft. 73. , of brittle and ductile, 73. , of floating and submerged, 93. , table of the specific weights of some solids, 105. Bohnenberger's electroscope, 404. Brisson and G. G. Schmidt's areometer, 101. Bronchi, 246. Bunsen's battery, 417. C. Calorimotor, Hare's, 415. Calotype paper, 345. Camera obscura, 315, 344. Capillary tubes, 108. Carlisle and Nicholson's discovery, 421. Cartier's scale, 105. Cathode, pole, 437. Caustic lines, 268. surface, 269. Cavendish's double barometer, 400. Celsius's thermometer, 488. Central motion, 158. Centripetal forces, 159. Centrifugal force, 162. Centre of gravity, 61. of a straight line, 64. of homogeneous triangle, 64. of triangular pyramid, 64. of a cone, 65. of a regular prism, 65. of a beam must lie as closely as pos- sible below the centre of suspension, 69. Chemical actions of the voltaic piles, 421. Chladni, 216, 233. Chordae vocales, 246. Circuit, different forms of the galvanic, 412. , theory of constant, 435. , Becquerel's, 435. , force of the galvanic, 444. , Becquerel's constant, 416. Climate on land and at sea, 572. Clock, the pendulum of a, 172. Clouds and mist, 596. Cloud, cirrus, 598. , cirro-cumulus, cirro-stratus and nim- bus, 599. , fleecy, 599. , stratified, 599. -, feathery, accumulated, 599. Co-efficient of friction, 175. Colladon and Sturm, experiments of, 115. Color of the spectrum is simple, each, 287. , complementary of the, 2S9. , natural, of bodies, 289. of contrast, 313. of thin plates, 335. of the sky, 606. Colored rays are unequally refrangible, the differently, 286. rings, (with a colored plate,) 335. secondary images, 312. shadows, 314. Combined electricities, 390. Combustible air, 116. Common syphon, 127. Communicating vessels, 89. Communication of electricity, 373. Compass, the tangent, 443. , declination, 357. , mariner's, 357. of inclination, 358. Composition of forces, 43. Composite eyes, 297. Compound microscope, 320. Compressibility, 30. Concave spherical mirrors, of, 262. mirrors, images, produced by, 265. Condenser, the, 396. Condensing pump, the, 139. Conducting tubes, influence of the, 183. Conductors and non-conductors, 369. Connection between the particles of a li- quid, 110. Constant battery, the, 416. Construction of the voltaic pile, 407. of the barometer, 121. Contact, theory of, 436. Contrast, colors of, 313. Convex lenses, simple eyes with, 298. mirrors, 268. Cornea, 298. Coulomb's plan, 352. Cubic expansion, 490. Current, magnetic actions of the, 454. , magnetization by the galvanic, 454. , as a moving force, application of the galvanic, 456. , induction of the, 470. , by the influence of terrestrial mag- netism, direction of, 463. and magnets, fotation of movable, 469. and animal electricity, thermo-elec- tric, 479. Crystaline lens, 298. Crystalization, 78. Crystalography, 79. INDEX. 629 Crystals, 78. Cylinder, the inclined, D. Daguerre's discovery, 344. Daniel's battery, 417. hygrometer, 591. Davy's discovery, 344, 423. Dechalle's experiments, 155. Declination of the magnet, 354. compass, 357. , variations of, 360. Delezeune, table of dilute sulphuric acid, 107. Density, 39. De Romas' experiments, 617. Despretz's experiments, 549. Dew point, 592. , the, 595. Differently (the) colored rays are unequally refrangible, 286. Dilute sulphuric acid, table of, 107. nitric acid, table of, 107. Diminution of magnetic force by distance, 364. of electrical power with the increase of distance, 387. Dioptrics, 270. Dipping needle, 358. Direction of motion, 148. of magnetic, declination, inclination, 354. Disc, a, 66. Dispersing power of different substances, 291. Distance of distinct vision, 301. Distinct vision at different distances, 299. Distribution of electricity on the surfaces of conducting bodies, 387. Divisibility, 29. Db'bereiner's lamp, 146. Dollond's achromatic telescopes, 292. Double touch, the, 354. refraction, 341. Dufay's invention, 373. Duration of the impression of light, 309. E. Earthquakes, influence on the magnetic needle, 361. Earth, actions of lightning upon the, 619. Echo, reflection of the, 224. multiple, 225. Efliux, velocities of the, ISO. of liquids, reaction created by the, 186. Elastic fluids, 116. Elasticity, 72, 125. of liquids, 115. Electric light in the air and in other gases under the pressure of the atmosphere, 398. Electric light in rarefied air, 399. fly-wheel, 401. currents, capacity of metals for con- ducting, 452. currents by magnets, induction of, 473. fluids and the natural condition of bodies, of the, 371. pistol, 374. forces, 387. telegraph, 458. current on a conducting circuit with- in itself, action of an, 470. Electrical actions, 368. diminution of power with the in- crease of distance, 387. Electricity, of the two kinds of, 370. during a thunder-storm, 617. , communication of, 373. by induction, 375. , of combined, 370. , direct proofs of the development of, by contact, 403. , distribution of, on the surfaces of conducting bodies, 387. , original discovery of atmospheric, 616. Electrifying machine, the, 381. machine, the steam, 384. Electro-chemical theory, 431. magnetic telegraph, 459. Electrodes, 437. Electrolytic law, the, 433. Electrophorus, the, 380. Electroscope of Bohnenberg, 404. Electrotype, 425. Elements, resistance of the, 450. Emission, or corpuscular theory, 326. Engine, the fire, 141. , the steam, 507. Equality of pressure, principle of the, 76. Equilibrium, 65. offerees, 43. , indifferent, 65. , stable, unstable, 65. , molecular, 72. of solids, 74. of heavy fluids, 83. of floating and submerged bodies, conditions of the, 93. of the force of tension, 502. Escapement, 173. Evaporation, 530. , production of cold by, 534. Expansion, 485. of solid bodies, the co-efficient of, 499. of fluids, 492. of solid bodies, 489. , cubic, 490. of gases, 493. Extensibility, 30. Eyes, composite, 297. , simple, with convex lenses, 298 , achromatism of the, 304. , vision with both, 307. 53* 630 INDEX. F. Fahrenheit's thermometer, 488. Falling stars, 614. Faraday, Mr., 206, 437, 471. Fechner's discovery, 438. Fire engine, the, 141. Fireballs, 614. Fixed air, 116. Fleecy clouds, 599. Floating bodies, 93. Fluids have the property of regularly pro- pagating to all parts the pressure exer- cised upon a portion of their surface, 76. , equilibrium of heavy, 83. , pressure of, 84. , magnetic, 349. , expansion of, 492. Fly-wheel, the electric, 401. of a steam-engine, 511. Focal lines, 268. distance, 279. Force, centrifugal, 162. of the galvanic circuit, 444. Forces, composition of, 43. , parallelogram of, 44. , of expansion of, 118. , centripetal, 159. Formation of regular air-waves in covered pipes, 227. of vapor, 498. Fourneyron, experiences of, 189. turbines, 190. Franklin's plate, 391. Freezing of water in a vacuum, 534. of mercury, 535. Friction, co-efficient of, 175. , sliding, 176. , rolling, 177. , resistance of, 177. Fusion, 494. G. Gadiat, simplifying turbines of, 190. Galileo, inclined plane of, 116, 120,152, 155. Galileo's telescope, 322. Gay-Lussac's areometer, 101. barometer, 122. Galvanometer, 441. Galvani's discovery, 402. Galvanism, 402. Galvanic circuit, different forms of the, 412. current, magnetic actions of the, 438. circuit, force of the, 444. piles, physiological actions of the, 419. Galvanic currents, generation of light and heat by, 420. , magnetization by the, 454. plication of the, 456. , as a moving force, ap- I Galvanic currents, on each other, recipro- cal action of, 465. Gases, 116. , measurement of the pressure of, 143. , absorption of, by liquids, 147. , motion of, 197. , the laws of the flow of, 202. , pressure of gases in the flowing out, 205. , expansion of, 493. for conducting heat, capacity of li- quids and, 548. , Gaseous bodies, 116. Gasometer, 197. Graduated, areometer the, 98. Gravity, 34. , centre of, 61. of liquids, the specific, 97. General idea of physics, 25. Generation of light and heat by galvanic currents, 420. Grimaldi and Riccioli, experiments of, 155. Grotthuss' discovery, 422. Grove's battery, 419. H. Hail and snow, 603. Hail-storm, 604. Hair-hygrometer, 590. Halos and parhelia, 612. Hare's calorimotor, 415. Heat, by galvanic currents, generation of light, 420. , of, 479. , latent,'496. , means of comparing quantities of, 536. , results of the experiments on spe- cific, 538. , existence of radiating, 539. , absorption of rays of, 543. , capacity of bodies to radiate, 542. , theoretical views concerning, 553. on the earth's surface, distribution of, 555. , Ingenhousz's apparatus for, 548. , reflection and diffusion of the rays of, 544. , capacity of bodies to transmit ravs of, 545. by conductors, distribution of, 547. , capacity of liquids and gases for con- ducting, 548. by chemical combinations, genera- tion of, 550. animal, 551. by mechanical means, development of, 552. Hearing, the organ of, 248. Height of the barometer, 121. Hell's achromatic telescopes, 292. Henley's discharging rod, 395. Hero's ball, 141. fountain, 142. Hoar-frost, 596. Homogeneous triangle, 64. INDEX. 631 Homogeneous, 287 Horizontal water-wheels, 189. Humboldt's description of the rainy sea- son, 602. Huyghen's theory of undulation, 327. Hydraulic press, the, 81. Hydrostatics, 80. balance, the, 95. Hygroscopic bodies, 147. Hygrometers, 590. of Daniel, 591. I. Ignis fatuus, 613. Images produced by concave mirrors, 265. by lenses, 282. , colored secondary, 312. Impediments to motion, 174. Inclined plane, the, 48. Inclination of magnets, 354. of magnetic needles, 357. , variations of, 360. Induction currents, 470. of electric currents by magnets, 473. Inertia, 33. Influence of light on chemical combina- tions and on decompositions, 343. Influence of conducting tubes, 183. Ingenhousz's apparatus for heat, 548. Insulated pile, the, 409. Intensity of tone, 223. of light diminishes inversely as the square of the distance, 256. of terrestrial magnetism, 361, 362. Interference of rays of light, 326. Iron becomes magnetic under the influ- ence of a magnet, 349. , influence of terrestrial magnetism upori, 362. Isochimenal lines, 570. Isothermal lines, 567. , causes of the curvature of the, 573. Jar, the Leyden, 393. K. Kobell's discovery, 428. Kryophorus of Wollaston, 535. L. Lamp, Db'bereiner's, 146. Lantern, the magic, 283. Larynx, 246. Latent heat, 496. of vapors, 530. Lateral pressure of gases in the flowing out, 205. Law of Mariotte, 128. of Ohm, 447. Laws of the oscillation of the pendulum, 164. Laws of the change of winds, 586. of the flow of gases, 202. of the vibrations of blades and rods, 242. , the electrolytic, 433. Lenses, convex, simple eyes with, 298. , magnifying the, 316. , refraction of light by, 274. Meniscus's, 275. Length of a wave, the, 202. Leslie's differential thermometer, 541. Lever, the, 54. Leyden jar, the, 393. Light, of, 252. , intensity of, diminishes, 256. , reflection of, 258. , refraction, 270. , white, 298. recomposition of, 287. , electric, in the air, and in other gases under the pressure of atmosphere, 398. , duration of the impression of, 309. , interference of rays of, 330. , refrangibility of, 331. , white, (with a colored plate,) 334. , polarization of, 337. , influence of, on chemical combina- tions and on composition, 343. in rarefied air, electric, 399. and heat by galvanic currents, gene- ration of, 420. Lightning conductors, 389, 398, 621. plate, a, 398. upon the earth, actions of, 619. Limits of visibility, 309. Linear-waves, 212. Lines, isothermal, 567. , isochimenal, 570. Liquids, equilibrium, 80. specific gravity of, 97. elasticity of, 115. compressibility of, 115. absorption of gases by, 147. in motion, lateral pressure of, 185. reaction created, by the efflux of, 186. , and gases for conducting heat, ca- pacity of, 548. Locomotive, the, 520. Baldwin's, 522. Long-sightedness, 303. Luminous point, 252. M. Machines of rotation, magneto-electric, 475. t water-column, 192. , the electrifying, 381. , the steam-electrifying, 384. Magdeburg hemispheres, 137. Magic disc, 310. lantern, the, 320. Magnet, influence of a, 349. , declination, inclination, 354. 632 INDEX. Magnets and currents, rotation of movable, 469. , induction of electric currents by, 473. Magnetic poles, 347. fluids, 349. actions of the galvanic current, 454. armatures, 351. north pole and south pole, 355. meridian, the, 356. needles, inclination of the, 357. equator, 359. force, diminution of, by distance, 364. Magnetism, intensity of terrestrial, 361. Magnetization of steel needles and bars, 353. by the galvanic current, 438. Magneto-electric, 470. machines of rotation, 475. Magnifying lens, the, 316. Manometers, 143, 201. Mariotte's law, 128. Mass, 37. Material pendulum, 170. Measures and weights, 36. Measurement of atmospheric pressure, 120. of height by the barometer, of the, 130. of the pressure of gases, of the, 143. Mechanical actions, the, 621. Meiszner's areometer, 105. Melloni's thermomultiplicator, 541. Meniscus lenses, 275. Mephitic air, 116. Mercury, of, 113. , freezing of, 535. Metals, conductibility of, 452. Meteoric stones, 614. Meteorology, 555. Method, 26. of mixtures, the, 537. Microscope, of the simple, 316. , the solar, 319. , the compound, 320. Middle-shot wheel, the, 189. Mirrors, reflection from curved, 261. , convex, 268. , of concave spherical, 262. , images produced by concave, 265. Mist and clouds, 596. Moisture, of atmospheric, 598. , degrees of, 591. , of the air in various districts, 595. Molecular forces, 32. equilibrium, 72. Monochord, an instrument, 241. Monsoons and trade-winds, 582. Motion and rest, 148. , uniform, the, 148. , the accelerated and retarded, 150. , centra], 158. , quantity of, 168. , impediments to, 174. , of fluids, 179. , of gases, 197. , of vibratory, 207. Motion occasioned by electrical reaction, 401. produced by the discharge of elec- tricity, 400. Mount d'Or, 124. Etna, 124. Lebanon, 124. Movable currents and magnets, rotation of, 469. Miiller (J.) mosaic composite eyes, 297. Multiple echoes, 225. Multiplicator, the, 441. Miinchow, 289. Muschenbrock, experiments of, 74. Musical notes, 236. Myopia, 303. N. Natural colors of bodies, 289. Needles, inclination and declination of magnetic, 357. Nesselgrabe, water-column machines, 192. Newton's industry, 161, 327. Nicholson's areometer, 96. Nicholson and Carlisle's discovery, 421. Niepce's discovery, 344. Nitric acid, table of, 107. Nobile's multiplicator, 442. 0. Oersted, experiments of, 115, 439. Ohm's law, 447. Giber's calculation, 300. Ombrometers, 600. Open pipes, the, 234. Optical axes, 342. Optometers, 303. Organ-pipes, 233. Organs of speech, the, 246. of hearing, the, 248. Origin of the winds, 581. Oscillations, 164. in the barometer, causes of the, 579. of the pendulum, laws of the, 164. Otto Von Guericke's invention, 132, 373. P. Papin's digester, 528. Parallelogram offerees, 44. Parhelia and halos, 612. Pendulum, of the, 163. , laws of the oscillations of the, 164. , the material, 170. of a clock, the, 172. Phenakistiscope, 310. Photography, 344. Physical actions of lightning, 621. Physiological colors, 312. Physics, what is understood by, 26. Picard's discovery, 400. Pile, construction of the voltaic, 407. INDEX. 633 Pile of Zamboni, 404. , the insulated, 409. , the closed, 410. , the dry, 410. properties of the dry, 411. , chemical actions of the voltaic, 421. , thermo-electric, 481. Pipes, organ, 233. , open, 234. Pistol, the electric, 374. Plane, inclined, 48. , Galileo's inclined, 151. of incidence, the, 270. Polarization of light, 337. Poles, magnetic, 347. repel each other, and contrary poles attract each other, 348. Poncelet's wheel, 189. Porosity, 30. Porta's invention, 315. Power of tension, 118. Presbyopia, 303. Pressure, principle of the equality of, 76. of fluids, 84. of air, 119. , measurement of atmospheric, 120. , table of the amount of atmospheric, 124. of gases, measurement of the, 143. of liquids in motion, lateral, 185. of gases in the flowing out, 205. of the atmosphere, and of the winds, 578. Prism, a, 272. Prisms, refraction of light in, 272. , achromatic, 292. Projectiles, 158. Psychrometer, 593. Pulley, the, 51. Pumps, the suction of, 125. , and forcing of the, 126. , of the air, 132. , condensing, the, 139. Pupil, 289. Q- Quality of tone, 223. Quantity of motion, 168. of rain, 600. Radiate heat, capacity of bodies to, 542. Radiating heat, existence of, 539. Rain, quantity of, 600. gauges, 600. between the tropics, 602. Rainbow, the, 608. Rapidity of sounds, 224. Rays of heat, reflection and diffusion of the, 544. , capacity of bodies to trans- mit, 545. Rays of heat, absorption of, 543. of light, interference of, 326. Reaumur's thermometer, 488. Reed-pipes, 242. Reflecting telescope, 321. Reflection of light, 258. of angles, 260. from curved mirrors, 261. Refracting angle, 270. telescopes, 322. Refraction, 270. , angle of, 270. of light in prisms, 272. by lens, 274. , double, 341. Refrangibility of light, 331. Regnault's investigations on heat, 539. Reichenbach's water-column, 192. Relation between the perception of the eye and the external world, 305. Resistance of friction, the, 77. Rest and motion, 148. Retarded and accelerated motion, the, 150. uniformly, 150. Retina, 298. Riccioli and Grimaldi, experiments of, 155. Ring colors, (with a colored plate,) 335. Rolling friction, 177. Rumford's differential thermometer, 540. S. Safety tubes, the, 143. Salifiable bases, 433. Salts, decomposition of, 423. Saussure's hair-hygrometer, 590. Scale of tension, 405. Scheiner's experiments, 302. Schweigger's multiplicator, 441. Scoresby's observations on snow, 603. Screw, the, 50. Secondary axes, 281. Secular variations, 360. Segner's water-wheel, 190. Sensibility of the balance increases with the length of the beam, the, 70. Shadows and half shadows, 253. colored, 314. Short-sightedness, 303. Simple eyes with convex lenses, 298. microscopes, 316. Sky, color of the, 606. Sliding friction, 176. Snow and hail, 603. Solar microscope, the, 319. Solidification, 497. Sound of tone, the, 223. , velocity of, 223. , rapidity of, 223. , reflection of, 224. Specific gravity of liquids, 39. - of some solid bodies, ta- ble of, 97. Spectrum, 285. Speech, organs of, 246. 634 INDEX. Statics, 43. Steam, the, electrifying machine, 384. engine, the, 507. Steel resists the magnetizing influence, 351. needles, magnetization of, 353. Stones, meteoric, 614. Storms, 588. Strength, 67. Strings, vibrations of, 240. Sturm's experiments, 115. Subjective colors, 312. Suction, the, of the pumps, 126. and forcing of pumps, 126. Sulphuric acid, table of dilute, 107. Suspension, 68. Syphon barometer, 122. , the, 121. , common, 121. T. Table of the specific weight of some solid bodies, 97. of density of liquids, 106. of the amount of atmospheric pres- sure, 120. Tangent compass, the, 443. Tangential forces, 159. Telegraph, the electric, 458. Telescopes, of Hell's Dollond's, 298. reflecting and refracting, 321. terrestrial, 325. Temperature in the upper regions of the air, decrease of, 576. , diurnal variations of, 561. of the ground, 575. , of the months, and of the year, mean, 562. of forty-three places, mean, 565. Tension of the vapor of water, estimate of the force of, 503. , scale of, 405. of vapors, maximum of the force of, 500. Terrestrial magnetism, direction of cur- rents by the influence of, 463. Thayer's discovery, 428. Theory of constant circuits, 435. of contact established by Volta, 436. Thermo-electric currents, and animal electricity, 479. piles, 481. Thermo-multiplicator of Melloni, 541. Thermometer, the, 485.- , Reaumur's, 488. , Fahrenheit's, 488 , Celsius', 488. , differential, Rumford's, Leslie's, 540, 541. , observations on the, 559. Trough apparatus, the, 412. Thunder-storm, electricity during a, 617. Time, of an oscillation, 165. Talbot's method, 345. Tones, 222. of stretched strings, 240. Torricellian experiments, 121, 128, 129. , vacuum of the, 121. , theorem, 179. Trade-winds and monsoons, 582. Translucent bodies, 253. Transmission of sound through the atmo- sphere, 217. of vibrations of sounds, 244. Transparent bodies, 253. Turbines, 190. Tubes, of the capillary, 108. safety, the, 143. , influence of conducting, 183. Tunica sclerotica, 298. Tympanum, cavity of the, 249. U. Udometers, 600. Undulatory theory, 327. Uniform motion, the, 148. Uniformly accelerated, 150. retarded, 150. V. Vapors, latent heat of, 530. in the air, distribution of, 589. Vapor, formation of, 498. , maximum of the force of tension of, 500. of water, estimate of the force of tension of the, 503. Variations of declination and inclination, 360. , secular, 360. Velocity of efflux, ISO. of sound, 223. Vertical water-wheels, 187. , under shot, 187. , over shot, 189. , middle shot, 189. Vessels, communicating, 89. Vibration, theory of, 326. Vibrations of different strings, 240. . of sound between solid, fluid, and aeriform bodies, 244. Vibratory motion, 207. Vision with both eyes, 307. Visibility, limits of, 309. Volta's theory of contact, 436. experiments, 402. Voltaic pile, construction of the, 407. , chemical actions of the, 421. Voigtlander's construction of the camera obscura, 316. Volcanic eruptions, influence on the mag- net, of the, 361. Volkmann's experiments, 305. Volumeter, 98. INDEX. 635 w. Water-column machines, 192, 195. Water, decomposition of, 421. contained in the air diurnal and an- nual variation in the quantity of, 593. , estimate of the force of tension of the vapor of, 503. in a vacuum, freezing of, 534. Water-spouts, 589. Water-waves, 209. Water-wheels, 189. horizontal, 189. : of Segner, 186. Wedge, the, 51. Wedgwood's discovery, 344. Weight, 36. of some solid bodies, table of speci- fic, 105. Weights and measures, 36. Windings on each other, action of the, Welter's invention, 143. White light, 285. recomposition of, 287. Will-o'-the-Wisp, 613. Winds, pressure of the, 578. , origin of the, 581. in higher latitudes, 585. , laws of the change of, 586. Wollaston's battery, 413. kryophorus, 535. Z. Zamboni's pile, 404. THE END. BLANCHARD & LEA'S CATALOGUE OP EDUCATIONAL AND MISCELLANEOUS PUBLICATIONS. attelr^^^ to furnish any information desired regardm" tLn Th ' T P ubhcati ons, and booksellers throughout this country ofcanadl who SftjS? 1 C ^ be had of a11 may not be kept in stock. Address, dlly order an J which , 1854. BLANCHARD & LEA, PHILADELPHIA. be had NEW AND MUCH IMPROVED EDITION-cLately Issued. PHYSICAL GEOGRAPHY. BY MARY SOMERVILLE r BY W. S. W. RUSCHENBERGER, M. D. f U. S NAVY In one large royal 12mo volume, of nearly 600 pages. ! extra cloth, $1 25 Half bound in leather, $1 35. The subject of Physical Geography is one of which the acknowledged i forcing its introduction into all systems of education which pretend to keep with the improvements and requirements of the age. It is no longer conKST * Jevd the scholar into a mechanical knowledge of the names of rivers H m sufficient to drill divisions of the earth's surface. A want is now fek of an ' " ' temt rial . an s now e o an acquainance w ih globe, externally and internally, and of the causes and ^^f^^S^SKS f *" forest and desert, heat and cold, tides, currents, rain, wind, and allthe other nhvscal h W ' occurring around us, which have so direct and immense an influence upon is all summed up ,n Physical Geography," which may be , c may e regare as t rese of all th t known on the natural history and present state of the eartlf and its SS^SS^^SS^ application of the priacipe. which are elucidated by the minute investigations of the observer Th.s vast and interesting subject has been successfully grappled by Mrs lomerv I who in the present volume has set forth, in a picturesque and vivid style?- polar yet condeni^' account of the globe, m its relations with the Solar System ; its geological forces hs^coZu ration and divisions mto land and water, mountain, plain, river, and lake ; its meteorology m nera 'nrr! duction., vegetation, and animal life; estimating and analyzing the causes at wo'r "and I ' influence on plants, ammals, and mankind. A study such as this, taken in conjunction ordinary political geography, lends to the latter an interest foreign to the mere cataJogu of nam and boundaries, and, in addition to the vast amount of important information imparted tendTto jmpress the whole more strongly on the mind of the student. Eulogy is unnecessary with regard to a work like the present, which has passed through three editions on each s,de of the Atlantic within the space of a few years. The publishers therefore only consider it necessary to state that the last London edition received a thorough revision at the hands of the author, who introduced whatever improvements and corrections the advance of sci ence rendered desirable ; and that the present issue, in addition to this, has had a careful examina ion on the part of the editor, to ad.ipt it more especially to this co.antry. Great care has beei sxercised m both the text and the glossary to obtain the accuracy so essential to a work of this nature ; and in its present improved and enlarged state, with no corresponding increase of price t is confidently presented as in every way worthy a continuation of the striking favor with whirh it has been everywhere received. From William Russell, Esq., N. E. Normal Institute Mass., March 14, ]fc54. Mrs. Spmerville's volume has been in use in rar own family class as an advanced text-book equalir acceptable to teacher and pupils. But the new edi- tion is studied with peculiar delight from its happy blending of the poetry with the philosophy of the sub- ject. I know of no class-book more instructive or ~~ *. .rviujwis 0,1111 UUilCt'rS. 1 HOnC U Will UC m^t-** iri1ur*>cf itirr adopted as such generally, for you have American- m re " ized it and improved it in other respects. From Thomas Sherwin, High School, Boston. From Samuel H Taylor, Esq . Philips Academy, I hold it in the highest estimation, and am confident Andover. Mass., Feb. 15, lf-54. that it will prove a very efficient aid in the education We have introduced your edition of Mrs. Somer- ot the young, and a source of much interest and in lies "Physical Geography" into our school, and struction to the adult reader. Snd it an admirable work. From Lieutenant Maury, U. S. N. National Observatory, Washington, thank you for the "Physical Geography;" it is e , ap , * nave keen reading it, and like it so much I have made it a school-book lor my children, whom I am teaching. There is, in my opinion, no work upon that interesting subjecton which it treats- l hysical Geography that would make a better text book in our schools and colleges. I hope it will b> BLANCHARD & LEA'S EDUCATIONAL PUBLICATIONS. NOW COMPLETE. A SERIES OF TEXT-BOOKS!^ ON PHYSICAL SCIENCE. HANDBOOKS OF NATURAL PHILOSOPHY AND ASTRONOMY, BY DIONYSIUS LARDNER, D. C. 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HYDROSTATICS, HYDRAULICS, PNEUMATICS, and SOUND. It will thus be seen that this work furnishes either a complete course of instruction on these subjects, or separate treatises on all the different branches of Physical Science. The object of the author has been to prepare a work suited equally for the collegiate, acade- mical, and private student, who may desire to acquaint himself with the present state of science, in its most advanced condition, without pursuing, it through its mathematical consequences and details. Great industry has been manifested throughout the work to elucidate the principles ad- vanced by their practical applications to the wants and purposes of civilized life, a task to which Dr. Lardner's immense and varied knowledge, and his singular felicity and clearness of illustra- tion render him admirably fitted. This peculiarity of the work recommends it especially as the text-book for a practical age and country such as ours, as it interests the student's mind by show- ing him the utility of his studies, while it directs his attention to the further extension of that utility by the fulness of its examples. Its extensive adoption in many of our most distinguished colleges and seminaries is sufficient proof of the skill with which the author's intentions have been carried out. From Prof. Kirkwood, Delaware College, April 12, 1S51 . After a careful examination, I am prepared to say lhat it is the most complete "Handbook of Astrono- my" with which lam acquainted. I trust the demand for the work will be commensurate with its merits. From Prof. A. C a swell, Broivn University. April 29, 1854. I regard it as a very useful and very convenient rpular compend of the sciences of which it treats, is full of information and well illustrated. It de- serves a place among the best educational treatises on Astronomy and Physics. From Prof. W. L. Broivn, Oakland College, Miss., March 29, 1854. I consider them most admirably suited for lle pur- poses designed by the author indeed, as the very best popular works on 'physical science with which I am acquainted. The k< Third Course" on Astrono- my, is especially valuable ; its magnificent engrav- ings and lucid explanations make it a most desira- ble text-book. From Prof. R. Z. Mason, McKendree College, III. In my judgment it contains the best selection of compact demonstrations and popular illustrations that we have yet received on the subject. Dr. Lardner has relieved it somewhat from the dry details of Mathematics, and yet there is such a close adherence to severe methods of thought as to satisfy the most rigid and careful analyst. From Rev. J. G. Ralston. Norrittown, Pa., March 22, 1854. Lardner's Meteorology and Astronomy is a fit com- panion for his First and Second Course. It is won- derfully minute, and yet not prolix. The principles of Astronomy are probably as clearly defined and judiciously arranged in this book as they can be. I expect to introduce it in my school. From S. Schooler, Esq., Hnnover Academy, For., April 16, Ib54. The three volumes constitute a body of information and detail on nearly the whole range of physical science which is not to be found together in any other publication with which I am acquainted. I hope that these works may be the means of inducing many of our youth to devote themselves to the de- velopment of the Laws of Nature, and the application of them to industry, and that they may be the vehicle for conveying sound information and food for thought to every man who aspires to be well educated. From M. Conant, State Normal School, Mass , April 11, 1854. This is a treatise admirably adapted to its purpose. For the accurate knowledge it unfolds, and the very popular dress it appears in, I think I have met with nothing like it. I shall advise the students of the. Normal School to add this to your edition of Lard- ner's Mechanics, &c. From Prof. E. Everett, -New Orleans, Feb. 25, 1854. I am already acquainted with the merits of this book, having had occasion to consult it in teaching the branches of which it treats, and I cannot give you a stronger assurance of my high opinion of it than the simple fact that 1 have selected it as the text-book of Physics in the course of study which I have just fixed upon for a new college to be established here. BLANGHARD & LEA'S EDUCATIONAL PUBLICATIONS. A COMPLETE COURSE OP NATURAL SCIENCE-(Just Issued.) THE BOOK OF NATURE; AN ELEMENTARY INTRODUCTION TO THE SCIENCES OF Physics, Astronomy, Chemistry, Mineralogy, Geology, Botany, Zoology, and Physiology, BY FREDERICK SCHOEDLER, Pn. D. * Professor of the Natural Sciences af Worms. FIRST AMERICAN EDITION, With, a Glossary, and other Additions and Improvements. FROM THE SECOND ENGLISH EDITION, TRANSLATED FROM THE SIXTH GERMAN EDITION BY HENRY MEDLOCK, F. C. S., &c. ILLUSTRATED BY SIX HUNDRED AND SEVENTY-NINE ENGRAVINGS ON WOOD. In one handsome volume, crown octavo, of about seven hundred large pages, extra cloth. $1 80. To accommodate those who desire to use the separate portions of this work, the publishers have prepared an edition in parts, as follows, which may be had singly, by mail or otherwise, neatly done up in flexible cloth, price 50 cents each. NATURAL PHILOSOPHY, .... 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It has been passed through the press under the care of a competent editor, who has cor- rected such errors as had escaped the attention of the English translator, and has made whatever additions appeared necessary to bring it completely on a level with the existing state of science. These will be found principally in the sections on Botany and Geology; especially the latter, in which references have been made to the numerous and systematic Government surveys of the several States, and the whole adapted to the nomenclature and systems generally used in this country. A copious Glossary has been appended, and numerous additional illustrations have been introduced wherever the elucidation of the text appeared to render them desirable. It is therefore confidently presented as an excellent Manual for the private student, or as a com- plete and-thorough Class-book for collegiate and academical use. far as my knowledge extends. It admirably com- bines perspicuity with brevity; while an excellent judgment and a rare discrimination are manifest in the selection and arrangement of topics, as well as in the description of objects, the illustration of pheno- mena, and the statement of principles. A more care- ful perusal of those departments of the work to which Books which treat of everything too often remind us of patent medicines, that are advertised to cure all the maladies that human flesh is heir to. But the volume before us does not belong to that genus. It is not the production of a quack, but is a truly scien- tific manual, almost a library on Physical Sciences, yet perfectly convenient, and valuable to the student as a work of reference. Though the whole range of sciences is embraced in it, yet it affords a much more minute and ample fund of instruction in these various departments than do many treatises which include only a single subject. Teachers will find it a valu- able work for their libraries. N. Y. Student. Composed by the same distinguished author, all the departments have a uniformity of style and illustra- tion which harmoniously link the entire circle to- gether. The utility of such a connected view of the physical sciences, and on such an approved basis, is beyond price; and places their acquisition within the reach of a vastly increased number of inquirers. Not only to such is it valuable, but to those who wish to have at hand the means of refreshing their memo- ries and enlarging their views upon their favorite studies. Of such a book we gpeak cordially, and would speak more at length, if space permitted. Southern Methodist Quarterly Revieiv. Froth Prof. Johnston. Wesleyan University, Ct., March 14, 1854. I dp not know of another book in which so much that is important on these subjects can be found in the same space. From Prof. Allen, Oberlin Institute, Ohio, April!, 1854. As a work for popular instruction in the Natural and Physical Sciences, it certainly is unrivalled, so my studies have been particularly directed has been abundantly sufficient to satisfy me of its entire reli- ablenessthat the object of the author was not so much to amuse as really to instruct. From Prof. Pearson, Union College, N. Y, Feb. 22, 1?54. It seems to be a book well adapted to imparting ai: elementary knowledge of Physics and Natural His- tory to students of our Academies and Colleges. From Prof. /. A. Spencer, N. Y. I am delighted with Dr. Schccdler's "Book of Na- ture ; :) its tone of healthful piety and reverence for God's word add a charm to the learning and deep re- search which the volume everywhere manifests. From W. J. Clark, Esq., Georgetown Female Semi- nary, D. C. As far as I have examined, it has afforded me great pleasure. It is the most valuable compendium of the subjects of which it treats with which 1 have ever met. From W. H. Allen, President ofGirard College, Philada. Though a very comprehpusive book, it contains about as much of the details of natural science as general students in this country have time to study in a regular academical course; and I am so well pleased with it that I shall recommend its use as a text-book in this institution. BLANCHARD & LEA'S EDUCATIONAL PUBLICATIONS. TEXT-BOOK OF SCRIPTURE GEOGRAPHY AND HISTORY (Just Issued.) OUTLINES OF SCRIPTURE "GEOGRAPHY AND HISTORY; Illustrating the Historical Portions of the Old and New Testaments, DESIGNED FOR THE USE OF SCHOOLS AND PRIVATE READING. BY EDWARD HUGHES, F.R.A.S., F.G.S., Head Master of the Royal Naval Lower School, Greenwich, &c. BASED UPON COLEMAN'S HISTORICAL GEOGRAPHY OF THE BIBLE. "With, twelve handsome colored Maps. In one very neat royal 12mo. volume, extra cloth. $1 00. The intimate connection of Sacred History with the geography and physical features of the va- rious lands occupied by the Israelites, renders a work like the present an almost necessary com- panion to all who desire to read the Scriptures understandingly. To the young especially, a clear and connected narrative of the events recorded in the Bible, is exceeding desirable, particularly when illustrated, as in the present volume, with succinct but copious accounts of the neighboring nations and of the topography and political divisions of the countries mentioned, coupled with the results of the latest investigations, by which Messrs. Layard, Lynch, Olin, Durbin, Wilson, Stephens, and others have succeeded in throwing light on so many obscure portions of the Scriptures, veri- fying its accuracy in minute particulars. Few more interesting class-books could therefore be found for schools where the Bible forms a part of education, and none, perhaps, more likely to prove of permanent benefit to the scholar. The influence which the physical geography, climate, and productions of Palestine had upon the Jewish people will be found fully set forth, while the nu- merous maps present the various regions connected with the subject at their most prominent periods. LIST OF MAPS. I. The World, showing the Settlements of the Descendants of Noah. II. Canaan in the time of the Patriarchs. III. Peninsula of Sinai, with part of Egypt; illustrating the Journeyings of the Israelites from Egypt to Canaan. IV. Canaa'n as divided among the tribes ; illustrating the period from Joshua to the Death of Saul. V. Syria; showing the Dominions of David and Solomon. VI. The Kingdoms of Judah and Israel. VII. Assyria, Chaldea, and Media. Countries of the Jewish Captivities. VIII. Palestine under the dominion of the Romans in the time of our Lord; illustrating the Gos- pels and Acts of the Apostles. IX. The Countries adjoining the Mediterranean; illustrating the Acts of the Apostles, tha Epistles, and the Apocalypse. X. Mediaeval Palestine in the time of the Crusades. XI. Christendom during the Crusades ; showing the extent of the Roman and Greek Churches, and the countries professing Mohammedanism. XII. Modern Palestine under Turkish dominion. We have given it considerable examination, and have been very favorably impressed with it as a work of rare excellence, and as well calculated to answer a demand, which, so far as our knowledge extends, has never yet been fully accomplished. Evangelical Repository. A concise and very convenient condensation of just such facts and information as the Biblical student and general reader want always at hand. We com- mend it without reserve. N. Y. Recorder. We have read it with care, and can recommend it with confidence. Indeed, we do not know of a more convenient and reliable handbook fora pastor, Sun- day-school teacher, or a general student to refer to for information in regard to Palestine, whether as to its physical features or its geography, its climate or its productions, its past history or its present condi- tion. Southern Presbyterian. From Prof. Samuel H. Turher, N. Y. Theological Seminary. It appears to contain in a compressed form a vast deal of important and accurate geographical and historical information I hope the book will have the wide circulation which iis merits entitle it to. I shall not fail to recommend it so far as opportunity offers. From Rev. Samuel Findley, President of Antrim College, Ohio, Feb. 18, 1854. We have long needed just such a book, and as soon as possible we shall make it one of the text- books of oar college. It should be a text-book in all our theological institutions. From Rev. Eliphalet Nott, President of Union College. N. Y., Feb. 20, 1854. Few more interesting class books where the Bible is used in schools can be found than the "Outlines of Scripture Geography and History," and it will prove, in families where the Bible is read, a valuable aux- iliary to the understanding of that blessed volume. It is therefore to be hoped that it will receive that patro- nage which it so richly deserves. From Prof. E. Everett, New Orleans, Feb. 25, 1854. I have studied the greater portion of it with care, and find it so useful as a book of reference that I have placed it on the table with my Bible as an aid to my daily Scripture readings. It is a book which ought to be in the hands of every biblical student, and I can- not but hope that it will have a wide circulation. To such as desire to borrow I answer, " I cannot loan it, for I am obliged to refer to it daily!" From William Russell, N. E. Normal Institute, Mass., March 14, 1854. It comprises the fullest and most instructive, as well as the most attractive course of lessons on its particu- lar subjects that has hitherto been offered in the com- pass of a single volume. From Prof. Sturtevant, Illinois College, March 25, 1854. Its thoroughness and comprehensiveness combined with conciseness and portable size, and especially its neat and beautiful maps, render it peculiarly adapted to Bible classes and Sabbath schools, and, indeed, to every religious family and every reader of the Bible. It is also very valuable to the student of Ancient History, whether sacred or profane. I have seen no work of the kind which pleases me so well. From Rev. J. G. Ralston, Norristown, Pa., March 22, 1854. I regard it as an excellent book, containing more information on the subjects indicated in the title than any other with which I am acquainted. It cannot fail to be a popular companion with every student of the Holy Scriptures. I take pleasure in commending it to the attention of my pupils. ^^1^L^!_^CATIO N AL PUBLICATIONS. NOW COMPLETE" SCHMITZ & ZUMPT'S CLASSICAL SERIES The publishers have much nl^c,, : . teachers, and its extensive introduction int many of on h T ^ " cholar ' and P^tical the objects of the distinguished editors have b^en fuUv c?rri/H S f minaries and co "eges, show that have been to present a uniform set of text-books based nth '" P re P aration - These objects education, conducting the student from the commen ^T 51? a PP roved 8 y stems of modern one definite plan, thus relieving the teacher froTthe c ** tO their concll ^on on works based upon different and conflicting systems h^"^ , PaSSI " g P ro g ress ively through been made, which are printed from the m^t cor^ ^ Sele 1 Ct ' n of classical au thors has with biographical and critical SSJ^^^^^S^ texts ' and are Accompanied , as i been done to convenient for use, while at the same ^l^S me ^ lSmo ' form > the ? "c low. Every care has been taken to secure the verbaTandlh 7 " e un P reced etedly tional works, while most of the volume! can hlhad in , * acc , ur f cy so necess "7 in educa- with leather backs and cloth sides " neat 6Xtra doth > or siron S^ half bound, The Series consists of the following works- ADVANCED DAMMAR OF THE LATIN LANGUAGE. Half bound, price the RULES F SYNTA ' S S H C ? L D J CTIONARY OF TH E LATIN LANGUAGE. In two parts, , and ENGLISH-LATIN. Complete in one very thick volume, of nearly 900 double- .olumned pages, full bound m strong leather. Price $1 30. Also, PART I, LATIN-ENGLISH, sold 'separate, full bound. Price 90 cents. PART II, ENGLISH-LATIN, sold separate, full bound. Price 75 cents. CORNELII NEPOTIS LIBER DE EXCELLENTIBUS DUCIBUS EXTERARUM GENTIUM, CUK \ms CATONIS ET ATTICI. With Notes, &c. Price in extra cloth, 50 cents ; half bound, 55 JL C. I . CJESARIS COMMENTARII DE BELLO GALLICO. With Notes, Map, and other illus- trations. Price in extra cloth, 50 cents; half bound, 55 cents. C. C. SALLUSTII DE BELLO CATILINARIO ET JUGURTHINO. With Notes, Map, &c Price in extra cloth, 50 cents; half bound, 55 cents. EXCERPTA EX P. OVIDII NASONIS CARMINIBUS. With Notes, &c. Price in extra cloth DO cents ; half bound, 65 cents. Q. CURTII RUFI DE GESTIS ALEXANDRI MAGNI LIBRI VIII. With Notes, Map, &c Price in extra cloth, 70 cents; half bound, 75 cents. P. VIRGILII MARONIS CARMINA OMNIA. Price in extra cloth, 75 cents; half bound, SO cts. T. LIVII PATAVINI HISTORIARUM, LIBRI I.. II., XXL, XXII. With Notes, two colored Maps, &c. Price in extra cloth, 70 cents ; half bound, 75 cents. M. T. CICERONIS ORATIONES SELECTS XII. With Notes, &c. Price in extra cloth. 60 cents ; half bound, 65 cents. ECLOG.E EX Q, HORATII FLACCI POEMATIBUS. With Notes, &c. Price in extra cloth, 60 cents; half bound, 65 cents. In its complete state, it will thus be seen that this Series presents a thorough and uniform course of instruction in Latin, from the rudiments to the lower collegiate classes. From among many hundred recommendatory notices with which they have been favored, the publishers append a few. From Prof. N. W. Benedict, Rochester University, N. Y. I have taken pains to examine the works and am rtappy to find them very superior for Ihe purposes designed. The selection made from Latin authors is a judicious one; the editorial labor is of the right kind; and the mechanical execution of the works, together with the low price at which they are afford- ed, constitute them a valuable aid towards the fur- therance of classical studies in this counlry. From Prof. W. H. Doherty, Antioch College, Ohio. I greatly admire the beautiful and most useful se- ries of Latin authors which you have published. I regard them as a real boon to all students of moderate means, they are so cheap, so comprehensive, and so correct. They constitute, in fact, an admirable course of Latin reading, and their wonderful cheapness places them wi'hin the reach of the humblest and poorest student. BLANCHARD & LEA'S EDUCATIONAL PUBLICATIONS. SCHMITZ & ZUMPT'S CLASSICAL SERIES (Continued.) From Prof. J. J. Owen, N. Y. Free Academy. With your classical series I am well acquainted, rnd have no hesitancy in recommending them to all my friends In addition to your Virgil, which we use, we shall probably adopt other books of the series as we may have occasion to introduce them. From Reginald PL Chase, Harvard University, Mass. I have taken time to give the two Grammars a par- ticularly careful examination, and I was not surprised to find them equally admirable in plan and execution with the other works of your series. They are pre- cisely what [ have been longing for. My pupils have provided themselves with them, and they will here- after, in common with the' other volumes of the series, lie required as text-books with all my scholars. In our Latin school no others will be allowed. From Prof. A Rollins, Delaware College. I regard this series of Latin text books as decidedly superior to any others with which I am acquainted. TheLivy and Horace I shall immediately introduce for the use of the college classes. From Prof. A. C. Knox, Hanover College, Ind. Having examined several of them with some de- gree of care, we have no hesitaiion in pronouncing them among the very best extant. From Prof. R N. Newell. Masonic College, Tenn., June 2, 1852. I can give you no better proof of the value which I set on them than by making use of them in my own classes, and recommending their use in the prepara- tory department of our institution. I have read them through carefully that I might not speak of them with- out due examination, and I flatter myself that my opinion is fully borne out by fact, when I pronounce them to be the most useful and the most correct, as well as the cheapest editions of Latin Classics ever introduced in this country. The Latin and English Dictionary contains as much as the sHvJenl can want in the earlier years of his course; it contains more than I have ever seen compressed into a book of this kind. It ought to be the student's constant companion in his recitations. It has the extraordinary recom- mendation of being at once portable and comprehen- sive. Among the various editions of the Latin Classics. Schmitz and Zumpt's series, so far as yet published, are at all times preferred, and students are requested to procure no other. Announcement of Bethany Col- lege, Fa. But we cannot forbear commending especially, both to instructors and pupils, the whole of the series edited by those accomplished scholars. Drs. Schmitz and Zumpt. Here will be found a set of text-books that combine the excellences so long desired in this class of works. They will not cost the student, by one-half at least, that which he must expend for some other editions. And who will not sny that this is a consideration worthy of attention? For the cheaper our school-books can be made, the more widely will they be circulated and used. Here you will find, too. no useless display of notes and of learning, but in foot-notes on each page you have everything neces- sary to the understanding of the text. The difficult points are sometimes elucidated, and often is the stu- dent referred to the places where he can find light, but not without some effort of his own. We think that the punctuation in these books might be im- proved; but taken as a whole, they come nearer to the wants of the times than any within our know- ledge. Southern College Review. UNIFORM WITH SCHMITZ & ZUMPT'S CLASSICAL SERIES, BAIRD'S CLASSICAL MANUAL. THE CLASSICAL MANUAL; AN EPITOME OP ANCIENT GEOGRAPHY, GREEK AND ROMAN MYTHOLOGY, ANTIQUITIES, AND CHRONOLOGY. Chiefly intended for the use of Schools. By the Rev. JAMES S. S. BAIRD, T. C.D., Assistant Classical Master, King's School, Gloucester. In one neat royal 12nio. volume. Price in extra cloth, 50 cents; half bound, 55 cents. This little volume has been prepared to meet the recognized want of an Epitome which, within the compass of a single small volume, should contain the information requisite to elucidate the Greek and Roman authors most commonly read in our schools. The aim of the author has been to embody in it such details as are important or necessary for the junior student, in a form and space capable of rendering them easily mastered and retained; and he has consequently notincum- bered it with a mass of learning which, though highly valuable to the advanced student, is merely perplexing to the beginner. In the amount of information presented, and the manner in which it is conveyed,, as well as its convenient size and exceedingly low price, it is therefore admirably adapted for the younger classes of our numerous classical schools. Although issued but very recently, this little work has commanded universal approbation ; and its immediate introduction into a large number of our best educational institutions, sufficiently proves that the author has succeeded in filling a vacancy among our classical text-books. From Prof. R. W. Newell, Masonic College, Tenn. I cannot help thinking that in none of your works have you so effectually provided for the wants of the poor student as in this. From Reginald H. Chase, Harvard University. That invaluable little work, the Classical Manual, has been used by me for some time. I would i,oton any account be without it. You have i;ot perhaps been informed that it has recently been introduced in the High School of this place. Its typographical ac- curacy is remarkable. From Prof. J. S. Hart. Principal of the Philadelphia High School.' !; Baird's Classical Manual" is an admirable com- pend of the knowledge most indispensable to the stu- iient of Greek and Roman ajitiquities. From Prof. P. 13. Spear, Madison University, N. Y. I am persuaded, from the examination whic'h I V ave given it. that if a class were to be drilled upon such an '-Epitome" as this, nothing better would lay a foundation for a full and accurate knowledge of the Geography, Chronology, Mythology, and Antiquities of thtf Grteks and Romans. ARNOT'S ELEMENTS OP PHYSICS. ELEMENTS OF PHYSICS; OR, NATURALlffllO SOPHY, GENERAL AND MEDICAL, Written for Universal Use in Plain or Non-Technical Language. BY NEILL ARNOT, M. D. In one octavo volume, leather, with about two hundred illustrations. $2 50. BLANCHARD & LEA'S EDUCATIONAL PUBLICATIONS BOLMAR'S COMPLETE FRENCH SERIES. nranMOA THEORE AL AND PRACTICAL GRAMMAR OF of a correct pronunciation of the French. In on e P 18m.. vo^e, half bound E TELEMAQOE. In on'e BOLMAR'S SELECTION OF ONE HUNDRED OF PERRIN"? FARTT4, 1853. As far as I am able to judge, it is the best work of its class in any language. From Prof. N. TilHnghast, Bridgewater, Mass., May 12, 1853. It would not become me to speak of the scientific merits of such a work by such an author; but I may- be allowed jo say. that I most earnestly wish that it might supersede every book used as a text-book on We now take leave of this remarkable work, which we hold to be, beyond a doubt, the greatest and most remarkable of the works in which ihe laws of astro- nomy and the appearance of the heavens are de- scribed to those who are not mathematicians nor observers, and recalled to those who are. It is the reward of men who can descend fr>m the advance- ment of knowledge, to care for its diffusion, that their works are essential to all, that they become the manuals of the proficient aswell as the lexl-books'of the learner. AthencEum. There is, perhaps, no book in the English language on the subject, which, whilst it contains so many of the facts of Astronomy (which it attempts to explain with as little technical language as possible), is so at- tractive in its style, and so clear and forcible in its illustrations. Evangelical Review. Probably no book ever written upon any science, embraces within so small a compass an entire epitome of everything known within all its various depart- ments, practical, theoretical, and physical. Ex- aminer. There is not, perhaps, in the English language, a work, treating upon so abstruse a subject, certainly not upon Astronomy, written with so much concise- ness and explicitness, and yet in so easy and intelli- gible a style, with such an avoidance of technicali- ties, and which one that is not an adept in the science can read so understandingly. The very learned au- thor has done almost as much for the cause of Astro- nomy by the preparation of this work, by which the knowledge of it will be diffused among the people, as by his wonderful discoveries. N. Y. Observer. NEW PHYSIOLOGICAL TEXT-BOOK (Now Ready.) PHYSIOLOGY OF ANIMAL" AND VEGETABLE LIFE. A POPULAR TREATISE ON THE PHENOMENA AND FUNCTIONS OP ORGANIC LIFE. To which is Prefixed a Brief General View of the Great Departments of Human Knowledge, In one handsome royal 12mo. volume, of 234 pages, with over 100 handsome illustrations. Written by a man of Science, this work, though popular in its form and elementary in its teach- ings, avoids the objections usually urged against similar treatises, ofsuperficiahty and incorrectness. While its language and arrangement are such as to render it easily understood by the youthful student or general reader, its basis is strictly scientific, and on every point it will 1 level with the most advanced state of knowledge. BIRD'S NATURAL PHILOSOPHY. ELEMENTS OF NATURAL PHILOSOPHY fbeing an Experimental Introduction to the Phy- sical Sciences. Illustrated with over 300 wood-cuts. By GOLDING BIRD, M. D., Assisi Physician to Guy's Hospital. From the Third London edition. In one neat volume, royal 1. extra cloth, $1 25; strong leather, $1 50. lish language of this wide range of physical subjects. We are astonished to find that there is room in so small a bonk for even the bare recital of so many subjects. Where everything is treated succinctly, sjreat judgment and much lime are needed in making a selection and winnowing the wheat from the chaff. Dr. Bird has no need 'to plead the peculiarity of his position as a shield against criticism, so lon as his book continues to be the bejst epitome in the Eng- North American Review. From Prof. John Johnston, Wesley an Univ., Middletown, Ct. For those desiring as extensive a work, I think it decidedly superior to anything of the kind with which I am acquainted. 10 BLANCHARD & LEA'S SCIENTIFIC PUBLICATIONS. CARPENTER'S COMPARATIVE PHYSIOLOGY. New and. Improved Edition Now Ready. PRINCIPLES OF COMPARATIVE PHYSIOLOGY. BY WILLIAM B. CARPENTER, M. D. ; Author of " Principles of Human Physiology," &c. A new American edition, revised and improved by the author. WITH OVER THREE HUNDRED ILLUSTRATIONS. In one large and very handsome octavo volume, of 750 pages. The delay which has existed in the appearance of this work has been caused by the very thorough revision and remodelling which it has undergone at the hands of the author, and the large numbei of new illustrations which have been prepared for it. It will, therefore, be found almost a new work, and fully up to the day in every department of the subject, rendering it a reliable text-booh for all students engaged in this branch of science. Every effort has been made to render its typo- graphical finish and mechanical execution worthy of its exalted reputation, and creditable to the mechanical arts of this country. This work stands without its fellow. It is one few men in Europe could have undertaken; it is one, no man, we believe, could have brought to so success- ful an issue as Dr. Carpenter. VVe feel that this abstract can give the reader a very imperfect idea of the fulness of this work, and no idea of its unity, of the admirable manner in which material has been brought, from the most various sources, to conduce u its completeness, of the lucidity of the reasoning i contains, or of the clearness of language in which the whole is clothed. Not the profession only, but thf scientific world at large, must feel deeply indebted tc Dr. Carpenter for this great work. It must, indeed add largely even to his high reputation. Med. Times JOHNSTON'S PHYSICAL ATLAS. THE PHYSICAL ATLAS OF NATURAL PHENOMENA, FOR THE USE OF COLLEGES, ACADEMIES, AND FAMILIES. BY ALEXANDER KEITH JOHNSTON, F. R. a. S. ; &c. In one large imperial 4to. volume, strongly bound in half morocco. With Twenty-six Plates, Engraved and Colored in the best style, Together with over one hundred pages of Descriptive Letterpress, and a very copious Index, Price $12 00. The book before us is, in short, a graphic encyclo- paedia of the sciences an atlas of human knowledge done into maps. It exemplifies the truth which it ex- presses that he who runs may read. The Thermal Laws of Leslie it enunciates by a bent line running across a map of Europe ; the abstract researches of Gauss it embodies in a few parallel curves winding over a section of the globe ; a formula of Laplace it melts down to a little patch of mezzotint shadow; a problem of the transcendental analysis, which covers pages with definite integrals, it makes plain to the eye by a little stippling and hatching on a given degree of longitude ! All possible relations of time and space, heat and cold, wet and dry, frost and snow, volcano and storm, current and tide, plant and beast, race and religion, attraction and repulsion, glacier and ava- lanche, fossil and mammoth, river and mountain, mine and forest, air and cloud, and sea and sky all in the earth and under the earth, and on the earth, and above the earth, that the heart of man has con- ceived or his head understood are brought together by a marvellous microcosm, and planted on these little sheets of paper, thus making themselves clear to every eye. In short, we have a summary of all the cross-questions of Nature for twenty centuries and all the answers of Nature herself set down and speaking to us voluminous system dansun mot Mr. Johnston is well known as a geographer of great accuracy and research ; and it is certain that this work will add to his reputation; for it is beautifully engraved, and accompanied with explanatory and tabular letterpress of great value. AlhencBum. CHEMICAL TEXT-BOOK FOR STUDENTS- (Just Issued.) ELEMENTARY" CHEMISTRY, THEORETICAL AND PRACTICAL. BY GEORGE FOWNES, PH.D., &c. WITH NUMEROUS ILLUSTRATIONS. A NEW AMERICAN, FROM THE LAST AND REVISED LONDON EDITION. EDITED, WITH ADDITIONS, BY ROBERT BRIDGES, M. D. In one large royal 12mo. volume, containing over 550 pages, clearly printed on small type, with 181 illustrations on wood ; extra cloth, $1 35; strong leather, $1 50. We know of no better text-book, especially in the difficult department of organic chemistry, upon which it is particularly full and satisfactory. We would recommend it to preceptors as a capital " office book" for their students who are beginners in Chemistry. It is copiously illustrated with excellent wood-cuts, and altogether admirably "got up." N. J. Medical Reporter, March, 1554. A standard manual, which has long enjoyed the reputation of embodying much knowledse in a small condensation with masterly tact. His book is con- cise without being dry, and brief without being too dogmatical or general. Virginia Med. and Surgical Journal. The work of Dr. Fownes has long been before the public, and its merits have been fully appreciated as the best text-book on Chemistry now in existence. We do not, of course, place it in a rank superior to the works of Brande, Graham, Turner. Gregory, or Gmelin, but we say that, as a work for students, it is space. The author has achieved the difficult task of J preferable to any of them. Lond. Journal of Medicine, BLA.NCHARD & LEA'S SCIENTIFIC PUBLICATIONS. 11 NOW READY. HANDBOOK OF CHEMISTRY, Theoretical, Practical, and Technical. By A. F ABEL F C S~ and C L. BLOXAM. With a Recommendatory Preface by Dr. HOFMANN, and numerous illustrations on wood In one large and handsome octavo volume, of 662 pages, extra cloth, $3 25. It must be understood that this is a work fitted for the earnest student, who resolves to pursue for himself a steady search into the chemical mysteries of creation. For such a student the " Handbook" will prove an excellent guide, since he will find in it, not merely the most approved modes of analytical investigation but descriptions of the apparatus necessary, with such manipulatory details as rendered Faraday's "Chemical Manipulations" so valuable at the time of its publication. Beyond this, the importance of the work is in- creased by the introduction of much of the technical chemistry of the manufactory. Athenaum. THE PRINCIPAL FORMS OF THE SKELETON, AND THE FORMS AND STRUCTURE OF THE TEETH. By PROFESSOR R. OWEN. In one very handsome royal 12mo. volume, with numerous illustrations on wood. (Just Ready.) This volume will present in a concise and popular form a complete view of the most recent state of com- parative osteology; the correctness of which is sufficiently vouched for by the name of the distinguished author. A subject of so much interest to the man of science, and more especially to the geologist, cannot fail to attract general attention. TECHNOLOGY; OR, CHEMISTRY APPLIED TO THE ARTS AND TO MANUFACTURES. By Dr. F. KNAPP. Edit- ed, with numerous Notes and Additions, by Dr. EDMUND RONALDS and Dr. THOMAS RICHARDSON. With additional Notes by Prof. WALTER R. JOHNSON. In two large and very handsome octavo volumes, with about five hundred splendid illustrations. $6 00. PRINCIPLES ~OF THE MECHANICS OF MACHINERY AND ENGINEERING. By Prof. JULIUS WEISBACH. Translated and edited by Prof. GORDON, of Glasgow. With Addition?, by Prof. WALTER R. JOHNSON. In two large and very handsome octavo volumes, with about one thousand beautiful illustrations. $6 50. CARPENTER ON ALCOHOL-(NOW READY.) ON THE USE AND ABUSE OF ALCOHOLIC LIQUORS IN HEALTH AND DISEASE. By W. B. CARPENTER, M. D., author of " Human Physiology," &c. New edition, with Preface and Notes, by D. F. CONIHE, M. D. In one neat royal 12mo. volume, extra cloth. This new edition has been prepared with a view to an extended popular circulation of this valuable work, the notes by Dr. Condie containing explanations of the scientific terms employed. Copies in flexible cloth may be had free of postage by mail on remitting 50 cents to the publishers. A very liberal deduction will be made when quantities are taken for distribution by societies or individuals. DE LA BECHE'S GEOLOGY. THE GEOLOGICAL OBSERVER. By Sir HENRY T. DE LA BECHE, C. B., F. R. S , Director-General of the Geological Survey of Great Britain. In one large and handsome octavo volume, extra cloth, of seven hundred pages, with over three hundred wood-cuts. $3 50. This volume will be found to present a very complete summary of what has already been accomplished in the science of geology,vwhile at the same time it indicates to the student the mode and direction in which future researches should be pursued. BONAPARTE'S AMERICAN ORNITHOLOGY. In four handsome quarto volumes, with large and splendid colored plates. $25 00. BRODERIP'S ZOOLOGICAL RECREATIONS. In one neat royal 12mo. volume, extra cloth, 75 cents. BOWMAN'S HANDBOOK OF PRACTICAL CHEMISTRY, including Analysis. In one neat royal J2mo. volume, extra cloth, with numerous illustrations. $1 20. BEALE ON THE LAWS OF HEALTH IN RELATION TO MIND AND BODY. A Series of Letters from an old Practitioner to a Patient. In one neat royal 12mo. volume, extra cloth, bO nts. GRIFFITH'S CHEMISTRY OF THE FOUR SEASONS, SPRING, SUMMER, AUTUMN, AND WINTER. In one handsome volume, large royal 12mo., with many wood-cuts, 75 cents. POPULAR PHYSIOLOGY OF ANIMAL AND VEGETABLE LIFE. In one handsome royal 12mo. volume of 200 pages, with over 100 engravings on wood. (Now Ready.) See P. 9. PHYSICAL GEOGRAPHY. Bv MART SOMERVILLE. A new American, from the last and Revised London E. Ih^r Glossary, by W. S. W. RUSCHENBERGER, M. D., U. S. N. In one large royal 12mo. volume, extra cloth (See P.I.) DANA ON ZOOPHYTES AND CORALS. Being a portion of the ^^^lil^SSt i Exploring Expedition. In one large royal quarto volume, extra c loth, with an Atla s ot sixty m colored plates, handsomely and strongly bound in half morocco, 4 OU. EVANS'S YOUNG MILLWRIGHT'S AND MILLER'S GUIDE. Fourteenth Edition. E P. JONES. In one octavo volume, leather, with numerous plates, 82 50. GREGORY'S LETTERS TO A CANDID ENQUIRER ON ANIMAL MAGNETISM. In one large royal 12mo. volume, extra cloth, $1 00. . ~*Tm T-T \ T>r-c HUMBOLDT'S ASPECTS OF NATURE IN DIFFERENT LANDS AND DIFFERENT CLIMATE Translated by MRS. SABINE. In one large royal 12mo. volume, extra ciotli, H ~ WT ~~ ^ v v HALE'S ETHNOGRAPHY AND PHILOLOGY OF THE UNITED STATES EXPLORING EXPL- DlTIOiV. In one large imperial quarto volume, extra cloth, frl THOMSON'S DOMESTIC MANAGEMENT OF THE SICK ROOM. In one large royal PHILOSOPHY AND ASTRONOMY. In three very large royal 12.no. vols., of 2000 pages, with 1000 illustrations. $5 00. H7" See P. 2. SCHCEDLER'S BOOK OF NATURE. A Popular Introduction to the f Sciences i of ^ u ' o c c Chemistry, Mineralogy, Geology, Botany, Physiology, and Zoology. In one large, c with nearly 700 illustrations. $>L 80. ffcj* See P. 2. JOHNSTON'S PHYSICAL ATLAS OF NATURAL PHENOMENA. In one imperial quarto half bound in morocco, with 26 colored plates. $12 00. LLT feee f. iu. 12 BLANCHARD & LEA'S MISCELLANEOUS PUBLICATIONS. COMPLETE LIBRARY EDITION. LIYES OF THE QUEENS OF ENGLAND, FROM THE NORMAN CONQUEST: WITH ANECDOTES OF THEIR COURTS. Now first published from Official Records, and other Authentic Documents, Private as ivell as Public. NEW EDITION, WITH ADDITIONS AND CORRECTIONS. BY AGNES STRICKLAND. Complete in six very handsome crown octavo volumes, containing over THIRTY-SIX HUNDRED PAGES, and for sale in various styles of binding, at very reasonable prices. The publishers have great pleasure in presenting to the public this work in a complete form. During the long period in which it has been issuing from the press, it has assumed the character of a standard work, and as occupying ground hitherto untouched; as embodying numerous his- torical facts heretofore unnoticed, and as containing vivid sketches of the characters and manners of the times, with anecdotes, documents, &c. &c., it presents numerous claims on the attention of both the student of history and the desultory reader. A valuable contribution to historical knowledge. It contains a mass of every kind of historical matter of interest, which industry and research could col- lect. We have derived much entertainment and in- struction from the work. Atheiuzum. This interesting and well-written work, in which the severe truth of history takes almost the wild- ness of romance, will constitute a valuable addition to our biographical literature. Morning Herald. These volumes have the fascination of a romance united to the integrity of history. Times. Also, to be had separate, STRICKLAND'S LIVES OF THE QUEENS OF HENRY VIII., and of his Mother, ELIZA- BETH OF YORK. Complete in one very neat crown octavo volume, extra cloth, of over four hundred pages. STRICKLAND'S MEMOIRS OF ELIZABETH, Second Queen Regnant of England and Ireland. Complete in one very neat crown octavo volume, extra cloth, of nearly six hundred pages. ROMANTIC HISTORY OF THE HUGUENOTS. HISTORY OF THE PROTESTANT REFORMATION IN FRANCE. By MRS. MASSH, author of "Two Old Men's Tales," &c. 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There are occasional letters in these volumes, which, if they had fallen into the hands of the British government at that time, would probably have caused the author some trouble, though it was a period when party spirit ran very high, and state? men took the largest license. N. Y. Com- mercial Advertiser. BLANCHARD & LEA'S MISCELLANEOUS PUBLICATIONS. 13 Campbell's Chancellors and Chief Justices. LIVES OF THE LORD CHANCELLORS Keqjtrs of tlje rmt 6ml of FROM THE EARLIEST TIMES TO THE REIGN OF KING GEORGE IV. BY LORD CHIEF-JUSTICE CAMPBELL, A.M., F. R. S. E. Second American, from the Third London edition, COMPLETE IN SEVEN HANDSOME CROWN OCTAVO VOLUMES, EXTRA CLOTH, OR HALF MOROCCO. ALSO, TO MATCH. LIVES OF THE CHIEF-JUSTICES OF ENGLAND, From the Norman Conquest to the Death of Lord Mansfield, Second Edition. In two very neat volumes, crown octavo, extra cloth, or half morocco. Of the solid merit of the work our judgment may be gathered from what has already been said. 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ON THE LAW OF CONTRACTS, AND ON PARTIES TO ACTION EX CONTRACTS. By C. G. ADDISON, of the Inner Temple, Barrister at Law. In one large and handsome octavo volume. A NEW LAW DICTIONARY, Containing Explanations of such Technical Terms and Phrases as occur in the works of Legal Authors, in the Practice of the Courts, and in the Parliamentary Proceedings of the Houses of Lords arid Commons. To which is added an Outline of an Action at Law, and of a Suit in Equity. By HENRY JAMES HOLTHOUSE, Esq. Edited, from the second and enlarged English edition, with numerous Additions, by HENRY PENINGTON, of the Philadelphia Bar. In one large royal 12mo. volume, of five hundred double-columned pages. TURKEY AND ITS DESTINY. BY CHARLES MACFARLANE, ESQ. In two neat royal 12mo. volumes, extra cloth. NIEBTTHR'S ANCIENT HISTORY. LECTURES ON ANCIENT HISTORY: COMPRISING The History of the Asiatic Nations, the Egyptians, Greeks, Macedonians, and Carthaginians, BY B. G. NIEBUHK. 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In its present neat and convenient form, the work is eminently fitted to assume the position which it merits as a book for every parlor-table and for every fireside where there is an appre- ciation of the kindliness and manliness, the intellect and the affection, the wit and liveliness which rendered William Wirt at once so eminent in the world, so brilliant in society, and so loving and loved in the retirement of his domestic circle. Uniting all these attractions, it cannot fail to find a place in every private and public library, and in all collections of books for the use of schools and colleges, for the young can have before them no brighter example of what can be ac- complished by industry and resolution, than the life of William Wirt, as unconsciously related by himself in these volumes. DON QUIXOTE DE LA MANCIIA. Translated from the Spanish of Miguel de Cervantes Saavedra, by CHARLES JARVIS, Esq. 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The steady demand which still continues for it, notwithstanding the immense number of copies which have been circulated, sufficiently proves the necessity of such a work for all educated men, and the thorough satisfaction which it continues to give to all who consult its pages; and shows that the publishers have not miscalculated in bringing the work up to a late period, with notices of con- temporary events and people, while reducing the price to about one-half of the original subscription. The Illustrated Geographical Encyclopaedia. THE ENCYCLOPAEDIA OF GEOGRAPHY; Comprising a complete description of the Earth, Physical, Statistical, Civil, and Political. Exhi- biting its Relation to the Heavenly Bodies, its Physical Structure, the Natural History of each Country, and the Industry, Commerce, Political Institutions, and Civil and Social State of all Nations. By HUGH MURRAY, F. R. S. E., &c. Assisted in Botany, by Professor Hooker Zoolo- gy, &c., by VV. W. 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