EBER C, BYAM his book Number J THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA PRESENTED BY PROF. CHARLES A. KOFOID AND MRS. PRUDENCE W. KOFOID ECLECTIC EDUCATIONAL SERIES. THE ELEMENTS OF NATURAL PHILOSOPHY, SIDXEY A. NORTON, A.M. Three Hundred and J^'fty Illustrations. VAX ANTWERP, BRAGG & CO., 137 WALNUT STREET, 28 BOND STREET, CINCINNATI. NEW YORK. Entered according to Act of Congress, in the yoar 1870, by WILSON, IIINKLE & CO., In the Clerk's Office of the District Court of the United States for the Southern District of Oh' :. ECLECTIC II VAN AN CINCINNATI. PREFACE. THIS work is the result of many years' experience in teaching the science of Physics. In its preparation, the author has endeav- ored to keep constantly in mind that its value must depend on its availability as a text-book. Accordingly he has made such a selection of the facts and principles embraced in the wide range of Natural Philosophy as, in his judgment, is best suited to the requirements of the pupil. While due attention has been given to the recent progress in Physics, including the latest methods and inventions, it has not been forgotten that all facts are equally fresh to the tyro, al- though all are not of equal importance, as regards either their fitness for developing the theory of the science, or their applica- tion to the practical affairs of life. For this reason, nothing has been introduced for the sake of its novelty; nor have cardinal principles been omitted, because a former generation of pupils has studied them. It has been an object of careful thought to present the science, in all its departments, in a manner at once systematic and sym- metrical. Of course, no pretense is made of exhausting the sub- ject, but it is hoped that the student will find in this treatise all that is necessary for his purposes. While fully impressed that "there is no royal road to science," the author has yet endeavored iv PREFACE. to make the labor of the student as attractive and invigorating as possible. To this end, the subject has been treated not merely as a science to be learned, but also as a means of educational dis- cipline: the topics are considered in their logical order, method- ically developed, thoroughly illustrated and enforced. No pains have been spared to secure clearness of expression, precision in definitions, and accuracy in the statement of facts. The manuscript was read by Prof. Charles H. Smith, the proof sheets by Mr. H. H. Vail, and to these gentlemen the author returns his sincere thanks. Should any errors have escaped their notice, the author will thank any of his readers who will have the kindness to inform the publishers of such as he may find. The problems are placed in the appendix for greater conven- ience. If properly used, they will serve not only to test the knowledge acquired by the student, but also to lead him to think on the nature of the laws and principles required for their correct solution. TABLE OF CONTENTS. CHAPTER I. PAOB INTRODUCTION, 7 CHAPTER II. SOMATOLOGY, 13 The Universal Properties of Matter, 14 The Specific Properties of Matter, 26 Phenomena connected with Adhesion, 38 CHAPTER III. THE MECHANICS OP SOLIDS, 51 General Statics and Dynamics, 51 Statics, 74 Dynamics, ........... 106 CHAPTER IV. THE MECHANICS OF FLUIDS, 135 Hydrostatics, 135 Hydrodynamics, 160 Pneumatics, 171 , CHAPTER V. UNDULATIONS, 196 CHAPTER VI. ACOUSTICS, 212 The Nature of Sound, 214 The Theory of Music, 225 yi CONTENTS. CHAPTER VII. PAGE OPTICS, 238 The Reflection of Light, 247 The Refraction of Light, 257 Colors, 268 Vision and Optical Instruments, 284 Double Refraction and Polarization, 297 CHAPTER VIII. PYRONOMICS, 305 The Effects of Heat, 305 The Distribution of Heat, 332 The Sources of Heat, 345 The Dynamical Theory of Heat, 350 The Steam Engine, 356 CHAPTER IX. ELECTRICITY, 364 Magnetism, 364 Statical Electricity, 373 Dynamical Electricity, 391 Electro-Magnetism, 422 Electro-Dynamic Induction, 436 Magneto-Electricity, 437 Thermo-Electricity, 441 PROBLEMS, 445 .j;y NMII;. The following t:il>l< i lias boon prepared for the Con- venience of -chools in which the time allotted to the study of Natural Philosophy is not siiflieieiit for the mastery of the entire work. Tin- topics indicated till about ei-hty paires. The omis- sion of these \\ill irive the student a shorter course, which is still complete in it-elf. to be omitted in the shorter conr>e: 817 18 -582 624 689 7 378 380 587 ~'l<; 648 ^'^ 286 312 419 487 <;"> 610 us 1 682 747 759 NATURAL PHILOSOPHY. CHAPTER I. INTRODUCTION. 1. Matter is any thing that possesses extension and im- penetrability ; as earth, water, air. The different kinds of matter are called substances. 2. Force is that which causes any change in the form or condition of matter; as heat, electricity. We know very little of the ultimate nature of matter and force, because it is difficult to conceive of either alone. All the phenomena of the visible universe are caused by the action of force upon matter. 3. A body is any separate portion of matter, whether large or small ; as a cannon, a cannon ball. Every body is considered as made up o very small particles, called molecules, each of which is supposed to contain two or more still smaller particles, called atoms. It is also supposed that these atoms do not touch each other, but are retained side by side by means of certain forces known as molecular attraction*. The firmness of their union is modified by the presence of an opposing force called molecular repulsion. Heat is the principal, if not the only, repellant force in Nature. (7) 8 NATURAL PHILOSOPHY. 4. With respect to the coherence of its molecules, a body is said to be in one of three states: 1. solid; 2. liquid; 3. aeriform, or gaseous. 1 . A body is in the solid state when the relative position of its molecules can not be changed without the expenditure of considerable force; as ice, marble, iron. Bodies in this state are called vW /'/> , and retain whatever shape has been given them by nature or art. 2. A body is in the liquid state when the relative position of its molecules is easily changed; as water, oil, wine. Bodies in this state are called Liquids, and assume with readiness the shape of any vessel into which they may be poured. 3. A body is in the aeriform or gaseous state when its molecules tend to separate and occupy a greater volume ; as steam, air, oxygen. Bodies in this state are called form Bodies, Gases, or Vapors. The term fluid is applied to both liquid and aeriform bodies: as water, steam. The same substance may, at different times, be in either of these three states, according to the relations which c.\i-t between the molecular attractions and repulsions. Thus, by a mod- erate chanire in the temperature, water may be made to pass through the solid, liquid, and aeriform states; as ice, water, steam. So, also, many metals may hi- easily niched, and then changed into vapors. 5. The number of distinct substances is almost infinite; but every body consists, either (1.) of a single element, or, (2.) of several elements combined. With respect to the nu mix T of elements it contains, a body is said to be either (1.; simple or (2.) compound. 1. A simple substance contains but one element; as iron, gold, diamond. 2. A compound substance contains two or more elements ; as water, oil, alum. Then- arc .-ixty--ix elements now recn-jni/cd. but a more riiron.iis analysis may either increase or diminish this number. Very few elements are found native: by far the greater number are derived FORCES. 9 from their combinations. Only eighteen or twenty may be obtained in any considerable quantity. The rest appear to play a subordinate part in the structure of our globe, and are known only to chemists. 6. Forces are either Attractive or Repellent according as they cause the particles of matter (1.) to approach, or, (2.) to recede from each other. Force may act either (1.) only upon the molecules of matter and at distances which are inappreciable to our senses, or, (2.) also upon bodies taken as a whole, and at any distance, whether small or great. The forces of the first class are called the Molecular Forces, and are severally named (1.) cohesion, (2.) adhesion, (3.) affinity. Those of the second class are (1.) gravitation, (2.) light, (3.) heat, which always acts as a repellant force, (4.) electricity, which is both an attractive and repellent force. The forces of affinity, electricity, heat, and light, are so closely allied that many philosophers consider them as modifications of the same force, in the same sense that magnetism is a modification of electricity. We know that the action of either of these forces may induce the action of any other of them ; thus the action of affinity may induce heat, then light, as is shown by the burning of a candle. For this reason, they are called the coirdative forces. Heat, light, and electricity are sometimes termed the imponderable agents, from an erroneous notion that they are matter without weight. 7. All these are the forces of inanimate nature. Plants and animals live and move by virtue of higher vital forces, which control and modify all other forces in an entirely inexplicable manner. The forces already named are the only ones of which we have any knowledge. They produce, by their action on matter, secondary forces, which are employed by man in machines. Thus the molecular forces give strength and elasticity to springs. Heat develops the elastic force of steam, and, acting in conjunction with gravitation, raises winds which cause the waves of the seas. Gravitation is made serv- iceable to man in the force of running water, and in machinery moved by weights. The muscular strength of men and animals is the result of many forces, as heat, cohesion, affinity, modified by the vital forces. 10 NATURAL PI1ILOSOPHV. 8. The changes to which all bodies arc liable may be reduced to two classes: (1.) those by which the substance is not altered so a- to lose its identity, and (2.) tho.M- hy which its identity is entirely lost. Thus (1.) a mu>s of iron may be hurled from a cannon, or wrought into nails, or beaten into a plowshare, or, by contact with a magnet, become endowed with the property of attracting iron tilings, but, notwithstanding these changes of position, shape, and size, or even properties, we still recognize it as iron. So water may be converted into ice or steam and yet preserve its identity, for if the ice be melted or the steam condensed, the fluid water re-appears with its characteristic properties. So, also, if a bit of hard rubber or sealing-wax be rubbed with a silk handkerchief, it will become endowed with the property of attracting and then repelling small pieces of paper or pith, although we can not perceive any change in the structure of either. Such changes are called "/ changes. The agencies by which they are pro- duced are the physical forces, of which the principal are gravitation, cohesion, and the secondary forces. (2.) On the other hand, if the iron be exposed to moist air it crumbles to a red powder; if it be placed in weak sulphuric acid, it is converted into a green, crystalline solid. If steam he pa ed over red hot iron, it yields a combustible gas (hydrogen). If sealing-wax is burned, it away into colorless gases which can never again be united tn form wax. Such changes are called clu-miml 0, and the agencies by which they are caused art* called rhnninil forces. The principal chemical force is affinity. Light, heat, and electricity, in their action on matter generally product- physical changes, but they sometimes a i-t in producing chemical change, or they are evoked by the action of chemical affinity: thus, if \\e heat a strip of /ine, it increa-e- in >i/c, then melts, and, finally, if no air i- piv--nt, panel away in a Mate of vapor: but, on cooling, the vapor lir.-t become.- liquid, then solid, and, at last, con- PROPERTIES. 11 tracts to its original dimensions, showing that all these change* are physical. On the other hand, if zinc is strongly heated in the air, it burns away to a soft and bulky pow- der sometimes used as a white paint. This permanent change is due to chemical affinity, assisted by heat. 9. Two classes of properties correspond to these two classes of changes. (1.) Those which a substance may exhibit without undergoing any change itself, or causing any essential change in other bodies, are called physical properties. (2.) Those which relate to the permanent change which a substance may experience itself, or effect in other substances, are called chemical properties : thus, among the physical properties of iodine are its luster, weight, its purple vapor, etc.; among its chemical properties are its power of turning starch blue, of setting fire to phosphorus, of combining with other elements, etc. 10. The changes, forces, and properties relating to matter may thus be classified in two distinct groups. The study of the laws and phenomena which severally relate to each group has given rise to two distinct sciences, (1.) Natural Philosophy, or Physics, and (2.) Chemistry. CHEMISTRY considers those phenomena in which the sub- stances acted upon suffer a loss of identity. X ATTIJAL PHILOSOPHY, or PHYSICS, considers those phe- nomena in which the substances acted upon do not suffer a loss of identity. 11. The laws and phenomena which belong to the domain of natural philosophy are so varied and numerous that it has been found necessary to divide them into several branches of study; each of which is of sufficient impor- tance to merit the name of a distinct science. It will be found convenient to make an arbitrary division of Natural Philosophy into Physics and Chemical Physics. 12 NATURAL PHILOSOPHY. 12. PHYSICS considers the forces whose phenomena are never attended by chemical changes. It includes three branches : (1.) Somatology, which treats of the properties of matter. (2.) Mechanics, which treats of equilibrium and motion. (3.) Acoustics, which treats of sound. CHEMICAL PHYSICS considers the forces whose phenomena are sometimes attended by chemical changes. It also includes three branches: (1.) Pyronomics, which treats of heat. (2.) Optics, which treats of light. (3.) Electricity, which treats of electrical forces. Some of these branches are again subdivided, as will be seen hereafter. The mechanics of the heavenly bodies con- stitutes the science of astronomy. 13. Recapitulation. Bodies are classified : {Solid; as ice. Liquid ; as water. Aeriform; as steam. II. With regard to composition. { Sim P le 5 as ox ^ en - ^ Compound ; as water. S< it nces which treat of the action of force upon inanimate matter are: t Somatology. Physics. \ Mechanics. Natural Philosophy, which includes 1 .^ f onomcs. w. P tics ; . v Electricit. Phyriw. . Electricity. Chemistry, which treats of Chemical Affinity. Forces in their action upon matter are either attractive or repellant I. t Cohesion. Act only on molecules. Molecular, -j Adlu-ion. ( Affinity. 8OMATOLOOT. General. 13 Act also upon bodies. (Electricity. Heat. Light. [ Universal. Gravitation. II. {Gravitation. Never cause loss of identity. { Physical. Cohesion. Adhesion. Sometimes attend loss of identity. { Chemico-Physical. {Light. Heat, Electricity. Always cause loss of identity. { Chemical. { Affinity. CHAPTER II. 14. By studying the properties of iron, it is found that they may be divided into two classes : one class includes properties which it possesses in common with all other sub- stances ; the other class includes properties which are peculiar to iron, and which distinguish it from all other kinds of matter. Thus, (1.) a mass of iron occupies a certain portion of space to the exclusion of all other bodies ; that is, it pos- sesses extension and impenetrability ; it also has weight : but every other substance, whether solid, liquid, or aeriform, possesses extension, impenetrability, and weight. Properties which belong to all bodies are called universal properties. (2.) Besides these, iron is endowed with other properties peculiar to itself. Thus, iron not only possesses extension, but has a peculiar crystalline form ; it not only possesses weight, but every piece of iron weighs 7.8 times as much as an equal bulk of water ; it has a certain hardness, strength, 11 NATURAL PHILOSOPHY. flexibility, and a familiar luster. Properties which are pe- culiar to a substance, and serve to characterize it, are called 15. The Universal Properties of matter are (1.) exten- sion, (2.) impenetrability, (3.) weight, (4.) mobility, (5.) inertia, (6.) divisibility, (7.) porosity, (8.) compressibility, (9.) expansibility, (10.) indestructibility, (11.) elasticity. The first two of these may be termed the essential prop- erties of matter, since they serve to define it. The last nine may be conceived of as not applying to atoms, but only to bodies, and hence may be termed general properties. The most important Specific Properties are (1.) elas- ticity, (2.) tenacity, (3.) hardness, (4.) brittleness, (5.) duc- tility, (6.) malleability. Besides these might be named others, as color, transparency, taste, odor, as well as the relations which bodies bear to heat, sound, and electricity. THE UNIVERSAL PROPERTIES OF MATTER. 16. Extension or Magnitude is that property by virtue of which a body occupies a certain space. Extension has three dimensions length, breadth, and thickness. No one can conceive of a body which does not possess all these. As a necessary consequence, every body lias a certain si i ape or figure. The figure of solids is per- manent; the figure of fluids varies with the shape of the vessel which contains them. The amount of .-pace that a body occupies is termed its Volume or l>ulk. 17. For the purpose of measuring length, England and the I'liiteil State- have adopted an arbitrary unit called the Yard, with its multiples and divisions, rods, inches, etc. The unit adopted by France is the metre, which is the forty millionth part of a meridian of our globe, and is e'|ii;il to inches used in the V. S. coa-t Mirvey. All tin- l-'ivjirh measure increase .-mil r lh<- im-ivuM-, the (ireek prefixes drr.-i 'I";, hecto WEIGHT. 15 (100), and kilo (1000) are used: for the de- crease, the Latin prefixes deci ( T V), centi ( T ^), mille (j^ny) are used. A decimetre is drawn on the margin in comparison with a scale of inches. It will be seen that one inch is a trifle longer than 25 millimetres. The units of surface and volume, derived from the linear unit, are called the square inch, cubic inch, etc. The wine gallon of the United States con- tains 231 cubic inches. The English imperial gallon contains 277.274 cubic inches. The French unit of volume, called the litre, is a cubic decimetre, containing 61.022 cubic inches or 2.113 wine pints. 18. Weight is due to the force of gravitation, by virtue of which every particle of matter attracts every other particle toward itself. A falling body is drawn by the attraction of all the particles of the earth toward the center of the globe ; but, when the body is not free to fall, the force which the earth's attraction exerts upon it is expended in pressure against its sup- port. This pressure is called absolute weight. Hence, weight is the measure of the earth's attraction, and must vary as the attraction varies. This definition limits weight to bodies on the earth, but, as the attraction of gravitation is universal, a body would possess weight if removed to any of the heavenly bodies. 19. The unit of weight adopted by the United States and England is the avoirdupois pound, of 7,000 grains. The French unit, called a gramme, is the weight of a cubic centimetre of distilled water at 39. 2 F. A gramme w - = >J - 05 = - c t FIG. 1. 16 NATURAL PHILOSOPHY. equals 15.434 grains. A kilogramme equals 15434 grains, or 2.2046 avoirdupois pounds. '. hi ^Pounds, of one Cubic Foot at 62 F. Potassium 53. Wrought Iron 480. Copper 556. Lead 712. Gold 1224. Platinum 1373. Hydrogen 0.005592 Nitrogen 0.07841 Air 0.080728 Oxygen 0.089256 Water 62.418 Mercury 848.75 20. Impenetrability is that property by virtue of which two bodies can not occupy the same portion of space at the same time. When a solid is immersed in a fluid, it displaces a quantity of fluid equal to its own volume. Thus, if a pebble be dropped into a tumbler full of water, enough water will overflow to equal the size of the pebble. Even a needle will displace its own bulk, for, although no one may be able to detect any change of level on the addition of a single needle, if many needles are dropped into the tumbler, the water will overflow as before. If one end of a glass tube be closed by the thumb, and the other end plunged into a vessel of water, the water can not enter the tube because of the impenetrability of the air en- closed in the tube; but, when the thumb is removed, the air will be expelled, and the water will rise to the level of that in the vessel. 21. This property belongs to all bodies, solid, liquid, and gaseous, though there are some apparent exceptions. Thus, in the last example, the water will rise a little way in the tube; but this occurs because the air is compressible. A nail may be driven into a board without increasing its size, but this is effected by separating the fibers of the wood and crowding them together to make room tor the harder body. If a long and slender test tube be half tilled with water, and strong alcohol be poured in carefully so as not to mix tin- liquids until the tube is quite full, and then the liquids be thoroughly shaken together, the mixture will no longer fill the tube. The reason for this i-^ not that the particles of water and alcohol penetrate each other, but that the smaller particles occupy a portion (if the -pace between the particles of tllC Other. Space utterly devoid of matter is termed a vacuum. MOBILITY. 17 22. Mobility is that property by virtue of which the position of a body in space may be changed on the applica- tion of sufficient force. A body in the act of changing its place is said to be in motion. Rest implies permanence of position. The motion or rest of a body is determined by its rela- tion to some given point; but, as this point may itself be fixed or moving, motion or rest is either (1.) absolute or (2.) relative. 23. Absolute motion is a change of place with regard to a fixed point : relative motion is a change of place with regard to a point in motion. Absolute rest is permanence in place with reference to a fixed point: relative rest is permanence in place with regard to a point in motion. Strictly speaking, there is no such condition as absolute rest, as the earth and all the heavenly bodies are known to be in motion. The motion of the heavenly bodies with reference to ideal fixed points in space are examples of absolute motion. Every particle on the earth's surface partakes of all the motions of the earth, daily, annual, and cyclic, therefore the terms absolute motion and rest, when applied to bodies on the earth, have reference to objects that appear fixed. A person seated on a steamboat in motion is in a state of relative rest with regard to the parts of the vessel, but is in absolute motion with respect to the harbor he has left, and to the water about him. If he walks toward the stern of the boat as fast as the vessel moves forward, he is in a state of absolute rest with regard to the harbor he has left or the water around him, but in relative motion with regard to the parts of the boat. 24. The rate of motion of a body is termed its velocity. It may be found by dividing the space by the time. The formula [1.] v = s -t-t expresses the relation between space, time, and velocity, and may be used to find the third quantity when the other two are known. From the formula given, other formula} may be obtained; thus, from [1.] we find s = vt and t = 8 -j- v. N.P. 2. 18 NA T URA L PHIL OS OP II } \ Table of Telocitles. Feet Miles per second, per hour. Man walking 4.4 3 Man running 14.66 10 Swift trotting horse 40. 27 A moderate wind... 10.26 7 A storm 73.33 50 A rifle ball 1466.66 1000 Sound 1118.6 762 Swiftest railway train 0.02 Initial velocity of a can- non ball 0.44 The earth in its orbit 18-97 A point on the Equator 0.2l Light 185500. Electricity 288000. 25. Inertia is that property by virtue of which a body tends to retain its present state, whether of motion or rest. This is a purely negative property of matter, and implies that motion and rest are equally natural to a body. A body dropped from a balloon in mid air falls because of the earth's attraction. A bullet fired in the air does not stop because the explosive force of the powder will carry it no further, but because other forces bring it to rest. 26. Many common phenomena may be explained by the inertia of matter. If a boy wishes to leap a broad ditch, he starts with a run, that the inertia of his body may be added to the muscular effort of leaping. With the same velocity, the inertia increases with the weight of the body. A small boy in running will easily "dodge" a larger, because the heavier boy will be unable to change his course at once. If a person descends carelessly from a car in motion, the upper part of the body retains its onward motion, while the feet are prevented from doing so by the friction of tin- ground, and lie is thrown forward. Si i a person standing in a wagon partakes of its condition of motion or rest. If it is suddenly started from a state of rest, his feet are drawn along by the friction .gainst the bottom, before the head can aeijuire the motion, and the person tails i>ackward. If the carriage is suddenly -topped when in rapid motion, the person is thrown forward. If a e;ird is balanced on the fop of one of the lingers of the left hand and a penny placed on it, a sudden blow given by the nail of the middle finger of the DI VISIBILITY. 19 C 8 7 6 5 4 3 2 A. right hand, will drive the card away and leave the penny on the finger. In this case the friction of the card against the penny will tend to carry it along with it, but the motion communicated will be so small that the coin will be moved but little. This experiment has been explained by saying that the inertia of the coin retains it in its place; but it really moves a little, as may be ascertained by placing the card and penny on the edge of a smooth table, and strik- ing away the card as before. The inertia of the air may be proved by the resistance it offers to a body moving through it. Thus, if we endeavor to carry an open umbrella, with the concave side forward, we shall need to employ considerable force to overcome the resistance of the air. Wind is only air in motion. If air had no inertia, it would not require force to set it in motion nor to stop it. 27. Divisibility is that property by virtue of which a body may be divided into distinct parts. A geometrical magnitude, as a line, may be supposed to be divided into an infinite number of parts. Let A B be the line to be divided. Draw D B and A C at right angles to it at its extremities and lay off, on AC, A 2, 23, 34, etc., each equal to DB, join D with each point, then D 2 will cut off one-half of A B, D3 will cut off one-third of A B, D 4 one-fourth, etc. Now as the line AC may be taken of infinite length, there is no limit to the number of equal parts which may be taken on it; consequently there is no limit to the number of parts into which A B may be divided. 28. The practical division of matter by mechanical means is subject to limitation, but wonderfully minute particles may be obtained by repeated subdivisions. Gold may be hammered so thin that fifteen hundred leaves, placed one upon another, will not equal the thickness of a single leaf of ordi- nary foolscap. The gilt wire used in embroidery has a surface of gold even thinner than this. It has been calculated that its thickness does not exceed one twenty-five millionth of an inch: if this calculation is correct, then, by the aid of a microscope, a particle of gold may be distinguished which does not weigh one two-million-millionth part of FIG. 3. 20 NATURAL PHILOSOPHY. a grain. The microscope has proved the existence of animals not larger than the particle of gold just mentioned, yet as these animals are furnished with organs of nutrition and locomotion, as well as the larger animals, their several parts must be inconceivably small. Blood is composed of a colorless liquid in which float red, flattened globules, so small that there are over a million of them in a single drop. 29. The wonderful divisibility of matter in solution may be readily shown by a few simple experiments. If a drop of nitric acid is allowed to remain for a few moments on a copper coin, it will dissolve an almost imperceptible amount of copper. Wash the coin in a tumbler full of water; the water will hardly be tinged in color. Now add some strong ammonia, and the liquid will be changed to a beautiful blue, showing the presence of copper in every drop of the solution. It has been estimated that a single grain of copper may thus be divided into one hundred million parts. * 30. The film of a soap bubble before bursting is less than one millionth of an inch in thickness; but, as this film possesses all the properties of water, a molecule of water can not be more than a millionth of an inch in diameter. Odors demonstrate the presence of particles whose size and weight must be infinitesimal. A single grain of musk will diffuse a perceptible odor through a large room for years, without appreciably losing in weight. 31. Certain facts in chemistry have led to the belief that there is a limit to the divisibility of mutter, and that there are particles called Atoms, incapable of further subdivision. By the conditions of this hypothesis : 32. An Atom is a particle of matter infinitely hard, in- finitely .-mail, and possessing a definite si/e, shape, and weight. Nothing is known of the ultimate structure .f atoms, but it has Tin- same facts may In- shown l>y taking a tiimhlrrof water and add- ing a drop of cadi of tin- following solutions : 1. Sulphate of iron ami ferrocyanide of potassium. J. Act-tale of lead and sulphuric acid. 3. Boiled starch and tincture of iodine. POROSITY. 21 been conjectured that they are spheroidal in shape, that some are larger and some heavier than others. That they are spheroidal in shape is a conclusion attained from the porosity of bodies. That they vary in size has been deduced from the fact that hydrogen will escape from a closely packed piston which retains oxygen and nitrogen. That they vary in weight seems probable, from the fact that the elements unite in a definite and invariable ratio to form chemical compounds. Thus, if the atom of hydrogen is assumed as unity, the atoms of the other elements will weigh respectively : oxygen, 16 ; sodium, 23 ; iron, 56 ; silver, 108 ; lead, 207, etc. 33. Porosity is that property by which spaces exist be- tween the molecules of a body. Pores are of two kinds, (1.) Physical Pores, which are so small that the surrounding molecules are at insensible distances from each other; (2.) Sensible Pores, which are actual cavities or cells that may be discerned by the eye or by the microscope ; as the cells in bread and in sponges. 34. In common language, a porous body is one that con- tains sensible pores. The porosity of some woods is evi- dent to the eye. The microscope reveals the presence of many thousand pores in every square inch of skin on the human hand. Many of the phenomena of the organic world are due to the existence of sensible pores. The presence of sensible pores is turned to practical use in filtering. A piece of unsized paper is folded in a conical shape and inserted in a funnel. Liquids, containing suspended matters, having been poured into this, pass through clear, leaving the solid particles behind. A milk strainer acts on the same principle. 35. The term porosity, as applied in the study of Natural Philosophy, generally relates to physical pores. All bodies possess these pores, and it is supposed that their atoms do not touch each other. All bodies, with one apparent excep- tion, expand by heat. This is not due to any change in the size of the atoms, but to the increase of the spaces between them. Iron and lead are made smaller by ham- mering, because the atoms are driven closer together. Water may be shown to possess pores by dissolving sugar in a cup 22 NATURAL PHILOSOPHY. full of hot water ; two or three spoonfuls may he added IK- ton- the cnjt overflows. If a jar he filled with alcohol to a certain height, a large quantity of cotton may he forced into it without raising the level. Fig. 4. ( Jasi-s are so porous that, if a ves- s.-l he filled with air, another gas may he introduced, and will fill the vessel as though the air were not there. The explanation of these experiments must be that the atoms of sugar and water, alcohol and cotton, or the two gases, are mutually arranged between the pores. 36. Bodies vary greatly with respect to the pores they contain. Those that have many and large pores are called rare bodies; those that have small pores are called dense bodies. Fig. 5 shows the size of one grain of air, of water, and of platinum. The term mass is used to denote the amount of matter contained in a body. If gravity were invariable, the terms mass and absolute weight Fio. 4. WATER. SlMIKHF. OK Alll WKl<;IIIMf On <;u.\IN. Fio. 5. SPECIFIC GRAVITY. 23 might be used interchangeably, as mass is the amount of matter in a body, and weight is the pressure exerted by it in consequence of gravity. The terms are not identical, as a little reflection will show. An iron ball will contain the same amount of matter or mass in every conceivable place, but if it weighs one hundred and ninety-four pounds at the equator it will weigh one hundred and ninety-five pounds at the poles, because, as will be shown hereafter, the force of gravity varies in different places. The mass of a body contained in a unit of volume is its density; the weight of the same unit is its specific weight. Hence, mass and density are invariable terms. 37. Specific gravity is the relative weight of any body compared with that of an equal volume of water or of air. Air is the standard of comparison for all gases and vapors, and water is the standard for both solids and liquids. The specific gravity of air being unity, that of chlorine is 2.47, of water, 773. The specific gravity of water being unity, that of air is .0013, of platinum, 21.5. In other words, specific gravity is the ratio which shows how many times heavier a body is than an equal bulk of air or of water, as a cube of platinum is 21.5 heavier than an equal bulk of water. Although the terms density and specific gravity involve different quantities, they are used interchangeably without sensible error. For, since the weights of the water or air and the body to be com- pared are ascertained in the same place, they will be alike influenced by gravity, and the specific gravity will be an invariable quantity. 38. The specific weight of any body is equal to the pro- duct of its specific gravity multiplied by the weight of the unit of water, or of air, as the case may require: thus, for liquids and solids : [2.] Sp. W. = 998.7 oz. X Sp. Gr. Since the weight of a cubic foot of water is nearly 1,000 ounces, that of the same bulk of any solid or liquid is nearly as many thousand ounces as are denoted by its spe- cific gravity. 24 NATURAL PHILOSOPHY. The mass of any body is equal to the product of its density and volume; its absolute weight is equal to the product of its specific weight and volume. Therefore for cubic feet of either liquids or solids [3.] W = V X Sp. W. = V X Sp. Gr. X 62.42 Ibs. Thus the weight of a cubic yard of lead is 27 X H.35 X 62.42 = 19,128 pounds. For aeriform bodies whose volume is stated in cubic inches, [4.] W = V X Sp. Gr. X 0.31 grains. Thus the weight of a gallon of chlorine is 231 X 2.47 X 0.31 = 176.87 grains. 39. The method of finding specific gravity will be given in its proper place. As there will be frequent occasion to refer to specific gravity, a table of the most important sub- stances is inserted at this point: Specific Gravities Compared. 32 F. 62 F. Ratio of air to water 1 to 773.2 1 to 816.8 Ratio of water to air 1 to .00129363 1 to .0012243 One cubic inch of air at 60 F. weighs 0.30954 grains. One cubic inch of water at 60 F. weighs 252.456 grains. Specific Gravity of the same Body in different States. Air = l. Water =1. Gases. Liquid. Solid. Ammonia 0.596 0.731 Carbonic acid 1.529 0.83 < hlorine 2.47 1.33 Sulphurous :i cid 2.247 1.38 As Vapors. Alcohol 1.613 0.792 Ether 2.589 0.715 Water 0.622 1. <).'.:; Mercury <;."7; 13.596 l.V.'.is Iodine s.Tir, l.'.M* Sulphur 2.230 2.086 l! if COMPRESSIBILITY. 25 Table of Specific Gravities. GASES. Air 1. Hydrogen 069 Nitrogen 972 Oxygen 1.106 LIQUIDS. Water, distilled 1. Sea water , 1.026 Olive oil 0.915 Sulphuric acid 1.84 SOLIDS. Cork 0.24 White oak 0.86 Ebony 1.331 Glass 3. Potassium 0.86 Platinum 21.53 Gold 19.26 Silver 10.5 Copper 8.85 Iron. Lead . 7.78* .11.35 Saturated brine 1.205 Iron pyrites 5. 40. Compressibility is that property by virtue of which the volume of a body may be diminished. This is a consequence of porosity. Rare bodies are much more compressible than dense bodies. Gases may be made to occupy a hundred times less space than they do under ordinary circumstances. Many gases, under great pressure, become liquids; others, as oxygen, nitrogen, and air, seem to have no limit to their compressibility. Liquids possess this property in so limited a degree that they were once supposed to be incompressible. Solids are all compressible. 41. Expansibility is the converse of the preceding. The volume of all bodies, except clay, is increased by heat. With equal incre- ments of heat, gases expand most, liquids next, and solids least. When a diving-bell is sunk in the sea, the water compresses the air and rises within the bell to a certain height, although it can not fill the bell because the air is impenetrable, When the bell is raised, the air ex- pands and recovers its former vol- ume. If a flask is nearly filled with FIG. 6. 26 NATURAL PHILOSOPHY. water and then inverted in a basin, a little air will be inclosed at the top of the flask. If the Husk is wanned, the air expands and expels a portion of the water. On cooling the flask, the air resumes its former bulk. 42. Various units have been adopted for the measure- ment of intensity of pressure. Thus, pressure may be estimated at so many pounds to the square inch, or to the square foot. The pressure of one atmosphere is a unit in very common use. The atmosphere presses on every square inch of all surfaces at the level of the sea with a force of about fifteen pounds, hence all other pressures may be taken as so many times greater or less than this, or, as so many atmospheres. Units of 'Pressure. I'uii lulu on each Pounds on each In >'jti:in- inrli. square foot. atmospheres. Water, 1 foot deep, at 39.2 F.~ 0. 1335 r>2.42:> 0.02l)o Water, 1 foot deep, at 62 F 0.4330 152.355 0.0294 30 inches mercury, at <>2 F 14.7225 2120. 1. 1 inch mercury, at .",2 F 0.4912 7o.7:j 0.0334 1 foot of air, at 32.. O.ooiMi 0.0807 0.00004 1 pound to the square inch. 2.:J ft. water. 2 in. mercury. 0.008 43. Indestructibility is that property by virtue of which a substance resists annihilation. Whatever changes man may impose upon matter, it still continues in Mime form, and may at any time he recoirni/.ed as matter. Thus, all the change- ih-erihed in i S. > caused no loss in the substances acted upon. Wood, in burnini:, pa.es away in smoke, leaving only a .-mall propi.riiiin <>f a.-hes; yet the a>he- and the Mnoke contain all the mutter nf the wood. SPKCIFIC PROPERTIES OF MATTER. 44. Most of the specific properties of matin- are de- pendent un the molecul&r attractions, aflinitv, cohesion, and adliesiim, modified by the molecular repulsion of heat and. perhaps, of electricity. ADHESION. 27 45. Affinity is that force which causes the atoms of unlike substances to unite and thus form new bodies. For example, when a nail is exposed to moist air, the iron combines with the oxygen of the moisture and forms a coating of rust, which is an oxide of iron. 46. Adhesion is the force which causes the molecules of different kinds of matter to cling together. Thus, adhesion causes the dust to cling to every thing it falls upon, chalk to cling to black-boards, mud to clothing, dew drops to leaves, and icicles to eave-troughs. Under the name of Friction, it diminishes the work of moving forces, (1.) by stiffening the joints of machines, and (2.) by increasing the resistance to be overcome. Friction often acts as a mechanical advantage, as in preventing our feet from slipping when standing or walking, in retaining nails and screws in their sockets, and in enabling locomotives to ascend gradients. 47. The force of adhesion gives value to the cements. No better proof can be desired that adhesion is not the same for all substances, than the great variety of cements employed for different materials; thus, glue is used for wood, the gum resins for glass, mortars for brick, etc. The adhesion of good glue and of the best hydraulic cements is about five hundred pounds to the square inch, that of ordinary mortars is much less. 48. Cohesion is the force which causes like molecules to unite in one mass. This force retains the particles of a cannon ball or of a lump of ice in a single piece. It is strongly exerted in solids, less strongly in liquids, and is entirely absent in aeriform bodies. Liquids. In large masses of liquids the force of cohesion is overcome by the force of gravity, which tends to bring all their molecules to the same level ; in very small masses the cohesive force is the stronger, and causes them to assume a spheroidal form. 28 NATURAL PHILOSOPHY. This is shown in drops of dew, in globules of mercury, and in small drops of water rolling upon a dusty table. The same fact is ex- emplified in the following pretty experiment: fill a tall wine-glass half full of water and earei'iilly pour upon the water an equal quantity of alcohol so as not to mix the two liquids, then drop a very little olive oil through the alcohol ; it will assume the shape of a spheroid and rest in the middle of the glass. The experiment may be made more striking by pouring into a clear glass bottle half full o!' a saturated solution of sulphate of zinc, some distilled water, and dropping through the water a little bisulphide of carbon, colored by iodine. The spheroid may be made larger than the neck of the bottle. Solids. When the cohesion of solids has been once destroyed it is often difficult to cause the particles to re- unite. Broken metallic castings may be remelted, and made to cohere in the same or a different form on cooling. Particles of loose sand jammed forcibly together, as, for instance, by a cannon ball, will cohere like stone. In like manner broken ice can be cemented together in one transparent mass by pressure. Two dull leaden bul- lets will not unite because the surface is covered by the oxide; but if each be cleanly cut by a sharp knife so as to present a smooth and bright surface, they will unite on being pressed tightly together, with a slight twisting motion. Two plates of polished glass will cohere, under pressure, so forcibly that they may be worked as a single piece. The slightest film of paper or even dust is sufficient to prevent this action. 49. Adhesion and cohesion differ from affinity in this, that their action on bodies does not effect any essential change in the properties of the bodies. They differ from cadi other in this, that adhesion acts between unlike par- tides, and cohesion between like particles. Heat generally increa.-es the force <,f afiinity, Itut it tends to weaken the force of ci.hoion. It is probable that all >olids may be converted to liquids, and even to vapor-, by sullicient heat, and that all gases and liquids may ! rh:m.ir-d to solids by a .-uflicicnt reduction of tem- perature, a i-ted by pre-^ure, although then' are many solids that have not been liquefied, and many gases that have hitherto resisted all endeavors to charge their state. COHESION. 29 50. The cohesion of the particles of a solid may be estimated l>y the kind and amount of resistance which its particles offer to a strain tending to rend them. The force which causes the strain may be applied I. In the direction of the length of the body : (1.) By a direct thrust, as when a weight, resting on a column, tends to crush it. (2.) By a putt, as when a weight, stretching a string, tends to tear it in pieces. II. Transversely, or across the length : (3.) By bending, as when a bow is strained and tends to break. (4.) By twisting, when the strain tends to wrench the particles asunder. III. A body may be subjected to several strains at the same time. 51. These relations are made more evident by the follow- ing table: Direction of force. Kind of stress. Kind of strain. Kind of fracture. I Longitudinal. ( (L) Thrust Compression. Crushing. I (2.) Pull. Stretching. Tearing. II. Transverse. { ^ Bendin S- Bending. Breaking. <> (4.) Twisting. Torsion. Wrenching. III. Combined. (5.) Distortion. Detrusive. Shearing. 52. Experience teaches that the effect produced by any strain will vary greatly with the material on which it acts, as well as with the intensity of the force. Thus, a sufficient force will cause fracture in any solid; a less force may produce a permanent or a transient change in its shape. 53. Elasticity is the property by virtue of which bodies altered in form or volume by any external force, resume their original shape, when that force has ceased to act. The change of form or volume is due to the strain, which compresses, stretches, bends, or twists the body. The 30 NATURAL PHILOSOPHY. energy with which the particles resume their original posi- tion, is due to their elastic force. Up to a certain limit, which varies with the substance, the elastic force is exactly equal to the stress, and the elasticity is therefore perfect. Beyond that limit, brittle bodies break; the molecules of most other solids are forced into new relations with each other, by which the bodies assume a permanent change, or set, with new relations to elasticity similar to the first. Thus, when a wire has been permanently lengthened by a them is removed, they immediately retrain their original volume; therefore, all J ln'nl.< arc j>n-frrtl// rln#tic.. 56. Solids possese this property in different degrees. India rubber, ivory, ^lass, and marble have considerable elasticity; lead, clay, and fats have very little. STRENGTH. 31 If a ball of ivory or of glass be dropped on a slab of marble, it will rebound to a height nearly equal to that from which it fell. If the slab had been smeared with oil, it would be found that the ball had left a circular impression on the plate, and had itself received a blot of oil; on repeating the experiment, it will be seen that the size of the spot on the table and on the ball increases with the height from which it falls. From this experiment it appears (1.) that, at the moment of shock, the ball was compressed, (2.) that its rebound was caused by the effort to regain its original shape, and (3.) that its elastic force increases with the strain. 57. The elasticity of traction is shown by the strings of musical instruments, which are made more or less tense, by stretching, at the will of the performer. 58. Flexibility should not be confounded with elasticity. A wire of soft iron is very flexible, though but slightly elastic. A steel sword blade has been bent double and on the removal of the force, has straightened itself perfectly, showing that it is both flexible and elastic. Threads of glass are even more elastic than steel, though not as flexible. 59. The elasticity of torsion is manifested in the ten- dency that twisted yarns and strings have to untwist. 60. The practical applications of the elasticity of bodies are innumerable. The elasticity of aeriform bodies is turned to account in foot balls, air cushions, springs, etc. The elasticity of solids is applied in the springs used in watches, clocks, carriages, bows, balances, etc. The value of corks is due, in great measure, to their elasticity. 61. The ultimate strength i> the cohesion with which a body resists a stress tending to produce fracture. The proof strength equals the greatest strain that may be borne with safety; it varies from one-tenth to two-thirds of the ultimate strength. The kind of strength which a body manifests in any instance, is called its resistance to the strain employed; as n-Mstance to compression, etc., except that: The resistance which bodies offer to forces tending to pull their particles apart is called Tenacity. 32 NATURAL PHILOSOPHY. 62. All kinds of strength increase, to a greater or less degree, with the area of the cross section of the body, and all, except tenacity, decrease when the length is increased. The only effect of increase of length upon tenacity is that the weight of the body is added to its load. The annexed table shows the comparative strain, expressed in pounds avoirdupois, that may be borne by rods not exceeding a foot in length and whose cross section is one square inch. The first column shows the force required by theory to double the length of the bars, a thing impossible to be done, except in the case of india rubber. 63. Table. Materials. M. "lulus of elasticity. Resistance to fracture. By crushing. Tenacity. By breaking. By wrencli'g. \crii)icnt which shall exactly represent the strength of the material, and also because slight imperfections and im- purities of tin- material produce marked change in the result. The following deductions from many experiments are, however, of general application: 65. The strength of a fabric depends not only (1.) on the nature of the materials, as has been shown; but, also, STRENGTH. 33 (2.) on the distribution of the strain, and (3.) on the mode in which the materials are arranged. The long continued action of a small strain will often produce fracture in a bar that would originally have re- sisted a much greater force for a short time. Every strain that exceeds the limit of elasticity tends to weaken the substance, until at last it yields readily. A continual jarring or pounding so alters the molecular condition of iron, that after a while it becomes extremely brittle ; for this reason axles in carriages and railway cars should be subjected to frequent tests. A sudden shock causes a greater strain than a continued force of equal amount. A horizontal beam, supported at both ends, will sustain twice the force, when distributed throughout its length, that it will when concentrated at the center. 66. It has been demonstrated that the most advantageous form for iron beams is one which has its greatest depth at the center, and a cross section resembling Fig. 8. Of two rectangular beams, having the same area, that which has the FIG. a. greatest depth will be the stronger : for this reason, beams and rafters are placed so as to receive the stress on their edges. The most economical arrangement of a given mass of ma- terial is that of a hollow tube. This arrangement is seen in the bones of animals, stalks of grain, and quills of birds. A hollow cylinder may be made of twice the strength of a solid cylinder containing an equal weight of the same material. An easy illustration of this fact may be had by resting the ends of a flat sheet of paper on sup- ports and ascertaining the force F IO . necessary to break it down ; and then repeating the test after having coiled the paper into a tube. N. P. 3. 34 NATURAL PHILOSOPHY. 67. A hollow rectangular tube, whoso height considerably exceeds its breadth, is stronger than a round tube of the same mass. This form is applied in the Victoria bridge, at Montreal, and in the Great Eastern steamship. The center tube of the Victoria bridge is three hun- dred and thirty feet long, sixteen feet broad, and nearly twenty-two feet high. It is made of boiler iron, about one half inch in thickness, and strongly braced with lateral irons. The ordinary pressure of a railway train passing through it is scarcely noticeable. 68. The tenacity of a substance is increased by drawing it into the form of a wire. Hence, cables made of fine iron wire twisted together, are far stronger than chains of equal weight, and are now coming into general use. There are many suspension bridges in this country and in Europe made of wire cables. The suspension bridge across the Ohio river at Cincinnati, has a span of one thousand feet. 69. If wood were as durable as iron, its lightness would make its use preferable in all cases where tenacity is re- quired. Thus, pine, which has nearly half the tenacity, has only one tenth the weight of cast iron ; so that, for equal weights, pine has more than four times the tenacity of cast iron. It would be impossible to build such roofs and bridges of iron as have been built of timber, because the strength of the material would not be sufficient to support its own weight. It is evident that the effective strength of any fabric is merely that which is not employed in supporting itself, and that when a certain size is passed, every additional part only adds to the load without increasing the strength, and thus weakens the whole. For this n-Msmi m:my inventions, that :ippi-ar faultless in model, fail when made of full si/c. 70. There is therefore a limit of magnitude which no structure, natural or artificial, can .surpass, so long as their materials are unchanged. Thus, insects arc proportionally stronger than mammals, the smaller quadrupeds are capable HARDNESS. 35 of feats of strength and agility impossible to the larger. Whales would be incapable of motion if their enormous weight were not sustained by the buoyancy of the ocean. 71. The hardness of a body is measured by the readiness with which it is worn or scratched by another substance. For the purpose of determining the relative hardness of minerals, the following arbitrary scale has been adopted, in which any sub- stance is scratched by those below it : Scale of Hardness of Minerals. 1. Talc, 4. Fluor spar, 7. Quartz, 2. Gypsum, 5. Apatite, 8. Topaz, 2.5 Mica, 5.5 Sea polite, 9. Sapphire, 3. Calc-spar, 6. Feldspar, 10. Diamond. 72. A body which neither scratches nor is scratched by any given mineral of the table, is said to be of the degree of hardness represented by that mineral. Thus, there are fifty-three minerals whose hardness is 4, or equal to fluor spar. The diamond can be cut only by means of its own powder; talc, or soapstone, is easily cut with the thumb nail. Few of the metals are as hard as glass; some, as lead and potassium, are very soft, and mercury is a fluid, from which it appears that hardness bears no relation to the density of a body. As a general thing, metals are softer than their alloys. 73. Brittleness is the property which renders a body capable of being easily broken or pulverized. Thus, hard bodies are generally brittle, and so too are most elastic bodies, when the limit of elasticity has been exceeded. 74. Ductility is the property by virtue of w r hich a body may be drawn into wire. Platinum has been drawn into aoooo f an i ncn i Q diameter. 75. Malleability is the property by virtue of which bodies may be rolled or hammered into sheets. Gold leaf may be made less than - f an i ncn thick. 36 NATURAL PHILOSOPHY. Most metals are both malleable and din-tile, though not in equal degrees. Antimony, bismuth, and some others, have neither pro- perty. 76. Some metals are most readily malleable under the hammer and others under rollers. Elevation in tempera- ture is generally attended with an increase of malleability and ductility ; copper, and its alloys, and lead being the prominent exceptions. Iron and glass are very malleable and ductile at a red heat. Zinc can be rolled with best success at a temperature between 226 F. and 300 F. Although the tenacity, ductility, and malleability of metals are alike dependent on the force of cohesion, yet the same metal does not always manifest the same relative degree of each, as may be seen by the following table: Tenacity. Ductility. Malleability. Under tin- l.amni.T. Under rollers. 1. Iron, Platinum, Lead, Gold, 2. Copper, Silver, Tin, Silver, 3. Platinum, Iron, Gold, Copper, 4. Silver, Copper, Zinc, Tin, 5. Zinc, Gold, Silver, Lead, 6. Gold, Zinc, Copper, Zinc, 7. Lead, Tin, Platinum, Platinum, 8. Tin. Lead. I ron. Iron. 77. Some of the effects of heat upon cohesion have already been noticed. Among the permanent changes pro- duced by heat are : (1.) HARDENING. Many substances, if suddenly cooled after having been strongly heated, become harder, more brittle, and more elastic than before. If steel is raised to a white heat and then plunged into a bath of cold water or mercury, it is rendeivd almost as hard as the diamond, very ela.-tie, and so brittle that it is suitable only for the di<-> used in coining and en^raviii.ir, and lor the hardest files. (2.) BOFTENDrO. Metals and jrlass are annealed by being slowly cooled from a hid) temperature. Annealing gen- 37 orally increases the flexibility, softness, and ductility of bodies. When metals have become brittle through excess of strain in rolling, wire drawing, twisting, hammering, or other mechanical means, their properties may be restored by annealing. (3.) TEMPERING. Steel is wrought into any form required in the arts when it is in its softened condition. It is then strongly heated and suddenly cooled, but, as this hardening procsss renders it too brittle for ordinary purposes, some- thing of its elasticity is sacrificed, and a portion of its hardness removed by reheating the steel to a lower temper- ature and then cooling it gradually. This process of an- nealing is called drawing the temper, or tempering. The temper required depends on the use to which the steel is to be applied, and may be regulated by varying the tempera- ture of the second heating; the higher the heat, the softer will be the steel. If a steel knittiug needle be hardened, then brightened and re- heated, the film of oxide on its surface becomes, at a temperature of 428 F., of a light straw color, then through intermediate hues to violet yellow (509 F.), blue (560 F.) ; at 977 F. the steel passes to a red heat. These colors guide the workman in the effects he wishes to produce. Light yellow indicates the heat required for surgical instruments, in which a keen edge is required ; a deeper yellow, fine cutlery; violet is the tint for table knives, requiring flexibility more than a hard but brittle edge; blue for springs, sword blades, and other flexible instruments. 78, The effect of rapid or slow cooling of glass is about the same as in steel. Melted glass dropped into water solidifies into the curious toy knows as Prince 'Rupert's drops. The body of these drops is so hard that it will bear a smart blow; but if the tail be broken, the whole flies into minute particles with considerable violence. This brittle- Fl - 10 - ness is prevented in glass utensils by careful annealing. As soon as glass vessels are blown they are placed in a long furnace, in which the heat, at first very great, gradually 38 NATURAL PHILOSOPHY. diminishes from one end to the other. Through this fur- nace they are slowly drawn, and thereby are cooled so gradually and equably that their molecules assume the most stable position with regard to each other, and all are alike affected by any shock. Heat produces on copper and bronze, effects precisely the reverse of those manifested by steel. When they are cooled slowly they become hard and brittle, but when cooled rapidly, soft and malleable. 79. Recapitulation, Properties of matter : Essential. Universal. Specific. , Extension, \ Impenetrability. ( Weight, Mobility, Inertia, Divisibility, Porosity, Compressibility, Expansibility, Indestructibility, - Elasticity. j Elasticity, (Tenacity. C Hanlix Involving permanent displace- Brittleness, ment of particles. 1 Ductility, I Malleability. General. Involving strain of particles. PHENOMENA CONNECTED WITH ADHESION. 80. Two facts relating to the force of adhesion have already been noticed: (1.) that it exists only between unlike molecules; (2.) that it varies with the kind and the >tate of matter. To these may be added, (3.) that it increase- with the number of molecules in contact. As only the exterior particles of solids can hi- brought in con- tact with others, this statement, when applied to solids at rest, become.-., Adhesion increases with the extent of surface. ADHESION. 39 81. With regard to the second fact, it is evident that, as there are only three states of matter, all the possible varie- ties of adhesion must fall into some one of their combina- tions, taken two and two. It will be convenient to indicate these by Roman numerals, thus: T. IV. f Solids to gases. iquids. -, v Gases to solids. VI. solids. J Solids to solids. II. {Solids to liquids. III. Liquids to solids. J Liquids to liquids. VII. Liquids to gases. VIII. Gases to liquids. IX. Gases to gases. 82. The adhesion of solids to solids has found sufficient illustration in cements and in friction (46, 47). As all attractions are mutual, it is hardly necessary to make any distinction between the three pairs connected by braces, except it be for the purpose of giving prominence to either body in any special case. Thus, when lycopodium or powdered resin is strewn in patches on a board, and water is sprinkled upon it, (II) the drops that fall on the powder attract the particles to themselves and roll about in globules, covered by the adherent solid ; (III) the drops that strike the clean surface of the board adhere to it and flatten. Either case illustrates the adhesion between the solid and the liquid. Some of the nine varieties of adhesion, given in the table above, have received specific names, and are of sufficient impor- tance to merit separate treatment: others are unimportant in every re- spect. 83. Capillary action. If a clean glass plate is placed vertically in a basin of water, the liquid will rise on each side to the height of nearly one-sixth of an inch. In this case, it is evident that the force of adhesion between the liquid Fio. 11. 40 NATURAL PHILOSOPHY. and the solid (III) is greater than the cohesion of the liquid molecules. An inspection of the diagram shows that any particle of the glass near the normal surface of the liquid can have no influence in producing this elevation. A par- ticle at d, or e will attract the upper portion of the liquid down with as much force as it tends to raise the molecules beneath it. It follows, therefore, that the whole weight of the liquid column must be supported by the narrow line of solid particles, 6c, near the top. To these particles the nearest molecules of the water adhere, and support, by their cohesion, the second line of molecules of water; these, in turn, support other molecules, and so on until the weight of the column equals the cohesion of the upper line to the second. 84. A second plate of glass will support an equal weight of the liquid; therefore, if a second plate be placed parallel to the first, the weight of the water supported will be double that of a single plate. If the plates are brought so near each other that both plates may act on the same molecules of the liquid, the water Avill rise between the plates. The nearer the plates the higher will be the column of water. Two plates, one hun- dredth of an inch apart, will support a column of water two inches high. 85. If the two plates are in- clined toward each other, and are in contact at one vertical cil-c, the water will ri>e Ix-tween them to heights varying in- \er~i-ly as the distance between the plates. The outline of the surface thus formed has been designated the equilateral hy- perbola. FIG. 12. CAPILLARY ATTRACTION. 41 86. Finally, if the molecules of the liquid are attracted in all directions, as they would be if a tube were substi- tuted for the glass plate, the liquid will rise to twice the height produced by two plates separated by an interval equal to the diameter of the tube. A tube, one hundredth of an inch in diameter, will support a column of water four inches high. 87. Because these phenomena are best exhibited in tubes whose internal diameters are so small as to resemble hairs, that variety of adhesion ivhich causes liquids to rise on solids i# termed Capillary Attraction. The height to which a liquid will rise, varies with the nature of both the liquid and the solid; thus, in the same glass tube, a solution of carbonate of ammonia will rise a little higher than water; nitric acid three-fourths, and alcohol a little more than one-half as high as water. On the other hand, mercury will not wet glass, although it rises freely on lead, zinc, and some other metals. In fact, it may be demonstrated that liquids will not rise on solids unless the adhesive force is more than half the cohesive force. Therefore, although mercury is attracted by glass, yet as this attraction is less than twice the attraction be- tween the molecules of the mercury, the phenomena mani- fested when glass is placed in mercury are directly opposite to those already described as taking place between glass and water. The most satisfactory experi- ments to illustrate capillary ac- tion, are conducted in glass tubes of the shape represented in Fig. 14, which any one can readily make for himself. Water poured into A assumes a concave sur- face in both branches, and rises FIG. M. in the smaller branch above the level of the larger. Mer- B B' 4:2 NATURAL PHILOSOPHY. cury, poured into B, assumes a convex surface in both branches, and is depressed in the smaller branch. In a greased tube, water is depressed. A needle, slightly greased, will float on water, because, not being wet by the liquid, it produces a depression, in which it is supported. 88. From these general facts it is easy to deduce the fol- lowing laws of capillary action, when applied to small tubes: 1. Liquids ascend in tubes when they wet them, and are depressed when they do not. 2. The ascent and depression increase as the diameters of the tubes decrease. 3. The ascent and depression vary with the nature of the substances used. 89. Familiar illustrations of capillary attraction are seen in the action of the wicks of lamps and candles. If one end of a towel is plunged in a basin of water and the other end is left hanging over the edge, the whole will become wet. Blotting paper is useful because it readily draws ink into its pores : the pores of letter paper are closed by sizing. In France, dry wooden wedges are driven into holes drilled in rocks, and then wet with water; the fibers of the wood, by absorbing the water, expand with so much force as to split the rocks. Water can not be poured out of a full tumbler without running down on the outside of the glass, because of the capillary attraction. 90. Capillary action is of immense importance in the operations of nature. It draws the water necessary to the support of vegetation to the surface of the Around, in the drmi-hts of summer. It is one of the principal causes f I he ax-cnt of sap in plants, and plays an essential part in the circulation of the liquids in animal tissues. 91. Solution. If a lump of snirar is dipped in water, the liquid will rise by capillary attraction until the whole mass SOLUTION. 43 is moistened. If sufficient water be present, the adhesion of the solid to the liquid (II) will be sufficient to overcome the cohesion of the solid, so that it will entirely disappear in the liquid, thereby forming a solution. Each drop of the solution has the sweetness of the sugar and the fluidity of the water, thus showing that the adhesion is perfect, because it is shared by every molecule. When the adhesive force of each molecule has reached its limit, no more of the solid will dissolve, and the solution is then said to be saturated. 92. The solvent powers of liquids vary exceedingly. An ounce of cold water can dissolve hardly a grain of sulphate of lime, although it readily dissolves one thousand grains of sugar. Many substances that do not form solu- tions with water are readily dissolved by other liquids. Water is the best general solvent; alcohol is the proper solvent for resins; ether and benzine, for fats; bisulphide of carbon, for sulphur and phosphorus; mercury, for lead and some other metals. The solvent powers of every liquid are limited, both as respects the number of substances soluble in it, and the amount of any one neces- sary to complete saturation. As a general thing, however, when a liquid has been fully saturated with one solid, it is still capable of dissolving others. When a solid disappears in an acid, as copper in nitric acid, the action is twofold; first, a chemical action, by which the solid and liquid unite to form a substance different from either, as nitrate of copper; second, a simple solution, by which the compound thus formed is dissolved in the liquid. 93. The adhesion of gases to liquids (VIII) is illus- trated by the solution of gases in water and other liquids. Water dissolves all gases; but in proportions varying (1.) with the nature of the gas, (2.) the temperature, and (3.) the pressure. The following table shows the solubility of several of the gases in water or in alcohol, in open vessels and at the freezing point: 44 NATURAL PHILOSOPHY. Solubility of Gases. Volumes of gas absorbed by one volume of water, of alcohol. Nitrogen .............................................. 0.0204 0.12 Sulphurous arid .................................... 68.8610 328.0200 Hydrochloric acid ................................. 506. Ammonia ............................................. 1049.7 The rapidity with which water absorbs ammonia may be prettily shown by the following experiment: having fitu-d a glass tube, tapering at one end, to the cork of a large bottle, fill the bottle with dry ammonia gas. Then invert the bottle, and place the mouth of the tube in water. After a little time the water will absorb so much of the ammonia as to leave a par- tial vacuum in the bottle; the external pressure of the atmosphere will then drive the liquid up the tube, forming a fountain of greater or less force, proportioned to the size of the upper diam- eter of the tube. 94. The weight of any gas absorbed by Fl<1 - 15 - a liquid, increases directly with the pres- sure; that is, if the pressure is doubled or tripled, the weight of the gas absorbed will be doubled or tripled. It will be shown hereafter that the effect of pressure on a ame laws as the adhesion of liquids to solids 111 . with tliis important difference, that .irases are very compre^ible. When water is heated in irluss vosels, the air may be seen to leave the water and collect in bubbles ABSORPTION. 45 on the side of the vessel, where they often remain for some time. Porous solids, as meerschaum, plaster of Paris, freshly burned charcoal, and metals in the state of fine powder often absorb large amounts of gases. The follow- ing table exhibits the number of volumes of several of the -uses absorbed by one volume of charcoal and of meer- schaum : Absorption of Gases. Charcoal. Meerschaum. Nitrogen 7.2 1.6 Oxygen 9.2 1.49 Carbonic acid 35. 5.26 Ammonia 90. 15. 96. A piece of freshly burned charcoal, exposed to the atmosphere for a few days, will often increase one-fifth in weight. This phenomenon can be explained only by the supposition that the solid, by reason of its porous condition, offers a very large extent of surface, to which the gases adhere and become condensed. Finely divided platinum absorbs two hundred and fifty times its volume of oxygen. When iron, reduced by hydrogen, is poured from the re- duction tube, it condenses the oxygen of the air so rapidly that the iron becomes ignited. 97. The absorptive power of freshly burned charcoal is of great economic value. The variety known as bone black is used for clarifying sugars. The brown sirups are filtered through a layer of this charcoal twelve or fourteen feet in thickness, and are thus obtained perfectly clear; all the coloring matters, whether solid or liquid, being absorbed. Porter, filtered through animal charcoal, loses much of its bitterness, and all of its gases. All varieties of charcoal are efficacious in destroying noxious effluvia, not by preventing decay, but by absorb- ing the gaseous products of decomposition. 98. Vesicular condition. In clouds and fogs the moist- ure is in the liquid state, and is supported above the earth by the adhesion of liquids to gases (VII). I', NATURAL PHILOSOPHY. It has been supposed that each drop of water forms a vesicle or bladder, by inclosing a molecule of air. The hollow vesicle exposes a larger surface than a solid drop of the same size, and continues to float until the drops become heavy enough to overcome the adhesion of the air, when they fall as mist or rain. 99. The mechanical transportation of dust, snow, and other light bodies by the winds, is due to the adhesion of solids to gases (IV). Although this appears to be a trivial matter, yet, if this action is continued for a long series of years, it affects great physical changes, as is seen in the dunes of France and England, and in the ever shifting sands of the deserts of Africa. DIFFUSION OF FLUIDS. 100. The adhesion of liquids to liquids (VI), and of gases to gases (IX), affords phenomena so similar that they may be considered together under the general theme of dif- fusion of fluids. The adhesion of some liquids, as oil and water, is so feeble that they can not be made to unite permanently by any amount of stirring and shaking. On the other hand, most liquids will mix readily with each other, though in various proportions ; some, as water and alcohol or glycer- ine, are miscible in all proportions; others may be mixed only to a limited extent. Thus, if water and ether are shaken together, and then allowed to stand, they will, in a great measure separate, each liquid dissolving about one tenth (f the other. In like manner, if two gases which do not act chemically upon each other, are placed in the same vessel, they will form a permanent mixture. 101. The tendency of fluids to mix with each other is termed Diffusion. Diffusion may take place without me- chanical action, and even in apparent opposition to the attraction of gravitation. Thus, if a tall jar is partially filled with a solution of blue litmus, and sulphuric acid is poured rnivfully through a Imi.ij funnel, reach- ing to the bottom of the jar, the line of separation between the two DIFFUSION. 47 fluids will be at first distinctly marked. This will soon disappear; the acid will gradually rise and the water will sink until the two are perfectly mixed. This will, however, require some time, and the pro- gress of diffusion may be traced, from hour to hour, 1)\- watching the gradual change from blue to red. The experiment may be repeated with almost any two liquids of different specific gravities, as alcohol and water, alcohol and turpentine, or the saturated solution of any salt and pure water. It is advisable to color one of the liquids with a little cochineal or alkanet root. The rate of diffusion will be found to vary with the nature of the substances used, and is uniform only in dilute solutions. FIG. 16. 102. The diffusion of gases may be illustrated by an apparatus consisting of two bottles, connected by a long glass tube. Fill the upper with the lighter gas, as hydrogen, and the lower with a heavier, as chlorine. In the course of two or three hours the two will mix perfectly and per- manently. The green color of the chlorine enables us to trace its gradual ascent. This experiment should be performed only in diffused daylight, or in a darkened room, to avoid an explosion. The experiment may be modified by filling two jars over a pneu- matic trough, one half full of hydrogen, the other half full of air, so that the water shall stand at the same level in both. If, now, we pass a few drops of ether into each jar, the same quantity of ether will evaporate in both, and ultimately cause the same depres- sion of water level, but the diffusion will be much more rapid in the hydrogen. 103. The diffusion of gases is of the greatest importance in maintaining the purity of the atmosphere. The constituents of the air are of different specific gravities, and would arrange themselves with the heaviest at the bottom, were it not for this beneficent law of 48 NA T URA L miL SOPHY. nature. The noxious products of combustion and decay would then be found at the surface of the earth, and would produce the most disastrous consequences. As it is, they arc rapidly diluted when formed, and soon are so perfectly dis- seminated through the atmosphere, that the most accurate chemical analysis fails to find any essential difference in the air of mountain, plain, or valley. 104. Osmose. The diffusion of fluids may take place when they are separated by a porous partition or septum. Inasmuch as the phenomena are greatly modified by the presence of the septum, the diffusion of fluids through septa has been termed osmose. Tie a long glass tube to the mouth of a membranous bag or a bladder. Fill the bag with strong brine, sirup, or alcohol, and then immerse it in pure water. After a while it will be found that the liquid has risen in the tube, and that the outer vessel contains some of the liquid which was in the in- terior. Hence, a current has been produced in two directions. The one passing to the liquid which increases in volume is called end- osmose, the other is called erosmose. The rate of diffusion, and (he vol- ume of water diffused, is greater in osmose than in simple diffusion. FIG. 18. The cause of osmose has not been clearly explained, but the conditions of its action seem to Itc: 1. That the liquids he capable of mixing. 2. That the septum have a L:reatcr adhesion for one liquid than the other. Experiments in osmose may be conducted by using, in- DIALYSIS. 49 stead of the bag in Fig. 18, an inverted funnel, having its mouth closed by a strip of any animal membrane, or by parchment paper. 105. Dialysis is the application of osmose to the separa- tion of the constituents of a liquid. Alcohol, hydrochloric acid, and substances capable of forming crystals, when in a state of solution, readily pass through septa. On the other hand, gelatine, gum arabic, and other substances that do not crystallize, do not exhibit this property. Hence, if a solution contain crystallizable and gelatinous substances, the former will suffer osmosis, and the latter will remain above the septum. 106. The osmose of gases may be shown by a striking experiment : Take a glass funnel with a long delivery tube. Close its mouth by a septum of plaster of Paris. This may be done by making a moderately thick paste of the plaster with water on a plate, inverting the mouth of the fun- nel therein, and then suffering the plaster to harden, and to dry thor- oughly. Now attach the open end to a flask containing water and fitted with a jet pipe extending beneath the water, as in Fig. 19, and invert over the septum a jar filled with hydrogen. The endosmose of the hydrogen will be so rapid as to force out the water from the jet tube in a miniature fountain. Remove the jar, and air will bubble through the water, show- ing the escape of the hydrogen through the septum. Fig. 19. India rubber balloons, filled with hydrogen, soon become flaccid, from the escape of the hydrogen into the air, N. P. 4. 50 NATURAL PHILOSOPHY. 107. Although the nature of osmose can not be satis- factorily determined, it is manifest, from the porous nature of vegetable and animal membranes, that it must play an important part in the operations of life. We know that poisons may be absorbed through the skin. It is probable that the ascent of sap in plants, and the various processes of secretion in animals, are either controlled or essentially modified by osmotic action. 108. Recapitulation. The varieties of adhesion are : I. Solids to solids J Cements, < Friction. III. Liquids to solids f Capillarity, <> Filtration. II. Solids to liquids Solution of solids- VIII. Gases to liquids Solution of gases. V. Gases to solids Absorption of gases. VII. Liquids to gases Vesicular condition- IV. Solids to gases Sand hills. VI. Liquids to liquids Diffusion of liquids. IX. Gases to gases Diffusion of gases. Osmose Diffusion through septa- MECHANICS. 51 CHAPTER III. 109. It has been shown that motion is caused by the action of force upon matter; but we can readily conceive that two or more forces may so act upon a body that their effects will mutually counteract each other, and that no motion will ensue. In this case, the forces are said to be in equilibrium, and the body is said to be at rest. 110. Mechanics is the science which treats of equilibrium and motion. That part of it which relates to equilibrium is called Statics, and that which relates to motion is called Dynamics. In the present treatise, no attempt will be made to separate statical and dynamical propositions, as the study of either presupposes the student to have some knowledge of the other. As a general rule, the facts in dynamics will be considered last. 111. Inasmuch as mechanics relates to all bodies, whether solid, liquid, or aeriform, it has been found convenient to divide the science into three divisions: 1. The mechanics of solids, called statics and dynamics. 2. The mechanics of liquids, called hydrostatics and hydro- dynamics. 3. The mechanics of gases, called pneumatics, or aero- statics, and aerodynamics. GENERAL STATICS AND DYNAMICS. 112. The forces considered in mechanics may be reduced to gravity, elasticity, and muscular strength. If a force acts but for an instant, it is called an impulsive. force. If its action is continued, it is called an incessant, or continuous force. A continuous force may be regarded as 52 NATUllAL PHILOSOPHY. a series of impulsive forces, acting in exceedingly brief but equal units of time. If the impulses are equal in intensity, it is called a constant force; but if their intensity changes, it is called a variable force. 113. Since motion is produced by the action of force upon matter, it must vary with the kind of force producing it. An impulsive force produces -uniform motion a contin- uous force acting alone produces varifd motion. I. UNIFOK.M MOTION is that in which equal spaces are described in equal times. A body once set in motion, would, by virtue of its inertia, continue moving in a straight line with uniform velocity forever, were there no opposing forces. But as every moving body meets with resistances, such as gravity and friction, it must soon be brought to rest unless impelled by a continuous force. Continuous forces may produce uniform motion when the successive impulses are exactly equal to the resistance. Thus, a railway train moves with uniform velocity when the friction and the resistance of the air have increased so as to be in equilibrium with the motive power of the en- gine. Thus, also, the earth revolves on its axis, in exactly uni- form motion. The time of one revolution is divided into 86,400 equal parts, one of which is called a second, and constitutes the unit of timr. Tlie velocity of a body is the space described in a unit of time. II. VARIED MOTION is that in which unequal spaces are described in equal successive units of time. If a body describes a greater space in each successive moment, the motion is acn l> rtl; but if the space is less, the motion is retarded. A constant fon-r acting alone upon a body will produce accelerated motion. \ falling Ixxly may l>e taken ;i< :m example of this kind of motion. Tlu- moment it is Unsupported, gravity causes it to defend, suul if MOMKXTL'M. 53 this force, and all opposing forces, were then annihilated, it would fall with uniform motion; but gravity continues to act with new im- pulses at each moment, and thus forces the body downward faster and faster. This illustration is not perfect, because the resistance of tlu- air increases as the square of the velocity of the body, and, if the body continues long in falling, will at last produce uniform motion. A constant force opposing the previous motion of a body produces uniformly retarded motion. Thus, when a body is thrown vertically upward, gravity retards its motion every instant and will finally bring it to rest. The velocity in uniformly varied motion, at any moment, is ike space a body would describe, by lirtue of its inertia, in Hie next subsequent unit of time, were all forces acting upon it to cease. 114. Momentum. When a body is in motion, the effect may be measured by the time that would be required to stop the motion by a pressure of uniform intensity. This pressure, multiplied by the time througli which it acts, is equal to the mass of the body mmltiplied by its velocity. This last product is the momentum of a body, or, as it is sometimes called, its quantity of motion. Of two equal masses, that which has the greater velocity will have the greater momentem; of two unequal masses, having the same velocity, the heavier mass will have the greater momentum. The momentum is, therefore, depend- ent on the weight and the velocity, and may be estimated by the following rule: the momentum is equal to the weight multiplied by the velocity. [5.] M = WXV. The momentum of a thirty pound cannon ball, moving with a velocity of one thousand feet per second, is equal to thirty thousand pounds that i<, it is equal to the momentum of a body weighing thirty thousand pounds and moving one foot per second. From these considerations it is evident that the momentum of a large body mov- ing slowly may be no greater than that of a small body moving rapidly. Thus, the momentum of an enormous but slow sailing ship may be no greater than that of a swift steam tug. The momenta of very large masses, as icebergs, are irresistible by any human power, even though their motion be so slow as to be almost imperceptible. 54 NATURAL PHILOSOPHY. LAWS OF MOTION. 115. The deductions in mechanics are based upon three axioms, known as Newton's laws of motion. FIRST LAW. Every body continues in a state of rest, or of uniform motion in a straight line, unless acted on by some ex- ternal force. This is called the law of inertia, because it depends on that property of matter. It is difficult to furnish examples which will perfectly illus- trate this law, because all bodies on the earth are constantly acted on by one or more external forces. The following are given as approxi- mate illustrations: That a body can not set itself in motion is evident from our expe- rience. Mountain cliffs remain for ages, until worn away by winds, rain, frost, or other agencies. That a body tends to move in a straight line may be seen by roll- ing a ball along the ground, or on the floor, or on a smooth sheet of ice; the fewer the obstacles in the way, the more direct will be its course. The same experiment shows that the fewer the obstacles, the more uniform will be the rate of motion, and the longer will it con- tinue in motion. 116. Whatever tends to oppose or retard motion is called the Resistance. The resistances which a moving body en- counters are, mainly, gravity, friction, and the resistance of the medium surrounding it, as air or water. There are some apparent exceptions to the law of inertia. A heavy ring may be so struck by the hand that it will proceed a little dis- tance, on a level surface, and then return to the hand. In this eas.-, the hand not merely gives the ring an impulse forward, but imparts a rotary motion in the opposite direction. The rotary motion soon destroys the impulse forward, and causes the body to change its direction. 117. SECOND LAW. Mnflnn, <>/ <-!if iimfiun, it pro- portional to the force impressed, and is in the direction of the line in which that force acts. In order to comprehend the action of a force, throe things must lie known: M.) its intensity, (2.) its direction, (3.) its point of application. MOTION. 55 1. The intensity of a force is the energy with which it acts. This may be expressed in pounds, and may be repre- sented by a straight line. Thus if we represent a force of one pound by a line an inch long, any multiple of the force will be expressed by a line of corresponding length. 2. The direction of a force is the line along which it acts. 3. The point of application of a force is the point upon which it exerts its action. 118. If a given force generates a given motion, a double force will generate double the motion. It must not be sup- posed that twice the velocity will actually be realized. Thus, if an engine can propel a steamboat ten miles an hour, two engines of the same power will not double its speed, because the resistance of the water increases as the square of the velocity. 119. A body may be acted upon by a single force, or by several forces at the same time. By the terms of the second law, each will produce the same effect as if it acted alone. Motions are, therefore, classified, with reference to the number of forces employed, as simple and compound. 120. Simple motion is produced by the action of a single force. Compound motion is produced by the joint action of two or more forces. The following are selected from the many cases that may occur : CASE I. If several forces act upon the same point in the same direction, their effect will equal their sum. Thus, if a carriage be drawn by two horses, one exerting a force of two hundred pounds, and the other three hundred pounds, then their combined effect will be the same as that of a single horse pull- ing with a force of five hundred pounds. A single force that represents the effect of several forces acting together, is called their resultant. The forces which combine to make up the resultant are called its components. 56 NATURAL PHILOSOPHY. When these forces produce motion, the sum of the velocities of the components will equal the velocity of the resultant. Thus, if a boat, impelled on quiet water by oars at a rate of four miles an hour, enters a river, flowing in the same direction at a rate of three miles an hour, the speed of the boat will become seven miles an hour. 121. CASE II. If two forces act upon the same point in opposite directions, their resultant equals their difference. If the carriage be drawn forward with a force of three hundred pounds and backward with a force of two hundred pounds, an effect of one hundred pounds will remain in the direction of the greater force. If, in the previous example, the boat proceed up the river against the current, it will have a velocity of one mile per hour in the original direction. 122. CASE III. If two forces which act upon the same point are represented in intensity and direction by the adjacent sides of a parallelogram, the diag- onal will represent their resultant in in- tensity and direction. Suppose a boat to be rowed at the rate of four miles an hour, in the direction A B, across a stream running at three miles an hour, in the direction AC. The boat will move in the direc- tion A D, the resultant of these components, at the rate of five miles an hour. This proposition is called the parallelogram of forces, and the operation of finding the resultant when the components are given is called the composition of forces. When the forces are at right angles to each other, the find- ing of the resultant is an easy geo- metrical problem of finding the hy- potenuse when the two sides are given. Many familiar natural phe- nomena may be explained by this principle. A bird, in flying, beats the air with wings inclined toward each other. The resistance t.f the. air is perpendicular Fio. 21. MOTION. 57 to their surfaces. Draw A F and A G perpendicular to each wing, and lay off on them A E and A D, to represent the force of each wing. Now complete the parallelogram A E C D, and draw its diagonal A C. This will be the resultant of the two forces, and the bird will move as if impelled by the single force A C. A bullet dropped from the topmast of a ship in rapid motion, will strike the deck precisely where it would have fallen had the vessel been at rest. The reason of this is, that the ball, which falls by the action of gravity, also partakes of the motion of the vessel, which carries it forward as fast as the ship moves. 123. Conversely, when the resultant of two forces is given, the components equivalent to it may be found. This operation is called the resolution of forces. Represent any force, equal in C intensity to ten, by the line A C. On this line an infinite number of parallelograms, ABC B', ADCD', AECE', may be constructed, any two adjacent sides of which may be considered as the components of A C. Thus, if A B be drawn equal in intensity to eight, A B x at right angles to it will equal 6. -xE As an illustration, take the sailing of a sloop under a wind oblique to the course of the boat. Represent the course of the wind by the 58 NATURAL PHILOSOPHY. R line V m. Its force may be resolved into two components ; the one t tf, tangent to the sail, and producing no effect, the other, m n, per- pendicular to the sail. As the sail is oblique to the axis of the boat, this force will tend to give the boat a lateral motion, called the lee- way. Therefore, _this force is again decomposed by the keel and the rudder, and the useful component impels the sloop on its course. 124. CASE IV. When more than two forces act upon the same point, the final resultant may be found by combining any two for the first resultant, then a third force with the first resultant, then a fourth force with the second resultant, and so on, until all the forces have been combined. Thus, in Fig. 24, Ar is the re- sultant of AB and AC; A? y the resultant of A r and AD; A R the resultant of A r 7 and A E, and, con- sequently the resultant of the four forces, A B, A C, A D, and AE. 125. CASE V. When two parallel forces act upon a line, B C, their resultant will also be parallel, and will have its point of application at a distance from either force, inversely proportional to its intensity. If the forces lie in the same direction, the resultant will equal their sum, as in the case of horses attached to the same whippletree. If the forces F and F' lie in opposite directions, as in Fig. 25, the resultant F F' will equal their difference, and lie in the direction of the greater force. When opposite parallel forces are equal, they produce no progressive motion, hut cause the body on which they act to revolve aliotit a point midway between the two forces. Such a >\>tem is called a counle. By the application of these principles, an approximate answer may be obtained lor problems who.se accurate solution requires the FIG. 24. FIG. 25. ACTION AND REACTION. 59 FIG. 26. higher mathematics. Thus, suppose a known vertical force, acting upon the point L, to be resists! ly two forces, acting on each side of it, at angles respectively forty and thirty degrees, and suppose the value of these components to be required. Represent these forces by the lines L G, L X, L E, and set off on LG the value of the vertical force, in any convenient unit, as one inch, or one foot. Through G, draw lines so as to complete the parallelogram. The sides of the parallelogram L X and L E will be the forces required, and their lengths, measured by a scale of equal parts, will give their ratio to each other, and to the known force L G. This is the method by construction. In the case supposed LG = 1, LE = 0.67, LN = 0.52, an answer correct to two places of deci- mals. Conversely, had L E and L X been known, their resultant, L G, equals the force necessary to counteract them, or 1.00. 126. THIRD LAW. Action and reaction are always equal, and are in opposite directions. A weight, suspended from a hook, is retained in its place because the hook reacts with a force equal to the pull of the weight. When a ball is fired from a cannon, the cannon recoils with a momentum equal to that of the ball, but the backward motion is much less because of the greater weight of the cannon. A rocket rises from the reaction of the air against its expanding gases. A bird, in flying, beats the air with its wings, and by giving a stroke whose reaction is greater than the weight of its body, rises with the difference. When a pugilist strikes his antagonist, his fist sustains as great a shock as it gives, but is usually less sensitive to injury than the part on which it strikes. 127. When a moving body encounters another, the effects of action and reaction are modified by elasticity, and other circumstances. The reaction of solids may be shown by balls of different material and size, hung from a frame, so that their diameters shall lie in the same straight line. 128. Non-elastic solids. If two balls, of soft wax or clay, be suspended, and one be let fall upon the other at 60 NA T URA L PHIL OSOPIIY. rest, the first will communicate a part of its momentum to the second, and both will move forward with the original momentum. The velocity of the two will be dimin- ished in proportion as their combined weight exceeds that of the falling ball. If both are dropped to- ward each other, they will come to rest, on striking, if their momenta are equal. This will be the case if equal balls are dropped with equal veloc- ities. If their momenta. are unequal, they will move, after collision, in the direction of the greater, and with a momentum equal to the difference of the original momenta. 129. Elastic bodies. In perfectly elastic bodies, the force of elasticity is exactly equal to that of compression, and in such bodies the effect of reaction is of the same kind as that of action. Suspend two equal ivory balls from the frame in Fig. 27. If b falls upon &', it will lose half its velocity in com- pressing &', and the body b' will destroy an c, and would rise as far a> /> fell, were it not for the want of perfect elasticity. If the two balls are dropped with unequal velocity, in the same direrti.m, each will move, after colli>i<.n, with the previous velocity of the other body. For, as before, b f gains what b loses. COLLlSHty OF BODIES. 61 If the balls collide from opposite directions, each will rebound with the previous velocity of the other body. 130. Bodies striking a fixed plane. Let a ball be thrown in the direction I N, upon a hard and smooth plane A B, and suppose both bodies to be perfectly elastic. The force of the collision at N, may be resolved into two com- .. |JV K ponents; the one, N D, perpen- dicular to A B, which repre- sents the elastic force, tending to urge the ball in the line N P, and the other component, N E, parallel to A B, repre- senting its velocity in the direction of the plane. Complete the parallelogram, NERG, its diagonal, N R, will repre- sent the direction the ball will take after impact. A careful measurement will show that the angle, I N P, is equal to the angle PNR. The angle, INP, formed by the direction of the inci- dent body and the perpendicular, is called the angle of inci- dence, and the angle, P N R, formed by the perpendicular and the direction of the body after reflection, is called the angle of reflection. Their equality is expressed by the following law: The angle of incidence is always equal to the angle of reflection. This law applies exactly to the reflection of sound, light, and heat, and of perfectly elastic bodies. If either body is imperfectly elastic, the component, N G, will be proportionally smaller; hence, the body will pro- ceed, after reflection, in a line nearer the plane than N R, and the angle of reflection will be greater than the angle of incidence. These facts may be readily exemplified by bounding balls of differ- ent elasticities, as rubber, ivory, marble, clay, putty, etc., upon a hard floor, and are well shown in the game of billiards. 62 NATURAL PHILOSOPHY. 131. Reaction in soft bodies. In the previous cases, the reaction has been supposed to be instantaneous, but if the reaction is gradual, its destructive effect will be less. Thus, if a man leaps from a height into deep water, the particles of the water separate, and, though the reaction is the same as though he alighted on a solid plane, it is diffused through a sufficient interval of time to become comparatively harmless. In like inamuT stones may be caught in the hand with impunity, if the hand is allowed for a time to partake of the motion of the stone. 132. Even soft bodies require some time for the displace- ment of their particles. If the surface of water be struck sharply by the open palm, the blow is resisted almost as well as by solids. This power of resistance for the moment is exemplified by the sport of ''skipping stones" along the surface of smooth water. Leaden bullets will become flat- tened if fired obliquely upon water. 133. Diffused action. If a blow be struck on a large body, the effect on each particle will be inversely propor- tional to the mass. Thus, if an anvil be laid on the chest of a man, he may receive a heavy blow on it without detri- ment, because the blow is first diffused through the anvil, and then deadened by the expanded lungs of the man. 134. Striking force. In these examples, bodies have been considered as under the influence of momentum, which expresses the intensity of the moving force. The energy of a force is its power to perform work, that is to overcome resistance through a certain space. This is called the vis viva, or striking force. Thus, the momenta of two balls, weighing five and ten pounds, will he the same if the lighter hall moves with twice (lie velocity of the heavier; hut if both strike a clay hank, the swifter hall will penetrate twice as far a- the other, or perform doiihle the work. This differ- ence is due to their striking force. 135. Either momentum or vis viva may be taken as the measure of a force. The iiioninifinii ivprr.-enN thr amount of pressure which, if applied to a moving body for one sec- COLLISION. 63 ond, will bring the body to rest. With a given mass, the momentum is proportional to the velocity of the body. The vis viva represents the energy required to keep a body in motion with a constant velocity. Suppose a locomotive to double its velocity : it encounters twice as many points of resistance, and strikes each of these with double velocity; hence, to maintain a double velocity, its energy of motion must be increased four times. If it trebles its velocity, its energy must be increased nine times, etc. That is, with a given mass the vis viva is proportional to the square of the velocity. The work which a moving body can do through a certain space before it is brought to rest is the measure of its energy at any moment. Its average velocity will be only one-half of the initial velocity, and, hence, The vis viva equals one-half of the product of the mass multiplied by Hie square of Hie velocity. [6-] * = 136. Destructive effects of collision. When railway trains come in collision, the engines are shattered by their striking force, while the momentum of the trains following each has been known to pile thirty cars one above another. The collision between two ships of equal size is the same as if either, at rest, had been struck by the other with twice the velocity. When a large ship runs down a small vessel, it suffers little injury, because of its stronger build and greater mass. Even light and soft bodies, as air and water, have tremendous power when moving rapidly, as in hurricanes and storms. CENTER OF GRAVITY. 137. A body, unsupported, falls to the ground; and, if supported, exerts a certain pressure, called its weight. These are but special examples of a force, of whose nature nothing is certainly known, which acts upon all particles of matter in the universe, and constantly tends to make them 64 NA T URA L PHIL OS OP II Y. approach each other. Newton has shown that the motions of all the heavenly bodies are due to this force, which he called Universal Gravitation. As applied to bodies on or near the earth, it is called Terrestrial Gravitation, or simply Gravity. 138. It will be shown (213) that gravity acts with equal intensity upon the particles of all bodies, however they may differ in form, size, or state. The direction and point of application of gravity will now be considered. The direction of gravity. Weights dropped at differ- ent places on the earth's surface will fall toward a point at, or near, the earth's center. Hence, the direction of the force of gravity may be considered, without sensible error, as the line joining the point of application and the earth's center. This direction may readily be found, at any place, by a plumb line, which consists of a heavy weight suspended by a light and flexible string. If a plummit hangs so that the weight dips in a vessel of water, the line and the surface of the water will be at right angles to each other. The direction of the line at any place is called the vertical, and IT a line at right angles to it is called a horizon- tal line. If two plumb lines are placed near each other, their lines v" of direction will be sen- sihly parallel, because their lengths are incon- H^^^^^H siderable in comparison with the radius of the earth. Hence, the di- rection sol' the force of gravity on particles near each other arc parallel. In Fi ( ir. 21), vertical lines on the earth are designated by V, and horizontal line.- by H. V'"" POINT OF APPLICATION. 65 139. The point of application of gravity. As gravity acts in a vertical direction upon each particle of a body, its effect on the body, taken as a coherent mass, will be the same as the resultant of an infinite number of equal and parallel forces. When the form and dimensions of a body are known, this resultant may readily be calculated by Case V (125), but in all cases it may be determined by experiment. Let A B be any body ; represent the force of gravity on each point by the dotted vertical lines, and their resultant, G E, by the arrow. Then, if any point, as C, in the direction of this resultant be supported, the body will remain at rest, and all the forces will be expended in pressure on the fixed point C. If, now, we suspend the body by a string in the direction of the line D E, it will still remain at rest, because the line is the prolongation of the direction of the resultant. If, however, we were to attach the string to a point at P, outside of the direction D E, the body would not remain at rest. The resultant, acting at C, will be decomposed into two parts, the first acting in the line C H, representing the w T eight supported by the point P, and the second acting in the direction C I, which would move the body toward the vertical, P K. Therefore, a body supported by a fixed point, can not remain at rest unless the direction of the resultant of gravity passes through that point. Now suspend the body at another point, as Z, the direction will change its position ; but whatever be the number of directions thus found, they will all intersect in a common point, as G. 140. The common point of intersection cf the resultants of the forces of gravity in all positions of the body is called the center of gravity. This center may readily be found in a board, or a plate of lead, by suspending it at various points. A plumb line attached to each point of suspension, will show the direction of the resultants. N. P. 5. 66 NATURAL PHILOSOPHY. The center of gravity may be regarded as the point of application of the force of gravity on all the particles of a body, since it is the only point common to all the result- ants. Hence, in calculations, the weight of a body may be considered as concentrated in the center of gravity. The ver- tical line passing through the center of gravity is called the line of direction. When the center of gravity is supported, the body will remain at rest, because any resultant will be supported when this point is supported. Therefore, the center of gravity is the point about which all parts of a body balance. 141, In bodies of uniform density the center of gravity will coincide with the center of the figure. When such a body is symmetrical, the determination of the center of gravity becomes a simple geometrical problem. Thus, the center of gravity will lie : 1. In a straight line, at its center. 2. In a circle, at the intersection of any two diameters. 3. In a parallelogram, at the intersection of its diagonals. 4. In a triangle, at the intersection of the lines drawn from the vertices of the angles to the middle point of the side opposite, and at a distance from any such middle point equal to one-third of the length of the given line. 5. In a sphere, at its center. 6. In a cylinder, at the center of its axis. 7. In a parallelopipedon, at the intersection of its diag- onals. 8. In a pyramid, on its axis, one-fourth of its length from the base. Tin-.- n-iilN may be verified by balancing bodies, of the figures described, at the points designated. For tbe first four, figures may be made of thin sheets of pasteboard, wood, or metal; for the re- mainder, the solids may he made of light wood, hard soap, etc. When the fi^im- is irregular, the center of gravity may be deter- mined by suspending it so that it will move freely from any two CENTER OF GRAVITY. 67 {mints, not lyintf in the same line of direction, as described in (139). The intersection of the two lines of direction will be the center of gravity sought. FIG. 32. FIG. 33. 142, The center of gravity may lie entirely outside of the body, as will be its position in a ring, a hollow box, or ball, or cask, yet even in this case its properties will be the same as if included in the mass of the body. 143. When two bodies are connected so as to form a rigid mass, the center of gravity will be at a distance from either body, inversely as their weights. In Fig. 34, if the weights are equal, they will be bal- anced at the middle point of the (~J\ c /^\ bar connecting them ; if A is the FlG ^ heavier, the center of gravity will lie nearer it. Thus, if A weighs four pounds and B one pound, the center of gravity will lie four times nearer A than B. When more than two bodies are connected, the center of gravity of the compound body is found by taking them successively in pairs, in the manner described for finding the resultant of several forces. (124.) When a body is not of uniform density throughout, the determination of the center of gravity is similar to that of two bodies connected. 68 NATURAL PHILOSOPHY. 144. Equilibrium of heavy bodies. Although a body will remain in a state of rest when its center of gravity is sup- ported, yet, as the center of gravity always tends toward the lowest possible position, the equilibrium of a body supported on a fixed point, will depend on the relative position of that point to the center of gravity. There will thus be three states of equilibrium : (1.) stable, (2.) unstable, (3.) neutral 1. A BODY IS IN STABLE EQUILIBRIUM if it tends to re- turn to its original position after it has been somewhat dis- placed. This will always be the case when any change of position elevates the center of gravity. A pendulum oscil- lates about its position of stable equilibrium, and will finally come to rest in that position. 2. A BODY is IN UNSTABLE EQUILIBRIUM when it tends to depart farther from its original position, after it has been slightly displaced. This will be the case when the point of support is below the center of gravity, for the center of gravity will then be higher than in any adjacent posi- tion, and when removed from the vertical above the point of sup- port, will not stop until it has gained the lowest possible position. This is illustrated in balancing a pencil by its point on the tip of the finger. Once balanced, it will remain in equilibrium until it is disturbed, but the least displace- ment will throw the line of direc- tion beyond the point of support, and the pencil will fall. If, now, we attach a couple of knives on cadi side of the pencil, like the balls in Kiir. 35, the center of gravity of the compound body will he below the point of support, and the body will be in .-table equilibrium. ILIBRIUM. 69 The conversion of unstable into stable equilibrium, may be illus- trated by suspending a pail from the end of a stick lying on the edge of the table Fig. 36. Now place a second stick, E G, with one II FIG. 36. end against the corner of the pail, and with the other end in a notch cut in the horizontal stick C D. By this contrivance, the center of gravity is brought under the edge of the table, and the whole will therefore be in stable eqilibrium. The pail may now be filled with water without changing the equilibrium. 3. A BODY is IN NEUTRAL EQUILIBRIUM when it remains at rest in any adjacent position after it has been displaced. This will be the case when the point of support coincides with the center of gravity, as when a wagon wheel is sus- pended on its axle. A perfect sphere, resting on a hori- zontal plane, is in neutral equilibrium, because its center of gravity is neither raised nor lowered in any adjacent posi- tion. The following figure represents three cones : A in FIG. 37. The stable, B in unstable, and C in neutral equilibrium, position of the center of gravity is indicated by g. 145. The relation which the center of gravity bears to equi- librium, may be shown by the following simple contrivance. 70 NATURAL PHILOSOPHY. Thrust two half knitting needles and one whole one through a cork, at right angles to each other, and support the apparatus on two wine glasses, by one of the shorter needles. By pushing the vertical needle up or down, the center of gravity FIG. 38. can be altered at pleasure, and the apparatus brought into either stable or unstable equilibrium. In performing this ex- periment, the student should carefully notice the position of the center of gravity, when the apparatus best exhibits the slate of stable equilibrium, for this is the position required in a good balance. 146. This experiment shows that the preceding distinc- tions apply to bodies resting on two or more fixed points. The pressure on these points is manifestly equal to the resultant in the line of direction. Thus, a book is in stable equilibrium when resting on its side, and in unstable equilibrium when standing on its edge. When a body, supported on two points, is in equilibrium, the line of direction will pass through the line connecting the points of support. Thus, a man standing on stilts is in a state of unstable equilibrium. So, also, is a man walking on a tight rope. The latin- uses a long pole, which he elevates or depresses, t<> a-ist him in keeping the center of gravity vertically over the rope. A person walking on the thin edge of a plank throws out his arms for the same reason. 147. The stability of bodies. When a body has but one point of support, or rests upon ;i line, it is easily moved from the vertical, and can not be said to possess stobUihj. This property depends on the relation which the center of gravity bears to at lea>t three point-, not in the same straight line, which constitute, the base of the body. The base of a body supported on le^s, as a table, i> the polygon formed by lines connecting the bottom of the legs. A bdy re-tin^ on a hsisc is .-table, when the line of direction fulls within the ban-. The stability of such bodies EQUILIBRIUM. 71 may be estimated by the force required to overturn them. If its position can be changed without raising the center of gravity, the slightest force would be competent to move it, if friction did not oppose. If its position can not be changed without raising the center of gravity, then the force required to move it must be sufficient to raise the entire body to the same height that the center of gravity would be elevated. To illustrate this, let the diagrams, Fig. 39, represent sections drawn through the center of gravity of different solids, and denote their centers of gravity by G. To turn either of these bodies over the edge E, the center of gravity must pass through the arc G T, and be raised through the height H T. A careful inspection of these figures will lead to the following deductions: The distance, H T, increases as the ratio of the height to the base decreases: therefore, (1.) the stability of bodies of the same height and similar figure is increased by widen- ing the base. The distance, H T, increases in proportion as the center of gravity is lowered: therefore, (2.) the stability of bodies is increased by bringing the center of gravity to the lowest possible position. As a corollary to this; (3.) of bodies having the same height and base, but of dissimilar figures, the pyramid is the most stable. Now, if the similar sections, in Fig. 40, inclined more or less from the perpendicular, be compared, it will be seen, (4.) that the stability of bodies is greatest when the line of direction passes through the center of the base. So long as the line of direction, G D, falls within the 72 NATURAL PHILOSOPHY. base, the body will stand, but its stability will be less in proportion as its distance from the center of the base in- creases, until the line of direction falls exactly through the edge, E. In this position the body is in a state of unstable equilibrium, and will be overturned by the slightest force. Finally, (5.) when the line of direction falls without the base, the center of gravity will be unsupported, and the body will fall. 148. A sphere remains at rest on a horizontal plane, be- cause the line of direction passes through the point of sup- port, but if the plane be inclined, the line of direction will fall with- out the base, and the sphere will roll" downward. So, any body on an inclined plane, will not slide down the plane, until the line of direction has fallen so far forward as to overcome the friction of the plane. 149. Practical applications. (1.) Stability dependent on extent of base: candlesticks and inkstands are made with broad bases. Stone walls are broader at the Imse than at the top. Tall monuments are made with their sides in- clined, and often have very Isirirr bases. The le^s of chairs are inclined outward. A child's hijrh chair has a very wide _. i Stability dependent on the height of the center of gravity: a load of hay is more easily overturned than the same woiirht of stone. In loading a wa.iron or a ship, the heavier articles should le placed at the bottom. (3.) Stability dejM-ndent, on the line of direction. There are Fio. 41. RECAP/TULA TION. 73 many towers in Italy, as at Pisa and Bologna, which incline far from a perpendicular position, but in these the line of direction still falls within the base. 150. General considerations. The center of gravity in man lies between his hips, his base is the area inclosed by his feet. The different attitudes assumed by persons in standing or moving are the ivsults of instinctive efforts to keep the line of direction within the points of support. In standing, a man widens his base by turning out his toes, or by using a cane. In moving about, the center of gravity is perpetually changing, and the positions of the several parts of the body are changed to correspond. Thus, when a person rises from a chair, he either throws his body forward, or draws his feet backward, to bring the center of gravity over his feet. In running or ascending a hill, a person throws his body forward so as to carry his weight with less effort. In descending a hill, he leans backward, so that his weight shall not cause him to fall forward. A man standing with his heels against a vertical wall, finds it difficult to stoop to the floor without falling. When a person carries a load, the effort is to preserve the line of direction, common to himself and the load, within his base. If the load is in his right hand, the person inclines his body to the left, and throws out his left hand as an additional assistance. If the person carries the load on his head, or an equal portion in each hand, there is no tendency to lean to either side. If the load is on his back, he bends forward ; if carried in his arms, he leans backward. 151. Recapitulation. I. Mechanics considers r Equilibrium of Motion of r Solids Statics, -I Liquids.. Hydrostatics, v Gases Aerostatics. f Solids. ...Dynamics, j Liquids..Hydrodynamics, ..Aerodynamics. II. Motion is classified With regard to a given ( Absolute, point. \ Relative. ( Uniform, Witli regard to rate, j y ar ; e( j f Simple, L With regard to force. 74 NATURAL PHILOSOPHY. III. {1. The inertia of bodies. 2. The action of forces. 3. Action and reaction. IV. f Stable support above center. Equilibrium is \ Unstable support below center. I Neutral support at center. STATICS. 152. Hitherto we have considered the action of forces as directly applied to bodies; but there are many instances in which force acts indirectly, through the intervention of some instrument. Thus, it is possible to arrange the burning coals in a grate by the direct application of the hands, but it is certainly safer and more convenient to apply the requisite force to a poker, which will com- municate it to the coals. The poker then becomes a machine. 153. A machine is an instrument by means of which a force, applied at a certain point, is made to exert force at another point, more or less distant. The effective force generally differs in intensity from the force applied. The force employed in a machine is called the power. The resistance overcome by a machine, at the point where the power acts, is called the weight or load. It may be con- sidered as a force acting in a direction opposite to that of the power. The work is the product of either the power or the load, by the vertical space through which it moves. 154. The foot-pound. In order to estimate the efficiency of any force, an arbitrary unit of work has been adopted, called the foot-pound. The foot-pound is the mechanical value of a force capable of raising one pound through a vertical space of one foot. The work of the power is, therefore, equal to the product of an equivalent weight in pounds multiplied by the vertical height in feet through HORSE-POWER. 75 which it passes. The work of the load is found in a similar manner. Thus, to raise a load of one thousand pounds of water thirty- three feet high, requires a power equal to thirty-three thousand foot- pounds. 155. Horse-power. To estimate the work of any force, acting through a limited period of time, another unit has been adopted, called the horse-power. A horse-power is the mechanical value of a force capable of raising thirty-three thousand pounds one foot in one minute. Its work is, therefore, equal to thirty-three thousand foot-pounds in a minute. Thus, one horse-power can raise one thousand pounds thirty-three feet high in one minute, or five hundred and fifty pounds one foot high in a second, or one million nine hundred and eighty thousand foot-pounds in an hour. 156. No machine can create power. It is merely an inert instrument for the advantageous application of power. In explaining the theory of machinery, many circumstances are at first neglected which must afterward be taken into account. Thus, it is assumed that the parts of a machine move without friction, without resistance from the air, that they have neither weight nor inertia; also, that the ropes and chains employed have neither thickness, stiffness, nor weight. As these conditions are never satisfied, a part of the power must be expended in the machine itself, and hence power is partially lost when applied to machines. 157. The work of the power is always equal to the work of the load. Hence, if any machine will enable us to lift a weight of ten pounds by a power of one pound, (1.) the power must move ten times the space traversed by the load ; (2.) as the spaces are traversed in the same time, the power must move ten times as fast as the load. Therefore, the following laws are applicable to machines of every kind: 76 NATURAL PHILOSOPHY. 1. The power -multiplied by Hie vertical trength. By using a crow-bar, a man may rai-r a large stone, which he could not stir with his liaml-. TIIK LEVER. 77 4. It enables us to employ other forces than our own, as the strength of animals, the forces of wind, water, and steam. 5. It enables us to utilize the products of nature. It is the knowledge of machinery that distinguishes civilized nations from savages, since by it we have mills for weaving cloth, forging iron, grinding flour, etc. 160. All machinery may be reduced to six elementary forms, called simple machines. The simple machines are (1.) the lever, (2.) the wheel and axle, (3.) the pulley, (4.) the inclined plane, (5.) the wedge, (6.) the screw. A combination of two or more of these constitutes a compound machine. 161. A lever is an inflexible bar moving freely about a fixed point, called a fulcrum. The arms of the lever are the parts into which the fulcrum divides it. When the arms are not in the same straight line, it is called a bent lever; otherwise, simply a lever. There are three classes of levers, depending on the rela- tion of the power, load, and fulcrum. In levers of the first kind, the fulcrum is between the power and the load, as in Fig. 42, I. In levers of the second kind, the load is be- tween the power and the ful- crum, as in Fig. 42, II. In levers of the third kind, the power is between the load and the fulcrum, as in Fig. 42, III. The lever acts on the principle of parallel forces. The power and the load will FIG. 42. be in equilibrium when they are inversely as their distance from the fulcrum. 78 NATURAL PHILOSOPHY. [9.] P : L : : W F : P F ; or, P X P F = L X W F. [10 .] P = ^S [11.] L= PX 1? P F. W F. 162. STATICAL LAW. The product of the power multiplied by its distance from the fulcrum, is equal to the product of the load multiplied by its distance from the fulcrum. A statical law expresses the relation of the power and load when a machine is in exact equilibrium. To produce motion it is necessary that one product should exceed the other. The greater product will determine the direction of the motion. EXAMPLES. In a lever of the first kind, sixteen inches long, with the fulcrum four inches from the load, a power of one pound will balance a load of three pounds. In a lever of the second kind, sixteen inches long, with the load four inches from the fulcrum, a power of one pound will balance a load of four pounds. On a lever of the third kind, sixteen inches long, with the power four inches from the fulcrum, a po\ver of one pound will balance a of one-fourth of a pound. 163. Familiar illustrations. A poker is a lever of the first kind, when it raises the coals in the grate by resting on the bars of the grate as a fulcrum. A crow-bar is used KM;. 43. Fid. 44. as a lever of the first kind when we pn-ss downward to rai~r the loud above a block used as a fulcrum. Fig. 43. It is also used as a lever of the second kind, when one end rests on the Around as a fulcrum, and \\c lift upward to raise the load. Fioiuid lever, may be employed. When a compound l<-vcr is in equilibrium, the power iHH/fiji/inl hif tin' fonfiinird fii-mlud <>t' t/n dlterncite arm*, i-nmnn in-i,if the wheel and the axle. WHEEL AND AXLE. 85 [12.] P : L :: BF : AF; or, PX A F = L X B F. [13.] P = L J AF. [14.] L = PX AF BF. STATICAL LAW. The power multiplied by the radius of the wheel equals the load multiplied by the radius of the axle. EXAMPLE. When the wheel is six feet in radius and the axle six inches, a power of one pound will sustain a load of twelve pounds. 176. In the various forms of this machine, the load is generally attached to a rope coiled around the axle; the power is applied in various ways. The form represented in Fig. 50 is that used in warehouses, in which the power is applied by means of a rope coiled on the wheel. When the rope on the wheel is unwound, that on the axle is wound up, and the load raised. As radii are proportional to their circum- ferences, it is manifest that the rope unwound from the wheel will be as many times longer than that wound up on the axle, as the load exceeds the power. The power may also be applied to pins project- ing from the wheel, as in the steering apparatus on large vessels. 177. It is not nec- essary that the power be applied to a com- plete wheel, since a single spoke will an- swer. This modifica- tion is the windlass employed in raising water from wells. The winch constitutes the power arm the radius of the axle the load arm. In the windlass used on ships there is no fixed handle, or winch, but handspikes are fitted into slots cut in the axle, and are shifted as occasion requires. When the windlass has a vertical axis, it con- stitutes a capstan. Fig. 52. This is turned by men walking around it, and pressing against handspikes inserted in 52. the top or drum. 86 NATURAL PHILOSOPHY. FIG. 63. 178. The effective power of this machine may be aug- mented by increasing the radius of the wheel, or by dimin- ishing that of the axle; but very large wheels are too un- wieldy, and very small axles too weak for practi- cal use. These inconveniences may be obviated by making the axle of two parts, with different ra- dii, having the same rope so at- tached that, as it winds around the thicker, it unwinds from the thinner. This contrivance is called the differential wheel and axle. The effect is to shorten the rope by which the load is suspended, by the difference between the circumference of the two parts, but the height through which the weight is raised is only half this shorten- ing of the rope. Hence, the efficiency of the differential wheel and axle may be found by this rule : The power multiplied by the radius of the wheel, equals the load multiplied by half the difference of the radii of the two parts of the axle. By making the two parts of the axle of nearly the same size, the effective power m:iy l>u increased to any required amount. 179. The power of this machine may also be augmented, on the principle of the compound lever, by combining several, in such a way that the axle of the first may act on the wheel of the second, and so on. Several wheels and axles combined in one machine are called a train. A train of wheels is frequently connected by cogs, as in clock-work. The cogs on the wheel- an- called teeth, those on the axles, leaves. The axle itself is termed a shaft, or pinion. The mechanical power of a train of wheels may be WHEEL AND AXLE. 87 found in the same way as for a compound lever. Since the cogs are proportionate to the radii of the wheels and pinions, the statical law may be thus stated: The power FIG. 54. multiplied by the continued product of the teeth in each wheel, equals the load multiplied by the continued product of the leaves in each pinion. FIG. 55. In Fig. 54, the power is represented as acting on the wheel which carries the first pinion P. By this arrangement, a small power is capable of raising a large load, but with a corresponding loss of velocity. The arrangement may be reversed for the sake of augment- 88 NATURAL PHILOSOPHY. ing the velocity, at the expense of the power. Thus, in a watch, power is applied to a wheel that revolves once in four hours, to give the second hand a revolution once in a minute. 180. Toothed wheels are of three kinds, spur, crown, and bevel. Spur wheels have their teeth in the direction of their radii, as in Fig. 54. Crown wheels have their teeth parallel with their axes, as , wheel shown in this figure is called a lan- tern. Bevel wheels have Fio. 56. , their teeth oblique to their axes, as in Fig. 56. 181. Wheels are also connected by endless bands, as in Fig. 57. In this case, the motion is communicated by the friction of the bands on the circumferences of the wheels. The whirling ta- ble, Fig. 93, con- sists of two wheels thus connected; on tn i-ii ing the large wheel around once, the smaller is made to revolve as many times as its circum- ference is contained in the circumference of the larger. It i- ii-ed to give great speed to the axis of tin- smaller wheel. 182. The pulley. If a e,,,d. fastened at one end to a THE PULLEY. 89 FIG. 58. hook, supports a weight at the other end, it is manifest that the stretching, or tension, of the cord will be transmitted throughout its whole length, and exert a force on the hook equal to the load. If, now, the cord be passed over the hook and one end held by the hand, the tension of the cord will remain the same, and the hand must exert a force equal to the load. No mechanical advantage will be gained in raising the load in this manner, beyond a change in the direc- tion of the power. In fact, there will be a loss, resulting from the friction of the cord upon the hook. We may diminish the friction, by passing the cord over a wheel revolving on the hook as its axis, but can not lessen the tension of the rope. Such a wheel is called the sheave of a pulley. A pulley is a small grooved wheel, revolving about an axis, and having a cord passing over its circumference. Pulleys are called fixed or movable, according as their axes are fixed or movable. 183. In the use of the fixed pulley there is neither gain nor loss to the power, but only a change in its direction. This is often as great an advan- tage as an increase of the power would be. Thus, if a fixed pul- ley be attached to the rafter of a warehouse, a man standing on the ground may raise weights to any floor of the building. It is, besides, so much easier for him to pull the rope down than it would be to lift the weight di- ivrtly up. that he can afford to overcome the friction of the pullry in addition to the load. By the use of two fixed pulleys, horizontal motion may be converted into vertical, as in Fig. 59. FIG. 59. 90 NATURAL PHILOSOPHY. 184. Movable pulley. If a cord be attached at each end to a hook, and a weight hung by a ring at the center of the * r . cord, the tension of the cord will be transmitted throughout its length. If we suppose the cord to be divided into two parts, each part will support but half the load, and, therefore, have but half the tension. Therefore, if a fixed pulley take the place of one of the hooks, the power required to support the load will be one-half the weight of the load. If it is desired to elevate the load, the friction may he diminished by substituting a movable pulley for the ring. Fig. 61. FIG. o. If one end of the cord be attached to the top of the movable pulley, as in Fig. 62, the tension of the cord produced by the load will be distributed in three equal portions. Consequently, the tension of the part attached to the power will he measured by one-third of the load, and the combination will he in equilibrium when the power is one-third of the load. SPANISH BURTONS. 91 In the arrangement of Fig. 63, the power is one-fourth of the load. In this, there are two fixed and two movable pulleys, each pair secured in a framework called a block. A combination of blocks, sheaves, and ropes is called a tackle. 185. As fixed pulleys do not increase power, the gain in the last three examples must be due to the division of the tension among the parts of the rope supporting the movable block. Hence, representing the number of these parts by n, [15.] L = [16.] P = - n STATICAL LAW. The load equals the power multiplied by tie i (limber of parts of the cord engaged in supporting the movable block. 186. This law applies only when one continuous cord passes through the whole system, and when its parts are parallel. Movable pulleys are very seldom used alone ; they are generally combined with fixed pulleys which serve to change the direction of the power. These combinations may contain from one to ten pulleys in each block. When the fixed and mov- able pulleys are equal in number, the parts of the string supporting the load will be twice the number of movable pulleys, as in Figs. 61 and 63. 187. Spanish burtons are pulleys contain- ing more than one rope. Such a system, with two ropes, is represented in Fig. 64. The rope, P B A D, sustains a tension equal to the power; consequently, the portions, A B, A D, each have a tension equal to the power. The rope, A C B, sustains the tensions, A B and B P, and, therefore, has a tension of twice the power. Therefore, the united ten- sions of the ropes supporting the movable block, A, will be four times the power. In Fig. 65, each pulley has a separate rope. The pulley, FIG. 64. 92 NA T URA L PHIL OS OP 11 Y. B, receives half the load attached to A, C half of B, and so on; hence the power increases by the geometrical ratio of 8421 2 2. Therefore, the load will equal the product of the power multiplied by '2 used us a factor as many times as there are movable pulleys. Although the power increases rapidly by this system, yet it is practically of little value because of its limited range. In the common system, the motion may be continued until the fixed and movable blocks come in contact; but in this system, only until D and E come together, at which time the other pulleys will be far apart, because C rises halt' as last as D, B one-fourth and A one-eighth as last. 188. The inclined plane is a hard, smooth, inflexible surface, inclined obliquely to the resistance. When a weight is placed upon such a plane, a part of the pressure is resisted by the FIG. 66. plane, while the remainder tends to cause the weight to >lid- or roll down the piano. Thus, in Figs. 66, 67, and (>.s, the weight of the body lies in the line of direction of L-ravity, L G. This may be resolved into two components, vi/,. : L N. acting perpendicularly to the plane, and com- pletely resisted by it, and L K, acting opposite to the direction of the power, and to be counterbalanced by it. It i- manifest that the component, L N, shows how much of the weight is supported by the plane. If the plane were vertical, L N would be zero, and if the plane were hori- THE INCLINED PLANE. 93 zontal, the whole weight would be supported by it. Con- sequently, the other component, L E, which represents the power necessary to sustain the load, will increase as the plane becomes steeper. It is also manifest that this component, L E, will vary with the direc- tion of the power. There may be three cases. FIG. 68. 189. In the first case the power acts parallel with the plane, as in Fig. 66. In the parallelogram, E L N G, the sides L G and E N are equal; hence, E N may be taken as the weight of the body, or load. The triangles, ABC and L E N, are similar, and hence, Power : load : : L E : E N; or, : : B C : A C. [17.] P = LXBC AC. [18.] L = PXAC BC. STATICAL LAW. The power equals the load multiplied by the ratio of the vertical height of the plane to its length. EXAMPLE. The power required to keep a barrel, weighing two hundred pounds, on a plank twelve feet long, with one end on the ground and the other in a wagon three feet high, will be fifty pounds. This is the most advantageous way of applying the power, for its whole effect is expended in raising the load. If the power be directed below the plane, a part of it will be expended in increasing the pressure on the plane; and, if directed above the plane, a part of the power will be used in diminishing the pressure ; and hence, only the i'emaining part is available in drawing the load up the plane. That is to say, in all other cases a greater power will be required to raise the same load. 190. In the second case the power acts parallel with the base, as in Fig. 67. The triangles, L E N and L N G, are each similar to ABC, and we shall find, 94 NATURAL PHILOSOPHY. Power : load : : L E : E N ; or, : : B C : A B. [19.] P = [20.] L AB. BC. STATICAL LAW. The power equals the load multiplied by the ratio of tfie vertical height, of the plane to its base. 191, Third case. In any other direction of the power, the triangles formed will not be similar, and no simple expression of equilibrium can be given, beyond the general law of (157.) * 192. Familiar examples. The grandest examples are found in roads, which are seldom perfectly level. In ascending mountains the roads wind about, so as to increase the length of the incline. So, also, a careful driver, in ascending a steep hill, -will guide his team from side to side of the road, preferring to increase his distance for the sake of lightening his load. On a level road, the power of the horses is expended in overcoming friction, which, on common roads, varies from one eighteenth to one fiftieth of the load, and on iron railways, from one one-hundred-and-fortieth to one two-hundredth. On a road rising one twentieth, that is one foot in twenty, the horse must lift one twentieth of the load besides overcoming friction. Beck- oning friction at one eighteenth, the whole power (jV + fV) necessary will be almost double that required on a level road. On a railway, with the same grade, the power required will increase from T ^ to TOT + ^ = Tftf> or eight times that required on a level. This rapid increase indicates the reason why steep planes are less admissible on railways than on common highways. *The general proportion for inclined planes is P : L : : sine of in- clination of the plane : cosine of the angle formed by the direction of the power and the plane. Suppose the weight to be concentrated in the point L, and the line A C to pass through it; then, I '!-. 08. P : L :: sine BAG : cos. CLE. In Fiir. '.'.. Cot. CLE radius /. P : L : : sine BAG : 1. In Fig. 67. CLE^ IJAC.-md is the compli-im-nt of K L N; hence, 1' : L :: siiu- BACj < < . I: \ C. The method l>y construction may al.so be applied. (125.) THE WEDGE. 95 193. The wedge is a movable inclined plane. If, instead of moving the weight along the inclined plane, Fig. 67, the plane had been pushed under the load, the same advan- tage would have been gained. Therefore, since in the wedge the power is always exerted parallel to the base, P : L :: BC : A B. [21.] P=^ AB. [22.] L = PXAB BC. FIG. 69. STATICAL LAW. The power is to the load as the height of the wedge is to its base. 194. As commonly applied for sepa- rating surfaces, a double wedge is used, as A C A' in Fig. 69. As each face meets with half the resistance, the power is to the resistance as half the thickness of the wedge is to the length, B C. 195. These laws are of little practical value, beyond the general deduction that the efficiency of the power increases with the thinness of the wedge. The reasons for this are : 1. The power is applied, not by a continuous force or pressure, but by percussion, for which we have no numerical standard of comparison. 2. The surfaces to be separated generally assist the action of the wedge, by their elasticity, at the moment of impact, and, frequently, by the leverage of the faces to be cleft, 3. The value of the wedge is often dependent entirely upon friction, as is the case with nails, pins, and the key- stones of arches. If it were not for friction, the wedge would recoil after every blow. 196. Practical applications. The wedge is especially useful where very great force is to be exerted through very small space. Masses of timber and stone are cleft by wedges. Ships are raised by 96 NATURAL PHILOSOPHY. FIG. 70. wedges driven under their keels. The most extensive application of the wedge is in tools for catting and piercing, as knives, awls, hatchets, chisels, nails, etc. The angle varies with the purpose for which the instrument is designed. Although the mechanical power is increased by diminishing the angle, yet the strength of the tool is diminished in the same proportion. Accordingly, in tools used for cutting wood, the angle is about 30 ; for iron, from 50 to 60 ; for brass, 80 to 90. 197. The screw is another variety of the inclined plane, as may be shown by winding a triangular piece of paper around a cylinder. Fig. 70. The hypotenuse will form a spiral path about the cylinder exactly resem- bling the threads of a screw. The ratio of the base, AB, to the cir- cumference of the cylinder, will determine the number of turns the triangle will make, and, by conse- quence, the number of parts into which the height, OB, will l)o divided. Each of these parts, as be, corresponds to the vertical distance between the threads of the screw. As in the w r edge, the power acts parallel with the base; the action of the screw is, therefore, the same as the second case of the inclined plane; hence, STATICAL LAW. TJie power is to the load as the vertical distance between two adjoining threads is to the circumference of the screw. 198. In actual practice, the screw consists of two parts: (1.) a convex grooved cylinder, or screw, S, which turns within (2.) a hollow cylinder, or nut, N, whose concave surface is cut witli a thread exactly corre- spondinir to the threads of the screw. The power is employed either to turn the -crew within an immovable nut, or to turn the nut about a fixed screw. THE DIFFERENTIAL SCREW. 97 In either case, it is generally found convenient to apply the power at the end of a lever, fitted either to the screw or to the nut. This renders the contrivance a compound machine, whose advantage may be found by the following STATICAL LAW. The power is to the load as the vertical 'Usance between two contiguous threads is to the circumference described by the power. P : L :: be : 2*R; or, :: be : 6.2832 FP. [2 3.] P = LX6 1_ [24] L -,PX 6.2832 FP 6.2832 F P. be. EXAMPLE. If the threads of the screw are one inch apart, and the lever is four feet long, a power of one pound will exert a pressure of 301.6 pounds. 199. The mechanical efficiency of the screw may be in- creased by lengthening the lever, or by dimishing the dis- tance 'between the threads; and, as we may modify the screw in both these ways at once, to an indefinite amount, the pressure which may be exerted by a screw is limited only by the strength of the materials. To obviate the practical difficulty of making the lever too unwieldy, or the thread too delicate, John Hunter invented the differential screw. This consists of the ordinary | ^^^ right handed screw, into the end of which works a left handed screw, so that the two move in opposite directions. The distance between the threads of the second screw is somewhat less than that between the threads of the first. This second screw is prevented from turning round, but may move up and down. On turning the lever of the larger screw, it twill descend through its nut, and, at the same time, the smaller screw will ascend within it; consequently the plate, N. p. 7. 98 NATURAL PHILOSOPHY. D, will descend the difference between the pitch of the two threads. Therefore, with the differential screw, the power is to the weight as the difference of the distances bet WITH the threads of the two screws is to the circumference described by the power. This principle is employed in the micrometer screw, which is an apparatus used to measure very small distances. 200. Practical applica- tions. The screw is used for compressing cotton, hay, and goods, for expressing the juices of plants and fruits, to raise buildings, to elevate grain and water, to propel ships, and to fasten securely the framework of structures of all kinds. Fig. 73, is the ordinary press used for copying letters. FIG. 73. COMPOUND MACHINES. 201. One of the most useful of these contrivances, is the endless screw, which is so secured by its shoulders that it has no longitudinal motion. Its thread works obliquely into the teeth of a wheel, which supplies the place of a nut. Ci-anes and der- ricks are combina- tions of pulleys with a wheel and axle. Fl0 - 74 - One form of the crane is shown in Fi_r. 7.">. This contains the wheel and axle, G, two fixed pulleys, E and F, and one movable pulley, P. The vertical axis, A, is supported by suitable framework. HUMAN MECHANISM. 99 The power of any compound machine may be found by estimating the effect of the parts separately, and then com- pounding them. 202. The human mechanism exhibits many examples of simple machines. Thus, the nodding of the head il- lustrates a lever of the first kind, in which the load is the weight of the head ; the fulcrum, the atlas bone, and the muscles of the neck, the power. When a man stands on his toes, the floor is the fulcrum, the power is ap- plied at the heel by the tendon A chillis, and the weight of the body falls between the fulcrum and the power. This is a lever of the second kind. We employ a lever of the third kind, in raising the fore-arm horizontally. The hand, and any thing it contains, is the weight, the elbow-joint the fulcrum, and the power is applied by a muscle attached to the fore-arm, a little in front of the joint. Fig. 76. In biting by the front teeth, we em- ploy a lever of the third kind. The force exerted by the muscles which raise the lower jaw is enormous. In man it can not be less than three hundred pounds, and in the tiger it must exceed t\vo thousand pounds. The muscle which directs the eye downward and inward, passes through a cartilaginous pulley attached to the frontal bone. Some of the teeth are wedges, capable of cutting like chisels. Throughout the entire frame, we have surprising examples of econ- omy of material to the end designed ; combining lightness, force, firmness, elasticity, leverage, motion, resistance, security, and grace. These contrivances are so numerous, and so wonderfully constructed, that a volume would be insufficient to describe them. FIG. 75. FIG. 76. 100 NATURAL PHILOSOPHY. 203. Recapitulation. Machines are classified as simple and compound. 1. Leverage, I. Simple machines employ r Lever. \ Wheel and axle. 2. Tension of ropes. < Pulley. {Inclined plane. Wedge. Screw. II. Machines are compounded : 1. By repeating the same simple machine ; as the compound lever, the burton, the differential screw. 2. By uniting two or more simple machines ; as the endless screw, IMPEDIMENTS TO MOTION. 204. It has already been stated that power is generally lost in machines through rigidity, and the mutual adhesion of the materials, and the consequent diminished mobility of the parts of the machinery. For this reason, the results actually reached in practice are somewhat less than those determined by the statical laws. Therefore, in calculating the useful work of any machine, due allowance should be made for the various impediments to motion. If (1.) the purpose for which a machine is designed' is merely to support a load, the greater the impediments the less will be the power required: but, (2.) if the object sought is to move a load, the greater the impediments the greater will be the power re- quired. In the first case, the impediments may constitute the entire mechanical advantage of tin- machine, as is shown bv the incalculable utility of friction in nails and screws, when employed in holding different materials together. So, also, friction is ncce.-sary in almost every application of power, whether employed in simple motion or applied to machines. Without friction, the wheels of a locomotive would turn on the rails without moving forward, belts would slide on their FRICTION. 101 i pulleys without starting them, all knots would readily untie, and nearly all manufactured articles separate into the parts of which they are composed. In the second case, any impediment to motion is a mechanical disadvantage, involving a loss of power. -rC" 205. Friction is termed sliding, when one surface slides over another, as a sleigh upon ice; and rolling, when one surface rotates on an- other, as a carriage wheel on the ground. Sliding friction has been deter- mined for many different surfaces by the apparatus shown in Fig. 77. Blocks of different materials, carrying varying weights, were made to move over various surfaces, by means of weights placed in the pan, P. The quotient obtained by dividing the force necessary to move the body, by its weight in pounds, is called the coefficient of friction. This quantity, therefore, represents the friction due to the normal press- ure of one pound. Roll- ing friction is determined by substituting, in place of the block, a cylinder about which were placed cords, loaded at each end, with equal weights, cc c'c'. The following results have been determined by experiments : FIG. 77. FlQ. 78. 206. 1. Friction increases with the roughness of the surfaces, because a rough surface contains many projections which fit into corresponding cavities of the opposing surface, and these projections must be either lifted out, bent down, or broken off in moving. 102 NATURAL PHILOSOPHY. 2. Rolling friction is less than sliding, because a rolling motion avoids the breaking down of the minor inequalities of the surface. 3. Friction is generally diminished by polisliing the surfaces, and by the interposition of unguents, because the projections are smoothed down and the cavities are filled up. 4. Friction is greater between soft bodies than hard ones, be- cause soft bodies allow the opposing surface to sink some- what into them, and thus increase the number of particles to be abraded. 5. Friction is generally greater at starting than after motion has commenced, because, if either surface is compressible, the contact becomes more intimate after a period of rest. If wood rests on wood, friction at starting attains its max- imum in a few minutes; but when metals rest on wood, the maximum intensity is not attained for several days. 6. Friction is greater between surfaces of the same materials than between those of different //'//'/>, because cohesion is added to the usual adhesion. Hence, it is usual to make axles of materials different from those of their supports. 7. Friction is very nearly proportional to pressure. 8. Friction is not affected by extent of surface, except within extreme limits. A brick will slide as easily on its side as on its edge, because the weight is distributed equally among all points in the surface on which it rests. Therefore, although there are more points in the side than in the edge, yet, as each point in the side receives a less friction than one in the edge, the sum of the friction of all the points will be the same. Besides these, other factors of friction sometimes need to be con- sidered. Thus, in ordinary vehicles, the inequality of the ground and the rapidity of motion increase the friction on hard ground, hut do not on soft. The width of the tire does not ailed friction on hard roads, hut on soft roads the friction i.s diminished l.y the use of broad tires. The friction of carriage wheels is inversely proportional to the diameter of the wheel. COEFFICIENTS OF FRICTION. 103 207. Table of Coefficients of Friction. Materials. 1 Unctuous Without unguents. | surfaces. Starting. Friction or motion. Oak upon oak fibers parallel .625 .540 .619 .137 .194 .162 .478 .324 .619 .138 .194 .172 .152 .217 .108 .143 .085 .077 .076 .075 .144 .107 Oak upon oak fibers cross \Vrous[lit iron upon oak Wrought iron upon wrought iron . Brass upon cust iron 208. The Friction of Wagons on Lerel *Roads. Loose sand 0.25 Common by-road 0.1 Dry highway 0.025 Macadamized road 033 Well paved road 014 Kailroads 0035 to .0059 209. The rigidity of cords, passing over wheels, also occasions a loss of power in transmitting motion, which varies with the materials and the circumstances attending their use. Thus, it has been found that the loss due to this cause is 1. Directly proportioned to the suspended weight. 2. Directly proportioned to the diameters of the cords. 3. Inversely proportioned to the diameters of the wheels. 4. And is greater in tarred than in white ropes, and in strongly twisted ropes than in those loosely twisted. 210. Resistance of fluids. The resistance which a moving body encounters in air or in water, is only an effect of the transference of motion. The moving body constantly sets in motion the particles of the surrounding fluid, and effects this by the loss of an equal amount of its own motion. It has been found that the resistance of fluids to bodies mov- ing in them is directly proportioned: 104 NATURAL PHILOSOPHY. 1. To the density of the fluid; for the moving body will displace its own bulk of either water or air; but as the water is eight hundred and twenty-nine times heavier than air, volume for volume, the weight of the fluids displaced will be exactly as their densities. The resistance of a square plane, of one foot area, moving in water with a velocity of one foot per second, is 0.975 pounds. 2. To ike square of tlie velocity of the moving body; for very swift motions the resistance increases even more rapidly. The resistance of the air to a cannon-ball, mov- ing with a greater velocity than twelve hundred feet per second, is greater than would be expected under the law. The increase seems to be due to the fact that air flows into a vacuum at the rate of twelve hundred and eighty feet per second, and, consequently, under very high velocities, the ball is retarded not only by the resistance of the air, but also by having the pressure of the atmosphere on the advancing side not counterbalanced by the pressure on the other. 3. To the extent of surface of tJie moving body; for the larger the body, the greater will be the mass of the fluid set in motion by it. 4. The form of the surface also influences the resistance. Thus, if the resistance to a given plane surface be taken as unity, an umbrella of the same area of section at the tips will meet with almost double (1.94) the resistance, when the concave surface is presented to the air; and only about three-fourths the resistance (.77), when its convex surface is presented. For this reason, the bows of fast sailing ves- sels are made sharp, so as to divide the water readily. It has also been found that the shape of the .-tern <>f a vessel nioditie- thi- reH.-tance. "). Large bodies encounter proportionally fa r<'.taiice is a.- the squares of their diameters; but their weight, which is one of the RECAPITULATION. 105 factors of their momentum, increases as the cubes of their diameters. Thus, if two balls have their diameters in the ratio of one to two, the area of resistance will be as one to four, but if their velocities are the same, their power to overcome resistance will be as one to eight. 6. Bodies of the same figure and volume, moving freely within a fluid, will be enabled to overcome resistance in pro- portion to the square root of their density. Balls, one-fourth of an inch in diameter, falling through the air, will soon reach the limit of accelerated velocity, through the resistance of the air, and will attain a final velocity as follows: lead, one hundred and eighteen feet per second ; water, thirty-six feet; cork, eighteen feet. 211. The useful effect of a machine, is that fraction of the power which is applied to its proper work after over- coming the various impediments to motion. As no two machines are exactly alike, the fraction which expresses the average work is not likely to be exactly applicable in any special case. Nevertheless, the following table will give some general idea of The Useful effect of Machines. Lever 98 Wheel and axle 90 Pulley 40 to .80 Endless screw 50 Chain pump 50 Undershot wheel 27 to .45 Breast wheel 45 to .65 Overshot wheel 60 to .80 Screw press 33 j Turbine wheel 60 to .90 212. Recapitulation. The useful effect of machines is lost, (1.) Either within the machine itself; or, (2.) By external impediments. The impediments to motion may be classified : 1. Friction, either internal or external. 2. Rigidity of cords and belts. 3. Resistance of fluids. 106 NATURAL PHILOSOPHY. DYNAMICS. 213. Gravitation. We have learned (1.) that the force of gravitation tends to make all bodies approach each other; (2.) that, for our globe, the direction of gravity is toward the earth's center, and (3.) that the point of application is at the center of gravity of the body. If we attach to a spring balance, balls of the same material but of different size, the tension of the spring, due to the force of gravity acting on the balls, will be proportional to the number of particles in each ball. If two of these balls be dropped from a height, they will reach the ground in very nearly the same time, although the resistance of the air is slightly in favor of the larger ball. If the balls were of the same weight but of different material, as lead and cork, the difference in bulk would cause so great a differ- ence in the resistance of the air, as to make the cork fall perceptibly slower. If, however, any two bodies whatever, as a bullet and a feather, be allowed to fall through a perfect vacuum, they will reach the ground at exactly the same time. Therefore, (4.) gravity acts with equal intensity on every particle of matter, and (5.) is measured by the weight, which is proportional to the quantity of matter. Now, if we catch balls dropped from different heights, we shall find that the swiftest balls are those which have fallen through the greatest spaces, thus showing that the motion is accel- erating, and if this experiment could be con- ducted in a vacuum, we should find that the increase of velocity is uniform, which proves (6.) that for bodies near the surface of the earth, gravity is a constant force. 214. The velocity attained by bodies falling freely through the air, increa.se.s so rapidly that it is a difficult matter to FALLING BODIES. 107 determine with precision the spaces passed over in successive seconds. GALILEO determined the laws of falling bodies, by rolling very smooth balls down a polished groove cut in a plane, which he inclined at different angles of elevation. In the study of the inclined plane, we learned that the weight, or gravity, of any body resting upon it, is resolvable into two portions, one producing pressure on the surface, and the other tending to produce motion down the plane. As this latter portion bears the same ratio to the whole force of gravity as the height of the plane does to its length, we may diminish it at pleasure by lowering the height. We shall thus diminish the initial velocity, so as to make the motion slow enough to be accurately measured. Nevertheless, as this ratio is invariable for the same plane, only the absolute motior will be changed. The motion of the body will be accelerated by the same law of constant forces, and pass, in successive moments, through spaces bearing the same ratio to each other as if it fell freely through the air. 215. To repeat the experiment of Galileo, stretch two parallel wires between the walls of a room, at any con- FIG. 80. venient angle, as in Fig. 80. On the lower ware hang a pulley with a weight suspended beneath it, and on the upper wire fasten any convenient index, as a bell, or slip 108 NATURAL PHILOSOPHY. of paper, to be moved by the top of the pulley, b. Sup- pose the angle of inclination of the wire to be such that, in the first second, it passes over the space, as; in two sec- onds it will pass over the space, as' ; in three, as", and so on. If, now, we measure these spaces we shall find that the spaces passed over in each successive second, viz.: as, ss', s' s", etc., increase in the order of the series of odd numbers, 1, 3, 5, 7, etc., or at the rate of two spaces for each second. This law of increase is a direct consequence from the nature of constant forces. For, as gravity may be considered as exerted in an infinite number of equal successive impulses, the final velocity, at the end of any second, will be due to the aggregate of all the impulses during the whole time of fall. Hence, the average velocity will be that at the middle of the interval during which it falls, and the final velocity will be double the average velocity. 216. The average velocity of the first second carried the pulley over the space, as, and the final velocity is double the space, a s. Therefore, if gravity were now to cease to act, the velocity already acquired will be sufficient to carry the body in the next, and each succeeding second, through twice the space, as. But during the next second, the fresh impulse of gravity will carry the body over a space equal to as; consequently, in the second second, the body will pass over three spaces, each equal to as, or s s f 3 a s, as determined by experiment. In two seconds the body will have passed over a s', which is equal to 1 + 3 = 4 spaces, and, as before, its final velocity will be double its average velocity. Since it has moved four spaces in two seconds, in the next two its acquired velocity would carry it over eight spaces, which is the same as a velocity of four spaces for one second. But as gravity adds a new increment at each second, it will traverse 4+1=5 spaces in the third second, and will have descended, in three seconds, through a#", which equals 1 + 3 + 5 = 9 times the .-pace, // & The final velocity will FALLING BODIES, 109 be 9 X 2-i-3=6 spaces. By similar reasoning, the body will be found to pass over seven spaces during the fourth sec- ond, and to have fallen through sixteen spaces at the end of the fourth second, and so on. 217. We may express these results by the following table, wherein t represents the number of seconds in any given time of fall. The last term in each series is merely a gen- eralization of the whole, derived by simple inspection of the previous terms in each series. Number of Spaces fallen Velocities Total space seconds. each second. acquired. fallen through. 1121 2344 3569 4 7 8 16 5 9 10 25 6 11 12 36 t (2t 1) 2< < 2 It is evident that these results will always be the same, whatever be the inclination of the plane, or the space passed over during the first second. If, in the actual experiment, the height of the plane had been one foot and the length sixteen feet, the pulley would have traversed, in the first second, one foot, in the second, three feet, in the third, five feet, and so on. Therefore, a body falling freely through the air would pass, in corresponding time, through sixteen times these spaces ; or it would fall, in the first second, sixteen feet, in the second, forty-eight, in the third, eighty, etc. * 218. It has been determined, by careful experiment, that in the latitude of New York, a body will fall, in a vacuum, through 16.08 feet in one second, and thereby acquire a final velocity of 32.16 feet. This last value is called the incre- "The apparatus devised by Atwood and by Morin will attain the same result, but as the description of either is of little use without the appa- ratus, the simple method of Galileo has been preferred. 110 NATURAL PHILOSOPHY. ment of velocity due to gravity, and is generally represented by <; = 32.16 feet. The space passrd over during the first second is %g = 16.08 feet. If we now employ the constant -\ r LAW. TJie total space described by a falling body f tfie end of any given second, is equal to tfie product of tfie square of the number of seconds, into the space dwrihnl f lie first second. Tim-, tin- total fall during nine seconds is 16.08X81 1302.48 feet. 220. Wo may combine the preceding formulas by braic pnin-.-M-s and determine five other values For each term, some of which may be of service. Thus, by eliminating t FALLING BODIES. Ill in [26.] and [27.] we find v* = 2gS; or, [28.] v = \/2g8. If g be taken as 32.16, [29.] v = 8.02 l/& Therefore, the velocity acquired by any body falling through a given height is equal to the square root of the Jieight multiplied by 8.02. So, also, from [27.] we find [30.] t=V 2S-t-g which is very nearly the same as ] vS. The number of seconds re- quired for a body to fall through a given space is very nearly one-fourth of the square root of the height, expressed in feet. 221. These formulas are also applicable for any constant force whose intensity, g, may be found. In any inclined plane, g is diminished, in the ratio of the height to the length, and becomes gh-^-L The total space, S, is iden- tical with /. If these changes be made in the preceding formulas, a new series will be found, applicable to bodies on inclined planes. Formula [27'.] becomes [31.] l = 4tl/ h, from which we derive, [32.] t = I -=- 4 V h. Therefore, when the heights of planes are equal, the times of descent are pro- portional to their length. Formula [28.] becomes v = V 2 g h S -r- 1. S and I cancel each other, and v = V 1gh\ or, [29V] = 8.02l/T, a formula identical with [29.] whenever S represents any vertical space. Therefore: 222. The final velocity of a falling body is propor- tional only to the vertical distance through which it falls, and is altogether in- dependent of the path it follows. Thus, a body, Fig. 81, starting from A, will have the same velocity on reaching the level, 6c, whether it falls through either of the grooves or vertically through ab. The time FIG. 81. 112 NATURAL PHILOSOPHY. of descent will be shortest on the vertical, but on any other line than the vertical, on the groove /. This curve is known as a cycloid. In the cycloid, the curve falls more rapidly at first, and the body acquires at the start a greater velocity than is possible in the other grooves. Another cu- rious property of the cycloid is that the body will descend the whole length of the curve in the same time as from any intermediate point, as /. 223. If a body is thrown downward, to the constant force already found must be added the impulsive force given the body. This is proportional to the velocity imparted and the time of its action. Thus, if a body be thrown downward with a velocity of fifty feet per second, and is three seconds in falling, gravity alone would carry it 3 2 X ISjV = 144 J feet ; the impulse acting through three seconds would carry the body 50X3 = 150 feet, and therefore the total height of the fall is 144| -f 150= 294 feet. 224. If a body be thrown upward, the direction of the body is opposite to that of gravity, and consequently its velocity will be diminished each second by the quantity g = 32. 16. Therefore, the time of its rise will be found by dividing its original velocity by g, that is t = v-i-g, an equation identical with [26.] Hence, the time of ascent is the same as that of a descending body, having an equal final velocity. From [29.] S = v 2 -v- 64.32, the height in feet, to which a body ascending vertically will reach, is equal to the square of its velocity divided by 64.32. 225. The results thus attained by theory are never realized in practice, on account of the friction on inclined planes, and the resistance of the air in every 0886, as ha* l>een shown in the previous section. 226. Projectiles. If a body In- hurled in an oblique or horizontal direction, as when a lall is shot from a cannon, the horizontal distance, measured from the point of <>rcc when ma alone is taken into account, hut is a variable force when the distance between two masses varies -eii-ihlv. It art- as a constant force on all l>ot> nu-asim-d : 1. By the weight of bodies. J. By the increment of velocity of falling bodies. 3. By the vibrations of a pendulum. This last point is a deduction from the following section. THE PENDULUM. 234. About the year 1581, Galileo noticed that a lamp, swinging by a chain from the ceiling of the cathedral in Pisa, performed its vibrations in equal intervals of time. This observation led him to the invention of the pendulum. It was first employed in clocks by Huyghens, in 1656. If a heavy bob, as B, Fig. 84, be suspended from a point, A, by means of a fine string, it will be at rest only when in the line of the vertical, AC. If the bob be raised to B, it will tend to move through the curve, B C, . T precisely as a ball would roll down an inclined plane of the same height, H C. The force of gravity, B G, will be par- tially resisted by the string, acting in the line B L, and the remaining component of gravity will force the ball in the line B T. Moving slowly at first, it will gradually gain in velocity, and on falling the whole height, H C, will have acquired sufficient momentum to carry it very nearly to D, an equal distance on the other side of the vertical. Thence it will return toward B, to repeat the vibrations, until the resistance of the air shall bring it to rest. This pendulum may be considered simple, although it is really compound. A simple pendulum is conceived to be a heavy material particle, suspended by a line without w r eight, and oscillating about a fixed point. G f T"' c i O L N 118 NATURAL PHILOSOPHY. 235. The motion of the pendulum, from B to D, or from D to B, is called a vibration or oscillation. The time of vibration, is the time occupied by the pendulum in describing this arc. The amplitude of vibration, is measured by the angle BAG, or by the arc B C, divided into de- grees, minutes, and seconds. The center of suspension, is the point about w r hich the pendulum vibrates. The laws of the pen- dulum may be found, experimentally, by using simple pendulums of different lengths and weights, as shown in Fig. 85. 236. Since the vibrations of any given pen- dulum are caused by gravity alone, the time of vibration will not vary with the quantity or quality of the weight suspended. Thus, if the ball c be copper and d wood, they will vibrate in the same time. Neither will the time sensibly vary if the amplitude of vibra- tion does not exceed certain limits ; because the increase in the length of the arc is so compensated by increased velocity of the fall, that the same pendulum will describe an arc of five de- grees in about the time required for an arc of five minutes. 237. The length of the pendulum is a very important consideration, for it can be proved, mathematically, that the time of vibration of a simple pendulum in a very small arc, is equal to the ratio of the circumference of a circle to its diameter (expressed by * = 3.1416) multiplied by the time of falling vertically half the length of the pendulum. Now, if we make %l equal to X in the formula [.'>().] t = V 2 S -f- above and below this point insert two bits of knitting needles, or, preferably, knife edges. The bar, made to swing from either point, will vibrate in about one second. If the vibrations from the two centers are not performed in exactly the same time, the bar may be adjusted by ele- vating or depressing the center of gravity. This may be done by placing a coil of fine wire about the bar, where patient trial shall determine it is needed. When the times of vibration from either point of suspension are the same, the distance between them is the length of the pendulum. If the precise time of this vibra- tion is known, the length of a seconds pendulum can be cal- culated. A shorter rod may be used to attain the same result. 244. Suppose such a bar to be suspended from S, and a pound weight, W, to be attached to the bar exactly at O ; then, since all the matter of the pendulum may be considered as concentrated in the center of oscillation, without regard to the quantity of matter, any addition at that point will have no influence on the time of vibration, although the bar will then have a new center of gravity, as at G'. If this weight be applied below the point O at W, its effect will be not only to depress the center of gravity, but also that of oscillation, and thereby lengthen the pendulum. If the weight is applied between S and O at \V". its effect will IM- to raise the center of ii>n, except at the center of oscillation, lengthens or shortens the pendulum. COMPENSATING PENDULUMS. 123 245, If, now, the weight is applied above the center of suspension, at W", it tends to retard the vibration of the bar, because the particles above S move in exactly opposite directions from those below. The time of vibration is thereby lengthened, and, consequently, the center of oscilla- tion is lowered. We may lower the center of oscillation to any extent by increasing the weight, or by increasing its distance above S. Every successive addition, while it raises the center of gravity, lowers the center of oscillation. If sufficient addition be made above S, the center of gravity may be made to coincide with the center of suspen- sion ; the bar will be in a state of neutral equilibrium, and if set in motion will tend to rotate continually. Now, as we can raise the center of gravity as near the center of suspension as we please, without making them co- incide, we may so increase the distance of the center of oscil- lation that it shall be below the bar. The bar may be made to vibrate in two, three, or even five seconds, which correspond to the vibration of pendulums whose lengths are 156.4, 351.9, and 977.5 inches. 246, The utility of a pendulum, as a measure of time, depends upon the perfect equality in the times of its vibra- tions. It is, therefore, essential that the distance between the centers of suspension and oscillation should be inva- riable. In ordinary clocks, heat tends to lengthen, and cold to shorten, the pendulum, and hence such clocks are apt to go too slow in summer, and too fast in winter. This ten- dency may be counteracted by raising the bob to make the clock go faster, and by lowering the bob to make the clock go slower. 247, Compensating pendulums are those which are made self-regulating, by constructinir them of two substances, in such proportions that the change in length of one upward is exactly compensated by an equal change of the other downward. 124 NATURAL PHILOSOPHY. Thus, the gridiron pendulum, Fig. 88, consists of a series of five steel bars, expanding downward, and a series of lour brass bars, ex- panding upward. In this the length of the steel bars is l - that of the brass. The mereurial pen- dulum, Fig. 89, beating seconds, lias, at the end of a steel rod, a stirrup holding one or two glass cylinders, each containing a column of mercury about 6.7 inches high. 248. The mode in which the pendulum is ap- plied to clocks is shown in Fig. 89. The pendu- lum rod passing between the prongs of a fork, /, communicates its motion to the rod, r, which oscillates on a horizontal axis, . To this axis is fixed the escapement, PP', terminated by two pro- jections, or pallets, which work alternately in the teeth of the scape wheel, S. This wheel, acted on by the weight, W, through a train of wheels (not shown in the figure), tends to move in the direc- tion of the arrow. If the pendulum is at rest, the wheel is held at rest by the pallet, P / , and with it all of the clock work. Now, if the pendulum be moved to the posi- tion shown by the dot- ted line, P is raised, and the wheel escapes from the pallet, and the weight causes the wheel to turn until its motion is arrested by the other pallet, P', which has been brought in contact with another tooth of the wheel in consequence of the motion of the pendulum. In this manner the descent of the weight, and the consequent movement of the clock-work is rcgul.-itrd by the pendulum. The faces of the pallets are slightly incliiu-d. so that each Moth of tin- wheel, Oil - Infifmlr ; hence, at Cincinnati, it should be about nine degrees twenty-five minutes per hour. THE BALLISTIC PENDULUM. 127 cricket player soon learns by experience at what point he can strike the most effective blow with his bat. In axes, ham- mers, etc., the head is made heavy, so that the centers of gravity and percussion are very near each other. As the center of oscillation is sometimes outside of the body, so, also, a hammer may be so made, or held, as to have no center of percussion within it. Such a body will expend part of its impulse in a strain upon its axis. 251. A beautiful illustration of the center of percussion is seen in the ballistic pendulum, an instrument employed to measure the velocity of pro- jectiles. This consists of a heavy mass of wood, sus- pended at the end of a long iron bar. If a cannon ball strikes the ballistic pendulum at the center of percussion, it simply makes it swing like a pendulum ; but if the im- pact is at any other point, a part of the force tends to tear it away from its axis. The velocity with which it begins to move when the cannon ball first strikes it, may be determined by observing the length of the arc through which the mass is driven ; the weight of the mass being also known, the momentum and velocity of the ball may be calculated. 252. Recapitulation. The pendulum may be simple or compound. The length of a pendulum is the distance between the centers of suspension and oscillation. The time of vibration depends, 1. On the force of gravity. 2. On the length of the pendulum. 3. On the amplitude of vibration. 128 NATURAL PHILOSOPHY. CIRCULAR MOTION. 253. Suppose a ball to be whirled in a circle, by means of a rubber cord held by the hand. The ball will tend to fly off, and will exert a certain tension on the cord, which will be resisted by the elastic force of the rubber. The ball is, therefore, revolving by reason of two forces, viz.: the impulse given by the hand, and the restraining power of the cord. Circular motion is always produced by the action of two forces, which are called the centripetal and ccntrifinjal forces. The centripetal force acts along the radii of the circle, and tends to draw bodies toward the center. The centrifugal force acts at right angles to the radii, and tends to make bodies fly farther from the center, in the direction of the tangent to the circle. In the previous example, the elas- ticity of the rubber represents the centripetal force, and the tension exerted by the ball, the centrifugal force. 254. It is only when these forces are exactly equal, that circular motion can be maintained; for if, at any time, the centripetal force is destroyed by breaking the cord, the ball will fly off in a tangent. If the centrifugal force is destroyed, the cord will draw the ball again to the hand. If either force were weakened, the ball would describe some other curve than a circle. If both forces are increased or diminished in the same proportion, the effect will be merely to increase or diminish the amount of motion. 255. If a stone be hurled from a slinf circular mo- tion. Suppose a body at the point a, to be under tin- influence <>f t\\<> CIRCULAR MOTION. 129 forces, viz.: (1.) a constant force acting at infinitely small intervals, and capable of moving the body in the direction of a fixed point, C, with a force equal to a&; and (2.) an impulsive force at right angles to the constant force, and represented both in intensity and direction by a d. Under the joint action of these forces, the body will move in the diagonal a. a', which will also measure the in- tensity with which it would continue in the same direction forever, were the constant force to cease. But the constant force acts in the second in- stant with equal intensity, o / 6 / , to- ward the point C, and, therefore, the line traced in the second instant will be a' a". In like manner, the body will pass, in succeeding instants, over lines which form the perimeter of the polygon, a a', a" a'", etc. 2s ow, as the instants of time considered are infinitely small, the perimeter of the polygon will not differ from a circle whose center is C. To determine the measure of these forces, we find, by Geometry (325), a b : a a :: a a' : ao; or, a b = a a' 2 -r- a o; but a b represents the centripetal force, and its equal, the centrifugal; a a' represents the velocity of the body, and ao the diameter of the circle in which it revolves. Therefore, the centrifugal force equals the square of the velocity, divided by twice the radius of the circle in which the body revolves : [43.] C = 2r 256. To ascertain the relation of centrifugal force to gravity, we have only to compare the spaces in feet through which a body would move in a second under gravity alone, and under the centrifugal force alone. Thus, we know that a body whose weight, or gravity, is W, will fall in one sec- ond g = 16.08 feet. Hence, W_:C ::* N. P. 9. : or, [44.] *- U6 r 130 NATURAL PHILOSOPHY. That is, The centrifugal force of a body is equal to the prod- uct of its weight by the square of its velocity j r wrond in feet, divided by 32.16 times the radius of the circle expressed in feet. 257. A different expression may be given to this formula, by employing, instead of velocity (1.) the number of sec- onds required to perform one revolution =t t or (2.) the number of revolutions performed in one second = n. Since the circumference of a circle equals 2 jt r, if v is made to represent the space described in one second, the number of seconds required to make one revolution is t = 2jtr-+-v. Whence, v 2 == 4 * 2 r 2 -j- t 2 . Substituting this value in [44.], W 4?i 2 r 2 Wr 4jt 2 [45.] = x=x Again, the velocity is the number of revolutions, or frac- tion of a revolution, made in one second; or v = 2nrn. Whence, v 2 =4 ft 2 r 2 n 2 . Substituting this value in [44.], W 4rt 2 [46.] C = X4* 2 r 2 ?i 2 =Wrn 2 X :=Wrn 2 Xl.2275. The last formula may be thus expressed : The centrifugal force of a body revolving in a circle is equal to the product of its weight by the number of feet in tJie radius of the circle, mul- tiplied by the product of the square of the number of revolutions per second by 1.2275. If, for example, a sling two feet long whirl a ten pound weight at the rate of five revolutions per second, the centrifugal force is 10 X 2 X 5 2 X 1-2275 = 613.75 pounds, or it would require that foree to re- tain it in the sling. To retain any weight in this slinniit the pressure in a like manner to those of a third series, and they onward, PRESSURE. 137 so that every molecule in the vessel will both receive and transmit an equal pressure. Therefore, each piston will be thrust outward with a force proportional to the number of molecules beneath it, and as these molecules are of the same size, the pressure on each piston will be proportional to its area; 1 will be pressed outward with a force of one pound, 2, by a force of two pounds, 3, by three pounds, etc. It will be found necessary to apply the amount of force thus indicated to keep the pistons in place. Any portion of the sides of the vessel, or any solid immersed in the fluid, will in like manner sustain pressure in pro- portion to the area of its surface. 268. It is also evident that the pressure . J^^ exerted on the surface at any point must be \* ^~ perpendicular at tiiat point, for if it is not, it may be resolved into two portions, one F|i . perpendicular and the other parallel to the surface of these, the former would exert pressure and the latter would produce motion in the fluid. 269. From similar experiments, Blaise Pascal deduced this important law: 1. Fluids submitted to pressure transmit it undiminished in every direction. The following corollaries are a necessary consequence: 2. The pressure sustained by any surf ace is proportional to its area. 3. The direction of the pressure at any point is perpendicular to the surface at that point. No apparatus can perfectly demonstrate these laws, because no liquid is without weight. A rough demonstration can be had by fitting open tubes to two necks of a Woulfe's bottle full of water, and thrusting a cork into the other neck. The height to which the water will rise in the tubes will be proportionate to the force of the thrust. 138 NATURAL PHILOSOPHY. EFFECT OF GRAVITY. 270. Fluids also exert pressure in consequence of their weight. Suppose the vessels A B C D filled with any liquid to the level C D, and con- sider each divided into an infinite number of strata by horizontal planes, in- dicated by the lines of the diagram. Each stra- tum may then be con- sidered as a cylinder ex- erting a pressure on its base equal to its own weight. By Pascal's law the weight of each stratum above will be transmitted to each stratum below in the ratio of their areas, so that the pressure sustained by any section, as A B, G L, G R, will be equal to the weight of a column of liquid whose base equals the area of the section and whose height equals its depth. 271. Several important conclusions may be deduced from this: 1. The pressure on the bottom of a vessel is independent of the form of the vessel. This may be illustrated by Haldat's apparatus, Fig. 101. Fill the bent tube with mercury to the level c, and pour water in the larger 1 till it reaches the index rod o. The water will press the mercury as high as the ring a. Now replace the larger vessel M by the smaller P, and fill with water to the index rod, when the mercury will rise to the same height as l.efoiv, thus showing that the pressure is independent of the quantity of water, or of the shape of the vessel. 2. The pressure is proportioned to the density of the liquid. In the last experiment, if the depths of the two liquids are measured, it will !>< found that the water column is l.".G times longer than the column of mercury. UPWARD PRESSURE. 139 FIG. 101. 3. The pressure exerted by a fluid is proportional to its depth. Tie a piece of sheet rubber over one end of a long open tube. On pouring water into the tube the rubber will be distended in proportion to the depth of the water. 272. The upward pressure of liquids is easily shown by reversing the last experiment : i. e. by thrusting the closed end of the empty tube into water, when the rubber will be driven into the tube farther and farther as the depth increases. It is generally demonstrated by taking an open tube having disks of lead, or leather closely fitting the lower end. Support the disk by a thread until the tube is plunged in a vessel of water. The disk will then be retained in its place by the upward pressure. If now the tube be carefully filled, the disk will FIG. 102. 140 NA T URA L PHIL OS OPH T. FIG. 103. not fall off until the sura of the weights of the interior column and the disk exceeds the weight of the exterior column. 273. The lateral pressure of liquids is shown by the velocity with which they escape from orifices at different depths, A fine illustration is shown in Fig. 103. This consists of a tall jar with a stop-cock near the base, and made to float on the surface of some liquid. If the jar he filled with water, and the stop-cock be closed, the lateral pressures at L and I/ will be equal. Hence, equilibrium will be preserved and the jar will remain at rest ; but on opening the cock, the pressure at L is removed, and the lateral pressure at I/ will be effective in driving the float in the direction of the arrow and opposite to the course of the stream. 274. The pressure on the bottom of a vessel is equal to the weight of a column of fluid having the same base as the vessel, and a height equal to the depth of the fluid in the vessel. If the fluid is water, since a cubic foot of water weighs 62.42 Ibs, the total pressure equals the product of the area of the base in feet, by the depth in feet, and this by 62.42. Thus, suppose a cubical vessel two feet on each side. The pressure on the bottom will be t-qual to 2 X 2 X 2 X 62.42 = 499.36 ll.s. The pressure upon a body sunk to any depth may be calculated in the same way. 275. The lateral pressure may be computed for the whole side, or for a piston in the side, by the following rule: The lateral pressure upon any >iiriar<- is equal to the weight of a column of the fluid, the area of \vho><- la.^- equals the area of tin- .-urfarr, and whose height is the FLUID PRESSURE. 141 depth of the center of gravity of the surface below the level of the fluid. The center of gravity will be at the mean depth of the surface. Suppose a square gate, C, in a canal lock lias its upper edge 9 feet, and its lower 11 feet from the surface. The area will be 4 feet, the mean depth 9 -f- 11 -H 2 = 10 feet: hence, the pressure will be 4 X 10 X 62.42 = 2496.8 tt>s. It i> important to observe that this pressure has nothing to do with the length of the vessel in the direction A B, or in other words with the amount of back-water; so that the gates of a canal lock sustains a pressure proportioned only to the depth of water and its own area. 276. Since the area of any given body remains constant, the fluid pressure which it may be made to sustain, will vary as the depth. A body submerged in fresh water sustains a pressure on each square incli at the depth of one foot of 62. 42-=- 144 = 0.4335 pounds. The compression of water is so slight that even for oceanic depths the pressure on each square inch may be taken without great error in multiples of this factor. Thus the pressure on each square inch at 10 feet will equal 4.335 pounds; at 100 feet 43.35 pounds; at 10000 feet 4335 pounds, or over two tons. Empty bottles hermetically sealed have been sunk in the open sea with the uniform result that, at no very great depths, either the bot- tles have been crushed, or the corks have been forced through their in k-. So pearl divers find it impossible to pass beyond a certain depth. When a ship founders at sea, the enormous pressure at great depths forces the water into the pores of the wood, and so increases its weight that no part ever comes again to the surface. 277. Pascal demonstrated the same fact for vessels con- taining fluids, in 1647. He fitted to the upper head of a strong cask a tube of small bore about forty feet long. The cask being filled with water he succeeded in bursting it 142 NATURAL PHILOSOPHY. by pouring a very small quantity of water into the tube. As an ounce of water will fill a tube j 1 ^ of an inch in diameter and 40 feet long, even that quantity would have sufficed for a tube - s of an inch in diam- eter has an area of only ^TT f a square inch, so that the ounce pressure would multiply itself 277 times for each square inch on the vessel, which becomes 17.34 pounds for each inch. Either head of an eight gallon cask would have to sustain about 2500 pounds, and the total pressure on the cask would have exceeded 15,000 pounds. The pressure would have been the same whatever the diameter of the tube, provided the length was unchanged : thus, had the tube been an inch in area, the pressure must have been 0.4335 X 40 = 17.34 Ibs. to the square inch. Pipes conveying water from high reservoirs should be of great strength. A four-inch pipe, laid 100 feet below the level of the reservoir, sustains an inter- nal pressure of more than 6000 pounds on each foot of its length. When a drain beeomas clogged, the pressure of the accumulated water is sometimes sufficient to burst it. 278. As fluid pressure is transmitted undiminished in all directions, it will not be affected by bends in the tube. The hydrostatic belloivs consists of two boards, AB, united by stout leather, and a small tube, c, communicating with the interior. Water poured into the tube will lift the upper hoard with a force proportioned to the height of water in the tube. Each foot in height represents a pressure of 0.4335 pounds to the square inch: then-Ion-, if the upper board has an area FIG. KM;, UN;. THE HYDRAULIC PRESS. 143 of one hundred square inches, and the height of the tube is three feet, the weight capable of being supported on A will equal .4335 X 100 X 3 = 130.05 pounds. 279. If A had been made to rise toward an immovable bar placed above it, any substance between the board and the bar would have been compressed with the force of 43,35 pounds for every foot in the height of the tube. By increasing the length of the tube, the pressure will soon become great enough to rupture the bellows. The same effect may be produced, if, instead of lengthening the tube, a piston is employed to force water down the tube. By Pascal's law, a pressure equal to that upon the piston would be communicated to each equal area in the bellows. 280. Bramah's hydraulic press is constructed on this principle. FIG. 107. Within the collar of the iron cylinder, B, a cast iron ram, P, worka water tight. The substance to be pressed is placed between the ram, 144 NATURAL PHILOSOPHY. P, and the immovable plate, Q. Water is brought by a force pump into the small cylinder, A, and is thence driven by the piston, r, through the tube, K, into the larger cylinder. The advantage gained will be in proportion to the areas of the two cylinders. If the large cylinder is one hundred times the area of the small cylinder, one pound applied at the piston will produce a pressure of one hundred pounds on the ram. The efficiency of the press is further increased by the handle, M, a lever of the second class. If the distance of the fulcrum to the applied force is ten times the distance to the weight, a power of one hundred pounds will transmit one thousand pounds to the piston, and tend to raise the ram by a force of one hundred thousand pounds. 281. In this press very little power is lost by friction, and, practically, the advantage gained is limited only by the strength of the materials. Like all other machines, it is governed by the law of virtual velocities (157) and works very slowly. In the example supposed, one hundred parts of water driven out of the small cylinder would raise the ram but one part. The hydraulic press is used wherever great power is to be transmitted through small space, as in extract- ing oils from seeds and crude fats, in pressing cotton, hay for shipment, and in various other industrial uses. Two of these machines were employed to raise the immense tubes of the Britannia Bridge to their proper elevation. Such was the force employed to drive the water into the cylinder, that it was sufficient to raise a jet twenty thousand feet high, or over the peak of Chimbora/o. With such pressures, the weight of the water in the smaller cylinder becomes inconsiderable. EQUILIBRIUM OF LIQUIDS. 282. A liquid is not at rest unless its particles ar<> somehow restrained by a vessel or its equivalent. When the liquid is in equilibrium, the force of gravity tends to bring each molecule as near the earth's center as possible. This condition i- att;iincl only when the surface is perpen- dicular to the force of gravity. EQUILIBRIUM OF LIQUIDS. 145 283. As two verticals, near each other, are sensibly parallel, any liquid surface included between them is level or horizontal. Whatever be the shape of the vessel, its surface will be level. In :i cnminon teapot, the water in the pot is always at the same level as that in the spout. So, a liquid poured into any system of communi- cating vessels, will rise to the same level in each. A common ex- FIG. 108. pression for this fact is " Water always seeks its lowest level." On this principle, water is conveyed from reservoirs through pipes to supply cities: the water will rise in the pipes to the exact level of the reservoir, and would rise to the same level in fountains, were it not for the resistance of the air, and other impediments to motion. FIG. 109. 284. Many natural phenomena depend on the same principle. The crust of the earth is made up of various materials, arranged in strata, as in the diagram. Some of N. P. 10. 146 NATURAL PHILOSOPHY. these, as clay or dense rock, can not be penetrated by water; others, as gravel or sand-stone, will permit it to trickle through them. Let the shaded portions of the dia- gram represent the impermeable strata, and the light por- tions the porous strata. The rain falling upon the surface at dcbe, will seek its lowest level, and, as it can not penetrate the underlying rock, will accumulate in whatever natural basins it affords. Thus, 1. Whatever rain falls upon the surface b will sink as low as possible, and finally come to the surface as a spring, at s. 2. The rain falling upon c and d will find a natural reservoir at waudw', the overflow at w passing to the lower level at w': A shaft sunk to either of these points would make a well. 3. The rain falling upon e would be confined between two impervious strata, one of which would prevent its pass- ing to lower levels, and the other prevent a natural outlet. For this reason it must descend to its lowest level between the strata. A tube sunk through the intervening strata to the porous stratum, as at A, would allow the water to rise in it to a height proportioned to the amount of accumulation in the reservoir. Such wells are Artesian, because they have been long employed for obtaining water at Artois, in France. The Artesian well at Louisville, Ky., was sunk to the depth of two thousand and eighty-six feet, and delivers, every twenty-four hours, at a height of one hundred and seventy feet above the surface, over three hundred thousand gallons of water, at a constant temper- ature of 76.5 F. 285. A spirit level is used to determine horizontal lines, B a . _^ and operates on the principle that water always seeks its level. Flli - "" This consists of a closed glass tube, slightly curved, and nearly filled with sonic liquid not easily fro/en. The tnlx- is then so arranged, in a bra.-s ca-c, that when the apparatus is perfectly horizontal, the small bubble of air, B, will lie exactly at the highest point. BUOYANCY OF LIQUIDS. 147 286. As the verticals drawn at two distant points incline toward each other, large surfaces of liquids are curved, to correspond with the general form of the earth's surface. The surface of a large body of water is easily proved to be convex, by the phenomena presented by ships sailing from the shore. The hull first disappears, then the lower sails, and so on, until, at last, the whole sinks below the horizon. The amount of curvature increases as the square of the distance, as shown by the following table : Distance in miles 1234 567 89 10 Curvature in feet .667 2.67 6. 10.67 16.67 24. 32.67 42.67 54. 66.67 From this it appears that if the eye of the observer were at the water's edge, an object eight inches high would be visible at the distance of a statute mile. At the distance of ten miles, the height of a visible object would be over sixty-six feet. A mountain, a mile high, could be seen at a distance of almost ninety miles. 287. As the earth revolves on its axis, the surface of the ocean at rest is actually perpendicular to the resultant of gravity and the centrifugal force. Under 'the influence of gravity alone, the surface of the ocean "would be spherical, but in consequence of the centrifugal force, it is spheroidal, being elevated at the equator and depressed at the poles. This spheroidal surface is the ti*ue level of the ocean ; a horizontal plane at any point is the apparent levd. 288. The attractive force of the sun and moon constantly disturbs the true level of the ocean ; the attractive force of the earth as constantly tends to bring the water to a level; hence the periodical oscillations of ebb and flow in the tides. BUOYANCY OF LIQUIDS. 289. When any solid is immersed in a fluid, every por- tion of its surface will undergo pressure, proportional to its depth. The horizontal pressures on the sides of the cube, Fig. Ill, will all be equal and opposite, and will 148 NATURAL PHILOSOPHY. have no tendency to move the solid in any direction. The upper face will be pressed downward by the column MABN, and the lower face will be pressed upward by the column MCDN. The solid is, there- fore, urged upward by a force equal to the difference between these two pressures, which is evidently equal to the weight of the column of the fluid having the same base and the same This force is called the buoyant effort Fio. ill. height as the solid, of the fluid. Now, as the force of gravity tends to lower the body, and as the buoyant effort tends to raise it, the effect of buoyancy will be to lessen the weight of the body. Conse- quently, a solid immersed in any fluid loses an amount of weight equal to the weight of an equal volume of the fluid. 290. This principle was discovered by Archimedes about 230 B. C. It may be verified by hanging to one arm of a balance a hollow cylinder, A, having a solid cylinder of copper, B, which exactly fits within it, suspended from the scale pan by a hook. Having first counter- poised the beam by weights put in the other scale pan, immerse the copper mass, B, in water. The cylinder will then lose a portion of its weight, and the equilibrium will be destroyed. On filling the bucket, A, with water, the equilibrium will be again restored; thus proving that the loss of weight occasioned by the immersion of the solid in water, is exactly equal to the weight of an equal volume of water. The same truth is exemplified by the fact that a ma-s i,f -tone can be more easily lifted at the bottom of the sea than on land, bein# lighter by the weight of an equal bulk of water. FLOATING BODIES. 149 291. When different solids are thrown into a given liquid, (1.) those that are heavier than an equal volume of the liquid will sink; (2.) those that are of the same weight for equal volumes will remain at rest in any position in the liquid ; (3.) the others will float. When a solid floats on a liquid, the weight of the solid will be exactly equal to the buoyant effort of the liquid which it displaces. Hence, A floating body displaces its own weight of the fluid. This principle may be proved by the apparatus in Fig. 113, which represents a vase with an L tube, to the base of which a stop cock, r, is attached. Pour in an amount of any liquid, and mark the level by the ring, a. Now place a floating body in the liquid it will raise the level of the liquid. By means of the stop cock, r, draw out enough liquid to reduce the level again to a. The weight of this liquid will be found exactly equal to that of the floating body. Many solids that sink in oil or alcohol will float on water ; some woods that sink in fresh water will float on salt water; iron and copper will float on mercury, but gold and platinum will sink in it. FIG. us. 292. If liquids which do not mix are poured into the same vessel, the lighter will rise to the surface, as oil does upon water. An interesting experiment may be made by pouring several liquids, of different densities, into a tall jar; as coal-oil, or naphtha ; alcohol reddened by cochi- neal ; water saturated by carbonate of potassa and tinged with litmus ; and mercury. These, shaken together, will come to rest arranged in the order of their densities. The experiment may be fur- ther varied by floating balls of cork, wax, wood, and glass on the different surfaces. -== 293. If dense solids are fashioned into FlG - 114 - thin-walled vessels, so as so displace a volume of water whose weight is greater than their own, the solids will float; 150 NA T URA L PHIL SO PHY. thus, iron, wrought into ships, not merely floats, but, as in the Great Eastern, has an enormous capacity for carry- ing its machinery and cargoes. 294. The Cartesian diver well exhibits the principles of flotation. This toy, which is made in various shapes, con- sists, essentially, of a figure connected with a hollow bulb, having a small opening be- neath. The bulb is filled with water and air to such an extent that, when placed in a vessel nearly full of water, it just floats. The mouth of the vessel is tightly covered with sheet rubber or moist bladder. On applying pressure to the rubber by the fingers, several facts may be noted. 1. That pressure is transmitted undiminished. The air trans- mits the pressure to the water, and this compresses the air in the bulb, and drives the water within it. 2. That the pressure is in all directions; for the result is the same in every position of the vessel. 3. That the pressure is as the depth ; for less pressure is required as the figure sinks. 4. Before the pressure is applied, the figure is lighter than the water and floats; on forcing water into the- hulb, it becomrs h. ;i\i. i and sinks. By carefully regulating the pressure, the figure inny In- brought to rest at any depth. 295. In like manner, fishes are enabled to float at any depth by expanding or contracting an air bladder with which they are provided. The weight of the human body is about the same as that of an equal bulk of water. When the lungs are well filled with air, the body i.- lighter, FIG. in. CENTER OF BUOYANCY. 151 but, when the air is expelled, the body is heavier than water. Therefore, if a person lies on his back in water, so as to leave only his mouth and nostrils out of water, he is not likely to sink. Drowned persons rise when enough gases have been generated through decomposition to render the body specifically lighter than water. The buoyancy of swimmers is increased by the use of life preservers, which are bags filled with air or cork. As the buoyant effort of a liquid increases with its density, ships draw less water in the ocean than in fresh water; so, also, it is easier to swim in salt water than in fresh. On the same principle, farmers determine the saltness of brine by observing whether an egg or a potato will readily float in it. 296. As the weight of a solid may be considered as emanating from its center of gravity; so the upward press- ure of a liquid acting upon a floating body, may be con- sidered as acting at a single point, which is called its center of buoyancy. This point will evidently coincide with the center of gravity of the liquid displaced, and may be re- garded as the center of support of the floating body. Thus, in the figure, G represents the center of gravity of the solid, and O the center of buoyancy of the fluid. A floating body will be in equilib- . * FIG. 115. num only when the cen- ter of gravity and the center of buoyancy are in the same vertical line. 297. The equilibrium will be either neutral, unstable, or stable. 1. The equilibrium is neutral, when the form of the body is such that the relative positions of the centers of gravity and buoyancy can not be changed. This will be the case with spheres of uniform density. 152 NATURAL PHILOSOPHY. 2. The equilibrium will be unstable, when the center of gravity is over the center of buoyancy. The least force will then overturn it. 3. The equilibrium will be stable, when the center of gravity is under the center of buoyancy. If the body is disturbed from this position, it will constantly tend to re- sume its original position. 298. The stability of ships increases with the breadth of the part submerged, and also increases in proportion as the center of gravity is lowered. For this reason, vessels must either carry heavy cargoes over their keels, or make up the deficiency by ballast. In small boats, the equilibrium is stable so long as the passengers are kept near the bottom of the boat; but when they rise, the center of gravity is elevated, the equilibrium is thereby rendered unstable, and any unguarded movement will overturn the boat. SPECIFIC GRAVITY. 299. To determine the specific gravity of a substance, it is necessary (1.) to select some standard for comparison; (2.) then to find the weights of equal volumes of the stand- ard and the body under consideration ; and, finally, (3.) to divide the weight of the body by the weight of an equal volume of the standard. The quotient will be the specific gravity of the substance. 300. The standard usually taken for aeriform bodies is air, but it is probable that hydrogen will soon come into general use. The standard for all liquids and solids is distilled water. As all bodies vary in size with the changes of the weather, all observations should be reduced to the same conditions of temperature and atmospheric pressure. The normal pre.-Hin- adopted in this country is thirty inches of the barometer; in France it is 760 in m. 29.922 inches. This item may be neglected, except in the case of aeriform bodies. SPECIFIC GRAVITY. 153 The usage respecting temperature is still unsettled : many retain the old English standard, 60 F., although the ten- dency is to adopt the French, which is the freezing point of water, 32 F., for all bodies except water, which is taken at 39.2 F., its point of greatest density. Observa- tions at any other temperature are easily reduced to the normal by means of tables, specially prepared for that pur- pose. 301. Having this standard, the formula for the specific gravity of solids and liquids becomes, rj - n Weight of given volume of substance L4/ ' J Weight of equal volume of water ~~ Spe< lfic %^' When any two of these are given, the other can be found. Therefore : (1.) The weight of any given volume of a body equals the specific gravity of the body multiplied by the weight of an equal volume of water. (2.) The weight of any body divided by its specific gravity will equal its loss of weight in water, or equal the weight of an equal volume of water. (3.) As one cubic inch of water weighs 252.456 grains, the volume of a solid may be found by dividing its loss of weight in water by 252.456 grains. The quotient will be the volume of the solid expressed in cubic inches. 302. The specific gravity of solids is found by the appli- cation of the principle of Archimedes (289). Weigh the body in air (= W), then suspend it by a hair and find its weight in water (=W). The difference in weight is the weight of an equal volume of water (= W W'). Therefore, the specific gravity may be found by dividing its weight in air by its loss of weight in water. [48.] Sp. gr. =W-s- (W W). Thus, a mass of lead weighing a pound in air weighs 14.6 ounces in water. Its specific gravity is, therefore, 16 * (16 14.6) = 11.4. 154 X.I T URAL PHILOSOPHY. 303. If the body is lighter than water, sink it by attaching a heavy mass, whose weight in air and in water is known, and find the weight of the combined bodies in air and in water. The loss of the combined bodies is evidently the weight of water equal to their united volume. If the loss sustained by the heavy body alone is taken from this, the remainder will be the weight of water equal to the bulk of the lighter body. Therefore, the weight of the lighter body in air divided by this remainder will give its specific gravity. Thus, attach a pound of lead to two ounces of cork. The weight in water will be 8.6 ounces. The loss of both bodies is 9.4 ounces, but as the previous example shows the lead loses 1.4 ounces, the weight of a volume of water equal to the cork is 8 ounces. There- fore the specific gravity of the cork is 2 -f- 8 = .25. 304. If the solid is soluble in water, weigh it in some other liquid, and allow for the difference between its specific gravity and that of water. Thus, 131 grains of nitrate of baryta lost 32 grains when weighed in absolute alcohol, having a specific gravity of .8. Its specific gravity, as compared with alcohol, is 131 -=- 32 = 4.1 ; then 4.1 multi- pi it -d by .8, the specific gravity of alcohol, equals 3.28, the specific gravity of the salt. 305. The specific gravity of liquids is found (1) by the specific gravity bottle. Counterpoise a small flask by a weight in the other arm of the balance, and w r eigh exactly one hundred or one thousand grains of water into the flask. Mark the volume of the water by a line cut in the glass. Now empty out the water, fill the flask as high as the line with the liquid whose specific gravity is sought, and weigh. The weight of the liquid in grains divided by one hundred or one thousand is its >|M-ifir gravity. The figure represents an clf^aiit 11,-,. form of the one hundred grain flask. Thus a loo grain flask contains 79.88 -rains of alcohol; hence, the specific gravity of the alcohol is 0.7938. HYDROMETERS. 155 (2). By the specific gravity bulb. Suspend any insoluble solid by a hair, and, having determined its weight in air, find its loss of weight in water, and also in the liquid. The loss of weight is equal to the weight of the fluid displaced by the same volume: hence, the loss in the liquid divided by the loss in water equals the specific gravity of the liquid. The figure represents a glass specific gravity bulb containing mercury. It can easily be made out of a small test tube, and loaded with shot instead of mercury. Suppose the air weight of the bulb is 480 grains; its water weight, 400 grains; its weight in alcohol, 416 grains. The losses will be, re- spectively, 80 and 64 grains ; then 64 -=- 80 = .8, the specific gravity of alcohol. Y\G. 117. 306. Either of these meth- ods affords accurate results, but for rapid determination, hydrometers are used. These instruments are of two kinds. (1.) Hydrometers of constant volume. (2.) Hydrometers of constant weight. 1. Nicholson's hydrometer. This instrument, shown in Fig. 118, consists of a hol- low cylindrical vessel, B, to which is attached a lead basket, C. The basket is made heavy to bring the ap- paratus into a condition of stable equilibrium. A wire FlG - 118 - at the top of the vessel sup- ports a pan, A, and has a fixed point, O, marked on it. To use the apparatus for determining the specific gravity 156 NATURAL PHILOSOPHY. of liquids, it is only necessary to determine the total weights required to bring the hydrometer to the point O, in distilled water, and in the given liquid. Thus, suppose the hydrometer weighs 1000 grains, and it in- quires 500 grains additional to sink it in water and 200 grains to sink it in alcohol. Then, the total weights are 1500 and 1200 grains. 1200 -T- 1500 = 0.80, the specific gravity of the alcohol. It may also be used for solids. As before, suppose that 500 grains will sink the hydrometer in water to the fixed point, O. Place any solid, not too heavy, as a bullet, on the pan, A, and add weights until the hydrometer sinks to O. It is evident that the weight of the body and the added weights are together equal to 500 grains. Then, if 100 were added, the weight of the body, in air, must be 400 grains. Now place the body in the basket, C; of course, as the body is submerged, it will be buoyed up by a weight equal to the volume displaced. It will be necessary to make good the loss, by adding weights to the pan, A, enough to bring the hydrometer to the fixed point once more. Suppose 50 grains are required; then, as this equals the weight of a volume of water the size of the solid, 400 -r- 50 = 8, the spe- cific gravity required. When the solid is lighter than water, it is necessary to fasten the solid to the basket, C, before submerging it. 307. A floating body has a constant weight, but dis- places a greater volume of light than of heavy liquids. Hence, if these relative volumes may be found, the specific irravity of any liquid may be calculated by dividing the volume which a floating body displaces in water, by the volume which it displaces in the given liquid. On this principle hydrometers of constant weight are constructed. The common form consists of a irla-s stem, near the bot- tom of which are blown two small bulbs. Sonic mercury or shot i< placed in the lower bulb, to Bfcrve as ballast, and the point to which the inMrumcnt sinks in pun- water is marked on the stem. It is then graduated ly placing the BE A UME'S H YDR O METER. 157 FIG. 119. instrument in a liquid whose specific gravity is known; the point to which it sinks is marked, and the intermediate space subdivided into a scale of degrees, according to the fancy of the maker. As a long stem would be inconvenient, it is customary to have two hy- drometers, one for liquids lighter than water, in which the zero point is near the bulb, and the other for heavier liquids, with the zero point at the top of the stem. 308. Thus Beaume's hydrom- eter for liquids heavier than water, sinks in pure water to the zero mark near the top of the stem ; in a solution containing fifteen parts of salt to eighty-five parts of water, it sinks to the mark 15. All the subdivisions of the stem are of the same size as those between and 15. As the specific gravity of the salt solu- tion is known to be 1.1095, the specific gravity correspond- ing to any degree may be determined. Let x equal the volume of water equal to the weight of the instru- ment to the zero point; then x 15 will be the volume of an equal weight of the salt solution. Therefore, x-*-(x 15) = 1.1095, from which, x, the number of equal parts displaced by water is found to be 152. The number of equal parts displaced by any other liquid will be 152 n, in which n represents the degrees on the scale. Conse- quently, the specific gravity corresponding to any degree on the scale will be found by the formula 152-=- (152 n} = specific gravity. For liquids lighter than water, Beaume made the zero point cor- respond to a solution containing ten per centum of salt, and marked the point at which the instrument floated in pure water as 10. By a similar calculation to that previously employed, the formula for the hydrometer for liquids lighter than water, is found to be: specific gravity = 146 -=- (136 + n). Alcohometers, lactometers, etc., have scales arranged to 158 NATURAL PHILOSOPHY. show the per cent, by volume or by weight of the liquid in a given solution. 309. The specific gravity of a gas is always found by direct weighings of equal volumes of air and of the gas. For this purpose, a large flask is weighed (1.) when en- tirely empty ; (2.) when full of air, and (3.) when full of the gas in question. The weight of the gas divided by the weight of the air, will be the specific gravity required. The accurate determination of the weights of aeriform bodies is attended with many difficulties, which can not be detailed here. As gases have weight, the principle of Archimedes applies to bodies weighed in them, as well as in other fluids. 310. The practical applications of specific gravity are numerous and important. It enables the manufacturer to know what degree of concentration a solution, or an acid, has reached. Thus, a Beaume's hydrometer stands in a well manufactured sirup at 35, and in strong sulphuric acid at 66. It often enables the merchant to determine the purity of the articles offered. Thus, the value of ardent spirits is dependent on the proportion of alcohol they con- tain. This is indicated at once by the alcohometer. 311. The famous problem offered Archimedes was to determine the purity of King Hiero's crown. Suppose the crown to have been an alloy of gold and silver, weighing 22 ounces in air, and losing 1.5 ounces in water. The general solution of this problem, as applied to any alloy, gold nugget, or other mineral, is as follows: Let M be the mass of the body, and m its specific gravity. Let H be the mass of the heavier substance, and h its specific gravity. Let L be the mass of the lighter substance, and I its specific gravity. Then, M = H -f- L. Since the volume of a substance equals its mass divided by its specific gravity, M IL REG API TULA TION. 1 59 From these two equations, it is found that - h The specific gravity of the mass can be determined the usual way ; the specific gravity of the components may be found by tables, or ascertained from fragments of the body. The proportions of the ingredients may then be found by the formulas. In the case of the crown as supposed, the gold, being the heavier, is found by the first formula. 312. Recapitulation. I. Liquids are both compressible and elastic. II. They transmit external pressure in every direction. 1. Undiminished. 2. Perpendicular to their surfaces. 3. Proportional to their areas. III. They produce pressure by their weight, and transmit this as if it were an external pressure. IV. A liquid always seeks its lowest level. The surface of a liquid in equilibrium is horizontal. 1. At any given vertical, an apparent level. 2. Between distant verticals, a true level. V. The upward pressure of a liquid upon a solid, wholly or par- tially submerged, is its buoyant effort. This is always equal to the weight of the fluid displaced. 1. A submerged solid loses weight, equal to the weight of the fluid of the same volume. 2. A floating solid loses all its weight, and displaces a volume of fluid equal to this weight. VI. The specific gravity of bodies is found by comparison with water or air. 1. By the relative weights of equal volumes. 2. By the relative volumes of equal weights. 160 NATURAL PHILOSOPHY. HYDRODYNAMICS. 313. If a vessel be filled with any liquid, the pressure at any point will be proportioned to its depth below the sur- face. Hence, if apertures, r, g, m, n, p, be made in the vessel, the liquid will flow out with unequal velocities, being less for r than for any point below it, and equal for any two points, as p and v, at the same vertical depth below the surface. FIG. 120. But the velocity does not increase in the simple ratio of the depth. The jet at v will tend to rise to the level at h, and fall- short of it only because of friction, the resistance of the air, and the weight of the particles falling back. If, then, the velocity at v is >uf}i-i-iit in carry the liquid through the vertical distance, hv, in opposition to gravity, this velocity must be equal to that which a body would acquire in falling through the same space. If the aperture were in the bottom of the vessel, the velocity of the escap- ing liquid would he the >ame as if it had i'allen freely through the vertical depth of the liquid above the orifice. MOVEMENTS OF LIQUIDS. 161 As the same fact is true of any aperture in the side of the vessel, the laws of escaping liquids are comprised in the following : THEOREM OF TORRICELLI. Particles of liquids, flowing from an aperture, Jiave Hie same velocity as if they had fallen freely in vacuo from a height equal to the vertical distance of the surface of the liquid above tfie center of the aperture. This distance is called, technically, the head or charge. 314. The velocity due to a body falling through any given height is expressed by the formula [28.] v = V 2 gh. As the factors 2 g are constant for the same place, the velocity ivith whidi a liquid escapes varies as tJie square root of Hie head. If we assume # = 32.16, the actual velocity of the liquid may be calculated by the formula v = 8.02 I/A. Conversely, [49.] 7i = v 2 H- 64.32: hence, if the velocity is known, we may calculate the head due to the velocity. As water and mercury would fall, in vacuo, from the same height in the same time, so they, or other liquids, will flow with the same velocity under the same head : there- fore, the velocity is independent of the density of the liquid. 315. The course of a stream, spouting out in any other direction than the vertical, is that of a parabola, and is governed by the law of projectiles. The range of a hori- zontal jet is easily calculated. For example: if the jet, g, is four feet below the surface, the velocity due to the head, h, is sixteen feet per second. If its elevation above the point where it strikes, 6, is nine feet, it will be three-fourths of a second in falling. Inasmuch as these two motions do not interfere with each other, the range will be found by multiplying the velocity by the time. (16 X J = 12.) The calculation may be simplified by the use of the following formula: R 2V^HE, in which R represents the range, H the depth below the surface of the liquid, and E the vertical distance of the aperture above the point upon which the .stream falls. N. P. 11. 162 NATURAL PHILOSOPHY. As H and E are parts of the same perpendicular, the value of R will he greatest when H = E. Therefore, the range will be greatest when the aperture is at the middle point. Further, since the product of H and E determines the range, their values may be interchanged without altering the value of K; therefore, two jets at equal distances above and below the center have the same range. These conditions are shown in the figure. 316. To calculate the volume of liquid discharged from- an orifice in a given time, multiply the area of the orifice by the velocity of the stream per second, and, then, this product by the number of seconds. Thus, if the jet g have an inch area, there will issue, in one sec- ond, a prism of water one inch in area and sixteen feet long, the contents of which is 1 X (16 X 12) = 192 cubic inches. If the given time be three minutes (=180 seconds), the discharge will be equal to 192 X 180 cubic inches, or twenty cubic feet. 317. The velocity of discharge will not be constant unless the liquid is kept at the same level. If a cylindrical vessel is allowed to empty itself through an orifice at the bottom, the velocity will be uniformly retarded as the sur- face of the liquid sinks. When motion, uniformly retarded, conies to an end, the average velocity is half the initial velocity (215) ; consequently, the quantity of liquid dis- charged from a vessel allowed to empty itself, is just half the quantity that would have been discharged in the same time if the original head had been maintained. Conversely, the time required to empty an unreplenishcd vessel is double the time required to discharge the same quantity of liquid if the original head is maintained. 318. The results thus given by theory are never attained in practice. Only the central part of the jet attains the theoretical velocity. The outer particles converge with less velocity, and, by their interference, retard the flow. By suspending in water small particles of amber or litmus, this convergence can be exhibited by the movement of the particles. In consequence of the interference of the cur- r/-:XA COX TRACT A. 163 Fio. 121. rents, the jet contracts on leaving the orifice, and at a distance from the orifice equal to half its diameter, the section of the stream is only .64 the area of the orifice. The point of greatest contraction, VC, is called the vena contracta. If the wall of the vessel is a thin plate, the area and head of the vena contracta must be considered as the real orifice in calculating the volume of liquid discharged. If the wall of the vessel has considerable thickness, or if a short tube is attached to the orifice, the rate of discharge is increased. A cylindrical tube, or adjutage, whose length is four times its diameter, in- creases the flow to eighty-four hun- dredths of that required by theory. The effect is still greater (.92) if the discharge tube is made conical both ways, first contracting like the vena contracta and then widening. On the other hand, if the discharge pipe projects within the vessel, the veloc- ity is impeded. 319. The lateral pressure ex- erted by a liquid in motion, is always less than when at rest. If water flows vertically through a long cylindrical pipe, it will ^ exert no lateral pressure. Suppose a reservoir of water to be connected by rubber tubing con- trolled by a clamp, C, to a pipe which is connected with a cistern having a discharge pipe, tin- pipe, and to the cohesion of the particles of the liquid. The re.-iManre to the flow incn-asrs, (1.) with the length of the pipe; (2.) with the number of bends and obstruc- RIVERS. 165 tions; (3.) as the diameter is diminished; and (4.) very nearly as the square of the velocity of the stream. The rate of discharge diminishes as the resistance increases, con- sequently, unless a large allowance is made for the resistance, the quantity delivered will fall short of the estimate. Under ordinary circumstances, the diameter of the discharge pipe should be at least one-half greater than that required by theory. 321. The size of rivers depends on the physical character of the countries drained by them. Their velocity is de- pendent on (1.) the volume of water to be discharged; (2.) the shape of the channel, and (3.) the slope of the bed. Thus the velocity of a river is greater during freshets than in dry seasons, and is greater in narrow and straight channels than in a broad or winding bed. By reason of the friction of the banks the velocity is greatest in mid channels, a little below the surface, and least near the banks. As the lateral pressure diminishes with the velocity, the more sluggish particles at the sides press upon the central portions, and thus heap them up, to produce equi- librium. This renders the surface slightly convex. 322. The smallest inclination capable of giving motion to water, is nearly one inch to fifteen miles. Three inches per mile, in a smooth, straight channel, give a velocity of three miles an hour ; three feet per mile are sufficient to produce a mountain torrent. The wearing away of the banks and bottom of a river or canal depends on the velocity of the current. A velocity of thirty feet per minute will not distuib clay or sand ; one of forty, will sweep along coarse sand ; of sixty, fine gravel ; of one hundred and twenty, rounded pebbles; of one hundred and eighty, angular stones. For this reason, rapid rivers are stony, slow ones sandy or muddy. If the velocity of rivers were not checked by friction, their force would be frightful. The Ganges, at a distance of eighteen hundred mik-s from its mouth, is eight hundred feet above the level of the sea. The velocity due to this fall is over one hundred and fifty miles per hour, which is more than fifty times the velocity actually attained. 166 NATURAL PHILOSOPHY. WATER POWER. 323. Flowing water acts as a moving power, (1.) by its weight, (2.) by the force of the current, or (3.) by the combined effect of both. The gross power of a fall of water is equal to the weight of water discharged in a unit of time multiplied by the head. Let H represent the head, Q the volume in cubic feet discharged per second, and 62.4 Ibs. the weight of one cubic foot of water; then, Q.H (62.4) = P, the gross power in foot- pounds per second. If the velocity of the stream is given, since [49.] H v 2 -T- 64.32, the formula becomes [50.] As the last factor does not differ greatly from unity, we may use the following rule for most purposes. Tfie gross poiver of a water fall in foot-pounds per second, is equal to the volume of water discharged, in cubic feet, multiplied by Hie square of Hie velocity, in feet. There is always a loss of energy, arising from the* shape- and fric- tion of the weir, so that the effective power is somewhat less than the gross. 324. Water wheels are either vertical or horizontal. In vertical wheels, the effect- ive power of the stream is applied to buckets or boards fixed to the circumference of the wheel. The wheel is con- nected with the machinery to IK- moved. Tin-re are throe varieties of vertical wheels: (1.) the overshot, (2.) the undershot, (3.) the breast In Ki... Ul. the overshot wJieel, wheel. Fig. 124, the stream falls into WATER WHEELS. 167 buckets at the top of the wheel, and acts principally by its weight. In the undershot wheel, Fig. 125, the stream strikes against boards at the bottom of the wheel, and acts by the force of the current. In the breast wheel, Fig. = 126, the stream may be made to act both by its weight and the force of the current. High breast wheels receive the stream in buckets above the axis; low breast wheels receive the stream on boards below the axis. FIG. 125. FIG. 126. 325. The availability of any wheel depends on the character of the fall. Undershot wheels are well adapted to low falls with large supplies of water. Overshot wheels are used with falls not exceeding sixty feet in height, and are efficient even with small streams. Breast wheels require a larger supply of water, but the fall is always less than their diameter. 326. The efficiency of a wheel is largely dependent on the shape of the buckets, or floats, and the readiness with which the water may escape after having been used. The actual 168 NATURAL PHILOSOPHY. impulse of the stream is only the excess of its velocity above that of the float boards : thus, if the stream has a velocity of eight feet in a second, and the float boards three feet, the velocity of impact is five feet. For these, and other reasons, the maximum effect of the wheel is always less than the effective power of the stream. Overshot and high breast wheels utilize from .6 to .8 of the power; low breast wheels, from .45 to .65, and undershot from .25 to .45. It is important to notice that the head is the same, whether the water flows from an orifice in a reservoir, or falls freely the same distance, as has been shown in (313). 327. There are two forms of horizontal wheels; (1.) the reaction, (2.) the turbine. The reaction wJieel may be repre- sented by Barker's mill, which acts on the principle of unbalanced lateral pressure (273.) A vertical axis, CD, which revolves upon a pivot, terminates in two hori- zontal pipes, A and 15, whose extremi- ties are curved in opposite directions. As the fluid escapes from the orifice in the ends of these pipes, the arms are driven around in opposite directions to the flow, and may be employed to com- municate motion to machinery. 328. There are three classes of turbines, and many vari- eties of each class. One of the most cfiicicnt was invented in 1827, by M. Fourneyron. Fig. 12t eflicirwy; and then (2.) to permit its escape with the !I IOM of motion. The TURBINE. 169 wheel is connected beneath the cylinder to the shaft, d, which passes upward through the center of the cylinder, and communicates its motion to the gearing at the upper end of the shaft. Turbines are FIG. 12s. FIG. 129. applicable to falls of any height, from nine inches up- ward, and will utilize from .75 to .90 of the power of the water. 329. If it were possi- ble for water to flow in a pipe entirely unimpeded, so that its velocity would ever be that required by theory (8.021/&), there would be no lateral pressure; and, if the pipe were pierced, no water would flow out. But when the velocity is diminished by friction, and other causes, a portion of the pressure is not carried off, and becomes a burst- ing pressure on the pipe. This pressure is unequal at different portions of the pipe. At the end, E, Fig. 130, where the water flows out, it is almost nothing, but in- creases toward the reservoir, as shown by the dotted line, being, at any point, equal to the difference between the calculated and actual velocity. If, now, the current of water be suddenly stopped, much of the momentum will be changed to lateral pressure, and the water will rise in the open pipes, a b c, to a height pro- portioned to the reaction of the momentum. This will be FIG. 130. 170 NATURAL PHILOSOPHY. greatest in the tubes near the end, E. In common house- hold water pipes, if the faucet is suddenly closed, a certain shock is felt near it, and, if the head is sufficient, the pipe will burst. 330. The hydraulic ram is a contrivance by which the impulse of running water, when suddenly checked, can fu- made available for raising a portion of itself to a consider- able height. Let K, Fig. 131, be a reservoir, from which the water flows through the pipe, P. to the orifice, o. Let a conical valve, C, be fitted to this orifice, of such weight as to remain down, and leave the orifice open, when it is opposed only by the steady pressure of the water in the pipe and reservoir. However, the water, by flowing through the ori- fice, soon acquires momentum sufficient to raise the valve, C, close the orifice, and thereby communicate a shock to the pipe. FIG. 131. A second valve, V, which opens into an air chamber, A, is made to rise by the impulse of the reaction, and allow the water to enter the air c-hamU-r, until the pressure of the inclosed air overcomes the shock of the water. The valve, V, now closes, C opens, and permits the water to flow out at o, as before. The aeeimmlated momentum a^ain closes C and forces a second portion of w.-iter into the air chamber, ami thus the action i- continued indefinitely. The confined ;iir KX>H ac.piires sufficient elastic force to drive the water in the chamber through the exit pipe, K, in a continued >tiv.mi. Much more water escapes at o between the pulsations than can be PNEUMA TICS. 171 raised in the exit pipe, E. The useful effect of this machine is the greatest when the height to which the water is raised does not much exceed the fall from the reservoir, but it diminishes as the height increases. With a low fall and only a moderate supply of water, a constant stream can be raised by this machine to a considerable height. A fall of two feet is competent to raise one-fortieth of the water expended, to a height of forty feet. 331. Recapitulation. Running water exerts power in proportion to the product of its volume and the square of its velocity, diminished by the impediments to motion. It acts as a motive power: Useful Effect. f Undershot. .25 {Vertical. j Breast. .60 ( Overshot. .75 f Turbine. .90 Horizontal. { Keact . on 4Q II. By the impulse of one part of the stream on another Hydraulic ram. .50 7^ THE MECHANICS OF AERIFORM FLUIDS. 332. Aeriform bodies are fluids which are highly com- pressible, elastic, transparent, and usually colorless. In an aeriform fluid, the repulsion of its molecules so far ex- ceeds their attraction for each other, that they tend to sep- arate and expand indefinitely into space, unless controlled by external forces, or pressures. The force with which an tu-riform fluid tends to expand, is called its elastic force or tension. 333. Aeriform bodies are divided into vapors and gases. 1. Vapors are produced by the action of heat upon solids and liquids, and readily return to their original state upon cooling. Steam is the type of all vapors. 172 NATURAL PHILOSOPHY. 2. Coercible gases are aeriform under ordinary circum- stances, but may be condensed into liquids, and even solids, by the aid of pressure and of low temperatures ; as chlorine, carbonic acid (CO 2 ). There are twenty-nine coercible gases. 3. Oxygen, nitrogen, hydrogen, carbonous oxide (CO), and nitric oxide (NO 2 ), have with great difficulty been also con- densed to liquids, in 1877. Before that date these gases were called permanent, because it was thought they could not be condensed by the means at the service of physicists. It is reasonable to suppose that as all gases have been condensed to liquids, so also all solids that are not decomposed by heat, may be changed, at temperatures sufficiently high, to liquids and to vapors. Therefore, the distinction between gases and vapors is merely conven- tional, as they differ from each other only in their specific properties, as density, odor, etc. 334. PNEUMATICS treats of the mechanical properties of aeriform fluids. The atmosphere, which is mainly a mixture of nitrogen and oxygen, will be assumed as the type of all bodies in the aeriform state. Whatever physical property is estab- lished regarding atmospheric air, is to be understood as applying to all vapors and gases. Air has been proved to possess extension and impenetra- bility, the essential properties of matter, and to have mobility, inertia, and momentum. Like all other fluids, it transmits pressure undiminished, in every direction ; but, as its compressibility far* exceeds liquids like water, the effect of pressure is not felt as instantaneously at long dis- tances us in the case of liquids. 335. Tli.- air i< kept in its place about the earth by tin- joint action of its molecular repulsion and the attraction of gravitation. Consequently, the atmosphere, at its upper limit, nm>t hav.- a definite surface, like the sea. At any point on the earth's >urface tin- air will exert, \>\ ivaxMi of gravity, a pressure due to a line of molecule-, extending from the point to the upper limit of the atmosphere. At ATMOSPHERIC PRESSURE. 173 any given elevation above the surface of the sea, the effect of gravity in producing upward, downward, and lateral pressures, will be the same as in liquids. 336. The pressure of the atmosphere was first ascertained by the experiments of Torricelli, in 1643. He filled a glass tube, nearly three feet long, with mercury, closed the open end firmly, and then inverted the tube in a cistern of mercury. On removing his finger, the liquid de- scended in the tube, and finally came to rest at the height of about thirty inches above the level of the liquid in the cistern, thus leaving a vacuum at the top of the tube. Now, as the weight of the mer- cury tends to make it flow out of the tube, the column must be sus- tained by an equal and opposite force. The philosophers of the day thought they explained the matter by saying that " Nature abhors a vacuum ;" but Torricelli reasoned that, in obedience to the law of equilibrium of fluid pressures, the force that sustains the mercury in the tube is the pressure of the atmosphere on the mercury in the cistern. Pascal confirmed Torricelli's explanation, by causing the experiment to be repeated on the top of a mountain. He thus reasoned: "If the height of the mercury is less at the top of a hill than at the bottom, it will follow that the weight and pressure of the air are the sole cause of the sus- 1 ><])>!< >n, and not the horror of a vacuum, since it is very certain that there is more air to weigh on it at the bottom than at the top, while we can not say that nature abhors a vacuum at the foot of a mountain more than at its summit." At the top of the Puy de Dome the column was found to be 174 NATURAL PHILOSOPHY. B Fia. 133. three inches lower than at the bottom, which settled the question. 337. The pressure of the atmosphere is, therefore, equal to the weight of a column of liquid which it will sustain. An instrument used for measuring atmospheric pressure is called a Barometer. The simplest form of the barometer is the Torricellian tube, but for convenience of transportation, other forms have been devised. Fortin's is one of the best. Fi^s. 133 and 134. It consists of a straight glass tube, about thirty -three inches long, filled with mercury, and dipping into a glass cistern containing the same fluid. The base of the cistern, mn, is made of leather, and can be raised or lowered by means of a screw, C. On using this barom- eter, the mercury in the cistern is brought to a level with the point of an ivory pin, a, by turning the screw, C, up or down. The scale, B, gives the exact height of the column above this point. The tube and cistern are protected from accident by a brass case. In traveling, the interior of the tube and cistern are filled with mercury by raising the screw, so as to prevent the accidental introduction of air. A thermometer is attached to the scale. As mercury ex- pands by heat, all barometrical observations should be ml need to the same temperature, by tables prepared for that purpose. It is essential to a first rate barometer (1.) that the mercury should be pure, (2.) that the scale should measure the exact distance between the levels of the mercury in the tube and cistern, (3.) that the vacuum at the top of the tube be perfect. With the bc>t precautions, it will contain a trace of tin- vapor of mercury. Air is excluded by ponrinir the mer- cury int> the tube, small portions at a time, and boiling it after each successive addition. CJ Fro. 134. PRESSURE OF THE ATMOSPHERE. 175 338. The pressure of the atmosphere may be estimated in pounds, or by the height of the barometer. At the level of the sea, the height of the column varies from 28 to 31 inches, the average being 29.922 inches. The weight of a column of mercury of this height, and one inch in area is 14.7 pounds. We say, therefore, that the press- ure of the atmosphere is nearly fifteen pounds to each square inch of surface. No other liquid is so serviceable in the construction of barometers as mercury. Barometers have been made, hav- ing their tubes filled with water and with sulphuric acid, but they are very expensive and unwieldy. The pressure of the atmosphere will sustain a column of water 13.6 times longer than the column of mercury, or thirty-four feet. 339. The pressure of the atmosphere may be illustrated by many simple experiments. FIG. 136. FIG. 135. 1. In the pneumatic inkstand, Fig. 135, the downward press- ure of the atmos- phere on the liquid in the tube sustains the ink in the bottle. AVhen the ink sinks down to the level of the neck, a bubble of air passes in and forces out a portion of the ink into the tube. 2. Fill a tumbler with water, and, having placed a thick slip of paper over its mouth, press the paper down tightly with the hand, and invert the glass cautiously. The hand may now be removed, and the water will be sup- ported in the glass by the upward pressure of the atmosphere on the paper, Fig. 136. 3. Take a small open tube, or a pipette, Fig. 137, plunge it vertically FIG. 137. 176 XA TURA L PHIL OSOPH Y. in water until it is filled, then close the upper end by the finger and raise the tube. The water will not run out, because the pressure of the air keeps it up. Remove the linger, so that the atmosphere may press above and below, and the water will fall by its o\vn weight. 4. Water will not How out of a small tap in a tight ban-el, because of the lateral pressure of the atmosphere. If this be counteracted by admitting air through an opening in the top, the water will run freely by its o\vn weight. Xo upper opening is required in beer barrels, because of the tension of the gases contained in the beer. 5. A boy's sucker is made by attaching a stout string to the center of a small circular piece of thick leather. The leather us first soaked in water, and then pressed firmly against the smooth surface of a stone, so as to exclude all the air. The two surfaces are now held to- gether by the force of fifteen pounds to the square inch, Fig. 138. On pulling the string, a vacuum is formed under a portion of the leather, and the weight of the at- mosphere on its upper side is borne by the hand. The weight of the atmosphere is thereby re- moved from this portion of the stone, and, if it is not too heavy, the pressure of the atmosphere on its under side will raise it up. 340. The tension of gases may be shown by the following experiment. Bend the closed end of a barometer tube, as in Fig. 139, and pour just enough mercury into tin- tube to fill the bend, as shown in the figure. The air inclosed in the short arm is now in its natural condition, under the press- ure of one atmosphere. If thirty indies of mercury be poured into tin- IOHL: arm, the ,. |( . I3y routined air will lie under the procure of two atmospheres, one of air and one of mercury, and will be reduced in volume one-half. If thirty inches more mer- cury be added, the pressure will lie three at inosphrres, and the FIG. 138. TENSION OF GASES. 177 volume will be reduced to one-third. And so on, for every like increase of pressure, the volume will be reduced to one-fourth, one-fifth, etc. Therefore, 1. The volume of a given weight of air is inversely as tfie pressure to whicJi it is exposed. This proposition is known as Mariotte's law, and is true for all gases, within small limits of error. As the density of a body is inversely as its volume, and as the pressure is always sustained by the tension of the air inclosed, 2. Tlie density and tension of a given weight of air are directly as the pressure to which it is exposed, and inversely as its vol- ume. 341. To prove the same law for pressures less than one atmosphere : Fill a long jar with mercury, and fill a baro- meter tube to within four inches of the top with mercury. Then invert the tube in the jar, and sink it until the level of the mercury in the jar and tube is the same. The confined air is now under the pressure of one atmosphere. On raising the tube, as in Fig. 140, the tension of the confined air equals one atmosphere minus the weight of the mercury in the tube. If the column of mercury raised is fifteen inches, the air will have a tension of one-half an atmos- phere, and will have doubled its volume. When the column of mercury is 20 inches the tension of the air will be one-third of an atmosphere (30 20 = 10), and its bulk will be trebled. Mariotte's law, therefore, applies both to condensed and rarified air. F ,, ; . 140 . 342. The tension of aeriform fluids, may be measured by manometers or gauges. One of the simplest forms is the closed manometer, Fig. 141, which acts on the principle of Mariotte's tube. It consists of a U tube, closed at one end, and half N. P. 12. 178 /'////. O.s'O/7/V. FIG. 141. filled with mercury. The closed end contains dry air, at the ordinary tension. When the open end communicates freely with the atmosphere, the level of the mer- cury is the same in both tubes. If the open end is connected with aeriform fluids whose tension is to be measured, as with the steam is in a boiler, the air will occupy one-half, one-third, one-fourth, etc., of its original space, according as the pressure increases to two, three, four, etc., atmos- pheres. Or if the pressure is less than one atmosphere, the air will expand as the pressure diminishes. 343. Bourdon's gauge, Fig. 142, is one of the most useful manometers known. It consists of a metallic tube, AB, closed at one end, B, and fixed at the other, A. The cross section of the tube is a flattened ellipse, having its greatest breadth perpendicular to the plane in which the tube is curved. When the pressure within the tube is greater than the pressure without, the tube be- comes less curved, or tends to straighten; when the pressure without is the greater, it becomes more curved. The extent of the motion depends on the elasticity of flexure in the tube. The movements of the closed end of the tube are communicated by the link, D, to an index, which moves along a graduated arc. The arc is graduated by comparison with other manometers. The tube and mechanism are contained in a brass box with ji glass cover. The sensibility of tin- gau.iro depends on the flexibility of the tube. Some are made to measure pressures of less than one atmosphere, and some of sev- eral liiindri'd. In steam gauges, the fixed end of the tube cominuui- Fio. 142. AIR PUMPS. 179 cates with the boiler, by the stop- cock, C. A modification of this gauge is well known in this country, under the name of Ashcroft's gauge. To measure pressures of less than one atmosphere, the tube is exhausted of air, and the fixed end hermetically sealed. The stop-cock is then removed. This gauge then becomes an aneroid barometer. AIR PUMPS. 344, An air pump is an instrument for removing the air from a closed vessel. Fig. 143 shows the Leslie air pump, and Fig. 144 the same instrument in section. The receiver, R, is connected FIG. 143. with the cylinder, C, by a long bent tube, terminating in a horizontal brass plate. The mouth of the receiver and the 180 NA TURA L PHIL OSOPII V. FIG. 144. surface of the brass plate are carefully ground, so as to bring them in contact at every point. The edge of the re- ceiver is smeared with grease, so as to render the connection as close as possible. When the piston, P, is raised from the bottom of the cylinder, the external air closes the upper valve ; the air in the receiver expands, opens the lower valve, p and fills the cylinder. When the piston is depressed, the lower valve closes, and the air in the cylinder is forced through the upper valve out into the atmos- phere. As the piston again rises, the upper valve is closed, the lower valve opens, and the confined air expands into the cylinder. At every ascent and descent of the piston, a portion of air is removed from the receiver, and this pro- cess may be repeated until the tension of the air remaining is not sufficient to lift the lower valve. The receiver is then said to be exhausted. The tension of the air in the receiver is measured by a gauge, which consists of a bent tube, leading from the re- ceiver to a vessel of mercury, H. The external air forces the mercury up the gauge, in proportion as the tension of the air in the tube is diminished. If the exhaustion were perfect, the mercury would rise to about thirty inches. The height of the gau^e indicates the difference between the pressure of the atmosphere and the tension of the air in the receiver. The air pump is also provided with a, stop-cock, S, Fig. 144, to close the communication between the cylinder and receiver when n^uiivd. The stopper, A, is u>ed to admit the external air to the receiver. A third valve, T, is usu- ally placed in the top of the cylinder to prevent I he external air from pressing on the piston. AIR PUMP EXPERIMENTS. 181 345. The" air pump may be used to perform a great variety of experiments, illustrating the properties of the air, only a few of which can be here given. 1. Tfie presence of air in bodies may be shown by placing a jar of well-water under the receiver. On working the pump, bubbles of air will be disengaged from the water. Having freed the water from air, fasten to the bottom of the jar bits of w r ood or other solids, and repeat the experi- ment. The formation of air bubbles will prove their porosity, and the presence of air in the pores. Many bottled liquors are charged with condensed gases. When the pressure is removed by drawing the cork, the thin liquids, like champagne, sparkle; viscid liquids, like ale, froth. 2. ExpangibiUty. Tie the neck of a fresh, flaccid bladder and place it in the receiver. On exhausting the receiver, the bladder will dilate, because the air within it expands. On re-admitting air to the receiver, the air in the bladder resumes its former volume. A shriveled apple, or a bunch of shriveled grapes will become plump in an exhausted receiver. 3. Pressure of tfie atmosphere. Take a small open receiver and close the upper end tightly with a piece of sheet rubber. On work- ing the pump the air w r ill be with- drawn from below the rubber, and the external air will press the rubber downward so as to fill the receiver. If the rubber is replaced by a piece of moistened bladder, Fig. 145, and the bladder suffered to dry, the external pressure will generally be sufficient to burst the bladder with a FIG 145. loud report. If the bladder is very stout, or the exhaustion incomplete, it may be necessary to weaken the strength of the membrane by puncturing it with the point of a pin. 182 NATURAL PHILOSOPHY. The Magdeburg hemispheres, Fig. 146, consist of two hol- low brass hemispheres, which fit together air tight. One of them may be connected with the air pump by a tube and stop-cock arrange- ment. On exhausting the air from the interior, the two hemispheres will be held together with a force of fifteen pounds to the square inch. If their diameter is three inches, the area of the section will be seven inches, and the force which holds them together will be over one hundred pounds. As the restraining force is the same in every position in which they are held, the pressure of the atmosphere is ifie same in every direction. Fig. 147 represents a tall receiver, which terminates in a metallic cap, furnished with a stop-cock, a screw, and an interior jet pipe. Exhaust the air from the interior and close the stop-cock. Place the mouth of the tube under FIG. 146. water and open the stop-cock. The pressure of the atmos- phere will drive the water up the pipe, forming what is known as the vacuum FI<;. \\i. fountain. Tin' iri itjlit ///'/>/ consists of a receiver which is connected to the air pump by an opening in the top. The lower end is closed by a piston or by a stout rubber bag. When the PROPERTIES OF AIR. 183 air is withdrawn from the receiver, the bag is forced upward, and carries with it weights attached below. If the receiver is five inches in diameter, nearly three hundred pounds will be lifted by the upward pressure of the atmospJiere, if the vacuum is complete. 4. When a heavy weight is thus sustained, the elasticity of the air may be shown, in a striking manner, by forcing dow r n the load by the hand, and then releasing it. The weight will then oscillate up and down, as if on an elastic spring. 5. The weight of air may be ascertained, by taking a vessel of known capacity and finding the difference of its weight when filled with dry air, and when exhausted of air. If the capacity of the vessel is one hundred cubic inches, the difference of its weight will be thirty-one grains. There- fore, the weight of one cubic inch of air is 0.31 grains. By the principle of Archi- 6. The buoyancy of air. medes (289), a solid im- mersed in a fluid loses an amount of weight equal to the weight of an equal volume of the fluid. Hence, every substance weighs less in air than in vacuo. Suspend to one arm of a balance a hollow globe, Fig. 149, or a ball of cork, and counterpoise it with a lead weight. Now place the balance under a receiver and exhaust the air. The cork will fall, and thus seem to be heavier than the lead. If a body is lighter than an equal volume of air, it will rise in it. Smoke rises in a chimney because air is rarified by heat, A soap bubble made from hot water and filled with warm air rises, because it weighs less than the air it displaces. If the soap bubble is filled with hydrogen, it rises rapidly until it bursts. FIG. 149. 184 NATURAL PHILOSOPHY. Balloons are varnished silk bags, filled with hydrogen or coal gas. The silk is strengthened by a netting of small ropes, which also serve to suspend a light basket. The buoyant effort of the air in raising a balloon is equal to the difference between the weight of the gas used and the air displaced by it. A spherical balloon, forty feet in diam- eter, will displace two thousand five hundred pounds of air, but will contain less than two hundred pounds of hydrogen. The lifting force of such a quantity of gas is over a ton. It is, therefore, capable of lifting the weight of the silk, and other parts of the balloon, the aeronaut, and a large quantity of sand used for ballast. If the aeronaut wishes to descend from a height, he allows some of the gas to escape, by opening a valve in the balloon. If he wishes to rise again, he throws out a portion of his ballast. The greatest height ever reached in a balloon is a little over seven miles. This was attained by an English aeronaut, named Glaisher, in 1861. 7. That air is necessary to combustion, may be shown by placing a lighted candle in a receiver. On working the pump, the candle will grow dimmer, burn blue, and finally go out. The smoke of the candle will be seen to descend, because there is nothing to sustain it. 8. That air is necessary to animal life, may be shown by placing a bird or a mouse in a receiver. On exhausting the air, the animal will give evident signs of distress, and will soon die. The relations of air to sound and heat will be considered hereafter. 346. The condenser is an instrument for forcing a large amount of air into a closed vessel. One of the best forms is shown in Fig. 150. It con>ists of a cylinder, C, in which a solid piston works air tight. There are two valves in the cylinder, (1.) the lateral valve, (i, which opens from the outside, and (2.) the lower valve, b, which opens from the inside. The receiver, R, may be CONDENSER. 185 connected by a screw to the cylinder, and may be opened or closed by means of stop-cocks arranged as in the figure. In using this instrument, the condenser and receiver are connected and the pis- ton driven down. This ac- tion condenses the air in the cylinder enough to close the lateral valve and open the lower. When the piston has reached its low- est point, all the air will be forced out of the cylin- der into the receiver. The confined air will have it* volume diminished and its tension increased. If the cylinder and receiver are of the same size, the condensed air will have a tension of two atmos- pheres. On raising the piston, the tension of the air in the receiver will close the lower valve, the external atmosphere will open the lateral valve, and again fill the cylinder. This operation may be repeated until the receiver is filled with air of the tension desired. When the receiver is thus charged, the stop-cock, V, is closed, and the cylinder is detached. By bringing the lateral valve in communication with a reservoir containing any gas whatever, this gas will be Withdrawn from the reservoir and forced into the receiver. In this manner liquids placed in the receiver may be charged with gases. FIG. 150. 186 NATURAL PHILOSOPHY. 347. An air gun consists of a charged receiver, properly connected to a gun barrel. After fitting a bullet to the bottom of the barrel, a trigger ^ turns the stop-cock, and the con- densed air rushes out with great force. A boy's pop-gun also illus- trates the tension of confined air. A fountain can be arranged to play by condensed air. Before charging the re- ceiver fill it partially with water, and connect to the stop-cock a tube reaching to the bottom of the receiver. When the air has been condensed and the stop- cock is opened, the air will force the water in a jet to a height proportional to the tension. The experiment may be varied by making the stream turn a hori- zontal tube, arranged on the principle of Barker's mill, Fig. 151. FIG. 151. THE HEIGHT OF THE ATMOSPHERE. 348. Mercury is about eleven thousand times denser than air, at the level of the sea. If air were every-where of this density, the height of the atmosphere required to bal- ance the column of mercury in the barometer would be 11,000 X 29.922 inches, or 27,400 feet. The pressure of air may, therefore, be reckoned as equal to a column 5.2 miles high, having throughout a density equal to that of air at the sea-level. This would be the actual height of the atmosphere if air were incompressible. We know that the air extends to a greater height, because aeronauts have actually ascended to higher altitudes. Moreover, as the air at any level is com- pressed by the weight of the column above it, the air must become rarer as we ascend from the level of the sea. If a barometer were carried one thousand feet above the sea-level, the column would descend about an inch. The air at this level sustain- a pressure one-thirtieth less than at the sea -level, and, in accordance with Mariotte's law, HEIGHT OF THE ATMOSPHERE. 187 it is proportionally of less density. Therefore, we shall have to ascend rather more than one thousand feet to re- duce the column another inch; and so on, in increasing ratio. At the height of 3.4 miles, the barometer will stand at fifteen inches, showing that one-half the atmosphere is below that level. Every additional ascent of 3.4 miles will reduce the pressure one-half, and consequently the density of the air. The following table is prepared in accordance with this rate of decrease : ^Pressure of the Atmosphere at different levels. Height above the sea in miles. 3.4 6.8 10.2 13.6 51 Height of the barometer in inches. Density of the air. Sea-level = 1. 30 1 15 7.5 3.75 * \ \ 1.87 & .0009 "3 ^TS 8 At the height of 13.6 miles the air would be rarer than hydrogen. At the height of fifty miles the mercury would be elevated about one-thousandth of an inch, and the air would be less than one thirty-thousandth of its density at the sea-level. At this height, therefore, the limit of the atmos- phere is practically reached. 349. The intense cold of the upper limits of the atmosphere, tends to diminish the ex- pansion of the air, by diminishing the repulsion between its molecules, so that it is probable that the height of the atmosphere does not exceed forty-five miles. This result is con- firmed by the phenomena of refraction of the heavenly bodies. Fig. 152 is an attempt to represent to the eye the decreasing pressure of the atmos- phere. Pressure in pounds to the square inch. 15 7.5 3.75 1.875 .9375 .0004 Fio. 152. 188 NATURAL PHILOSOPHY. 350. Heights are measured by the barometer, in accord- ance with the facts thus established. Observations are taken at two stations at very nearly the same moment. The differ- ence between the two barometric columns will represent the difference in the heights of the atmospheric columns above the two stations. Allowance must then be made for the temperature at the time of observation, and for the latitude of each station. Formulae have been computed for this pur- pose, but they do not fall within the scope of this book.* 351. Fluctuations of the barometer. The atmosphere may be regarded as an aerial ocean, in whose lower depths we live. From the extreme mobility of its particles, it is never perfectly at rest, but moves in immense waves above our heads. When the crest of one of these waves is over the barometer, the column rises; and then falls again, as the depression of the wave succeeds. Except for extraor- dinary causes, the range in height at the equator does not exceed one-fourth of an inch ; at New York the range is about two inches, and in Great Britain it exceeds three inches. The mean annual height at any station is the same from year to year. The mean annual height is greatest (30.04 inches) near the thirty-sixth parallel of latitude. 352. The barometer is subject to slight variations, which *An approximation to the vertical distance between the two stations may In- found by multiplying the dinVrenee of tin- logarithms between the two barometric columns by 601-~>!t r, t. This, inn-eased by f^- of Itself for every degree thai the mean temperature of the two .stations is above 32" F. f will give a result not far from the truth. ExAMi'LK. The barometric pressures at the bottom and top of a mountain u.-iv, respectively, ;>1.7ir> and "JT.Miti. The mean temperature K; i.-qiiiied, tin- dillerenee in height. Log. of the lower station, :;i.7J.~. l.f>Wll) Log. of tin- upper station, L'T.sMi 1,11., us I inference of logarithms of tin- two stations^ ~ .05632 60159 X .05632 = 3388 = approximate height. The coi red ion for tempera- 1 1 . r is (50 - 32 = 18), 18 X SSUo X 3388 = 137 feet ; 3388 { 137 - 325 feet = the height more nearly. WEATHER RULES. 189 occur at regular periods, from hour to hour and from day to day. The mean monthly height is greater in winter than in summer. The mean daily height occurs at about twelve o'clock, noon, and midnight ; the maximum height is reached between eight and nine o'clock ; the minimum, between three and four o'clock, both morning and evening. These hours are, therefore, the best for taking observations. 353. Besides these periodic variations, the barometer it, subject to accidental variations which increase with the lati- tude. It has been noticed that such accidental variations are often coincident with the changes in the weather, because the column of air is generally heavier in fail weather, and lighter in foul weather. The absolute height of the column varies with the altitude of the station, and affords, by itself, no indication of the weather ; hence, the weather marks, "fair, rain, wind," on some barometers, are absolutely worthless. The variations in the height of the barometer indicate changes in the pressure of the at- mosphere, which may be followed by changes in the weather. The following rules are generally reliable. Rules for predicting changes in the iveather: 1. The rising of the mercury indicates the approach of fair weather; the falling of the mercury indicates the approach of foul weather. 2. A sudden and great fall, is the sure forerunner of a violent storm. 3. When the barometer changes slowly, a long continuance of the weather indicated may be expected. 4. A sudden change of the barometer indicates that the change of weather will not be of long duration. 354. The body of a man of average size has a surface of about two thousand square inches. He, therefore, sus- tains, at the level of the sea, a pressure of thirty thousand pounds. It conveys a wrong notion to speak of this press- ure as a load ; on the contrary, the buoyant effort of the air lifts the man, and makes him press the ground more 190 NATURAL PHILOSOPHY. lightly than he would without it. The atmosphere acts on all sides of a body immersed in it, not as a weight, but as a crushing force. The reason w r hy we do not feel this com- pressing force is because the pressure is transmitted throughout the body by the blood and other fluids of the body. Hence, when the atmosphere tends to squeeze in the sides of the blood-vessels, it is met by an equal out- ward pressure, caused by the pressure of the atmosphere on the other parts of the system. \Ve may become sensible of this outward pressure by placing the hand on a small open receiver and exhausting the air from beneath it. The external air now acts as a load, holding the hand firmly to the receiver. The blood, in the under surface of the hand, distends the vessels, and, if the skin has been punctured with a pin, the blood is forced out. Cupping glasses are made to act on the same prin- ciple. 355. On ascending to great heights, the respiration is much accelerated, because of the rarefaction of the air. If the ascent is made rapidly, as in a balloon, other uneasy sensations are often felt, which are very likely occasioned by the expansion of the air inclosed in the body. If the ascent were made slowly, this air would have time to ac- commodate itself to its new conditions. If it be true that the "skin cracks and bursts, and the blood issues from the pores of the body," at high elevations, as is related by travelers in South America, the cause must be sought rather in the dryness of the air, or the greater cold, than in the diminished pressure. Men who descend in diving bells to the depth of thirty- four feet, endure the pressure of at least two atmospheres without serious inconvenience. MACHINES FOR RAISING WATER. 356. If we place one end of an open tube in water, and apply the mouth to the other end, \ve may cause the liquid to rise in the tube by suction. Correctly speaking, the LIFTING PUMP. 191 effect of the suction is to withdraw the air in the tube; the water is then forced up the tube by the pressure of the atmosphere on the surface of the water in the vool. The common suction, or lifting pump, acts on the same principle. It consists of a barrel, B, similar to the cylinder of the air pump, and, like it, fitted with a piston, P, work- ing air tight, and two valves, U and e, both opening up- ward. From the bottom of the barrel proceeds the suction pipe, C, which dips below the surface of the water to be raised. When the piston is worked, the air beneath it is rarefied more and more at each stroke; the pressure of the atmosphere on the water outside of the pipe, causes the water to rise in the pipe and enter the cylinder through the lower valve. Xow, on forcing down the piston, the lower valve, e, is closed, the water forces open the piston valve, U, and rises above it. When the piston is again raised, the upper valve, U, is closed, and the water above it is lifted to the spout of the pump. At the same time, the atmospheric pressure on the water in the reservoir, causes more water to rise into the barrel under the piston. 357. The length of the suction pipe can never exceed thirty-four feet, because the pressure of the atmosphere is 192 NA TURA L PHIL OSOm ) ". only capable of supporting a column of water thirty-four feet high. Owing to variations in atmospheric pressure, and the imperfect mechanism of the pump, the limit, in practice, is less than twenty-eight feet. There is, however, no limit to the height through which water may be lifted after it has once passed above the piston. In deep wells, the working barrel, containing the piston and both valves, is placed near the bottom. A long, vertical discharge pipe, through which the piston rod plays, connects the working barrel to the surface of the ground. The atmospheric pressure forces the water from the well into the working barrel ; the force applied to the piston lifts the water from the working bar- rel to the top of the discharge pipe. 358. In the forcing pump, the piston is made solid, and the upper valve, u t is placed in a lateral discharge pipe, d, connected with the bottom of the barrel. The lower valve and suction pipe are the same as in the lifting pump. When the piston is raised, the water passes up the suction pipe through the lower valve, e, into the pump bar- rel. On depressing the piston, the lower valve closes, and the water is forced through the upper valve, u, into the discharge pipe. On again raising the piston, the upper valve closes, and prevents the water in the discharge pipe from returning; the l<>\ver valve opens to admit more water into the barrel. At each depres- sion of the piston, more water is driven into the discharge pipe, until it is elevated to the required height. FIG. 154. 359. The water will be ejected from such a pump in successive impulses. When it is desired to make the stream continuous an air chamber is attached, as in Fiir. 155. When the piston descends, it forces the water through the valve, u, into the air chamber, A ; tin- water partially fills the chamber, and thus compresses the air. The tension of the compressed air increases as its bulk is diminished, and soon THE SIPHON. 193 FIG. 155. becomes sufficient to force the water in the chamber out through the tube, T, in a constant stream. 360. An ordinary fire engine consists of two force pumps, worked by long handles, called brakes, and having an air chamber common to both. The piston of one barrel descends as the other as- cends, by which means, a continuous stream of water is forced into the air chamber, and escapes through the dis- charging pipe. 361. The siphon is employed for trans- ferring liquids from a higher to a lower level. It consists of a bent tube w r ith two unequal arms, Fig. 156. In using the siphon the shorter arm is plunged in the liquid to be transferred. To begin the action, the air may be removed from the tube by suction at the lower end. The liquid will be forced up the shorter arm by the pressure of the atmosphere; it will then fill the tube and continue to flow through the siphon. After the suction is stopped, the liquid is pressed up in the shorter arm by the weight of the atmosphere on the surface, A B, minus the weight of the liquid column, MI. So, also, the liquid in the longer arm is pressed upward by the weight of the atmosphere, minus the weight of the liquid column, M K. Hence, the liquid is urged in the direction, C M F, by a force equal to the excess of the weight of M K, over that of M I. If M K and M I were equal there could be no flow in either direction. The greater the difference in the length of the arms, the greater will be the velocity of the flow. 362. These facts may be prettily shown by the siphon N. P. 13. 194 NA T URA L PHIL OS OP II Y. fountain. Close the mouth of a tall flask, R, with a cork, and insert two glass tubes, as shown in Fig. 157. The shorter arm should be drawn out at the upper end to a very fine bore. On exhaust- ing the air from the tube, the ordinary flow of the siphon will commence. If, now, the longer arm be lengthened, by attaching a rubber tube, the jet may be made to strike forcibly against the top of the flask. The force of the jet may be shown to be dependent on the difference of length of the two arms. As the greatest pressure on the sur- face, A B, Fig. 156, can never exceed one atmosphere, the vertical height, MI, of the column sustained can never exceed thirty-four feet, if the liquid is water, or thirty inches if the liquid is mercury. Fio. 157. Bv drawing the end of the long arm out to a fine tube, and giving i horizontal or upward direction, it may employed to advantage in illustrating the flow of liquids through orifices. The acid siphon, Fig. 158, has a suction tube attached for convenience in exhaul any body are disturbed by any external force, not too great, they will tend to resume their original positions by a series of movements, to FORMATION OF UNDULATIONS. 197 and fro, which gradually decrease in extent and finally cease. Such alternating motions are known as vibrations, oscillations, waves, or undu- lations, according to the circumstances under which they are pro- duced. 367. Any body may be thrown into vibrations of some sort, but the character of the waves formed varies (1.) with the state of the body, whether solid, liquid, or aeriform; (2.) with its form and specific properties, and (3.) with the nature of the disturbing force. Formation of undulations. If an elastic cord, AX, fixed at one end, be stretched by the hand grasping the other end, and the hand be jerked upward, an apparent move- ment will be transmitted along the cord, like the waves upon A x water. The first effect of the jerk will be to produce the crest, A EN, which rises above the position of repose. This will be succeeded by the corresponding hollow, N D O, depressed below the horizontal plane to the same extent. If the cord be jerked but once, the curve, A E N D O, will advance along the cord, as- suming successively the positions II and III until it reaches the end, X. It will then return in an inverted curve, IV, V, and VI, again to the hand. The curve, A E N D O, Fig. 1 62, is called a wave. A N O is the length of the wave. H E is the height of the wave. D P is the depth of the wave. A E N is called the phase of elevation of the wave. X D O is called the phase of depression of the wave. The greatest distance through which any particle moves is called the amplitude of vibration, or the intensity of the wave. It equals the sum of the height and depth of the wave, H E + D P. 198 NATURAL PHILOSOPHY. 368. Although the particles of the cord appear to move from one end to the other, it is evident that this is impos- sible, but that each particle has moved only up and down, successively passing through the highest and lowest points of the wave. A wave which moves in a certain direction by the successive motion of material particles, is called a progressive undulation. If a pebble be dropped into a placid pool, a circular elevation will be formed around the depression caused by the pebble. The gravity of the liquid particles tends to bring them to their former level, but their inertia will carry them below the horizontal plane, and, at the same time, extend the impulse to surrounding particles. In this way, progressive undulations will be produced in ever widening circles. Each undulation will consist of a phase of elevation and of depression. The motion of each particle, in obedience to the original impulse, and to the force of gravity, can only be up and down, as i,s proved by the alternate rise and fall of bodies floating on the surface. A progressive undulation is, therefore, merely an advancing form, and any apparent progression of the particles of the wave is merely an optical illusion. The circular waves of liquids decrease in intensity, and finally be- come inappreciable, because the number of particles through which the impulse is diffused increases as the circles widen. 369. The surface waves of fluids are propagated by gravity. All other waves are dependent, mainly, on the elastic force developed among the particles of a body by the disturbing force. Any body through which waves are transmitted is called a medium. Undulations may be confined to the body in which they are formed, or may be formed in one body and transmitted through several others. Thus, the vibrations of solids may be transmitted to water, to the atmosphere, or to other solids. 370. The undulations of solids are dependent on the degree of their elasticity and the manner l.y which it is developed. Solids of an elongated form. MS rods and tense cords, are subject to (1.) transverse, (2.) torsional. and (3.) longitudinal vibrations, arrordin-- a< their clastic force is developed by flexure, torsion, or traction. - D LXDULATIONS OF SOLIDS. 199 If a rubber tube be suspended from one end, and stretched by a weight at the other, and the weight be pulled down and suddenly let go. the cord will perform a series of longitudinal vibration*, causing the weight, A, to oscillate alternately above and below its normal position. If the weight be turned to one side, so as to twist the cord, and let go, the torsion of the cord will cause the weight to oscillate back beyond its original position, and then return in a series of torsional vibrations. If the cord be stretched and made fast at both ends, and then plucked at the center, by drawing it out and letting it go, it will oscillate to and fro in transverse vibration*, as shown by the dotted lines of the figure. FlG ' 163 In each case, the elasticity of the cord tends to restore it to the normal position, the inertia of the cord carries it beyond, and again develops the elastic force. The greater the disturbing force, the greater will be the amplitude of the vibration, E D ; but as the elastic force increases with the amplitude, the time of vibration will be the same. Thus the vibrations of an elastic body, like those of the pendulum, are isochronous, or performed in equal times. Therefore, the vibrations of the same body will be continued in equal times, though with decreasing amplitude, until they are brought to rest by gravity and the resistance of the air. The strings of musical instruments vibrate transversely. Such vibrations are called stationary, because all the parti- cles assume and complete their vibration at the same time. The motion from E to D is called a simple vibration ; the motion from E back to the same point is called a double or complete vibration. Hereafter the word vibration will be used to denote complete vibrations, unless the contrary is distinctly stated. 371. Let the cord AB be divided into any number of equal parts, and be fixed temporarily at the points of divis- ion, as N and X', and let the segments be set in vibration in contrary directions at the same time, as shown in Fig. 164. Now, if the points N and N' are set free, no 200 NATURAL PHILOSOPHY. change will take place in the vibrations of the cord. The cord will remain at rest at the points N and N', y-v /x v -I" an( l stationary undula- tions will be formed FlQ 164 along the cord, whose phases of elevation and depression will be alternately above and below the line A B. Rings of paper placed along the cord will be thrown into vibration at every other point than N and N'. Points at rest in a vibrating body are called nodes, as N and N'. 372. Progressive undulations may be converted into stationary. Suppose a progressive undulation to be started along the cord, AB, by a single jerk; and suppose the pulse, A ?n, to be completed in half a second. The advancing wave, E F, will reach the end of the cord in one second, and will then begin to return. At this moment, let an equal impulse be started at G. The two pulses will meet at the center of the cord in opposite directions ; the FIG. 165. advancing wave will tend to move the point m downward, the re- flected wave will have an equal tendency to move it upward. The point, m, being thus urged by two equal and oppo>ite forces at the same time, will become a node. The two halves of the cord will then vibrate independently of each other, in >tati.mary undulating. l',y timing the pulses, so that each shall oeeupy one-third. one-fourth, etc., of tin- length of the cord, three, four, etc., nodes will be formed along the string. The segments between the nodes vibrate independently of each other a~ stationary undulations, two, three, or four times faster than the cord vibrates a- a whole. The theoretical length of a wave is that of two segments, including one phase of elevation and one of NODES. 201 depression. The position of the nodal points can be ascertained by placing on the cord light rings of paper; these will be thrown off at any point other than a node. 373, A cord which vibrates transversely along its whole length, can be made to vibrate in any number of segments, FIG. 166. by gently touching it at one of its nodal points, one-half, one-third, one-fourth, etc., of its length, either at the mo- ment the cord is set in motion, or after it has begun to vibrate. The touch quenches the vibration at the point, and the string divides into two, three, four, or more seg- ments, according to the distance of the point touched from the end. Fig. 166. 374, The vibrations of all elastic solids bear a general resemblance to those of cords. Transverse vibrations may be excited in cords, rods, or thin plates, by percussion, or by the friction of a resined fiddle-bow. Longitudinal vibrations may be produced in cords and rods by rapidly rubbing them in the direction of their length with a bit of cloth or leather covered with powdered resin. The trans- verse vibrations of cords are maintained by the tension em- ployed in stretching them. All other vibrations are main- tained by the elasticity of the material. By so much as this molecular elasticity differs from that developed by ten- sion, will the rapidity of the vibration differ from the 202 NATURAL PHILOSOPHY. transverse vibrations of cords. The same rod will vibrate longitudinally much faster than transversely. 375. The nodal lines in plates may bo shown by a plate of glass or metal fastened in a horizontal vice. If the plate be covered with fine sand and set into vibration, the sand will be thrown off from the parts in vibra- tion and will gather about the nodal points. If the vibrations of the plate are quenched at any point by touching the plate, nodal lines will be formed sym- metrically on the plate, as shown by Fig. 167. In this way, an almost infinite number of nodal lines may be formed. If a thin goblet or finger glass be partially filled with water, and FIG. w*. then rubbed on the edge with a wet finger, the glass will emit a musical sound, and waves and nodal lines will be formed on the surface of the water. 376. Undulations in liquids, The circular waves formed on tin- surface y their strady aetion, enough of this sort of motion to produce the oceanic urn-nts. It is generally lie- lieved that the currents of the ocean are due to the difference in tern- UNDULATIONS IN GASES. 205 perature and density of its different parts, aided by the rotation of , the earth on its axis. .Ar" 381. Undulations in aeriform bodies. Surface waves, which are due to the force of gravity, may be produced in gases as well as in liquids. Aeriform bodies are also subject to undulations, caused by their elasticity, which are called waves of condensation and rarefaction. If the piston in the air syringe, Fig. 279, be driven to the bottom of the cylinder, and the pressure be suddenly removed, the elasticity of the condensed air will force the piston upward. If there were no resistance to be overcome, the inertia of the air would cause it to expand beyond its original volume. It would then contract again, and thus the piston would be made to oscillate about the position of repose. In the same way, the load attached to the weight lifter, Fig. 148, oscillates by the alternate rarefaction and condensation of the air within the receiver. 382. The same phenomena will take place in free air. Let a soap bubble, containing a mixture of oxygen and hydrogen, be exploded by the flame of a candle. The vapor formed by the chemical union of these elements fills a sphere many times greater than the soap bubble, and thus a rarefaction will be produced at the center of disturb- ance. The pressure of the surrounding air w r ill then cause the vapor sphere to contract; its elasticity will again impel it outward, and thus it will continue to oscillate by alternate rarefaction and condensation, until at length its oscillation ceases. The surrounding particles of air will partake of these motions. When the vapor sphere expands, the shell of air inclosing it will be condensed, and again expand as the vapor contracts. This aerial shell will, in like manner, act upon a second exterior shell ; it, in turn, upon another, and so on. Thus the initial force will be propagated in a series of alternate condensations and rarefactions, extending in spheres about the center of disturbance. These movements are analogous to the waves on the sur- face of liquids, extending in circles from the center ; the 206 NATURAL PHILOSOPHY. phase of elevation corresponds to the condensation, and the phase of depression to the rarefaction. An aerial wave consists of a condensation and a rarefaction. Fig. 169 is an attempt to represent to the eye four aerial waves. 383. The propagation of aerial undulations will be best understood by considering the motion of the particles along one of the rays of the sphere, as a x. a b c x .x! .'"r r N a"" //"' KM;. 170. Let the II|I|MT line <>f l.i- rcpi-.-cnt tin- iiir purticlrs alon^ one of the radii, in a state of rest, :mli*i'n-ity is feeble, so that their vibra- tions are slow and inaudible. Steel, glass, silver, brass, and cat -gut are sonorous, because these substances are highly Clastic, and possess sufficient force for rapid vibrations. Edison's phonograph is an interesting proof that sounds are due to vibrations. It consists of an elastic plate, to the center of which a bard stylus is so attached that it plays above a sheet of tin-foil, which is made to cover a cylinder whose surface is cut into the form of a screw. On turning the cylinder, and at the same time speaking (it the ela.-tic plate, the stylus forms indentations in the tin-foil which cor- r. -pond to the sounds uttered. After the tin-foil has In-, n indented, if the cylinder is n-v.lved as before, the sounds will be reproduced by tin- elastic membrane with greater or less fidelity. 396. Quality of sound. Noise is the sensation produced bv unequal "i % confused vibrations. A niu>ical sound is pro. duccd by vibrations ivrurriiii: at >lmrt and equal intervals. If the vibrations are rapid, the sound is high, or acute; /.v77-:.v>vrr OF SOUND. 215 but if slow, the sounds are low or grave. Therefore, the pitch, or tone, depends on tliy the vibra- tion of the column of air within the jar. At any height above or below this level, the inten- sity of the sound will he less- ened. The length of the air column diniiiiMi.-s u ih.- rapidity <.f vibration increases, and is always one-fourth of the length of the wave produced by the fork. Fio. 177. QUALITIES OF MEDIA. 217 399. Sympathetic vibrations are always produced when one sounding body vibrates near another capable of emitting the same tone. Thus, if the voice utters a prolonged tone near a piano, that wire will be set in vibration whose sound is in unison with the pitch of the voice. By changing the pitch, other wires will respond. This is because the sono- rous waves excite to vibration wires which are capable of vibrating at the same rate. 400. dualities of media. The experiment in (394) proves that sound diminishes in intensity as the air is rarefied. If the receiver be filled with other gases, it will be found that the bell has a feeble sound in gases lighter than air, as hydrogen, and an intense sound in gases denser than air, as carbonic acid. Hence, Hie intensity of sound depends on the density of the medium in which it is generated. These experiments are confirmed by the facts that the sound of a pistol fired on the tops of high mountains re- sembles the report of a fire-cracker, while a whisper is painfully loud to the occupants of a diving bell sunk to a considerable depth. The energy with which liquids and solids transmit sound, exceeds that of the atmosphere. Franklin found that a person with his head under water could hear the sound of two stones struck together at the distance of half a mile. The scratch of a pin at the end of a long stick of timber seems loud to a person whose ear is at the other end. 401. Mixed media. If the lungs be filled with hydrogen, the voice is weak and piping. A bell under a glass re- ceiver is less distinct than in the open air, although glass is among the best conductors of sound. A noise made under water is feebly heard in air, and vice versa. Hence, the intensity of sound i* diminisJied in passing from one medium to another. The conducting power of air is diminished when it is disturbed by alternating currents of different densities. For this reason, sounds 218 NATURAL PHILOSOPHY. are less distinct by day than by ni^ht. So, also, peals of thunder penetrate to a less distance than would be anticipated from their in- tensity. 402. Limits of hearing. All ears are deaf to some vibrations. The gravest sound perceptible to the human ear is produced by sixteen complete vibrations in a second; the highest sound is caused by thirty-eight thousand com- plete vibrations in a second. The auditory range is not the same for all persons. Some can not hear the highest notes of a piano, others are insensible to the note of a cricket, or even the chirrup of a house swallow. The hearing of these persons may be exceedingly acute within their limit; that is, they may be able to distinguish very feeble sounds, as the lowest whisper. Naturalists assert that many insects produce sounds that are perfectly appreciated by their mates, although too acute for human ears. 403. The distance at which sound is audible varies with it< original intensity and the circumstances which modify it. Still air, of great density and uniform temperature, is favorable to the transmission of sound. Under ordinary circumstances, a powerful voice is distinct at a distance of seven hundred feet. In the arctic regions. Lieutenant Foster conver.-ed with a sailor at the distance of a mile and a quarter. The cry of a sentinel, "All's well," has been conveyed, in still air, over calm water, ten miles. Winds and currents increase or diminish the conducting power of air, according to their direction and force. Tin- earth transmits sound further than air. The cannonading at Antwerp, in ls:Ji_'. was heard in the mines of Saxony, three hundred and twenty miles distant. 404. Acoustic tubes. If the sonorous wave is not per- mitted to expand, its intensity can lie maintained tor a great di>tance. This may be effected bv causing the wave to pa- through a tube. Speaking tubes are employed in buildings for transmitting messages from one story to another. If the tube terminate in a suitable sounding box, VELOCITY OF SOUX1'. 219 a complicated symphony, played hy a hand in the basement, is perfectly transmitted to an upper hall, though inaudible in the intermediate stones. 405. The speaking trumpets employed by firemen and mariners reenforce the voice by the vibrations of the column of air contained in the trumpet, and thus increase its in- tensity. The hearing trumpet is in principle the same, though its form is the reverse of the speaking trumpet. The sonorous wave which reaches the trumpet transmits its compression or rarefaction to portions of air smaller and smaller, and thus transmits it with increasing intensity. The form of the external ear is favorable to the collection of sound. The hand held concave behind the ear concen- trates the sound in the same manner. 406. Velocity of sound. Every one must have noticed that the flash of a distant gun is seen before the report is heard. Experiments based on this observation have de- termined that the velocity of sound in still air at 32 F. is one tln:"*nnd and ninety feet per second. The velocity increases as the temperature rises, at the rate of 1.12 feet for every degree Fahrenheit. At 60 F., sound has a velocity of eleven hundred and twenty-one feet per second. The velocity also varies with the direction and velocity of the wind. These facts enable us to compute the distance of a sound- ing body, when the time of transmission is known. When a flash of light accompanies the sound, the distance may be found by multiplying the velocity of sound by the number of seconds that elapse between the flash and the report. Thus, if when the air is at 80 F., five seconds elapse between a flash of lightning and the succeeding peal of thunder, the stroke is 1150 X 5= 5750 feet distant. In the same manner, we may estimate the height of a cliff by dropping a stone from the top and noting the number of seconds that elapse before the sound is returned to the ear. Suppose the time to be eight seconds. A j>urt of the time, r, was occupied by the falling body, the rest, y, by the sound ; hence, 220 NATURAL PHILOSOPHY. x + y = 8, but by the law of falling bodies x 2 X ISy? equals the height of the cliff; by the law of the transmission of sound, 1090 y also equals the height. Hence, z 2 . 16^ = 1090 y. From these two equations y ~ 0.77 -f ; therefore, the height of the cliff is 839.7 feet. 407. The different notes simultaneously produced by the instruments of an orchestra reach the ear of a distant auditor at the same moment. This proves that all sounds are transmitted wiifi Hie same velocity in the same medium. If this were not so, a musical performance would produce only discords to all except those in the immediate vicinity. This law is strictly true only for sounds not differing greatly in intensity, for it has been noticed that the report of a cannon is some- times heard before the command given to fire. Mathematical inves- tigations also lead to the conclusion that a very intense sound, like a peal of thunder, is transmitted with greater velocity than a gentler one. 408. The velocity of sound in gases is directly propor- tioned to the square root of their elasticity, and inversely as the square root of their density, vccve-i-d. This is shown by the following table : Telocity of Sound in Gases at 32 f 1 . I'"t. Feet. Air 1090 Oxygen 1040 Hydrogen 4164 Carbonic oxide 1107 Carbonic acid 858 Protoxide of nitrogen 859 In this table, the elasticity and density are due to the pressure of one atmosphere. By Mariotte's law the density varies with the elas- t icity, so that any decrease in density is counteracted by an equal decrease in elasticity. Therefore, sound will move up or down a mountain, or at any altitude, with the same velocity as at the base, if the temperature is uniform. The effect of heat on gases submitted to a constant pressure is to increase their elasticity without altering their den.-ity. Hence, as the heat is generally greater at lower alti- tii'l.-, tin- velocity of -Diiinl in air will generally be greater at the sea level than on mountain tops. Newton applied these facts in cal- culating the velocity of sound in air. The velocity obtained by theory is about one-sixth less than that found by experiment. This discrepancy is due to the fact that condensation develops heat, and CO-EXISTENCE OF SOUNDS. 221 rarefaction produces cold. Hence, the condensation of the sonorous wave is accomplished with greater rapidity, because the heat devel- oped increases the elastic force between the particles ; the rarefaction of the wave is also more rapid, because the cold produced diminishes the elastic force to be overcome. Therefore, the velocity of the wave must be augmented both by the heat and by the cold developed in its progress. This result would not follow if the heat were transmitted to contiguous particles. 409. The velocity of sound in liquids and solids is greater than in air, because their elastic force increases in greater ratio than their density. The velocity of sound in fresh water is four thousand seven hundred feet per second. In sea water it is a little more, and in alcohol nearly one- fourth less. The velocity of sound per second, in lead, is four thousand and thirty feet; in silver, five thousand seven hundred and seventeen feet; in steel and glass, sixteen thousand six hundred feet; in pine, ten thousand nine hundred feet; in ash, fifteen thousand three hundred and fourteen feet. The difference of velocity in solids and in air may be demonstrated by placing the ear at one end of a long bar or wall, while an assistant strikes a blow at the other end. Two sounds will reach the ear, the first through the solid, and the other through the air. The interval between them will vary with the length of the solid. The approach of a railway train may be soonest heard by applying the ear to the rail. The velocity of sound varies also with the mole- cular structure of the medium. Wood conducts sound in the direction of its fiber two or three times faster than across the grain. 410. Co-existence of sonorous waves. Many sounds may be transmitted at the same time in the same medium with- out modifying each other. A cultivated ear can readily distinguish the sound of each instrument in an orchestra. This i.< analogous to the little waves formed on the large billows of the ocean. A very intense sound deafens the ear so as to render feeble sounds inaudible. 222 XATURAL PHILOSOPHY. 411. Combinations of sonorous waves. Many feeble sounds separately inaudible, may unite to produce a sort of murmur, as is exemplified in tbe rustle of leaves, or the hum of a whispering school. Two sonorous waves, meeting in the same phase, form a resultant wave of in- creased intensity. 412. Interference of sonorous waves. If two sonorous waves of equal intensity, meet in opposite phases, both are destroyed, and silence results. The feeble sound of a tuning fork, held in the hand, is mostly due to the par- tial interference of the two waves produced, by each prong vibrating in an opposite direction. If a tuning fork, when vibrating, is turned slowly round, about a foot from the ear, four positions will be found in which the interference is total, and no sound is heard. If two tuning forks, vibrating respectively two hundred and fifty- five and two hundred and fifty-six times in a second, are sounded together, they will, at first, combine to produce a louder sound than either could alone, for both generate waves in which condensation corresponds with condensation, and rarefaction with rarefaction. At the one hundred and twenty-eighth vibration, one will have gained half a vibration on the other, and their phases are in complete op- position and there will be no sound, because the condensation of one wave is neutralized by the rarefaction of the other. For the next half second, the interference is less and less, and at the end of the second they airain combine. At every even nninbrr of half seconds the sound will be doubled in intensity, and at every odd number dest roved. This alternate combination and interference is known to musicians by the name of beats. The number of beats in a second is always equal to the difference in the two rates of vibration. If the forks vibrate in unison no beats will be heard. If one vibrates two hun- dred and fifty and the other vibrates two hundred and fifty-six times in a second, the number of beats will be six. 413. The reflection of sound is in accordance with the laws already deduced for the reflection of wave.-. (.'N7. ) A sonorous wave, reflected from a surface of <-OHH, In-able magnitude, is returned to the ear with more or less distincl- 11688, in proportion to the distance of the .-urface. The ECHOES. 223 repetition of a sound by reflection is called an echo. Articu- late sounds require a distance of one hundred and nine feet to produce a distinct echo, because the voice can not utter, nor the ear hear, more than five syllables in a second. At a distance of one hundred and nine feet, a monosyllabic echo may be perfect; but if a word of two syllables be pronounced, the echo of the first will be commingled with the direct sound of the second, and confusion will result. At a distance of two, three, or more times one hundred and nine feet, the echo will be dissyllabic, trisyl- labic, and so on. In Woodstock Park, England, is an echo from a reflecting surface twenty-two hundred and eighty feet distant, which returns seventeen syllables by day, and twenty by night. 414. Multiple echoes are those which repeat the same sound several times. This happens when two surfaces, as parallel walls, reflect the sound successively. An echo in Italy repeats the same sound thirty times. When a cannon is fired on the shores of Echo Lake, in New Hampshire, the sound is reflected from a succession of cliffs, at different distances, and produces an echo like a peal of thunder. The reverberation of thunder is also due to echoes, for sound is reflected not only from solid surfaces, but also from clouds, drops of water, and even on passing into air of greater density than its own. In foggy weather, sounds are rapidly enfeebled, because they undergo so many partial reflections. 415. The echo may be heard when the direct sound is inaudible. Thus, if the ear be placed in the focus of a con- cave mirror, the ticking of a watch may be heard at a distance, when it would be otherwise inaudible. The sound will be strengthened, if the watch be also placed in the focus of another mirror, opposite to the first, Fig. 174. The same effect may be produced in rooms having smooth walls of a continuous curved form. In such a chamber, a whisper at one focus will be audible at the other, because the undulations reflected from the different points of the walls will be collected at the other focus. The direct rays will be feeble in comparison, and on this account, two persons in the foci could converse, and yi-t be inaudible to a company at any place between them. Such whispering galleries 224 NATURAL PHILOSOPHY. are not uncommon. The dome of St. Paul's Cathedral, London, and of the Capitol, at Washington, are fine examples. 416. Resonance. The increased intensity produced by the commingling of the direct and reflected sonorous waves is called resonance. Resonance is specially noticeable in empty rooms, with bare smooth walls. If the rooms are small, the direct and reflected waves strike the ear at about the same time, and strengthen the original sound without diminishing its clearness. This will be the case, if the echoing walls are not distant more than thirty-five feet from the speaker, for at that distance the reflected wave will go and return in one-sixteenth of a second, which is found to be the limit of perceptibility. Such rooms are easier to speak in than the open air. In large halls, the direct and reflected waves only partially coincide, and the words are less distinct. If, however, the echoes are quenched by the furniture, or by the presence of an audi- ence, the direct waves only are heard, and the words are distinct. Some resonance is desirable, if the room is very large and the speaker's voice weak. The wall behind the speaker should be made ti> aid the voice, by being a good reflecting surface of proper shape. The ceiling should not be too high, and the room should be rather longer than broad. The echoes from distant walls should be broken up by galleries, and no large and distant surfaces should be parallel to nearer ones. 417. Sound may also be refracted, or bent out of its course, in passing from one medium to another. The laws of refracted sound are the same as those of light, and will be treated hereafter. 418. Recapitulation. 1. The quality of sound depends on the elasticity and form of the .-.norous body. 2. Tlu- pitch of sound depends on the nito of the vibrations. 3. The intensity of sound in< i 1. With the amplitude of the vibrations. 2. With the den-it y of the ireneratint; medium. .",. My the proximity of a n-,,n:int body. MUSICAL SOUNDS. 225 The intensity of sound decreases 1. As the square of the distance increases. In passing from one medium to another. Is maintained or strengthened by acoustic tubes. 4. The velocity of sound is not dependent on quality, pitch, or intensity, but varies with the elasticity and density of the medium. ( (1) May co-exist in the same medium. 5. Sonorous waves 4 (2) May combine and interfere. (_ (3) May be reflected or refracted. MUSICAL SOUNDS. 419. The ear recognizes all sounds of pure tone as agree- able. Nearly thirty -eight thousand different sound waves are possible, each one of which will, by itself, produce a pure tone. If all these were produced in succession, the most practiced ear would be able to distinguish, as distinct tones, less than the one-hundredth part of them. This is because two tones, whose rates of vibration are nearly the same, can be distinguished from unison only by the formation of beats. If the beats are not readily perceptible, the ear recognizes the sounds as the same. Any tone may be selected for a basis of comparison, to which all others are either higher or lower. 420. Suppose a guitar string, or wire, to be stretched across a sounding box, of the form represented in Fig. 178, which is called the sonometer, or monochord. When the whole length of the string vibrates, it produces a sound called the fundamental tone of the string. It may, of course, be any one of the thirty-eight thousand perceptible tones. Suppose the tone to be that due to one hundred and twenty-eight complete vibrations in a second, as meas- ured by the toothed wheel or the syren. Musicians have agreed to designate this tone as Cj. It corresponds to C, in the second space of the base clef. If, now, the bridge, B, be placed at half the length of the string, the half N. P. 15. 226 NATURAL PHILOSOPHY. string will make two hundred and fifty-six vibrations in a second, or twice as many as the fundamental. The tone produced is C 2 , which corresponds to middle C of the piano. If the string be again shortened, by placing the bridge at one-fourth its length, the number of vibrations will be again doubled, and the new tone, C 3 , will corre- spond to C, in the third space of the treble clef, due to five hundred and twelve vibrations per second. Every successive halving of the string will double the rate of vibration, and produce in succession C 4 , C 5 , and so on. On the other hand, if strings be taken two, four, eight times the length of the original string, the rates of vibration will be diminished in the ratio one-half, one-fourth, one-eighth, and produce respectively the tones C_,, C_ 2 , C_ 3 , corre- sponding to sixty-four, thirty-two, and sixteen vibrations pel- second. If these tones were produced in succession, the relation- between vibrations of the strings are represented by the numbers 1 : 2 : 4 : 8 : 16 : 32, etc. The ratio between any two tones is called an interval, ami indicates how much one sound is higher than another. The interval 1 : 2 which exists between the tones of the Beriee found is called an octave, because between any two tonei hearinir this ratio, other tones having simple relations may be placed, so as to form, with the two extremes, a series of ri'jht -oiimU having airreealile relations to each other. 421. These eight tones constitute the diatonic scale or gamut, in music. They are designated by the first seven DIATONIC SCALE. 227 letters of the alphabet. If the length of the string which sounds: the fundamental be assumed as 1, the relative length required to produce the other tones of the scale are : Tones CDEFGAB C Relative length of cord I I f I I f A i The relative number of vibrations corresponding to these tones is expressed by the reciprocals of these numbers, as follows : Tones CDEFGAB C Relative No. of vibrations.. 1 f f t f f V 5 2 Therefore, (1.) The number of vibrations per second is in- >> I'M-ly proportioned to tJie length of the string. These tones may also be produced by increasing the ten- sion of the string, without altering its length. This may be done by increasing the weights, P, by which the string is stretched. To double the number of vibrations, the stretch- ing weight must be quadrupled. Tones CDEFGAB C Relative stretching weight.. 1 f f f V 5 f V * 4 Therefore, (2.) The number of vibrations per second varies as the square root of the weight by which the string is stretched. As the elastic force of a string is dependent both on its density and diameter, these functions modify the rate of vibrations produced by strings of the same length and ten- sion. Their combined effect determines the weight of a string. A string four times as heavy as another, makes but half the number of vibrations. Tones CDEFGAB C Relative weight of string.... 1 ff |f T 9 5 f & & \ Hence, (3.) The number of vibrations per second varies in- > ra /// as the square root of the weight of a given length of string. 228 NATURAL PHILOSOPHY. All these laws may be proved by tin- sonometer. All are applied in the construction of stringed instruments. A bar}) or piano is a good example. The high notes are produced by short, thin strings; the low notes by long, heavy ones; the strings are brought to the proper pitch by tension, applied at the pegs. 422. The absolute number of vibrations per second in any tone may be found by multiplying the number found for C, by the fractions f, f, etc., which express the rela- tive number. Thus, the upper octave of the base clef is produced by the following series : Tones Cj D x E : F a Gj AJ Bj C 2 Absolute No. of vibrations.. 128 144 160 170| 192 213 240 256 The absolute number of vibrations in the higher scales is obtained by multiplying these numbers by two, four, eight, etc., while for lower scales the same numbers are divided by two, four, eight. Thus, the number of vibrations of A 3 is 213 X4 853 in a second. The actual number employed by orchestras in different cities is not the same. For this reason a congress of musicians has adopted the following scale, which gives all the tones of the lower octave of the treble in whole numbers. Tones C 2 D 2 E 2 F 2 G 2 A 2 B 2 C 3 New scale of vibrations 264 297 330 352 396 440 495 528 423. The length of a sonorous wave may readily be found by dividing the velocity with which sound travels in a second by the number of vibrations in the same time. In air at 60 F., sound moves about eleven hundred and twenty-one feet per second. The length of the wave C, is, therefore, 1121 -4- 128 = 8.7 feet. C 2 = 4.3 feet, C 4 = 1.1 feet. It must lie borne in mind that the length of the wave varies with the medium and the temperature. 424. The interval between any two tones is called a musical interval. Musical intervals an- named by the order of their position with respect to any note taken as the fun- damental, as seconds, thirds, fourths, etc. The interval of the fifth, a< C(J, or (J I) 2 , is expressed ly the ratio 3 : 2, or . The numerical value of any interval is obtained by MUSICAL SCALE. 229 dividing the number of vibrations in a given tone by the mimlH-r of vibrations in that preceding it. The table on this page is a summary of the results already obtained for two octaves of the diatonic scale. W- & o 4 . t- OQ pq "3 N OQ O an( l is the least interval usually regarded in music. Any less interval is called a comma, though this term is more specifically applied to the ratio between a major and minor tone f -r- y = f J. When two tones differ only by a comma, they are generally reckoned as of the same value in music, consequently the intervals f and ^ are taken as whole tones of equal value, and the intervals } -; and ri ,' as equal semitones, although they differ respectively by f^ and yff. The interval between C E, F A, or G B, contains two whole tones, and is called a major third; its value is f X V = ! The interval between EG, AC 2 , or BD 2 , contains one whole tone and one semi- tone, and is called a minor third; its value is f X If = f The in- terval, DF, differs from a minor third only by a comma; y X if X 425. The pleasure derived from music depends on the frequent recurrence of vibrations in the same phase. When different tones are produced in close succession, or simul- taneously, the effect on the ear will be more or less agree- able, according us the relations between their vibrations are simple or complex. If the ratio between any two sets of vi- brations can be expressed by whole numbers, less than five or six, the combination will be pleasant. Melody is due to the succession of single tones, having agreeable relations to each other. The air in a piece of music is an example of melody. A chord is due to the simultaneous production of two or more tones in agreeable relations to each other. A harnnniii is a melodious succession <>f chords. The air, in music, with the accompaniment, constitutes a harmony. Notes in unison are agreeable, IMT.IU-C their vibrations an- coinci- dent throughout. Next in order is the chord of the octave, because every alternate vibration of the higher tone coincides with the funda- mental, in the same phase. Then follow in turn the iifth, the fourth, the major third, and the minor third. The second and seventh are CHORDS. 231 by no means equally pleasant, because the coincidences are less fre- quent. Below, is an attempt to represent the relations between the simple chords. The dots represent the rarefaction of the wave, the lines the condensation ; the long lines mark coincidences in the phase of condensation. Unison. 1 : 1. As CC. Octave. 2:1. As CC 2 , DD 2 . gj| Fifth. 3 : 2. As CG, FC 2 . g | Fourth. 4:3. As C F, AD 2 . | Major third. 5:4. As C E, F A. | 'l*-' I '",' I ' ! Minor third. 6:5. As E G, A C 2 g I 426. Compound chords are formed of three or more tones, which, when taken two and two, are harmonious. A perfect major chord consists of three simultaneous tones, such that the first and second form a major third, the second and third a minor third, and the first and third a perfect fifth. Thus CEG or FAC 2 constitute a perfect major chord, because their intervals taken two and two are C E f , EG |, C G %. The ratios of this triad are very simple, 4:5:6, and the number of coincident vibrations very many. If the same intervals are taken in the order of a minor third, major third, and perfect fifth, the tones form a perfect minor chord. Thus, DFA or EGB ascend in the order DF -J, FA }, D A f , and form a perfect minor chord. 427. The diatonic scale is composed of unequal intervals, because this disposition of the vibrations is found to result in a greater number of concords than would be possible if the intervals were all equal. The scale has two modes. In the first, which is the most common, the first third is a major third ; in the other, the first third is a minor third : consequently, the modes are denominated the major and the minor mode. 232 .V.I TURAL PHILOSOPHY. The intervals in both scales are the same, though not in the same order. If the diatonic scale begins with C, the mode is major, and the semitones occur in the third and seventh intervals. If the dia- tonic scale begins with A, the mode is minor, and the semitones are found in the second and filth intervals. Because the ear seems to require that the seventh interval should always be a semitone, there is this additional peculiarity in the minor mode, that the seventh note is sharped, so as to make the last interval a semitone, as in the major mode. The sixth interval thereby becomes a tone and a half. The sharped seventh is called the accidental seventh, and is considered essential to the minor mode in the ascending scale. 428, Musicians interpolate other notes in the scale by means of sharps and flats, which are indicated by the signs $ and fc. A note is sharped or flatted by multiplying its value, respectively, by ff, or by ff. The tone of the note is thereby raised or lowered a chromatic semitone. If the lower note of the interval of a minor tone is sharpened, or the higher note flattened, the reduced interval is a diatonic semitone. Thus : D D Efe E t. . *i . t "; J The interval, D Efr or D# E, is ff , a diatonic semitone. D# and E|j are not identical, but because they differ only by a comma, they are considered equivalent in music. The difference between the interpolated sharp and flat in the interval of a major tone, as F# Gfc, is nearly equal to a chromatic semitone. Upon instruments capable of modula- tion, as the violin or flute, they are not played alike by a skillful performer, in solo pieces. Upon instruments with fixed keys, the accurate rendcriii- of .-harps ami Hats would require a key-hoard so large as to be exceedingly inconvenient. For this reason, all the whole tones are made equal and divided into two equal semitones, so that the sharp of one tone is made identical with the flat of the next higher. The octave is thereby divided into twelve equal intervals, called clir<>ins, horn. Trnrrnl bodies allow light to pass freely through them; as glass, water, air. 7'/v///x- lucent bodies transmit light so imperfectly that objects can not be clearly seen through them ; MS ground glass, horn. Opaffue bodies do not transmit light; as wood and the metals. 441. Luminous bodies are those in which light originate-; as the sun and burning bodies. Non-luminous bodies origi- SOURCES OF LIGHT. 239 nate no light, luit may be rendered temporarily luminous ly the presence of a self-luminous body; thus, a lighted candle renders adjacent objects luminous. 442. a The sources of light are (1.) mechanical action, (2.) chemical action, (3.) electricity, (4.) phosphorescence, and (5.) the heavenly bodies. Any solid, on being raised to 977 F., begins to emit light, of a dull, red color, and is then said to be incandes- cent. The light of incandescent bodies varies with the in- tensity of the heat. At 1280 F. it is bright red; at 1440 F., blue; at 2000 F., orange; at 2130 F., white; and it continues to increase in brilliancy above this temperature. A current of gas does not become luminous at 2000 F. Mechanical action may produce sufficient heat to render solids incandescent. Thus, sparks of light are produced when flint and steel are struck violently together. M>i artificial lights depend on the ignition of solid particles in the intense heat developed by chemical action. If oxygen and hydrogen are burned together an intense heat is pro- duced, but the light is feeble, because the product of the combustion is gaseous. If, however, a solid, as a bit of lime, is held in the flame, it becomes incandescent, and emits a light of great intensity. In ordinary combustion, the hydro-carbons contained in the oil, coal, gas, etc., are decomposed by the heat; the hydrogen then burns with a pale flame ; into this flame the solid particles of the carbon rise, become incandescent, and finally burn. The transient light of the electric spark and the brilliant glare of lightning are familiarly known, but electricity may be made to furnish a continuous and abundant supply of light Phosjihorescence is a pale light, emitted in the dark, with- out any manifestation of heat. The light of the glow- worm and the fire-fly are examples. In tropical climates, the sea is often covered with a bright phosphorescence, due 240 NATURAL PHILOSOPHY. to extremely small animalculse. Under certain conditions, rotten wood and decaying flesh become phosphorescent. Phosphorescence may also be developed in some minerals by heat, friction, and crystalization. The cause of the light of the sun and the fixed stars is unknown, but the prevailing opinion is that it is due to some form of mechanical action. The moon and the planets are non-luminous; receiving from the sun the light by which they shine. 442b. The velocity of light was first ascertained by Roemer, by means of the eclipses of the first satellite of Jupiter. Jupiter is a planet attended by four moons which revolve about it, as our moon revolves about the earth. These moons are observed by the telescope to undergo fre- quent eclipses, by passing behind the body of the planet. The exact moment when the moon becomes eclipsed, as would be seen by a spectator at the mean distance of the earth from the sun, is calculated by astronomers. Both the earth and Jupiter revolve about the sun, but in different periods; consequently, they are sometimes on the same side of the sun, and sometimes on opposite sides. In the former case, the earth is about one hundred and eighty- three millions of miles, or the whole diameter of its orbit, nearer to Jupiter than in the latter. Now, it is found by observation, that the eclipse of the first moon is seen about 16fJ minutes sooner when the earth is nearest to Jupiter than when it is most remote from him; therefore, the light must occupy this time in crossing the earth's orbit. The velocity of light is then about one hundred and eighty-five thousand five hundred miles in a second. The velocity of light has also been determined by direct '\|M-riment, and found to vary in different media; being, in water, one hundred and forty-four thousand miles per second; in glass, one hundred and twenty-eiirht thousand miles ; and in diamond, seventy-seven thousand miles. 443a. Luminous bodies may he considered as a collection SHADOWS. 241 of luminous particles, or points. A luminous point may be seen in all positions of the eye, if no opaque body in- tervenes ; hence, light radiates in aU directions from every luminous point. A single line of light is called a ray. A l ncll of light is a collection of rays from the same source. The rays of a pencil naturally tend to separate from each other, or to become divergent; but they may be so modified as to pass through a common point, or become convergent; hence, we may have diverging pencils and converging pencils of light. A collection of rays which are sensibly parallel is called a beam of light. In a homogeneous medium light moves in straight lines, for if an opaque body be placed in a direct line between the eye and the luminous point, the light is intercepted. A ray of sun light admitted into a dark room is seen to be straight, by illuminating the floating particles of dust in its course. 443b. Shadows. When light falls on an opaque body, the space behind the body, from which light is excluded, is called the shadow. If the source of light be a luminous point, the shadow will be bounded by the rays tangent FlG ]84 . to the surface of the body. A section of the shadow received on a screen will increase in breadth in proportion to the distance of the screen. If the source of light have a sensible magnitude, the opaque body will cast an independent shadow for each pencil of luminous rays. Let AB, Fig. 185, represent a luminous body, and CD the section of an opaque body. The pencil from the luminous point, A, will be intercepted between the lines, CF and DH, and the pencil from B will be intercepted between the lines, C E and D F. Hence, all the light will be excluded only between the lines, CF and D F, which inclose the true shadow, or umbra. The space beyond, between the lines, C E and C F, and N. P. 16. 242 NA T URA L PHIL OS OP II Y. between DF and D H, receives light from certain points of the luminous body, and not from others. It is brighter than the true shadow, but not so bright as the illuminated space, and is, therefore, called the partial shadow, or pe- numbra. FIG. 185. If the luminous body is smaller than the opaque object, the shadow will be larger than the body; thus, if the hand be held near a candle, a gigantic shadow of the hand may be thrown on a distant wall. If the luminous body is larger than the opaque object, the breadth of the umbra will gradually diminish to a point, but the breadth of the penumbra will increase with the distance to which it is thrown. 444. Images formed by direct light. If luminous rays are transmitted through a small aperture into a dark room, and are then received on a screen, they form inverted images of external objects. The luminous rays proceed in straight lines ; those from the top of the object, Fig. 186, are received on the bottom of the screen, and those from the base of the object on the top of the screen. The rays of light, therefore, must cross each other without interfer- ing. A darkened room, so arranged, is one form of the camera obscura. A single luminous point will give an image the shape of the aperture; if the, aperture is triangular, the image will be triangular. Hence, a luminous body will give an infi- nite number of superimposed triangular images; the union of all these partial images produces a total image of the INTENSITY OF LIGHT. 243 same form of the luminous object. Therefore, the image is independent of the shape of the aperture, if the latter is sufficiently small. The image will be indistinct if the aper- ture is large, or if the screen is too far removed. It will be distorted if the screen is not perpendicular to the direction of the rav>. FIG. 186. In accordance with these principles, the images of the sun which are formed on the floor when its light is transmitted through small openings in the blinds, are round or elliptical, according to the incli- nation of its rays to the floor. Similar images are formed on the ground by the solar light passing through the dense foliage of a forest. During an eclipse the images will be more or less of a crescent shape, in proportion to the obscuration of the sun. 445. The intensity of the light varies inversely as the square of the distance from the luminous point. Suppose a luminous point, or the flame of a small candle, to be placed in the center of a hollow sphere; the whole interior surface of the sphere will be lighted by the candle. Now, since the surfaces of spheres are as the squares of their radii, each square inch of the surface will receive four times as much light, if the sphere have a radius of one foot than if its radius were two feet, and nine times more than with a radius of three feet. 244 NA TURA L PHIL OS01 '// ) . This law may be proved, experimentally, by shadows. A board having a surface one foot square, placed one foot from a candle, will cast a shadow that will cover four square feet at double the distance, nine square feet at three times the distance, and so on. The areas in- crease as the square of t he- distance, and, consequently, the intensity of light on each square inch will decrease in proportion to the square of the distance from the lumin- ous point. 446. The relative in- tensities of two lights may be compared by an application of this law. Place an opaque rod before a vertical screen of white paper, or of ground glass, and arrange the lights so that each shall cast ;i shadow of the rod on the screen. Now move one of the lights backward or forward, until a position is obtained in which both the shadows appear equally dark. If the shadows are sensibly equal, the amount of light falling on the screen from each source must be equal also; the relative intensities of the two lights are then found by squaring the distance of each light from the screen. The light which we receive from the sun, at a distance of ninety- one million miles, is equal to the concentrated glare of five thou- sand five hundred and sixty -three wax candles at the distance of a foot. The light of the full moon is three hundred thousand times less than that of the sun. The brightest of the fixed stars shines with only one twenty-thousand-millionth part of the light which we receive from the sun. For this reason, tin- stars arc invisible when the sun shines, being lost in his superior brilliance. 447. The visual angle is the angle contained between two lines drawn from the center of the eye to the two ex- tremities of the object. (1.) For the same distance, the visual angle increases with the size of the object. (2.) For DISTANCE AND SIZE. 245 the same object, the angle decreases with the distance of the object ; thus, if the same object, A B, is removed to A' B', the visual angle decreases. Hence, if the size of an object is known, we may estimate its distance by its visual angle, having learned, by experience, to associate together distance and angular size. 448. The optic angle is the angle contained between two lines drawn from a luminous point through the centers of the two eyes when they are both directed to the same point. FIG. 189. The optic angle, BAG, increases with the nearness of the object. We may judge of the relative distance of an ob- ject by the muscular effort required to turn our eyes so as to direct them toward the object. Nevertheless, this power comes only from long experience, as persons born blind, whose sight has been restored by a surgical operation, im- agine, at first, that all objects are at the same distance. 449. Our estimate of distance is more correct when many objects intervene; the stars overhead all appear at the same distance, because we have no standard for compar- ison. Finally, the more distinct an object is, the nearer it seems to be. Distant mountains, if seen for the first time in pure air, appear nearer than they really are, and the reverse if the air is foggy. 246 NATURAL PHILOSOPHY. 450. Our estimate of size is closely associated with our judgment of distance. If the object is unknown, we form an estimate of its distance by comparison with that of known objects, and then estimate its size by the visual angle. Any thing that increases our estimate of distance also in- creases our estimate of size. The moon appears larger near the horizon than when above us, because it seems more distant by reason of intervening objects. So, also, objects, seen in a fog, often appear enormously large, because they appear to be distant by reason of their indistinctness. 451. Disposition of incident light When a pencil of light falls on any substance, it is separated into parts. (1.) Some of the rays are absorbed. (2.) Some are reflected, and (3.) some may be transmitted, or, with more or less change in direction, refracted. Absorption. A very thin plate of glass is almost perfectly transparent, but as its thickness is increased, its transparency is diminished, and it may be made so thick as to transmit no light. Eacli thin layer, therefore, weakens the vibrations, so that, if they pass through a certain number of layers, the undulations become so feeble as to be insensible. Even the purest air absorbs so much light that the atmosphere would not transmit the rays of the sun, if it had the depth of seven hundred miles. On the other hand, gold may be made so thin as to transmit light of a violet-green color. 452. Recapitulation. I. Bodies are classified, in accordance with their relations to light, in regard 1. To the emission of rays { Luminous. ( Non-luminous. ("Transparent. 2. To the transmission of rays < Translucent. (. Opaque. f 1. Altsnrl>rs is an example of a plain- mirror. The most common kind- of curved mirrors an- those whose eurvature is spherical. A convex spherical mirror is a portion of the surface of a spin-re, reflecting light from the external face: PLANE MIRRORS. 249 FIG. 192. a concave spherical mirror, is a portion of the surface of a sphere reflecting light from the internal face. 458. The formation of images by plane mirrors may be determined by investigating the images due to a series of points. Let M N be a plane mir- ror, and A a luminous point. The reflected rays will make the same angles with the perpendiculars, D P, as the incident rays, and hence the reflected rays will make the same angles with each other as they did be- fore reflection, but will appear to di- verge from the point, A'. By an easy geometrical construc- tion, it may be shown that if a pencil of rays, diverging from a luminous point, fall on a plane mirror, ike reflected rays will appear to diverge from a point similarly placed behind Hie mir- ror, and at a distance equal to that of the luminous point before the mirror. Of the great number of rays emitted from a luminous point and reflected from a mirror, a few enter the eye and form a virtual image of the point. The image is called vir- tual, because the image has no real existence, and the rays only appear to come from the other side of the mirror. Let A B be an arrow in front of a mir- ror, M N. The image of the point, A, will appear to come from A'; that of B, from B', and those of intermediate points on the arrow between A 7 and W. Hence, if an object be placed before a plane mirror, the image will be formed at an equal distance behind the mirror, of the same size as the object, and equally inclined FIG. 193. to the mirror. 459. The object and image have to each other twice the inclination that each has to the mirror. Hence, trees ap- pear inverted by reflection from a tranquil surface of water. 250 NATURAL PHILOSOPHY. If the mirror and object are parallel to each other, there is a semi- inversion in one dimension only. If a pri-son stands before a vertical mirror, the image of his right hand will be on the left side of his image. So, also, if a printed page is held before a plane mirror, the letters appear reversed in a horizontal direction, or right and left. Since the angle of incidence is equal to the angle of reflection, a person may see his entire image in a vertical mirror of half his length. 460. Multiple images. If two mirrors are at right angles, a luminous point placed between them will give three images. If the mirrors are inclined 60, five images FIG. 194. are produced, and seven if the angle is 45. The number of images increases as the angle diminishes, and would be infinite when the mirrors are parallel, if the light were not gradually weakened at each successive reflection. 461. The kaleidoscope is an optical toy which illustrates this property of inclined mirrors. It consists of a paper tube containing two or more long and narrow mirrors, ni- di m-d to each other; one end of the tube is closed by Around L'luss and the other by plain glass. Small bits of colored glass are placed in a cell between the ground irlass and another glass disk, leaving just room enough for the objects to tumble about as tin- tube is turned. On looking CURVED MIRRORS. 251 through the tube, the objects and their images are seen in beautiful forms. That there may be perfect symmetry in these forms, the angle of the mirror must be an aliquot part of 360. The best inclination for two mirrors is 30. Three mirrors are usually employed, furnishing three angles of 60 each. In a well constructed instrument, an end- iriety of beautiful and symmetrical figures may be obtained. 462. Curved mirrors may be considered as made up of an infinite number of plane mirrors, inclined to each other. Each ray of light will be reflected exactly as if it fell on a plane, tan- gent at the point of incidence. Let T T'" be a section of a small portion of a spherical surface. C will be the center of curvature. The line, C V, which passes through the vertex of the mirror is called the principal axis FlQ . 195 . of the mirror, and any other line, as CC', which passes through the center of curvature is called a secondary axis. Any radius, as C I, is perpendicular to the concave surface, and its prolongation, C' I is perpendicular to the convex surface. 463. Concave spherical mirrors. If a luminous point be on the principal axis, the image formed on reflection will vary in position with the distance of the point. If the point is at an infinite distance, the rays will be sensibly parallel to the axis. M H FIG. 196. (1.) In Fig. 196, the radii, C M, C B, CD, are perpendicular to the surface. The parallel rays, H B, G D, L A, will each be reflected so that the angle of incidence for each ray equals the angle of reflec- 252 NATURAL PHILOSOPHY. tion, and hence will converge after reflection. If the mirror is not more than 10 of angular aperture, all the rays will meet at F, very nearly half-way between the center of curvature and the mirror. This point is called the principal focus of the mirror. If the luminous point is at a finite distance, the rays will be divergent. (2.) If the point is at L, beyond the center of curvature, Fig. 197, the rays will converge, on reflection, to a point, /, between the center and the principal focus. (3.) Conversely, if the luminous point is FIG. 197. at /, rays will converge, on reflection, to the point L. The points, L and /, are, therefore, called conjugate foci. The nearer the luminous point, L, is to the center of curvature, the nearer will its conjugate focus, /, approach to the center. (4.) If the luminous point be at the center of curvature, all the rays will fall perpendicularly on the mirror, and will be reflected back to the center. In all these cases the focus is real, and on the same side of the mirror as the object. (5.) If the luminous point be at the principal focus, the reflected rays will be parallel, and there will be no focus. Fig. 196. (6.) If the luminous point be be- tween the principal focus and the mirror, the rays will diverge as it from a point, /, behind the mirror. Fig. 198. This point is called the virtual focux. When the luminous point is near the principal focus, the virtual focus will heat a great di-tance In-hind the mirror; hut as the luminous point approaches the mirror, the virtual locus also approach*- it; and (7.) when the luminous point is at tin- surface, the two coincide. 464. Secondary axes. If the luminous point be on a Fio. 198. FORMATION OF IMAGES. 253 secondary axis, the focus of any point, L, will be found on this axis, 1>\ the same reason- ing as in the preceding cases. Fig. 199. 465. The images formed by concave mirrors may be de- termined by finding the foci ' f -1 A 1 FlG - 199 ' for a series of points. A col- lection of these foci will constitute an image, either real or virtual. The real image will be formed when the object is beyond the principal focus. The image is real, for it may be re- ceived on a screen, or it may be seen by placing the eye in the direction of the reflected rays. 1. If the object is at an infinite distance, no image will be formed, but there will be a concentration of light at the focus. 2. Let the object be placed at a finite distance beyond the center of curvature, as AB, Fig. 200. From the point, A, draw the secondary axis, A E, and the incident rays, A D, AH. Make the angle of reflection, a DC, equal to the angle of incidence, ADC. The point, a, where the reflected ray cuts the secondary axis, is the conjugate focus of the point, A. Similarly, b is the conjugate focus of the point, B. FIG. 200. Between these two extremes, the images of the other points of the object will be found, and hence a b is the complete image of A B. The image is inverted, smaller than the object, and placed between the center and the principal focus. 254 NATURAL rniLosoniY. 3. The image increases in size as the object approaches the principal focus. At the center, the ima.uv is inverted, of the same size as the object, and at the same distance from the mirror. 4. If the object is between the center and the principal focus, as at a b, Fig. 200, the image will be at A B inverted, beyond the center, and enlarged. The nearer the object is to the focus, the larger will be the image, and the farther beyond the center. The real image is always inverted, and recedes from the mirror as the object approaches it, and vice versa. Reflecting telescopes give a small but very distinct image of the heavenly bodies, which are viewed after being enlarged by the use of lenses. Burning mirrors are concave reflectors, which collect the parallel rays of the sun at the principal focus. The light and heat increase in intensity as the area of the mirror exceeds the area of the focus. 5. No image is formed when the object is at the principal focus, for the rays are reflected parallel. This principle is applied in light-houses. The light is placed in the focus of a concave mirror, and its rays are reflected in parallel lines from every point of the mirror. 466, The virtual image is formed when the object is between the prin- cipal focus and the mirror. 6. Let A B be an object between the principal focus and the mirror. Draw the axes, C A, C B, and produce them behind the the mirror. The pencil at A will be reflected to the eye at E, appear- ing to radiate from a, in the same axis ; likewise those from B, as from 6. The image is virtual because it is behind the mirror, erect, as the rays do not cross each other, ami < n- larged, because the visual angle of the image is larger than that of the object. The visual angle is largest, when the object is near the CONVEX MIRRORS. 255 focus. As the object approaches the mirror, the image becomes smaller, and when the object is at the surface, the image is of the same size. 467. Convex spherical mirrors. In a convex mirror all the foci are virtual. They may be found in the manner already detailed for finding the foci of concave mirrors. In Fig. 202, the parallel rays, SI, T K, take, on reflection, the directions I M, K II, which appear to diverge from the point, F, which is the principal virtual focus of the mirror. This point lies very nearly half-way between the center of curvature and the mirror. F;;:;-C FIG. 202. Kays diverging from a luminous point, as L, at a finite distance from the mirror will form a virtual focus, I, between the principal focus and the mirror. Diverging rays are rendered more divergent by reflection from a convex mirror. 468. Formation of images in convex mirrors. Let AB, Fig. 203, be an object placed at any finite distance. The pencil from A appears to radiate from a, in the same axis, A C ; that from B, as if from b, in the axis, B C. Therefore, the image formed by convex mirrors is always virtual, erect, and smaller than the object. 469a. In all cases of spherical mirrors the diameter of the image varies with the distance of the ob- ject from the mirror ; hence, the size of the image is inde- M 256 NATURAL PHILOSOPHY. pendent of the area of the mirror. An increase in the area of the mirror increases the briyhtncts of the image, by inter- cepting more of the luminous rays proceeding from the object. 469b. Spherical aberration. The laws already de- duced for the formation of foci and images from spherical mirrors, are not strictly accurate unless the mirror is a very small portion of a spherical surface. If the aper- ture of the mirror exceeds 10, the rays reflected from the borders of the mirror meet the axis nearer FIG. 204. the mirror than those which are reflected from points nearer the vertex. The effect of this is to render the image indistinct or less sharply defined. This defect is termed spin-rind < I- rut Ion by reflection. Every pair of reflected rays succes- sively intersect each other, and their foci form a curved line, called a caustic by reflection. Fig. 204. Thus, the heart-shaped curve, formed by the reflection of a lighted candle from the concave surface of a tumbler containing milk, is a caustic. Surfaces generated by the revolution of parabolas about their axes, reflect without aberration. Hence, parabolic mirrors are used for the lanterns of locomotives, because, if a luminous point be placed in the focus of a concave parabolic mirror, all the rays which fall on the mirror will be reflected exactly parallel. The light thus reflected maintains its intensity for a great distance. 470. Recapitulation. The intensity of light varies: I. When emitted by luminous bodies: 1. With the source. 2. Inversely as the square of the distance. II. When rel!ert-(l from non-luminous lto7 Crown glass 1.534 Quartz crystal 1.548 Bisulphide of carbon 1.76S Flint glass 1.830 Diamond 2.4.".! Chromate of lend... .. 2.974 474. The direction of refraction depends on the relative velocity of lijrht in the two media. The velocity of light is least in the more hiirhlv refractive media. The refractive power increases, in ^i-m-i-al. with the spe- cific gravity of the -ul.-tance ; l m t inflammable bodies, like alcohol and the essential oils, have a irn-at-T refractive power than water, although their specific gravity is less. A TMOSPHERIC REFRA CTION. 259 In optic?, the word dense is used to signify of great refract- ive power, and rare, of little refractive power, without reference to specific gravity; in this sense water is rarer than alcohol. Laws of refracted light. 1. When light passes perpendic- itlnrhj from one medium to another, it is not refracted. 2. When lifjht passes obliquely from a rarer to a denser me- dium, it is refracted toward the perpendicular. 3. When light passes obliquely from a denser to a rarer me- dium, ii is refracted from the perpendicular. 475. Total reflection. As a consequence of the third law, when light passes from a denser to a rarer medium, the angle of refraction is always greater than the angle of inci- dence. Thus, if light passes from water into air, as the angle of the inci- dent ray, I. V, I", increases, the angle of the refracted ray, R, R 1 , R 2 , also increases. There will be found some ray, as L, where the angle of refraction is a right angle, and the ray, if refracted, would co- incide with the surface OB. But if the incident angle exceeds this limit, as T, the ray can not pass into the air, but will be totally reflected to T'. The limiting angle varies inversely as the refractive power: for water, it is 48 28', for crown glass, 40 49', for diamond 24 12'. This result may be shown by fill- ing a glass with water and placing in it a silver spoon. An eye, placed a little below the level of the water, may see a bright image of the part of the spoon immersed, reflected from the surface of the water. 476. Atmospheric refraction causes the heavenly bodies to appear higher than they really are, except when in the zenith. The nearer the sun or a star is to the horizon, the greater will be the effect of the refraction in increasing its altitude. The sun and stars are visible, even when they FIG. 207. 260 NATURAL PHILOSOPHY. are below the horizon. The refractive power of a gas in- creases witli its density, and, as the successive strata of the atmosphere are denser as they approach the earth, the rays from a luminary near or below the horizon are refracted more and more, describing a curve, and appearing to the eye to be in the direction of a tangent to this curve. Twi- light is due to the successive refractions and reflections of the sun's rays when it is below the horizon. 477. When the density of the atmosphere varies from its ordinary state, the unusual refraction thus arising pro- duces various phenomena. Distant objects, not usually visible, sometimes appear to be near and elevated in the air. The looming of objects at sea is due to an increase in the density of the strata near the earth's surface. The mirage of the desert results from a decrease in the density of the strata of the air caused by contact with FIG. 208. the heated -oil. Kays from an elevated object, M, Fig. 208, are transmitted through strata \vhich grow less refract- Mid. ultimately, the incident ray reaches the limiting and i- totally reflected. The ray then rises, and is refracted in a direction contrary to the (ir>t, until it reaehes the eye in the same direction as if it had proceeded from a REFRACTION BY PARALLEL PLANES. 261 point below the ground. Hence it gives an inverted image of the object, just as if it had been reflected at A, from the surface of a tranquil lake. This illusion often deludes the traveler in arid regions with the hope of finding water; but as he approaches it recedes, until, at last, the real ob- jects are seen by means of direct light. The inverted images of very distant ships are frequently seen at sea. This form of mirage is the reverse of the pre- ceding, because the lower strata of the atmosphere are ren- dered colder and denser than those above by contact with the water. Sometimes this phenomenon is combined with extraordinary looming, so that an erect image is observed in the air above an inverted image, when the ship is really below the horizon. 478. Refraction by regular surfaces. If a transparent medium is denser than the air, and is entirely surrounded by air, a ray of light, on entering the medium, will be refracted toward the perpendicular, and, on emerging from the medium, will be refracted from the perpendicular. The relative direction of the incident and emergent rays, will depend on the inclination of the two faces of the medium. 1. Parallel planes. When a ray of light is transmitted through a medium, bounded by plane and parallel surfaces, the incident and emergent rays are parallel, because the ray is refracted an equal amount at each surface, but in a contrary direction. The two refractions do not produce a change in the general direction of the ray, but simply produce a lat- eral aberration, whose amount increases with the thickness of the medium, and the obliquity of the incident rays. A pane of glas.s, whose sides are perfectly parallel, occasions no distortion of objects seen through it; if, however, the sides are not 262 NA T URA L PHIL OS OF in '. P", FIG. 210. parallel, the objects seen through the glass are distorted in proportion to the inequality in the thickness of the glass. 2. A prism is a transparent medium, having two plane sur- faces, not parallel. The prism may be a solid wedge of glass, ice, or crystal, or may consist of liquids inclosed in hollow prisms with sides of plane glass. Let A C B be the section of a prism, and O a luminous point. The incident ray, O D, on entering the prism is refracted toward the perpendicular, P P', because it enters a denser medium, and will proceed in the line, D K. On leaving the prism for a rarer medium, it will be refracted from the perpendicular, P' P", and will emerge in the direction, KH. The light is thus twice refracted toward the base of the pi*ism, and the eye which receives the emergent ray, K H, sees the object at O' nearer the summit of the prism than the real position of the point, O. 3. A lens is a transparent medium having two curved surfaces, or one curved and one plane surface. Lenses are usually made of crown or of flint glass with spherical sur- faces. There are six varieties of spherical lenses, viz.: A is a double convex, B is a plano-convex, C is a meniscus, con- / Fio. 211. vex on one side and concave on the other, the convex sur- face having the >hortcr radius. D is a Jmible concave, K is a plano-concave, and F is a concavo-convex, the concave sur- face ha v in ir the shorter radius. 479. Lenses arc divided into two groups, the first three are converyiny, and are thickest at the center; the others are FOCI OF LENSES. 263 diverging, and are thinner at the center than at the edges. The double convex lens will be taken as the type of the first group, and the double concave lens as the type of the second, as the properties of these lenses will represent those of the others. The right line, MX, which passes through a lens perpendicular to both surfaces is called the axis of the lens. The centers of curvature are the centers of the spherical surfaces. The double convex lens may be regarded as a series of prisms, whose bases are turned toward the axis, and the double concave lens as a series of prisms, whose bases are turned away from the axis. If the sides of each prism are infinitely small, the series will form a spherical surface. The per- pendiculars drawn to the points of incidence and of emergence will, evidently, correspond to the radii of the spherical surfaces. Hence, as a prism refracts light toward its base, a convex lens will refract light toward its axis, or tend to converge the rays ; and a concave lens will refract light away from the axis, or tend to disperse the rays. 480. The principal focus of a convex lens, 'is the point at which parallel rays unite after refraction. Any incident ray, as L B, will be twice refracted toward the axis, which it cuts in F. This focus is real, for the rays of the sun may all be col- lected at this point. The M ordinary burning glass is simply a large double convex lens. The dis- tance of the point, F, FIG. 212. from the center of the lens, is called the principal focal distance. This varies with the radii of curvature, and also with the index of refraction. In a double convex lens of crown glass, it is equal to the radius of curvature, and in a plano-convex glass it is equal to twice the radius. The greater the refracting power of the substance, the nearer will the principal focus be to the lens. 481. Real conjugate foci are formed when a near object is beyond the principal focus. Thus, if a luminous point 264 NATURAL PHILOSOPHY. be at L, Fig. 213, the diverging rays will converge on re- fraction to I, and, conversely, rays from / will converge on refraction at L. If a luminous point be placed at the DAB 11 FIG. 213. principal focus, Fig. 212, the emergent rays will be parallel. A lamp so placed will illuminate objects at great distances. 482. A virtual focus is formed when the luminous point is between the lens and the principal focus. Thus, rays diverging from L, will be rendered less divergent on refrac- FlG. 214. tion, and will appear to come from the point I on the axis. Thus, the virtual focus is on the same side of the lens as the object; the real foci are on the opposite side. 483. Secondary axes. If two radii, CA, C'A', Fig. 215, an- drawn parallel to each other, their tangents will also be parallel. Hence, a ray of light which reaches A at such an anirle that after refraction it takes the direction, A A', will emerge from A' as if trans- mitted through a medium with parallel faces. Therefore, the emeip-nt ray, K' A', will he parallel to the incident ray, K A. The lateral aberration caused by the slight thickness of the lens may be neglected, FORMATION OF IMAGES. 265 and the incident ray considered as in the same straight line with the emergent ray. The point, O, where the line, A A', cuts the principal axis, is called the optical center of the k-ns. Any right line which passes through the optical center without passing through the centers of curvature, is a secondary axis. A luminous ray, coinciding with a sec- ondary axis, suffers no deviation in direction. So long as secondary axes are nearly parallel with the principal axis, foci may be formed on them in the same manner as on the principal axis. A collection of these foci will determine the position of images formed by lenses. 484. Formation of images by convex lenses. Real images are formed when the object is at a finite distance FIG. 216. beyond the principal focus. Let A B be an object so placed. Draw a secondary axis, A a, from the top of the object A. Any other ray diverging from A, as A C or A E, after being twice refracted will cut the secondary axis at a. This point is the conjugate focus of A. In the same manner, the con- jugate focus of B will be found at b, and intermediate points on the object will have their foci between a and b. Hence, a real and inverted image of A B will be found at a b. Reciprocally, if a b were a luminous object, its image would be formed at A B. Hence, 1. If an object be placed more than twice the principal focal distance from a double convex lens, the image will be smaller than the object, real, and inverted. 2. If a small object be placed less than twice the princi- pal focal distance, but beyond the focus, the image will be larger than the object, real, and inverted. In both cases, 266 NATURAL PHILOSOPHY. the diameter of the object is to that of its image as the distance of the object is to the distance of the image from the lens. These principles can be verified by placing a candle at different distances from a double convex lens, and receiving its image on a sheet of white paper. 485. Virtual images are formed when the object is placed between the lens and the principal focus. In Fig. 217, draw the secondary axis, O a, through the point A. Every ray, as A C, after twp refractions, appears to emerge diver- Fia. 217. gent from this axis. The point, a, where the emergent ray, continued backward, cuts the secondary axis, is the virtual focus of A. The virtual focus of the point B, is at b. There is, therefore an image of A B at ab, virtual, erect, and larger than the object. In thi> <-a-c, the lens is a simple magnifying glass. The size of the image is independent of the area of the lens, but is greater as the lens is more convex, and the object nearer the principal focus. The iniML'f i- liri'iliffi- ;i- the area, or field of view increases, because more rays tVoin the object enter the lens. 486. The foci of concave lenses arc always virtual. Let L, Fig. 218, be a luminous point. The incident ray, LI, will be re- fracted at I, toward the per pen- L dirtilar, ('I, and, on emerging, it is refracted from the perpendicu- lar, G C', so that it is twice re- IVactcd away from the axis, L C'. A- this is the case with every ray, the emerging rays, G K, CONCAVE LENSES. 267 FIG. 219. M N, will appear to diverge from a virtual focus, I, which is between the principal focus and the lens. 487. The images formed by concave lenses are always virtual. Let AB be an object in front of a double con- cave lens. Draw the sec- ondary axis, A O. Each ray from the point, A, as A I, AC, is twice re- fracted, diverging from the axis, so that the eye, placed in the direction of the emergent rays D E and G H, receives them as if coming from the point a, where their prolongations cut the secondary axis. The rays from B appear to diverge on emerging from b. There- fore, the eye sees at a b an image of A B, which is always virtual, erect, and smaller than the object. 488. Spherical aberration by refraction is due to the fact that the rays refracted near the edge of the lens meet the axis a little nearer the lens than the focus of the rays passing through ,he center. The effect of spher- ical aberration is to render the image less distinct and well defined, and is a serious defect in the lenses used in pho- tography. If the angular aperture, which is obtained by drawing lines from the principal focus to the edges of the lens, does not exceed 10, the defect is not usually regarded. It may, therefore, be partially obviated by placing before the lens a diaphragm which cuts off the rays from the edges, and may be entirely destroyed by combining two lenses of suitable curvatures. 489. Recapitulation. Light is not refracted 1. In passing through a uniform medium, nor 2. When passing perpendicularly from one medium to another. 268 NATURAL PHILOSOPHY. Light is refracted in passing obliquely into a second medium, 1. Toward the perpendicular, when the second is the denser; 2. From the perpendicular, when the second is the rarer. {Double convex. I'hiiio-convex. Lenses are i Meniscus. {Double concave. Plano-concave. Concavo-convex. The effects of concave mirrors and convex lenses are analogous ; that is, when the object is 1. Nearer than the principal focal distance, The image is virtual, erect, and magnified. 2. At the principal focus, There is dispersion of light in parallel rays. 3. Beyond the principal focus, but less than twice its distance, The image is real, inverted, and magnified. 4. At twice the principal focal distance, The image is real, inverted, and of equal size. 5. At more than twice the principal focal distance, but finite, The image is real, inverted, and diminished. 6. At an infinite distance There is concentration of light at the principal focus. The effect of convex mirrors and of concave lenses are also analogous, forming images which are always virtual, erect, and smaller than the object. CHROMATICS, OR COLORS. 490. Decomposition of light. If a pencil of solar light be admitted into a darkened room through a very small aperture, it will form a round, white image of the sun, as represented at K, Fig. 220. If, now, a prism be placed in -ar the aperture in the path of the pencil* the rays will be unequally refracted, and will form on a screen an elon- gated, colored image, which is called the solar spectrum. \- ach ray forms an imairt' of the sun, the sju-ctrum may be considered as an infinite number of colored images, CHROMATICS. 269 overlapping each other from end to end. If any ray of the >jHvtrum be transmitted through a small aperture in the screen, and received on another prism, it will again be refracted, but will undergo no further change in color. Hence all the prismatic colors are simple. Newton dis- tinguished seven of these colors as primary, which are in order, beginning with the least refracted, red, orange, yellow, green, blue, indigo, mold. 491. White solar light is therefore composed of different colored rays. An additional proof of this is found in the fact that, when all the colors of the spectrum are recom- bined, they will reproduce white light. Thus, if all the rays of the spectrum are received on a convex lens, or on a concave mirror, a white image of the sun will be formed in the focus. If a circular card be painted with the seven colors, in sectors proportional in extent to the spaces occupied by these colors in the spectrum, then on revolving the card very rapidly it will appear of a white color, more or less pure according as the colors on the card more or less exactly imitate those of the spec- trum. Fig. 221. 492. Complementary colors are any two colors which combined will produce white. If the red rays of the spec- trum are intercepted, and the remaining colors are com- bined by means of a convex lens, the resulting image will 270 NATURAL PHILOSOPHY. be green. Hence, green and red are complementary, be- cause the two combined contain all the rays of white light. In this manner it is found that blue and orange, violet and yellowish green, indigo and orange yellow are complement- ary colors. FIG. 221. Complementary colors may be seen by gazing intently at any blight colored object for a few minutes, and then turning the eye toward a white wall. Thus, if the object be a bright red wafer, placed oil a sheet of black paper, the eye, on turning away, will retain *fl impres- sion of the wafer, in its complementary color, green. If tin obj.-ri is bright, the eye will sec a ring of a color complementary to that of the object before it is turned away; hence, a color tetwfs to pfoduce in the eye its complement. 493. When two colors are placed near ftch other, each color will 1x3 modified, as though mixed With th comple- ment of the adjacent color. If a red wafer In- placed Wide a green wafer, each color will be heightened, liccnii-.- the red wafer will tefld to tinge the adjacent nl.ject gm-n, <>r to make it greener; and thf given wafer will, in the same manner, tinge the red with red. I/ it be desired t> heighten a color, it should lc placed l, ( -ide it> complement, but if it be de- FRAUNIIOFEffS LINES. 271 sired to weaken its effect, it should be contrasted with others. Thus, a green dress or scarf increases the freshness of a rosy complexion. Florid complexions will bear dark hues in dress, but a pale face appears still paler when a black dress is worn. A yellow shawl and an orange dress, when worn together, appear mutually dull, but the contrast of either with an appropriate shade of violet would be pleasant and tasteful. 494. Fraunhofer's lines. If light be admitted through a very narrow slit and received on a good flint glass prism, it will be found not only that the colors of the spectrum M DARK H AT RAYS W, x, * 1 I JJJ J 2 S I CHEMICAL FIG. 222. are not continuous, but also that they are interrupted by numerous dark spaces, known as Fraunhofer's lines. On viewing the spectrum with a powerful telescope, two thousand of these lines are visible. Seven of these are more distinct than the rest, and are designated by the letters, B, C, D, E, F, G, H, to serve as means of refer- ence. The positions of these lines in the spectrum, due to solar light, direct or reflected from the moon and planets, is invariable, but their distances from each other vary with the material of the prism. Each fixed star has a stellar spectrum, which differs from that of the sun and other fixed stars, in regard to the number and position of the dark lines. 495. Dispersion of light. The index of refraction for the different colors is fixed with precision by ascertaining the refraction of Fraunhofer's lines, B, C, etc. The table on page 258 gives the indices of refraction for the line, E, in the yellowish-green rays, which is taken as the mean of 272 NATURAL PHILOSOPHY. all the rays. If similar prisms are made of different sub- stances, the mean refraction may be nearly the same, and yet the spectra they furnish be of very unequal lengths. The dispersive power of a medium indicates the amount of separation which it produces in the extreme rays, compared with the amount of refraction in the mean rays. Thus, the refractive power of flint glass is but little greater than that of crown glass, but its dispersive power is almost double. Table of Dispersive ^Powers. Oil of cassia 0.139 Bisulphide of carbon 0.130 Flint glass 0.052 Diamond 0.038 Green crown glass 0.036 Water 0.035 Alcohol 0.029 Quartz crystal 0.026 496. Chromatic aberration, As lenses are merely a series of prisms, with infinitely small faces, they disperse light like a prism. The violet rays, being most refracted, come to a focus, v, Fig. 223, nearest the lens, then the other colors in order, the red being the most re- no. 223. mote. Hence, if a screen be placed a little nearer the lens than the focus of the mean rays, the image will be fringed with red. If the screen is beyond the focus, the image will be fringed with violet, because the violet rays cross after coming to their focus, and form the outside of the diverging pencil. The difference between the focal distance of the red and violet rays causes what is called the chromatic aber- rnt'iun of the lens. The chromatic aberration of a quartz Jen- i- small, l>y reason of its low dispersive power. 497. Achromatism. If two prisms, exactly alike, are placed near cadi other, with their bases turned in a contrary direction, one will exactly neut rali/e the other, and the light will emerLT' 1 from the second a.- if from a medium ACHROMATISM. 273 with parallel faces. If, however, the first prism, B C F, be of crown glass, and the other of flint glass, the disper- sion may be destroyed without entirely neutralizing the refraction. Since the dispersive power of flint glass is almost twice that of crown glass, the refracting angle of the former must be made so much smaller than the latter, ^ that the dispersion of the two prisms shall be equal. The flint glass will then entirely neutralize the disper- sion of the crown glass, but will destroy only about half of its refractive power. On the same principle, an achromatic lens may be made by combining a double convex lens of crown glass with a concavo-convex lens of flint glass. The two lenses must have such curvatures that their AlHillvB focal lengths shall be as their dispersive powers. An achromatic lens is, therefore, free from chromatic aberration. 498. Homogeneous light is light of only one color. An almost colorless flame may be pro- FIG. 225. duced by burning pure alcohol, or by burning gas in a Bunsen's burner. If a platinum wire be dipped in any salt of sodium, as common salt, and held in a color- less flame, it vaporizes and yields a homogeneous yellow light. Every flame may be considered as the combustion of a body in the state of vapor. Several other substances yield characteristic colored flames ; thus, strontium gives a red color; potassium, purple; copper, green, but the light is never perfectly homogeneous. 499. Spectrum analysis. The spectra formed by artifi- cial lights are usually wanting in several colors, but yield the remainder with the same refrangibility as the corre- sponding colors in the solar spectrum. Their relative inten- sities will vary with the predominant colors of the flame. N. p. is. 274 NATURAL PHILOSOPHY. The spectroscope, Fig. 226, is an instrument used for analyz- ing flames. The light is admitted from the Bun sen's burner, E, through a narrow slit into one end of the tube, A, where it is condensed by lenses, and thrown on the prism, P. The refracted rays are thrown on the object glass of the telescope, B, and pass through it to the eye. The tube, C, contains, at the end nearest the prism, a lens, and at the other a scale divided into equal parts. When a bright light is placed in front of the tube, C, it casts a bright image of the scale on the prism, which is reflected into the telescope, B, so that the observer can n -ad off on the scale the exact position of the rays he is observing. It' platinum wires an- dipped in solutions of the metals to be ex- amined, and placed in tlie flame of the Bun-en's burner, K, their spectra may lie ..(.served lhn.ii-h the t.-lr-n.pc. !',. In this way it M found that sodium u'ives a bright, double, yellow line, identical in refraii'/il.ility with the dark line, D, in the solar spectrum. Potas- SPECTRUM ANALYSIS. 275 shim gives a red ray, in the position of the line, A, and a violet ray, between G and H. Any substance which can be volatilized will furnish a spectrum of a few bright lines, which always have the same relative position. This is also true of incandescent gases; hy- drogen gives three bright lines, which are identical in position with C, F, and G. These lines remain the same throughout a great range of temperature, and it is highly probable that they are not the same for any two substances. If several substances are mixed, each will give its own system of lines, as if it were burned separately. No chem- ical reaction is equal to this as a mode of detecting the presence of many substances. It is, in fact, difficult to obtain a flame which does not show the presence of sodium, as ynnnhrffUTF f a grain will give the characteristic yellow line of sodium. Since the year 1860, five new metals have been discovered by means of the spectroscope. Two of these, coesium and rubidium, are widely distributed, being found in many mineral waters, and even in tobacco. 500. Under extreme temperatures new lines are added to many spectra; and, under pressure, hydrogen may be made to yield a continuous spectrum ; that is, one in which no dark lines are found. Any incandescent solid will emit, at 977 F., only red rays, but as the heat increases the orange is added, and then the other colors in succession, until at 2130 F. the spectrum becomes continuous, con- taining all the colors, and, by consequence, the solid appears white hot to the naked eye. The lime light produced by the oxy-hydrogen blow-pipe affords a convenient method of obtaining a continuous spectrum. The electric spark ordinarily gives a discontinuous spec- trum, due both to the metallic connectors and to the atmosphere ; but if the spark be very intense the spectrum becomes continuous. 501. Absorption bands. If light which would give a continuous spectrum is passed through certain almost trans- parent and colorless solutions, and then examined, dark lines are found, which are due to absorption. Thus, solutions of didymium give two dark lines, one in the yel- low and the other in the green. The blood also produces two dark lines. This effect is produced, not only by light transmitted through a dilute solution, but also when a spectrum is thrown on a screen painted with blood. The gases also produce absorption bands. Nitrous acid, and the 276 NATURAL PHILOSOPHY. vapors of iodine and bromine, produce remarkable series of black bands. Even the atmosphere exerts an absorptive power, which is especially energetic when the sun is near the horizon. Some of the Fraunhofer's lines are undoubtedly due to the air, but the larger portion must have another cause. 502. If the sodium spectrum is formed in the ordinary way, and the lime light is transmitted through the sodium flames, a dark line is seen in place of the yellow sodium line, and the spectrum is said to be reversed. So, also, if two sodium flames are placed before the spectroscope, so that one must traverse the other, no spectrum is produced. In other words, sodium absorbs the same rays that it emits. This is found to be the case with so many bodies that it may be stated : 1. That every substance, when rendered luminous, gives out rays of a definite degree of refrangibility. 2. The same substance has the power of absorbing rays of this identical refrangibility. 503. Explanation of Fraunhofer's Lines. Kirchhoff sup- poses (1.) that the nucleus of the sun emits a continuous spectrum, containing rays of all degrees of refrangibility ; (2.) that the luminous atmosphere of the sun contains vapors of various metals, each of which would give its own system of bright lines ; (3.) that when the intense light of the nucleus is transmitted through this incandescent atmos- phere, the bright lines which would have been produced by the atmosphere are reversed; (4.) that Fraunhofer's lines are these reversed lines. Now, since very many of Fraunhofer's lines coincide with the bright lines of metals, it is fair to suppose that those metals exist in the solar atmosphere. Iron gives four hundred bright line- which coincide with 1-Yaunhofer's lines. Eighteen dillercnt metals give similar coincidences. Hence, we are led to suppose that the sun con- tains iron, nickel, calcium, magnesium, chromium, copper, sodium, aluminum, hydrogen, and a lew other elements. But no evidence ha- been L'iven of the presence of mercury, silver, lithium, gold, and many others. Tin- -trllar -p.-ctra al-o .-how .-imilar coincidences ; thu-. Sinus and Aldebaran are thought to contain sodium, magnoium, and hydrogen. PROPERTIES OF THE SPECTRUM. 277 The comets and nebulae give spectra with bright lines, which seein to show that these bodies are incandescent gases. 504. The properties of the spectrum are three; (1.) Lu- minous; (2.) Heating; (3.) Chemical; but all the rays do not possess them in equal intensity. The ordinates of the curves in Fig. 222 show the relative intensity of each prop- erty in a spectrum produced by a prism of flint glass. 1. The luminous intensity is greatest in the yellow and least in the violet. 2. A thermometer placed in different parts of the spec- trum will indicate an increase of temperature from the violet to the red. The point of maximum thermal intensity varies with the material of the prism. By using a prism of rock salt, which absorbs but little heat, the point of greatest heating power is found to be beyond the red rays. This fact shows that the spectrum contains dark rays of heat, invisible to the eye, which are refracted less than the red rays. 3. Light acts as a chemical agent, because it is essential to the healthy growth of plants and to various chemical changes. Thus hydrogen and chlorine combine slowly in diffused light, but with explosive violence in direct sun light. The relative chemical effect of the different rays may be de- termined by placing a film of chloride of silver in the spectrum. To accomplish this, dip a slip of paper in weak brine made from common salt; then dry the paper, and wash one side of it with a solution of nitrate of silver, and dry the paper again. A film of chloride of silver will thus be formed on the paper, which will remain white if the operation be performed in a darkened room. On exposing this paper to the solar spectrum, the chloride of silver will blacken, but with unequal energy in the different rays. A quartz prism is best adapted for these experiments, because L'luss prisms absorb a large portion of the chemical rays. The chemical effect is scarcely perceptible in the red and yellow rays; it is decidedly present in the blue, and attains its maximum 278 NATURAL PHILOSOPHY. intensity in the violet. The action extends even beyond the violet, which shows that the spectrum contains rays more refrangible than the violet, but not of sufficient intensity to be visible. If these invisible ultra-violet rays be concentrated by a quartz lens, they form a faint beam of lavender colored light. These rays also become visible when they fall on paper moistened with a solution of quinine, or on glass colored with uranium. This property is called fluorescence, and is due to the power which these substances have of changing the refrangibility of the rays. 505. Interference and combination, If the wave theory is correct, the luminous vibrations must produce all the phenomena of combination and interference, (377). These phenomena may be shown in various ways. One of the simplest is that afforded by the reflection of waves from both surfaces of very thin plates. If a convex lens, A B, Fig. 227, with a long ra- ,B dius of curvature, be firmly pressed on a plane glass, D E, a thin film of air will be inclosed between the two glasses, whose exact thickness at any point can easily be estimated. If a beam of homogeneous light be allowed to fall perpendicularly on the upper surface, a portion will be reflected from the convex surface, A C, and another portion from the plane surface, D E. These two systems of waves will intersect in crests and hollows, ac- cording as their paths differ by a whole number of undulations, or by an odd number of semi-undulations. At a certain distance from C, as at F, the two waves will meet in opposite phases and destroy each other, and the ring at F will appear black. At a greater distance, as at G, the waves will meet in the same phase and increase the ampli- tude of vibrations, and produce a bright ring the same color as the light. Other points will be found beyond G, in which the waves will meet in opposite or similar phases, and, consequently, a series of black and colored rings will be formed about the center, C. If the yellow sodium flame is employed, \ve shall have alternately black and yellow rings; if red light l>e employed, a similar system of red and black rings is produced, and so on for other colors. 506. If solar light be employed, each rin^ contains all INTERFERENCE. 279 the colors of the spectrum in order, from violet on the inner edge to red on the outer, because the different colors have different refrangibilities, and the rings are not exactly super- imposed. The smallest rings are the most brilliant, because the vibrations coincide the most frequently. These rings are known as Newton's rings, and by finding the thick- ness of the layer of air between the glasses, the following table has been constructed : Colors. Lengths of waves in parts of an inch. Number of waves in an inch. Number of waves in a second. Extreme red .0000266 37640 442000000000000 Red 0000 9 56 39180 458000000000000 Orange .0000240 41610 489000000000000 Yellow . . . 0000227 44000 517000000000000 0000211 47460 558000000000000 Blue ... 0000196 51110 599000000000000 Indigo 0000185 54070 634000000000000 Violet 0000174 57490 675000000000000 Extreme violet 0000167 59750 702000000000000 507. Similar phenomena of interference may be observed in other very thin plates, as in mica, soap bubbles, or in the film of oil on water, or alcohol on glass. Striated surfaces, formed by very fine parallel grooves, reflect bright colors for the same reason. This is the cause of the iridescence of mother of pearl, of labradorite, and of the changeable hues in the plumage of birds and the scales of insects. 508. Diffraction. When a pencil of light encounters an obstacle, the rays diverge from the edge of the obstacle as if from a new point. The light then enters the shadow of the obstacle, and is said to be diffracted. If a thin body, as a hair, is placed in a small opening, the diffracted rays cross each other and produce fringes of colored light, which are due to interference. Light is always diffracted when it passes the edge of an object, but it is rarely observed, because the fringes are illuminated by light from other sources, and quenched. 280 NATURAL PHILOSOPHY. 509. The color of light is determined by the frequency of its vibrations, and its brightness by the amplitude of its vibrations. The heating, luminous, and chemical rays of the spectrum are the same in kind, and differ from each other only as red differs from violet ; that is, in degree of refrangibility and rapidity of vibration. The retina of the human eye is so constructed that only rays of medium refrangibility and rapidity excite the fibers of the optic nerve to vibration. The appreciation of color varies greatly with different indi- viduals, but the reason of this is not yet understood. From observations made in animals, it would seem that certain fibers of the optic nerve are sensitive to one color, and others to another. The eye which is defective in these fibers is color blind, or unable to distinguish colors appro- priate to the lacking nerve fibers. Dalton could not distin- guish blue from crimson ; others confound different colors, and some can not distinguish colors at all, and yet in every other respect their sight is perfect. 510. The natural color of a body is due to the power it has of extinguishing certain vibrations and reflecting or transmitting others. A white screen placed in the solar spectrum appears of all the colors. A red screen appears brighter red in the red rays of the spectrum, and almost black in the blue. A red object can reflect only red rays, and absorbs the rest. Hence, the color of an opaque body is due to the light which it reflects. A body that reflects all the rays of the solar spectrum is white; a body that reflects no light, or but very little, is black. Most natural colors of bodies, when examined by the prism, are found to be compound. If all the solar \\y\\\ is transmitted by a transparent body it appears colorless. If it absorbs some of the rays, the emergent liirht will be of the color produced by tin- transmitted vibrations. Thus, red red. An ammoniaral solution Of OZide Of OOpper iran-mit- a v.-ry pure blue. Some bodies reflect THE RAINBOW. 281 one color and transmit another; thus, gold appears yellow by reflected light and green by transmitted light. 511. The rainbow is due to the combined effect of re- flection, refraction, dispersion, and interference of the solar rays in passing through drops of rain. For its formation, it is necessary (1.) that the sun shall shine during a shower, (2.) that the observer shall stand with his back to the sun, between the drops of rain and the sun. When two bows are visible, the inner and brighter is called the primary bow, the outer, the secondaiy bow. Each bow contains all the prismatic colors, so arranged that in the primary bow the red band is on the outside, and in the secondary bow on the inside. The common center of both arches is always in the prolongation of a line drawn from the sun through the eye of the observer. Fig. 230. 512. The formation of the primary bow may be ex- plained by tracing the course of the sun's rays through a drop of rain. Suppose the paraUel rays of the sun, S S' S" S'", to fall FIG. 229. on the rain drop. The ray, SI, which falls perpendicu- larly on the drop will suffer no refraction, but will be par- tially reflected back, as it enters and leaves the drop, in 282 NATURAL PHILOSOPHY. the line, S I. Any ray of little obliquity to the surface of the drop, as ST, will be refracted to i f , where it will be reflected to R', and then again refracted in the direction R' E', making a small angle with the incident ray, ST. The angle of deviation between the incident and emerging rays will increase until we reach a ray, S" I", about 59 from the axis, for which the deviation, S" V E", is the greatest possible. Beyond this limit the deviation of the emergent rays will again diminish, until we reach the ray, S'" I'", which is tangent to the top. Hence, of the incident rays near the limit of 59, those above V will emerge very nearly parallel to those below. The rays of the sun are thus dispersed by each refraction as by a nearly spherical prism, but will be more intense in the direction of the parallel rays, R" E", so that these only will bring to the eye the impression of color. Owing to the difference in the refraction of the different rays, the line of greatest intensity is not the same for the differ- ent colors. For the red ray, the angle, S" VE", between the incident and emergent pencils is about 42; for the violet, about 40, and for the other colors between these limits. If, now T , the line, s o c, Fig. 229, be con- ceived to pass from the sun through the eye of the observer, the angles S" V o and V o C, are equal, because the solar rays arc parallel. Hence, if the eye bo Flo taken as the center, the red rays will all be seen in a circle of 42 null us : the violet rays in a circle of 40 radius, and the other colors between these. As the THE SECONDARY BOW. 283 emergent rays are nearly, but not exactly parallel, they will be in a condition to combine and interfere, and will, of course, give rise to colored bands separated by dark spaces. The colors are much brighter by reason of combination, and purer by reason of interference, because a dark band separates each color from the other. The second band of each color is sometimes bright enough to be visible, and then forms a spurious bow below the primary. 513. The secondary bow is due to two reflections and two refractions. In order that the rays may descend to the observer, the incident rays must enter below the axis of the drop, as in Fig. 231. Only the rays which enter at a distance of about 71 below the axis, will emerge sufficiently parallel ^ to give a bright color at a great distance. The red band has a radius of about 51, and the violet about 54. As some light is lost at each reflection, the secondary bow 7 is fainter than the primary. The extent of the bow depends on the position of the sun. When the sun is in the horizon, the arches are semicircles; as it rises they diminish, the primary bow ceasing when its altitude is about 42, and the secondary when about 54. If the sun is at or a little below the horizon, and the observer is sufficiently elevated, a com- plete circle may be rendered visible. Such circular rainbows are often observed near waterfalls and fountains. Faint lunar rainbows are sometimes seen. The halos seen about the sun and moon are supposed to be due to light refracted by minute crystals of ice suspended in the air. 514. Recapitulation. When solar light is examined by a prism, it is found to consist of seven primary colors, which are interrupted by dark lines. Other luminous bodies yield spectra which resemble the solar spec- trum in many particulars. NATURAL PHILOSOPHY. All spectra have luminous, thermal, and chemical properties, but not in equal intensity. The spectrum analysis depends on the fact that every luminous body emits rays of definite refrangibility. The dark lines are explained by the fact that every luminous body- is capable of absorbing the rays which it emits. Luminous vibrations may be made to combine and interfere by re- flection, refraction, and diffraction. Colors are dependent on the frequency of the luminous vibrations. VISION AND OPTICAL INSTRUMENTS. 515. Camera obscura. One form of this instrument has already been described in section 444. The photographer's camera, Fig. 232, is constructed on the same principle. The box, C, is the dark chamber. The screen, E, is of ground glass, inserted in the movable frame, B. An achro- D FlG. 232. matic convex lens is placed in the tube, A, in order to render the image clear and well defined. The focus may !>< adjusted t<> ol.jeets at different distances l>v moving th',- screen, or the lens backward or forward. The image will be real, and smaller than the object, because the object is placed more than twice the focal distance in front of the lens. THE HUMAN EYE. 285 516. The draughtsman's camera is used for sketching natural scenery. The student can readily make an instru- ment of this kind by inserting a convex spectacle glass in an orifice at the top of a box, about two feet high, and placing a plane mirror at an angle of 45, so as to reflect the light from external objects downward through the lens. The image can be received on a paper at or near the bottom of the box. A shawl must be throw r n over the open side of the box, in order to shut out the extraneous light. 517. The human eye is very nearly spherical, and is about an inch in diameter. It consists essentially of (1.) three enveloping coats, and (2.) three refracting bodies. Fig. 233 presents these parts in horizontal section. (1.) The outer coat, or white of the eye, is a tough and opaque membrane called the sclerotic. In the front part of this, the transparent cornea, a, is set in like a watch-glass. The middle coat, k, is the choroid, which consists of a membrane, abundantly supplied with blood-vessels, and covered, on its inner face, by a dark, velvety substance, called the black pigment. The inner coat is the retina, m, which is mainly an ex- pansion of the optic nerve, n, with the addition of terminal 286 NATURAL PHILOSOPHY. nerve elements for the perception of light, spread out in very fine net-work on the black pigment. Near the junction of the cornea and sclerotic, the choroid becomes thicker, and terminates in the ciliary processes. To the outer portion of these is attached an opaque, contractile membrane, d, called the iris, because it is the colored por- tion of the eye. The iris is pierced by an aperture, called the pupil, through which the luminous rays pass to the bottom of the eye. (2.) Behind the iris, and supported by a suspensory liga- ment, attached to the ciliary muscle which proceeds from the ciliary processes, is the crystalline lens, f. This is a double convex lens, having its anterior face of less con- vexity than the posterior. The portion of the eye, e, between the cornea and the crystalline, is filled with a thin liquid, called the aqueous humor. Behind the crystalline is the chamber, h, which is filled with a jelly-like liquid, called the vitreous humor. The humors and the crystalline are each surrounded by a deli- cate membrane, or capsule. 518. If a luminous point be placed before the eye, the central rays pass through the cornea, and enter the aqueous humor. Of these rays, the more divergent are intercepted by the iris, and only those which are nearly parallel are admitted through the pupil to the interior of the eye. These are transmitted through the crystalline and the vit- reous humor, and finally fall upon the retina. The effect of these refracting bodies will be the same as that of a converging system of lenses, and they will, there- fore, tend to form, at or very m-ar the retina, an iinauc of tin- luminous point. The same being true of all diverging pencils proceed in. i: from an object, then- will be Conned on the retina an image of the object, which will be inverted, becaii-e the a.\c.- of the pencil.- cross each other before reaching the ret- VISION. 287 ina. The mechanical action of the eye is very similar to that of the photographer's camera. 519. The sensation of sight is due to the impression made by the image on the terminal percipient nerve ele- ments of the retina, and thence conveyed by the optic nerve fibers to the brain. These nerve elements are contained in u layer next the black pigment, and consist of a great number of very minute bodies, arranged side by side, and resembling rods and cones, standing perpendicularly to the surface of the retina. It is supposed that the waves of light falling upon this layer of rods and cones produce vibrations, which are conducted by the nerve fibers in such a way to the brain that it is excited and acknowledges the reception of the luminous image on the retina. 520. The impression made on the retina is not instan- taneous, and when once made continues, on the average, for nearly one-third of a second after the exciting cause has ceased to act. If, therefore, an ignited coal be whirled about rapidly, luminous rings are produced. Many optical toys owe their effect to the duration of the impression on the retina. The Thaumatrope, or "twirl me round," Fig. 234, consists of a card which is made to revolve by means of strings attached to FIG. its siiit'-. A horse may be so painted on one side and a rider on the other, that a rapid revolution of the card will cause the rider to appear seated on the horse. The same principle is applied in the familiar Zoetrope, by which an object painted in different positions appears to perform the motions of real life. 521. The accommodation of the eye to different distances is effected by the action of the ciliary muscle upon the crys- talline lens. When the eye is turned toward a distant object, the muscle relaxes and the lens is flattened; but, for near objects, the muscle contracts and the lens becomes more 288 NATURAL PHILOSOPHY. convex. In this way, the conjugate focus of the object is made always to fall upon the retina. The power of accom- modation is very great, and is exerted unconsciously with marvelous rapidity. Nevertheless, there is for all eyes a certain distance at which the parts of an object, as, for instance, the letters on this page, are seen with most dis- tinctness. This distance, which varies for ordinary eyes from five to ten inches, is called the distance of distinct vition. 522. The limits of distinct vision. In order that an object may appear distinct, the rays proceeding from it must enter the eye nearly parallel. If rays diverge from a point more than eighteen inches from the eye, those that enter the eye will be sensibly parallel. The nearer the object is to the eye, the more perfect will be the image, provided always that the rays are brought to a focus on the retina. If a printed page be brought too close to the eye, the letters appear more or less blurred, because the rays are too di- vergent to focus on the retina. For normal eyes, the far- thest point of distinct vision is infinitely distant, the nearest point about three and one-half inches. Far-sighted eyes are those whose nearest point of distinct vision exceeds ten inches, and near-sighted eyes are those whose farthest point of distinct vision is at a finite distance, varying from three inches to twenty feet. 523. The normal eye is very nearly round, and the prin- Fio. 235. cipal focus of parallel r:iy> falls <>n tho retina, as at E, Fig. 235. From this figure there are two principal devia- DEFECTS OF THE EYE. 289 tions, producing what are known as Myopic and Hyperme- ti-njilc vision. The myopic eye is an oblate spheroid, in which the retina, M, lies beyond the focus of parallel rays. For this cause, only divergent rays are brought to focus on the retina, and thus near-sightedness results. Such eyes will obtain relief by the use of concave glasses. The hyperraetropic eye is a prolate spheroid, in which the retina, H, lies in front of the focus of parallel rays. Hence, only the convergent rays come to a focus on the retina, and far-sightedness results. When such eyes deviate but little from the normal, the power of accommodation may be suffi- ciently active to produce perfect vision, but in other cases they will require the use of convex glasses. There are other anomalies of refraction in the eye, among which astigmatism is the most common. Persons so affected find it difficult to see horizontal and vertical lines distinctly at the same moment. The glasses used to correct astigma- tism are cut from cylindrical surfaces instead of spherical. Another defect of the eye is called presbyopia, because it is generally found only in old persons. This results from a gradual diminution of the elasticity of the crystalline lens, by reason of which the power of accommodation is weak- ened, and only distant objects are seen distinctly. This kind of far-sightedness may also be remedied by the use of convex glasses. * 524. Magnifying glasses. If an object be very minute, the image formed on the retina will be too small to affect the optic nerve. If the object be too near, the rays will not focus on the retina, because they are too divergent. Suppose a pin hole to be pricked in a thin card and placed between the eye and a printed page. Now, if the page be brought * It will at once be seen that it is an error to suppose that presbyopia is due to the flattening of the cornea, and that all treatment based on this theory is absurd. Either of the defects mentioned may be relieved by the use of spectacles ; but as there is great danger of injuring the eye by the abuse of spectacles, the glasses suitable for each case should be selected only by competent oculists. N. P. 19. 290 NATURAL PHILOSOPHY. very close to the eye, the outer divergent rays will be ex- cluded, and the eye will be able to converge the few nearly parallel rays to a focus, and thereby form a faint but distinct image. At the same time, the letters will appear magnified, because the visual angle is increased. A convex lens placed a little nearer the object than its focal distance will converge all the rays on the retina, thus preserving all the light while it magnifies the object by in- creasing the visual angle. Since the lens may be held close to the eye, the magnifying power may be found by dividing the distance of distinct vision by the focal distance of the lens. Thus, if a lens have a focal distance of one-half an inch, and the distance of distinct vision be assumed as ten inches, the lens will magnify twenty times in diameter or four hundred times in area. Lenses have been made having a focal distance of -$ of an inch, and a consequent magnifying power of five hundred diameters. With a powerful lens, the object must be very near the surface ; consequently, only the smallest portion of the object will be seen ; hence, the field of view diminishes as the mag- nifying power increases. Moreover, from the great nearness of the object, the outer rays are so diverging as to cause spherical aberration ; for this reason, only the central por- tion of a lens can be used, and this is termed its aperture. The diamond has nearly twice the refracting power of glass, and hence the same magnifying power can be attained with a lens of less curvature, and is consequently less subject to spherical aberration than those of glass. com P ara ti v e thicknesses and curva- Flo ggg tures of three lenses having the same mag- nifying power are shown in Fig. 236. The loss of light by absorption is in proportion to the thickness of the lens, and also to the size of the aperture. The illuminating power of a lens is the amount of light it eollert- from tin- ohjeet and trans- mits to the eye; hence, as hi^h magnifying powers require small apertures, their illuminating powers arc feeble and require that the illumination of the object should be intense. This is effected by con- len-iin^ the solar li^ht upon it l>y means of a concave mirror, or by a large convex lens. THE STEREOSCOPE. 291 From these considerations, it follows that microscopes of different local distances are required for different purposes. The magnifying glasses used for viewing pictures afford a large field of view and magnify but little; the smaller glasses used by watchmakers are of greater magnifying power. Pocket microscopes usually contain two or three lenses, acting as a single thick lens. They do not usually magnify more than from five to ten diameters. 525. The stereoscope. If a solid object, as a die, be held a short distance before the eyes, each eye will see the object from a different point of view ; and, consequently, . / FIG. 237. the two images formed on the retina will not be exactly alike. Fig. 237 represents a die as seen by the left and right eyes respectively. By the blending of these two images, the object appears solid. This effect will be pro- duced in the engraving, if a card be held between the two figures, and they are steadily looked at for a few seconds, one by the right eye and the other by the left. The stereo- scope, Fig. 238, is contrived to assist FIG. 238. FIG. 239. the eye in blending two slightly different pictures of the 292 NATURAL PHILOSOPHY. same object, taken from points of view related to each other in the same manner as the two eyes of the observer. These pictures are placed in the bottom of a box and viewed through two eye pieces, which are segments cut from a double convex lens. A diaphragm, D, Fig. 239, prevents each eye from seeing more than one picture. The rays of light from A, after emerging from the lens, M, reach the eye as if they came from C, while rays from B, after emerging from N, appear also to come from C. Thus the two pictures are blended in one, and appear to come from a solid object at C. 526. The magic lantern is an instrument by which trans- lucent objects are magnified and thrown upon a screen. FlO. 240. A lamp is placed in the common focus of a reflector, MN, and of a convex lens, A, so that a strong beam of light is thrown on the object inserted in the slit, C D. The magni- fying lens forms an image of the object on the screen, E F, placed at its conjugate focus. The objects are usually painted on glass, but the instrument may also be used to magnify photographs on glass, or natural translucent ob- jects, as the wings of insects pasted on glass. The image may be made as large as is desired, by adjust- ing the lens, B, but as the brightness of the image dimin- ishes in proportion as the object is enlar"\V large as the capitol at Washington could readily be perceived at the distance of our moon. Its highest magnifying power is over six thousand diameters. DOUBLE REFRACTION. 297 534. Recapitulation. f Sclerotic. Enveloping coats -I Choroid. The human eye consists of \ Retina. r Aqueous humor. Refracting bodies -I Crystalline lens. v Vitreous humor. The sensation of sight is produced by luminous undulations passing through (1.) the cornea, (2.) aqueous humor, (3.) pupil, (4.) crystal- line lens, (5.) vitreous humor, to the retina, and there exciting, in the layer of rods and cones, vibrations, which are conveyed by the optic nerve fibers to the brain. The ordinary defects of the eye are f Myopia. 1. Anomalies of refraction -I Hypermetropia. v Astigmatism. 2. Loss of power of accommodation Presbyopia. All optical instruments are combinations of either prisms, lenses, or mirrors. DOUBLE REFRACTION AND POLARIZATION. 535. If a crystal of Iceland spar be placed upon an ob- ject, as in Fig. 246, a double image will be perceived. This phenomenon is called double refraction. Most transparent crystals have the same property of refracting light in two separate pencils. The manner in which the incident ray is divided is shown in Fig. 247. Let a a; be a line joining the 298 NATURAL PHILOSOPHY. obtuse angles of a crystal of Iceland spar. It is called the axis of farm, and any plane, as adxc, parallel to this axis and perpendicular to any face o'f the crystal, is called the plane of principal section. Now, suppose a ray of light to proceed from a dot at i; it will be refracted in two rays, tV, ief ', and will give two images of equal inten- sity, one at o the other at e. The first of these rays, io', has a constant index of re- fraction 1.05, and is governed by the laws of single refraction. It is, therefore, called the ordinary ray. The other ray, ie / ) is called the extraordinary ray. 536. There is one direction in which the images coin- cide and the object appears single. This direction is parallel to the axis of form, and is known as the optic axis of the crystal. The amount of separation of the two images will be the greatest when the direction of the inci- dent ray is at right angles to the optic axis. If the eye be placed directly above the dot, and the crystal be slowly turned around, the ordinary image will remain stationary, while the extraordinary will revolve about it at varying dis- tances. Hence, the extraordinary ray has a variable index of refraction, and does not, in general, coincide with the plane of the incident ray. Crystals with but one axis are called uniaxal, as Iceland spar, tourmaline, sapphire, quartz. Most crystals are bi- axal; that is, they have two directions in which the image is single, as sugar, strontianite. 537. Both the ordinary and extraordinary rays have acquired properties which distinguish them from rays re- ceived directly from the sun or any self-luminous body, ami are said to be polarized. Li^ht may also be polarized by single n-iVaction, reflection, and absorption. A body capa- ble of polari/in-- li'jht is called a /Whown. Suppose a brain of -ohr light io have been transmitted through a doubly refracting crystal, ar, and one of the POLARIZATION. 299 FIG. 248. rays to be cut off by a screen, S. If the ordinary ray be allowed to pass through a second crystal, a' z', it will in general be separated into two rays, one ordinary, i'tX, and the other extraordinary, iV, but of unequal intensities. If the second crystal, which is called an analyzer, be turned around until the two principal planes coincide, that is, until their axes make an angle of or 180, the ex- traordinary ray disappears, and the ordi- nary has its greatest intensity. On turning the analyzer farther around, the ordinary ray gradually decreases in intensity, while the extraordinary ray re-appears and in- creases in intensity. When the principal planes are at right angles to each other, that is, when their axes have been turned 90 or 270, the ordinary ray disappears, and the extraordinary ray has its greatest intensity. If the screen be moved so as to cut off the ordinary ray and allow the extraordinary to fall on the analyzer, the extraordinary ray alone will be transmitted when the principal planes coincide, and only the ordinary when the principal planes are at right angles. At intermediate positions, the refraction is double, but of unequal in- tensity, except at the middle point of each quadrant. 538. Explanation of polarization. If we regard the waves of light to be those of crests and hollows (893), the vibrations will be transverse to the direction of propagation. Now, since common light will be equally transmitted in every conceivable direction, the transverse vibrations must take place in every possible plane. This can not be the case with polarized light, since its intensity varies from a maximum to zero as its direction to the medium which it encounters varies. It has, therefore, acquired sides ; that is, its transverse vibrations may be regarded as moving in a single plane, as east and west, or up and down, or right and left. Hence, polarized light consists of a system of vibrations moving in a single plane or in parallel planes. If, then, the adjoining figures repre- sent sections of two beams of light, the / FIG. 249. FIG. 250. 300 NATURAL PHILOSOPHY. radii of Fig. 249 will represent the transverse vibrations of common light, and the parallel lines of Fig. 250, the transverse vibrations of polarized light. Now, on the principle of the resolution of forces, polarized light may be considered as moving in a single plane, and common light as equivalent to a system of vibrations, moving in two planes at right angles to each other. Fig. 251. When the beam is polarized, the light is sepa- rated into two sets of vibrations, which move in planes at right angles to each other. In the case of the Iceland spar, the ordinary ray is polarized in a plane parallel to the optic axis, and the extraordinary ray in a plane at right angles to that axis. 539. Polarization by absorption. If a crystal of tour- maline be split into plates parallel with its axis, these plates will be doubly refracting, like Iceland spar. They also possess the property of rapidly absorbing the ordinary ray ; and hence, if a beam of solar light fall upon a plate of requisite thickness, only the extraordinary ray will emerge. For this reason, a plate of tourmaline is a convenient means for polarizing light, and also for analyzing light that has been polarized by other means. The tourmaline pincette consists of two such plates set in movable disks, a and 6, Fig. 252. If either plate be held between the eye and a candle, the light will be transmitted polar- ized in all positions of . 2:>2. the disk, (but colored by the accidental tint of the crystal.) If the two disks are placed in front of each it IKT, with their axes parallel, little cliaiiL r e will !< observed; but if the second or analyzing plate be slowly turned, the liirht will gradually become more feeble, and will entirely ili-apprnr when the plate has been turned 1)0. The effect of the tourmaline is analogous to that of two gratings with parallel bars. Fi.ir. -').'! If a card-board model of a wave of POLARIZATION BY REFLECTION. 301 FIG. 253. li.,'ht be presented to the grating, A, only the vertical portion will be permitted to pass. When this portion, which represents a polarized wave, reaches C, it will be stopped if the gratings at C are at right angles to A, but will pass freely if C be turned a quarter round. If either ray which has been polarized by transmission through Ice- land spar be examined by a tourmaline analyzer, it will be found that in certain positions of the analyzer all the light will be absorbed, but if the analyzer be turned 90, all the light will be transmitted. The ordinary ray will be trans- mitted where the extraordinary was absorbed, and absorbed where the other was transmitted. 540. Polarization by reflection. When light falls upon the surface of any transparent medium, the reflected ray is more or less polarized. Let AB, Fig. 254, be a plate of R' FIG. 254. FIG. 255. glass, and I C the incident ray. A small portion of the light will be reflected at each surface, in the direction, C R, ER', and the remainder transmitted. All the reflected light will be polarized when the angle of incidence is such that the reflected and refracted rays are at right angles to each other. This is called the polarizing angle. The polar- izing angle for glass is 54 35', for water 52 45'. * * The angle of polarization for light passing from air into a denser medium is such that the tangent of the incident ray, which is reflected polarized, is equal to the index of refraction for the reflecting medium. 302 NATURAL PHILOSOPHY. If the polarized ray tall upon a second plate at an equal angle, vix.: ">4 ;>"/, it will lie entirely reflected when the two plates are parallel, but if the upper plate be turned around this ray as an axis, so as to maintain the same angle of incidence, the ray will gradually decrease in intensity, and will entirely disappear when the two plates are at right angles to each other. Fig. 255. If the polarized ray be examined by an analyzer of Iceland spar, it will be refracted singly and ordinarily when the principal plane coincides with the plane of reflection ; singly and extraordinarily, when the principal plane is at right angles to the plane of reflection, and in all other cases will be separated into two pencils which are, in general, of unequal intensity. 541. Polarization by refraction. When light is polar- ized by reflection from the surface of a transparent medium an equal amount of the transmitted ray, E D, is polarized by refraction. But as the amount of light transmitted is much greater than that reflected, only a small portion of the transmitted ray will be polarized, and will emerge mixed with common light. If, however, several plates of glass or mica be laid one upon another, the light will be partially polarized at each refraction, and if eighteen or twenty plates be used, very nearly all of the transmitted light will be polarized. If light, polarized by refraction, fall upon a glass plate at its polar- izing angle, it will be wholly reflected when the surface is at right angles to the plane of refraction, and wholly transmitted when the reflecting surface is turned 90. Therefore, the planes of polarization by refract i< m and reflection are at right uncles to each other. If examined by an analyzer of tourmaline, or of Iceland spar, the reflected ray will be transmitted where the refracted ray is stopped, and stopped where the refracted ray is transmitted. 542. Rays of light, polarized in the same plane, may be made to interfere with each other in the same manner as rays of common light. The chromatic effects produced are exceedingly striking and beautiful. The simplest manner of producing these effects is by in- terposing a thin plate <>{' any doubly refraetiu: substance IK t ween the polarizer ami analv/.er. Thus, if a thin film of Iceland spar be placed IM-IWM-II the disks ..fa tourmaline R TA TOR Y POL ARIZ A TION. 303 Fio. 256. FIG. 257. pincette, with the axes of the tourmalines perpendicular, a beautiful series of colored rings traversed by a black cross be seen. Fig. 256. If the analyzer be turned, the colors will gradually change, and when the axes- are parallel, the tints will be comple- mentary to the first series, and the cross will become white. Fig. 257. Any uni- axal crystal will pro- duce similar effects. Biaxal crystals produce double systems of rings, with most curious and characteristic combinations. 543. Many other substances, as slices of quills, parings of horses' hoofs, grains of starch, compressed glass, gums, and jellies, will, under like circumstances, give similar colors and rings, and thereby indicate a doubly refracting structure. Whenever there is the least tendency to an axial arrangement in the molecular structure of transparent bodies, it may be determined, at least in part, by transmit- ting through the body a polarized ray. If polarized light be transmitted through unannealed glass, irregu- larly heated, compressed, or bent, the amount of molecular change in the glass caused by the disturbing force may be at once indicated and measured by the colors displayed, by viewing the transmitted ray through an analyzer. 544. Rotatory polarization. If two tourmaline plates be crossed, no light will be transmitted. If, now, a section of quartz crystal, cut at right angles to the axis, be placed between the polarizer and analyzer, more or less light will be transmitted, and to extinguish it, the analyzer must be turned through a certain angle. This phenomenon is called rotatory polarization. Some kinds of quartz turn the plane of polarization to the right hand and others to the left, and the crystals are 304 NATURAL PHILOSOPHY. termed right handed or left handed, according to the effect produced. The action of the plate is proportioned to its thickness, and is more energetic the greater the refrangi- bility of the ray. Thus, for a plate of quartz one twenty- fifth of an inch thick, a ray of red light requires the analyzer to be turned 17, and a ray of violet light, 44. If white light be used, the same crystal will give different colors as the analyzer is turned. 545. Certain liquids also possess the property of rotatory polarization. Thus, solutions of cane sugar, and oil of lemons, give a right-handed rotation; albumen, and solu- tions of uncrystallizable sugar, give a left-handed rotation. Hence, if a ray of polarized light be transmitted through a sirup of pure cane sugar, the strength of the sirup may be determined by the angle through which the analyzer must be turned to produce the violet tint. A mixture of two liquids, acting oppositely, will pro- duce a result equal to the difference between the two; hence, a simi- lar contrivance may be used to determine the proportion of cane and fruit sugars in a sirup, or to determine the adulteration of various essential oils. Other uses of polarized light. By viewing the heavenly bodies through an analyzer, Arago was enabled to decide that the moon and planets shine by reflected light, because much of their light is polarized. On the other hand, the fixed stars are self luminous, because their light is unpo- larized. Polarized light is of great value in microscopic investi- gations, because, by means of characteristic rings and axial lines, various bodies may be detected in very minute <|ii:uitities. Thus, the various kinds of starch give charac- teristic bands which serve to distinguish one from the other. 546. Recapitulation. fl>ouhlr refraction. Onlinarv rHYartion. a- j i .' ; Reflection. Absorption. HE A T. 305 CHAPTER VIII. FYRONOMICS. 547. The sensations of warmth and cold are due to the action of a force which every one recognizes as heat. These tt -rms are, however, merely relative, as the same substance may at the same time appear warm to one individual and cold to another. If we place the right hand in iced water and the left in hot, and then suddenly transfer both to ordinary cistern water, the sensations of either hand will be reversed. Our sensations, therefore, can not be used as a means of measuring heat accurately. We may accom- plish this result by means of the effect of heat on bodies not endowed with sensation. 548. The first effect of heat on any body, solid, liquid, or aeriform, is to expand it. The expansion of gases may be readily shown by the air thermometer. Fig. 258. This consists simply of a bulb of glass, with a long narrow stem, dipping into colored water. If the bulb be warmed by the hand, the air within will so ex- pand that a portion will be expelled and rise in bubbles through the liquid. On cooling, the por- tion of air remaining will contract to its former volume, and the water will take the place of the air expelled. The experiment may then be continued indefi- nitely. The expansion and contraction may be measured by the scale attached to the stem. If other gases than air are used to fill the stem, it will be found that all expand equally and regu- larly for successive increments of heat. Fio. 258. The expansion of liquids may be shown by a flask, hav- ing a long narrow tube fitted to its neck by a cork. Fig. 259. N. P. 20. 306 NATURAL FHILOSOrilY. FIG. 259. If the flask be filled with alcohol and plunged in boiling water, the expansion of the alcohol will be manifested by its rise in the tube. If other liquids are used to fill the flask, most of them will expand less than the alcohol, showing that different liquids expand unequally for the same increments of heat. A scale attached to the tube will convert the appa- ratiH into a thermometer, which may be termed mer- curial, alcoholic, water, etc., according to the liquid used. The expansion of solids may be shown by a Gravesande's ring. Fig. 260. A brass ball is so made that, at ordi- nary temperatures, it passes freely through the ring, ra. When the ball is heated, it expands, and will no longer pass through the ring. FIG. 260. The preceding experiments show an "increase in volume which is termed cubical expansion. In solids the expansion is sometimes measured in one direction only, and is then termed linear expansion. The pyrometer, Fig. 261, may be used to show the linear expansion of solids. A metallic rod, A, fixed at one end, B, presses at the other end FIG. 2fii. the short arm of tin- indrx, K. When tin- rod is lira ted, it and drives the index along the scale. By using rods of different EXPANSION BY HEAT. 307 substances, it will be seen that different solids expand unequally for equal increments of heat. 549. The unequal expansion of different metals is well shown by a compound bar, made by riveting together two bars of iron and brass, at different points along their whole length, as shown in Fig. 262. If the bar is straight at ordinary temperature, it will so bend when hot water is poured on it that the brass will be on the convex FIG. 262. FIG. 263. side of the curve, and bend in the opposite direction when cold water is poured on it. The brass expands and contracts more than the iron, and the bar curves to accommodate the inequality of the length which results. This principle has been applied to the construction of metallic thermometers. Clay does not expand by heat, but contracts permanently, by reason of chemical changes among its particles. In the experiments detailed, the bodies will be found to contract on cooling, and assume their original volume, as soon as they attain their former tempera- ture. Certain metals, as lead and zinc, are exceptions to this law of cooling, the contraction being at each time a little less than the ex- pansion. 550. From these experiments it is evident (1.) that the volume of all bodies is increased by heat; (2.) that this in- crease of volume is due to motion among the molecules of the bodies, which tends continually to separate them; (3.) that the intensity of the heat may be measured by the degree of the molecular motion. From these and other considerations, to be detailed hereafter, it is assumed that Heat is that mode of molecular motion which may be meas- ured by the expansion of bodie*. By this definition it is understood (1.) that the molecules of every body are in continual motion; (2.) that when this motion increases in intensity, the body becomes warmer; (3.) that when this motion decreases in intensity, the body becomes cooler. An older theory, which regarded heat as 308 NATURAL PHILOSOPHY. imponderable matter, has been generally discarded while some of its terms have been retained : hence, the student must remember that when heat is described as passing from one body to another, it means that the molecular motion of one body is communicated to the molecules of another, and not that any material agent has passed. 551. Temperature is the intensity of heat referred to some arbitrary standard. The standards assumed are those of melting ice and of water boiling under the pressure of one atmosphere, which are found by experiment to represent invariable temperatures. These temperatures are called, severally, the freezing and the boiling points. A tJiermometer is an instrument which measures temperatures. Thermometers may be formed of 212 anv substance in which the expansion on heating and the corresponding contraction on cooling may be determined. The mercurial thermometer con- sists of a capillary glass tube, at one end of which is blown a bulb; the bulb and part of the tube are filled with mercury. The mercury and the glass are both affected by heat, but, under the same circumstances, the mer- cury expands or contracts seven times as much as the glass. Therefore, if the instrument is warmed the mercury will rise in the tube; and if it is Fi.i.264. cooled, the mercury will sink in the tube. For the purpose of comparing one instrument with another, arbitrary scales have been devised, by which the variation in the mercurial column may be designated. The fVee/.iiiL r and boiling points are first determined by im- mersing the instrument in melting ice and in boiling water, and the height <>f the column in each case is marked on the tube or on the scale attached to it. These points being determined, the interval between them is then divided into any number of equal parts called degrees, and parts of the THERUOMETRIC SCALES. 309 same length are set off above and below the boiling and freezing points, as far as may be required. 552. Fahrenheit's scale is in common use in this country. It marks the boiling point by 212 and the freezing point by 32. The zero, or 0, of this scale was determined by a mixture of ice and salt. The scale used in France, and generally employed in scientific researches, is the centigrade, invented by Celsius. It marks the freezing point by 0, and the boiling by 100. Reaumur's scale, which is used in Germany and Spain, marks the freezing point by 0, and the boiling by 80. These scales are distinguished from each other by the letters F., C., and R. The divisions below zero are indicated by the negative sign; thus, 10 signifies ten degrees below zero; + 10, or 10 sig- nifies ten degrees above zero. The interval between the freezing and boiling points is, therefore, divided by Fahrenheit into 180, by Celsius into 100, and by Reaumur into 80 ; hence, 180 F = 100 C = 80 R, or l F = fC = fR. Bearing in mind that Fahrenheit's zero is 32 below the freezing point, one scale may readily be converted into another, thus: F = fC + 32 = fR + 32. C = (F 32) f r= f R> R = (F 32) f = | C. All these scales are alike arbitrary; but undoubtedly the most rational and conven- ient is the centigrade. 553. As mercury freezes at 37. 9 F., and boils at 662 F., it can not be used to measure temperatures be- yond these limits. Thermometers filled with alcohol are used to measure ex- treme cold, and various forms of metallic thermometers are used to measure extreme heat. The pyro- meter, Fig. 261 is an example. The air thermometer, Fig. 258, is very sensible to changes in tem- perature, but is affected also by changes in the atmosphere. FIG. 265. 310 NATURAL PHILOSOPHY. Regnault has devised an air thermometer which is by far the most reliable thermometer known. It is very sensitive and may be used for any temperature, but is too compli- cated for ordinary use. The differential thermometer, Fig. 265, has two closed bulbs filled with air and connected by a U tube, containing a little sulphuric acid. It indicates only the difference in tem- perature of the two bulbs ; if one is warmer than the other, the liquid in the tube will be forced toward the colder bulb. For very delicate investigations, the thermo-multiplier, described in (771), is now universally employed. 554. The coefficient of expansion is the small fraction which measures the expansion of a body on being raised from the freezing point to one degree above. The rate of expansion for all gases is very nearly the same, being 49 * 9 of their bulk for each degree Fahrenheit, or -%fa of their bulk for each degree centigrade. The rate of expan- sion for solids and liquids increases as the temperature rises. Between 32 F. and 212 F. this increase in rate is hardly ap- preciable, so that the coefficient of expansion will very nearly represent the expansion of each degree. For higher temper- atures, the increase in rate forms a considerable quantity. For this reason all thermometers should be graduated by comparison with Regnault's air thermometer. Thus, the tem- perature of 572 F., as measured by Regnault's thermometer, would be indicated by 586 F. if measured by an ordinary mercurial thermometer, because of the increase in the rate of expansion in mercury, as the temperature rises. Alcoholic thermometers are even less reliable, because the expansion of alcohol at all temperatures is exceedingly irregular. If a rod, whose length is taken as unity, have a coefficient of ex- pansion n-jin -nitr.l I iv ' ( , then its total Imirih after being heated one degree will be 1 -f . If the same substance be in the form of a square, the superficial contents, after heating one decree, will be (l -f-l) 2 =l -f l+#. Finally, if the same substance be in the EXPANSION. 311 form of a cube, the volume, on being raised one degree, will be (l +|) 3 = l-r + Jj+^r. Now, as | is a very small quantity, its powers, 55 , - 3 , may be neglected ; consequently, the superficial coefficient of expansion is nearly twice, and the cubical coefficient three times the linear coefficient. Table of Expansion from 32 F. to 212 JF*. Solids. Linear. Cubical. Flintglass T ^ T ^ Platinum Steel.... Brass Silver Tin Zinc Fluids. Cubical. Mercury ^ Water The fixed oils Ty - Alcohol , Air and the permanent gases. f 21 555. The amount of force exerted in expansion or con- traction is enormous ; for it is equal to that which would be required to stretch or compress the material to the same extent by mechanical means. Water, at the temperature of 128 F., is compressed .000044 of its volume by the pressure of one atmosphere. On being heated from 32 F., to 212 F., it expands .0466 of its volume. Therefore, to re- store boiling water to its bulk at freezing would require a pressure of over one thousand atmospheres. The expansive force of water for each degree F. is nearly ninety pounds per square inch. Hence, if a closed vessel be completely filled with cold water, it must speedily burst when heat is applied. A bar of wrought iron expands, for each degree F., with a force of nearly two hundred pounds to the square inch. This force had a curious application in the Museum of Arts and Trades, in Paris. The walls of an arched gallery had bulged outward by the weight of the arch. Iron bars were placed across the building and screwed into plates on the outside. The alternate bars were then heated, and as soon as they had expanded the plates were screwed up tightly to the walls. As the bars cooled and contracted, they drew the walls closer together. The operation was repeated until the walls had attained the vertical position. 312 NATURAL PHILOSOPHY. On the same principle tires are fastened on wheels. The tire, made a little smaller than the wheel, is heated red hot, and while expanded is placed in position. On cooling, it not only secures itself on the rim, but holds all the other parts of the wheel in position. It is often necessary to take into account the changes of length produced by heat. In railways, a small interval must be left between the ends of the iron rails. Iron bars built into masonry should be left free at one end. Brittle substances, as glass and cast iron, often crack on being heated suddenly ; because the outside is heated sooner than the inside, and thereby causes an unequal expansion. A sudden cooling, by in- ducing unequal contraction, has the same effect. The thicker the plate the greater the liability to fracture. 556. Water presents a singular exception to the general law of expansion and contraction by heat. If a flask, with a long and very slender neck, Fig. 259, be filled with boiling water and allowed to cool, the water will go on contracting, though irregularly, until it reaches the temperature of 39. 2 F. It then begins to expand, and continues to do so until it freezes. At 32 F. it occupies the same space that it did at 48 F. The maximum density of water is consequently attained at 39. 2 F., and above or below this temperature it expands. This fact is of infinite importance in nature. In winter, the lakes and rivers cool until they attain their maximum density throughout; if the cooling proceeds further, expansion begins at the surface, and the lighter though colder particles float upon the warmer water below. Hence, the freezing takes place only on the surface. At the moment of freezing, the water undergoes a sudden enlarge- ment, of about ten per cent, in volume, in becoming ice. The ice once formed covers the water like a blanket, and renders the fivr/ing process v.-ry -low. If the ice were specifically heavier than water, large ma-.-- would form at the bottom each winter, which the heat of the succeeding snnmirr would be unable to melt entirely, and thus our lakes would in time become solid. SPECIFIC HEAT. 557. The temperature of a body affords \\^ imliratimi of the amount of heat it rontuin.s. The / allowed to cool very slowly, without agitation, it may be cooled to 10 F. bclcuv it fivc/rs. When in this condition, a gentle jolt, or tin- addition of a bit of ice, will OHM immediate congelation, and the temperature will suddenly rise LATENT HEAT. 317 to 32 F. Tn fine capillary tubes, water has been lowered to 4F. without solidification. This fact probably explains why sap is not frozen in plants. The freezing point of water is lowered by the fuvsi-nre of salts in solution. Sea water freezes at 27.4 F. Saturated brine freezes at 4 F. In such cases nearly pure ice is formed by freezing. The water appi-ars to crystallize out, leaving the salt behind. Weak alcoholic liquors, like wine and cider, may be concentrated by exposing them to cold and removing the layers of ice as they form. 564. Change of volume. At the moment of freezing, water expands with great force. This fact is familiar to northern housekeepers in the breaking of utensils in which water is allowed to freeze. Service pipes often burst unless a little stream is permitted to trickle through them. Bomb shells an inch thick, filled with water, have been burst by the freezing of the water. Cast iron, bismuth, antimony, tin, zinc, and some of their alloys, also expand on solidify- ing. These substances give sharp casts, because, when the metal sets, the expansion forces it into the minute cavities of the mold. Most substances, except those enumerated, contract on solidifying ; hence, coins of copper, silver, and gold require to be stamped. 565. Latent heat. After a solid begins to melt, the temper- ature remains constant nntil the whole is melted. This fact may be verified by watching a thermometer immersed in a tumbler filled with melting ice. A large amount of heat must enter a pound of ice at 32, before it can be changed to water at 32. A pound of water at 212 mixed with a pound of water at 32, gives two pounds at the mean tem- pt rature of 122; but a pound of water at 212 mixed with a pound of ice at 32, gives two pounds of water having the temperature of only 51. In this case, the water has lost 161, while the ice has gained only 19, so that 142 have disappeared in changing the ice to water. The heat is not lost, for an equal amount will be given out if a pound of water is converted into ice, but because this is not sensible to the thermometer, the 318 NATURAL PHILOSOPHY. heat which a body absorbs or emits, in changing its mole- cular condition, is termed latent heat. The latent heat of water is of the greatest value in nature. 1. It retards the melting of snow. To change a pound of snow at 32 into water at 32, requires as much heat as to warm one hundred and forty- two pounds of water one degree. If it were not for this provision, the inhahitants of northern valleys would be exposed to terrific inun- dations at every approach of spring. 2. The melting of ice withdraws the heat from surrounding objects. A "thawing day" frequently feels very chilly. Near lake Erie the spring is so much retarded by the melting of the winter's ice, that generally the buds of trees do not swell until the danger of late frosts is past. 3. The freezing of water mitigates the sudden setting in of frosts, as the very act of freezing liberates sufficient heat to moderate the effect of the depression of temperature on surrounding objects. Hence, it is a common remark that the weather moderates on a fall of snow. 566. Every solid in melting has its own latent heat, which is called the fieat of fusion, or the latent heat of liquid*. The amount may be determined by the method of mixtures. The second column in the following table shows the number of pounds of water that would be raised one degree by the solidifying of one pound of each substance named. Latent Heat of Liquids. In F. Water - 1. Water 142.65 1.000 Zinc 50.03 .365 Tin '^-^ Sulphur 10.*-"' - 118 Lead 9.68 .<>7 Mercury r > 567. Freezing mixtures. In dissolving solids, as in molt- ing, a certain quantity of heat becomes latent. Thus, if snow and common salt !>< mixed together, the salt causes the snow to melt, and the water dissolves the salt, so that both EVAPORATION. 319 become liquid, and, by consequence, a large amount of heat is absorbed from the surrounding objects. This is the mixture used for freezing ice creams. Two parts of snow and one part of salt will reduce the temperature to 4 F. Two parts of snow mixed with three parts of crystallized chloride of calcium will produce a cold sufficient to freeze mercury, and if these substances, and the containing vessel, be previously cooled, a cold of 50 may be produced. A very convenient freezing mixture con- sists of five parts of common hydrochloric acid and eight parts of crystallized sulphate of soda, previously reduced to powder. 568. Vaporization. If a solid be exposed to sufficient heat, when the expansive force of the heat exerted between its molecules equals their cohesive force, the body melts. As the temperature rises, the expansive force becomes greater than the cohesive, and the liquid passes into the aeriform state, as soon as the excess of expansive force exceeds the atmospheric pressure. This, the third effect of heat, is termed vaporization. If vaporization takes place slowly and quietly, it is termed evaporation, but if the liquid is agitated by the formation of bubbles of vapor, the process is termed ebullition, or boiling. Some solids, as iodine, arsenic, and camphor, vaporize without becoming liquids. This is termed sublimation. 569. The laws of evaporation may be studied by intro- ducing a small quantity of ether, or other volatile liquid, through a barometer tube, into the Torricellian vacuum at the top. As soon as the liquid reaches the vacuum, it is instantly converted into vapor, and depresses the mercury by its elastic force; showing, 1. All volatile liquids in a nirinim are instantly vaporized. If successive small portions of the same liquid are used, the mercury continues to be depressed until a point is reached where the ether remains liquid. The space above is then said to be . it united, and the elastic force of the vapor has reached its maximum tension. If, now, the tube be heated, more ether will vaporize, 320 NATURAL PHILOSOPHY. and the mercury will be further depressed ; but if the tube be cooled, a portion of the vapor will be condensed into liquid, and the mercury will rise. Therefore, 2. In every space void of air the maximum tension of vapor correspond* with the temperature. If the tube be plunged in a deep bath of mercury, as in Fig. 140, and the saturated vapor be exposed to increased tension, by depressing the tube, a portion of the vapor will become liquid, and on raising the tube a fresh portion will vaporize under diminished pressure. Therefore, 3. Tfie maximum tension of saturated vapors is independent of tfie press- ure. Non-saturated vapors obey Mariotte's law. If the first experiment be per- formed with several different vol- atile liquids, Fig. 266, each having the temperature of 68 F., the mercury will be depressed, in inches, as follows : ether, 17 ; bisulphide of carbon, 12 ; alcohol, 1.7; water, 0.7. Hence, 4. At the same temperature, the saturated vapors of different liquids possess different elastic force. If two liquids which do not dissolve each other, as water and bisulphide of carbon, are placed in the same tube, the tension of the mixed vapors will equal the sum of the two taken separately This explains the remarkable fact that the same amount of water will evaporate in a space filled with air, as in a vacuum of equal volume. 570. Evaporation of water is ^roing on constantly in nature, and is OIK- of the me:m.- by which the earth is ren- dered fit for the maintenance of life. The principal cir- DEW POINT. 321 cumstances which influence the amount and rapidity of evaporation are as follows: 1. It varies with the temperature, because heat increases the elastic force of vapors. 2. It varies with the amount of the same liquid in the atmosphere. When the air is saturated, evaporation ceases; it is therefore greatest in air free from vapor. 3. It is assisted by the renewal of the air; because, if the air is not renewed it becomes saturated. Hence, evap- oration is more rapid in a breeze than in still air. 4. It varies with the extent of surface exposed; because, evaporation proceeds only from the surface. 5. It varies inversely with the pressure on the surface of the liquid, because of the resistance offered to the escape of the vapor. It is very rapid in vacuo and less rapid in space containing air. Evaporation may go on at very low temperatures. Mercury begins to evaporate at 60 F. Iodine, camphor, and some other solids vaporize at ordinary temperatures. Snow and ice disappear from the surface of the earth when there has been no thawing. Clothes are dried on a winter's day, when the thermometer shows a temperature below freezing. A warm sultry day is less favorable to evaporation than a cold day with a brisk wind. 571. Air is said to be saturated with moisture when it contains as much aqueous vapor as it can hold up at a given temperature. Air, at 32 F., can absorb yj-g- part of its weight of aqueous vapor. For every increase of 20, the capacity of air for moisture is nearly doubled ; at fifty- two degrees, air can absorb yfg-, and at seventy-two degrees, ^ of its own weight. If air, saturated with moisture, is cooled, a portion will be deposited as dew. The tempera- ture at which this deposit occurs is called the dew point. The more fully the air is saturated with moisture, the nearer will the dew point be to the temperature of the atmosphere. N. P. 21. 322 NATURAL PHILOSOPHY. The dew point may be determined with sufficient accuracy for ordinary purposes, by placing ice in a metallic vessel containing water, and noting, by a thermometer, the temper- ature of the water when the dew begins to form on the outside of the vessel. The higher the dew point, the more abundant will be the deposit. The "sweating" of pitchers is indicative of rain, because it shows that the air is nearly saturated with moisture, which will fall, if the temperature of the air is lowered below the dew r point. 572. Ebullition. Tlie temperature at which liquid* boll *x constant for the same substance, under like conditions. Several circumstances influence the boiling point. 1. The nature of the liquid. The following table gives the boiling point of several liquids under the pressure of one atmosphere. Table of Boiling Points. Protoxide of nitrogen... 157 F. Carbonic acid 108.4 Sulphurous acid -\- 17.6 Ether .. 94.8 Bromine 145.4 F. Alcohol 173.1 Water 212. Mercury 602. 2. The adhesion of the liquid to the vessel which contains it. Water sometimes boils in a glass vessel at 214, and in a glass vessel coated with shellac as high as 221. The ebullition then takes place in bursts, the temperature fall- ing at each gust of vapor to 212. By throwing iron filings into the water, the boiling point, in either of these cases, is reduced to 212. 3. Satis in solution generally increase the boiling point. Thus, a saturated solution of common salt boils at 227 F.; of nitrate of potassa, at 240 F. ; of chloride of calcium, at 355 F. Substances mechanically suspended, like bran, saw-dust, do not influence the boiling point. The vapor which arises from solutions is not permanently hotter than the steam from pure water. BOILING POINT. 323 4. Variations of pressure increase or diminish the boiling point, because n //'. foiling 'Points of Water at different 'Pressures. Boiling point, Barometer, F. inches. 184 16.676 190 18.992 195 21.124 200 23.454 205 25.46S 210 28.744 211 29.331 212 29.922 213 30.516 214 31.120 215 31.730 Boiling point, Pressure in F. atmospheres. 212 1 iM'J.r> 2 273.3 3 291.2 4 306. 5 318.2 6 329.6 7 339.5 8 348.4 9 356.6 10 415.4 20 574. The temperature of the boiling point of water is much reduced on ascending mountains, in consequence of the diminished atmospheric pressure. Soiling 'Point of Water at different Altitudes. Above the Mean height Temperature, sea-level. of barometer. F. Donkia (Himalaya) +17337 15.442 179.9 Mont Blanc 15650 16.896 185.8 Quito 9541 20.750 194.2 Mount Washington 6290 22.905 200.4 Madrid 1995 27.720 208. London 29.922 212. Dead sea (below) -1316 31.496 214.4 The observation of the boiling point of water at any particular elevation, gives a ready means of determining its elevation above sea- level, a difference of about 596 feet of ascent, producing a variation of 1 F. in the boiling point. 575. Marcet's globe is used to estimate the tension of high pressure steam. It consists of a small boiler, fur- nished with three apertures, through one of which a ther- mometer stem is pasn-d, air tight; through a second is inserted a glass manometer tube, whose lower end opm> under mercury placed in the boiler; the third aperture is furnished with a stop-cock. The boiler is half filled with SPHEROIDAL STATE. 325 water. On applying heat it will be found that so long as the stop- cock is open, the temperature of the boiling will remain steadily at 212 F. Steam, there- fore, at this temperature, has an elastic force equal to the pressure of one atmos- phere. On closing the cock, the steam, which continues to rise from the water, increases in elastic force, as is shown by the rise of mercury in the manometer. When the mercury in the manometer stands at thirty inches, the tension of the steam will be in- creased one atmosphere. At the same time the boiling point gradually rises, and at the pressure of two atmospheres equals 249. 5 F. The elastic force of the steam increases more rapidly than the rise of the boiling point, as is shown by the preceding table. For this reason, high pressure steam is more economical as a motive power than low pressure. Steam, heated apart from water, follows the general law for the expansion of gases. Such steam is called dry, or superheated steam, and is applied to the carbonization of wood, and the rendering of lard and tallow. 576. The spheroidal state is caused by the slow evap- oration of a liquid in apparent contact with a very hot plate. Drops of water scattered on a polished surface of high temperature do not flatten, but assume an ellipsoidal shape, and roll quietly about until they evaporate, without boiling. This experiment may be performed in a smooth metallic capsule, heated over a lamp. Into this any vola- tile liquid may be dropped from a pipette. Several phe- nomena are noticeable. 1. The temperature of the plate must be greater than the boiling point of the liquid. Thus, the plate requires to FIG. 268. 326 NATURAL PHILOSOPHY. be heated to 340 F. to produce the spheroidal state with water; with alcohol, 273; with ether, 142. 2. The temperature of the spheroid is lower than the boiling points of the liquids, being, for water, 206 F.; for alcohol, 168; for sulphurous acid, 13. 3. The spheroid does not touch the plate. By using a plane surface of silver, the light of a taper may be seen between the surface and the liquid. If the source of heat be re- moved, the temperature of the plate will fall until a point is reached when the liquid wets the surface, and then the liquid will boil violently. This may be shown by pouring a small quantity of water into a copper flask, intensely heated, and corking the flask while the liquid is in the spheroidal condition. For a time all is quiet, but when the flask lias cooled sufficiently, the water will be suddenly converted into KI.J. am. steam, and the cork ejected with violence. It is probable that boiler explosions are sometimes caused in a similar manner. 577. The explanation of these facts is that as soon as the drop reaches the hot surface a portion of it is converted into vapor, which both supports the spheroid and prevents the conduction of heat from the plate to the liquid. The temperature of sulphurous acid, in the spheroidal state, is 13 F. ; hence, it is capable of I'reexin^ water, although the capsule containing the acid may be ivbite hot. By using a mixture of ether and solid carbonic acid, even mercury may be I'm/en. So, ton, a moi-tened band may be drawn without injury through molten iron as it runs from the furnace. The moisture of the band is converted into a non-conducting envelope, which sullicieiit ly protect- the skin during the short period of its immersion. The most common illus- LIQUEFACTION OF VAPORS. 327 (ration of the spheroidal state, is that of a drop of water rolling about on a heated stove. 578. The liquefaction of vapors may be produced (1.) by cooling, (2.) by compression, and (3.) by chemical action. 1. A saturated vapor condenses at its boiling point. The process of distillation illustrates this principle. Dis- tillation is used (1.) to separate liquids from solids, as when water is distilled to free it from its impurities ; or (2.) to separate a volatile fluid from another less volatile, as when alcohol is distilled from fermented liquors. The mixed liquid is first heated in a retort or boiler, the vapors discharged are then condensed by passing them through a FIG. 270. pipe kept cool by being surrounded with water. Fig. 270 represents the common still. The boiler, , contains the liquid to be evaporated ; the spiral tube, called the worm, which is immersed in a tank of cold water, receives the vapors to be condensed. 328 NATURAL PHILOSOPHY. 2. If a closed cylinder be filled with the vapor of ether, and this compressed by a piston, as soon as the pressure on the piston equals the maximum tension of the vapor, the vapor becomes saturated, and if the pressure be continued, the vapor will be condensed to the liquid state. Faraday succeeded in liquefying gases by the tension of their own *SK, vapor. His method con- \ sists in inclosing in a ^J ^K bent glass tube the sub- stances by whose chemi- cal action the gas is pro- duced, and then sealing the shorter leg. In pro- portion as the gas is lib- erated, the pressure in- creases and ultimately it liquefies and collects in the empty end. The condensation is further assisted by immersing the shorter leg in a freezing mixture. Fig. 271. In this way cyanogen is readily liquefied by heating cyanide of mercury in the longer end. Larger quantities of gases are condensed by driving the vapors by means of force pumps into strong receivers. Under the joint influence of cold and pressure, nearly all the gases have been liquefied. 3. Sulphuric acid, chloride of calcium, and several other substances, have so strong an affinity for the vapor of water, that they will absorb it from the air even when it is not saturated. Such bodies, placed in a closed space, will quickly abstract all the moisture from it. 579. Latent heat of vapors. Since the temperature of a liquid is constant during ebullition, it follows that a con- siderable quantity of li<-at is rendered latent in producing the molecular chan.ir- from liquid to vapor. FIG. 271. LATENT HEAT OF VAPORS. 329 With the same source of heat, it takes about 5 times as long to change boiling water into vapor as to raise the same quantity 180 degrees, or from 32 to 212; hence, the latent heat of steam is 180 X 6J, or about 960. The latent heat of vapors is more accu- rately determined by distilling them, and noting the rise of temper- ature caused in the water surrounding the worm by a known weight of vapor. The application of both these methods for determining the latent heat of water may be readily made. FIG. 2:2. Arrange a glass flask and beaker, as in Fig. 272. Pour one ounce of water, at 32 F., into the flask, and 5J ounces at the same temper- ature into the beaker, and apply heat. Now note (1.) the time re- quired to raise the water in the flask to boiling, and that required to change the boiling water to steam. The latter will be 5 times longer than the former. (2.) When the water in the flask has been expelled, that in the beaker will be raised to the boiling point, showing that an ounce of steam is competent to raise 5 ounces of water from 32 to 212. Z,atent Heat of Vapors. Water 966.6 Alcohol 374.9 Acetic Acid.. . 183.4 Ether ,. 162.8 Bisulphide of Carbon 156. Bromine 82. 580. Cold produced by evaporation. Whatever be the heat at which a liquid evaporates, it grows sensibly colder in proportion to the rapidity of evaporation, unless it receives as much heat from external bodies as is rendered latent. 330 NATURAL A shower of rain cools the air by absorbing the heat during evapor- ation. For the same reason, the air of a heated room cools when water is sprinkled on the floor. Any nieehanieal eause that increases the evaporation enhances the effect. A breeze or current of air produced by fanning causes a more rapid evaporation of the perspiration, and thereby produces a refreshing cooln* In tropical climates water is cooled by the use of porous jars placed in a draft of air. A small quantity percolates through the pores, and, on evaporating, abstracts so much heat from the remaining liquid as to lower its temperature considerably below that of the surrounding air. Ether and other volatile liquids thrown in spray on portions of the body may so benumb them by cold as to render them insensible to pain during surgical operations. 581. Water may be frozen by its own evaporation, by placing a thin shallow capsule, filled with water, over strong sulphuric acid, under the receiver of an air pump. On exhausting the receiver, the sulphuric acid absorbs the vapors as fast as they are formed, and thus a very rapid evaporation of the water ensues, which effects the freezing of the water. A similar result is produced by means of the cryophorus. This con- sists of two glass bulbs, connected by a long tube. In making the instru- ment, one of the bulbs is partially filled with water, which is then made to boil briskly until the air is expelled by the steam, and the instrument is then hermetically sealed. On cooling, the spare above the water is filled only with its vapor. If, now, the empty bulb, A. is plunged into a free/ing mix- ture, this vapor is condensed as last as it is formed, and evaporation occurs so rapidly from the water in the other bulb, that it soon begins to freeze. Fig. 273. 582. If liquid carbonic acid lc cx|n.>rd io tin- air, if evaporat<- with siirh rapidity that a portion almost, instantly VOLUMES OF VAPORS. 331 solidifies, and produces a cold of 106 below zero. Mer- cury is easily frozen by pouring upon it this solid carbonic acid moistened with ether. Natterer obtained a cold of 220 F. by evaporating a mixture of bisulphide of carbon and liquid protoxide of nitrogen in vacuo. 583. When vapors are condensed they give out their latent heat. Water may be boiled in wooden tanks by forcing steam into it. Buildings are frequently warmed by the heat of steam generated in a boiler placed in the basement. To this end it is conveyed to the several apart- ments by coils of iron pipe. The whole amount of heat in the steam is the sensible, plus the latent heat : thus, at the boiling point a pound of steam contains 212 + 966.6 = 1178.6 tfiennal units. 584. Equal volumes of different liquids produce unequal volumes of vapor. The following table shows the volume of vapor furnished by one cubic inch of each of four liquids, at their respective boiling points. Cubic inches. Boiling point. Water 1696 212 F. Alcohol 528 173 Ether 298 95 Oil of turpentine 193 314 Water furnishes, bulk for bulk, a greater amount of vapor than any other liquid, one cubic inch expanding to nearly a cubic foot. The mechanical value of the expansive force of different vapors depends upon the bulk of vapor produced from an equal bulk of each liquid. The cost of fuel in generating vapor would be in pro- portion to the latent heat for equal volumes, but experiments show that, for equal volumes, the latent heat of these liquids is not far different. There would be, therefore, no economy in using other liquids in place of water in the steam engine, even if they cost no more than water. 585. The incandescence of bodies has already been con- sidered in (442 a ). 332 NATURAL PHILOSOPHY. 586. Recapitulation. The effects of heat are 1. The expansion and contraction of bodies. 2. The melting and solidifying of solids. 3. The vaporization and condensation of liquids. 4. The incandescence and cooling of solids. The measurement of heat may regard 1. The relative intensity Temperature. 2. The relative quantity Specific heat. 3. The amount absorbed or evolved during mole- cular changes Latent heat. THE DISTRIBUTION OF HEAT. 587. Any heated body returns, sooner or later, to the temperature of surrounding bodies. This tendency of heat to maintain an equilibrium of temperature, is due to a continued exchange of molecular motions by virtue of which every molecule tends to produce in contiguous molecules its own rate of vibration. Heat may be transferred from one body to another in three ways: 1. By conduction, or from molecule to molecule. 2. By convection, or by motion among molecules. 3. By radiation, or by thermal undulations through space. 588. The conducting power of a body increases, as a general rule, with its density. Hence the metals are good conductors ; porous solids, poor conductors ; and liquids ami gases, almost non-conductors. The conductibility of o/*Vx may be shown by equal sized rods, along which a number of small marbles arc fastened, at equal distances, with wax. Fig. 274. If one end of this rod be held in a hot flame, the heat will !>< propagated from molecule to molecule along the rod, and its gradual progress will bi! manifested by the successive dropping of the marbles, as the different sections of the rod attain the temperature of the fusing point of the wax. CONDUCTION OF HEAT. 333 FlG. 274. That different solids vary much in their power to conduct heat, may be shown by repeating this experiment with rods of copper, iron, brass, glass, etc. By placing thermo-multipliers at equal distances on similar metallic rods, the following table has been obtained. Relative Thermal Conductivity. Silver 100. Copper 73.6 Gold 53.2 Brass 23.$ Iron 11.9 Lead 8.5 Platinum 8.4 Bismuth 1.8 589. That liquids are poor con- ductors may be shown by passing the tube of an air thermometer through a funnel, so that the bulb shall be just below the surface when the funnel is nearly filled with water. Fig. 275. Now, if ether be poured on the water and ignited, the ther- mometer will be but slightly af- fected. Gases, when confined, are almost non-conductors of heat. Fibrous bodies, like wool and furs, owe their non-conducting properties largely to the air which is confined between their meshes. FlG. 275. 590. The conducting power of a body may be roughly estimated by the touch. Thus, sup- pose different substances to be compared at a common tem- perature (1.) much hotter, and afterward (2.) much colder than the hand. An iron rod, if heated above 120 F., will 334 NATURAL PHILOSOPHY. burn the hand, because it conveys its heat rapidly to the skin, and if cooled below F., will blister the lips, be- cause it conveys their heat away so rapidly. On the contrary, a bad conductor may be handled with impunity, within even greater limits of temperature. For the same reasons an oil cloth will feel warmer or colder than a carpet in the same room, according as their common temperature is greater or less than that of the skin. So, also, the oven girls of Germany, clad in woolen garments, enter ovens heated to 300 F. without inconvenience, although the touch of any metal while there would surely burn them. Common observation furnishes abundant illustrations of these facts. Water is sooner heated in a tin cup than in one of porcelain, because the metal is a better conductor of heat. Silver conducts away heat so rapidly, that if a silver spoon be smoothly wrapped with muslin, water may be boiled in it without injuring the muslin. Porous bodies, like ashes and plaster of Paris, are such poor conductors that, if the hand be protected with a thin layer of either, it may carry live coals without danger. So, also, woolen cloths, wrapped about heated irons, protect the hands of the laundress. 591. The practical applications of these principles are very numerous. Thus, non-conductors are used (1.) to prevent the escape of heat, or (2.) to exclude heat. 1. Close wooden boxes, Fig. 276, lined with felt, are used in Nor- way to economize fuel in cooking. For instance, a kettle containing water and vegetables is lir.-t heated on the stove to the boiling point, then placed within the felt box and tightly covered. By this means suilirirnt heat i- retained to cook the vegetables. Double doors and windows, which inclose a layer of air, prevent the escape of heat from our apartments. For the same reasons furnaces are lined with fire brick. So, also, straw is wrapped about tender plants to prevent the escape of their heat. In a -imilar manner a layer of snow pre- serves the warmth of the earth during the chilling blasts of winter. 2. Fire-proof safes are made with double walls inclosing non-con- USES OF NON-CONDUCTORS. 335 ducting substaiuvs, as plaster of Paris or alum. Ice may be kept t'rom melting by wrapping about it a thick blanket. Ice houses have double walls, inclosing a thick layer of straw, sawdust, or charcoal. FIG. 276. Water coolers are constructed in the same manner. The table mats placed under hot dishes protect the table. Furnace men and firemen wear thick woolen garments to exclude the external heat, because this is greater than that of their bodies. 592. The main object of clothing is to prevent the escape of heat from our bodies. The conducting power of the materials used for clothing is in this order: linen, cotton, silk, wool, furs. Hence, with equal texture, a woolen garment is warmer than one of silk, cotton, or linen. A bed quilt containing a layer of paper is warm, because the paper prevents the heat from escaping. The furs of animals in cold countries are finer and closer than those in warm countries. The feathers and down of northern birds form an almost perfect non-conductor. 336 NATURAL PHILOSOPHY. 593. Convection. If heat be applied to the bottom of a flask of water, containing a few fragments of cochineal or sawdust, the particles of the liquid will be seen to rise as they become heated and expanded, while other colder particles descend from the side to supply their place. These currents will then continue until the whole is heated. This process of circulation among molecules is termed convection. It may be applied to the heating of liquids and gases, but not of solids. In heating by convection, the fire must be applied beneath. Thus, on filling a test tube with water, and, holding it by the lower part so that the top is inclined across a hot flame, the layers of water at the top may be made to boil without communicating any heat to the hand, owing to the low conductibility of the water. In the process of cooling fluids, the currents are established in a contrary direction. The upper particles become specifically heavier and descend, thereby forcing the lighter particles upward to fill their place. Any thing that hinders this free circulation retards both the heating and cooling of the fluid. Thus, viscous liquids, like molasses or tar, heat and cool very slowly. 594. The convection of gases is more energetic than that of liquids, because their expansion by heat is greater. If "touch paper," containing chlorate of potassa, be burned in the vicinity of a heated body, the currents of air arising from it may be traced in the smoke. The air which thus rises is heated by convection. The column of :iir in :i chimney becomes heated by the fire, and i- therein- rendered -jieeilieally lighter than any external column of air and rises. I fence, the external air will enter the grate with a draft, proportioned both to the height of the chimney and the in- tensity of the fire. Fio. 277. WINDS. 337 595. In all cases of convection there must be two cur- rents in opposite directions. Thus, if a lighted candle be held in the crack of a door which opens between two apartments of different temperatures, a current of warm, air will drive the flame outward from the heated room, at the top of the door, while the current of cold air will drive the flame inward at the bottom of the door. 596. Winds. These two currents are always attendant on winds, although only the lower one admits of being accurately traced. The atmosphere is heated mainly by convection. The surface of the earth is warmed by the sun, which produces little direct action on the air. The layers of air in contact with the soil become heated and rise, while colder layers descend to supply their place; thus producing upward and downward currents. Moreover, since the earth is not heated equally in all places, a surface current of air will rush from colder toward warmer local- ities, while an upper current will proceed at the same time in a contrary direction, as in the case of the two rooms above mentioned. For this reason a surface wind might always be expected to flow from each pole toward the equator, and an upper current to flow from the equator toward the poles. The direction of these winds is modified by the daily rotation of the earth on its axis from west to east. In consequence of this rotation, fixed objects on the surface have a velocity of nine hundred and eighty miles per hour at the equator and a successively diminishing rate at higher latitudes, until at the poles the motion entirely ceases. The lower current, coming from the poles, partakes of the motion of the surface, and is, therefore, moving more slowly than those regions toward which it proceeds. Consequently the wind appears to come from a direction opposite to that in which the earth is moving, or from the east, with a velocity equal to the difference in the two rates of motion. Hence, it results that two constant surface currents are produced within the tropics on each side of the equator. Their direction will be the resultant of the effects due to the heat and the diurnal rotation. Therefore, north of the equator there will be a steady north-east wind, N. P. 22. 338 NATURAL PHILOSOPHY. and south of the equator a south-east wind. These winds are called trade winds from their importance to navigation. The upper trade winds proceed in the opposite directions, and are sometimes made manifest by clouds and volcanoes. As these winds go northward they become cooler, and gradually descend to the earth. The variable winds in our latitude are frequently caused by the meeting and crossing of the upper and lower currents. 597. Radiation. It is evident that the heat of the sun does not reach the earth by conduction or by convection, since heat is propagated by either of these methods with exceeding slowness. A heated body must, therefore, emit thermal rays which have the power of exciting vibrations in aether and other media, in the same manner as light. This emission of heat is termed radiation. The laws of radiant heat are identical with those of light, and the phe- nomena are in all respects similar. 598. The laws of radiant heat. If a heated body be suspended in space, a thermometer placed in any position around it, will indicate a rise in temperature; but if a screen be interposed, the thermometer will not be affected: hence, 1. Heat radiates in straight lines in all directions. Since heat is a radiant force, 2. The intensity of radiant heat is inversely as the square of the distance from its source. 3. The intensity of radiant Jieat w proportional to ifie temper- ature of its source. 599. Theory of exchanges. Since no body is known to exist at the temperature of absolute zero, all bodies must omit thermal waves of some degree of intensity ; while, at the same, time, they receive other waves from surrounding bodies. These waves, like those of liL r lit, may and do cross o-ieh other without disturbance. If the sum of the motion received is less than that emitted, the body becomes cooler, REFLECTION OF HEAT. 339 hut if greater, the body becomes warmer. If it receives hack just as much heat as it radiates, it remains at a uni- form temperature. If a thermometer be placed before a block of ice, its temperature will fall, because the ice and the thermometer are both sources of heat, and the thermometer receives less heat than it radiates. The ice does not radiate cold, for the opposite result would have been attained if the bulb of the thermometer had contained frozen mercury. 600. Bodies differ greatly in their radiating power; but this is dependent more on the nature of their surfaces than of their substances. Thus, if a canister of tin have one of its sides coated with lamp- black, another with paper, a third scratched or tarnished, and the fourth polished, and then be filled with boiling water, a delicate thermometer placed at each side in succession will indicate different temperatures. Lampblack has the highest emissive power known, the surfaces of paper, and similar loose materials are next in order; the polished metals are the poorest radiators, but gain in radiating power in pro- portion as their surfaces are tarnished. Hence, a bright silver tea- pot filled with hot water will retain its temperature longer than one of earthenware. Pipes for the conveyance of steam, should be kept bright until they reach the rooms where the heat is to be distributed, and there their surfaces should be blackened to increase their radiating power. 601. Radiant heat, incident on any surface, may be (1.) reflected, (2.) refracted, (3.) absorbed, or (4.) transmitted. 602. Reflection. Substances which reflect light well, are also good reflectors of heat. The proportion of incident heat reflected at an angle of forty-five degrees, from cer- tain polished surfaces, is shown by the following: Table of 'Reflecting ^Powers. Silver 97 Gold 95 Brass 93 Platinum .83 Steel 82 Zinc 81 Iron 77 Cast iron 74 340 NAT URA L PHIL OS OPH Y. Archimedes is said to have burned the Koman vessels before Syra- cuse by concentrating upon them the solar rays, by means of concave mirrors. To show that this feat is possible, Buffon constructed a concave mirror that ignited a plank of tarred wood at a distance of two hundred and ten feet. 603. Refraction. When a solar beam is transmitted through a prism of rock salt, and the spectrum is examined by a thermometer, we have the result sketched in Fig. 222, showing, 1. That the thermal rays extend through and beyond the visible spectrum, and are, therefore, of different refrangi- bility and wave length. 2. That the maximum heating effect lies beyond the red, or in rays of low refrangibility, and, consequently, of great wave length, but invisible to the eye. The thermal rays which accompany light are called lumi- nous thermal rays, and the dark rays are the obscure thermal rays. If a platinum wire is heated, it first emits only obscure rays ; as it becomes incandescent, it not only emits luminous rays, but also adds to the intensity of the obscure vibrations. Hence, the hotter a body the more numerous are the rays, and the more intense are each set of vibrations. The obscure and the luminous thermal rays are gov- erned by the same laws, but differ from each other exactly as one color differs from another. 604. Absorption and transmission. Most transparent bodies transmit the rays of heat from the sun as well as those of light; but will not equally transmit the thermal rays from artificial sources. Thus, the heat of the sun will readily pass through glass windows and warm a room, while the same thickness of glass would effectually shut off the heat of a fire. A substance that transmits heat is railed diatJiermanous, and one that is opa<|ii i to heat is called athermanous. Incident rays not transmitted are either re- flected or absorbed. Only the rays absorbed have any effect in warm ing th<- body. 1>[ATHERMANCY. 341 ^ 605. The diathermancy of a body varies both with the nature of the substance and the quality of the heat. The following table shows the proportion of one hundred inci- dent rays, coming from different sources, that will be trans- mitted by different substances, cut in plates 0.1 of an inch in thickness: Naked Incandescent Copper Copper flame. platinum. at 752 F. at 212 F. Rock salt 92.3 92.3 92.3 92.3 Sulphur 74 77 60 54 Iceland spar 39 28 6 Glass 39 24 6 Clear quartz 38 28 6 3 Smoky quartz 37 28 6 3 Alum 9200 Rock candy 8100 Ice 6 0.5 606. This table shows that diathermancy and trans- parency are analogous, but not identical properties. The different sources of heat correspond to different colored flames, and the plates or screens to different colored glasses. Plate glass is nearly transparent for all rays of light, as rock salt is diathermanous for all rays of heat. In either substance the vibra- tions not transmitted are mostly reflected. Red glass transmits only red rays, alum transmits only luminous thermal rays ; but these sub- stances absorb most of the other rays. Luminous or thermal rays which have traversed one plate will traverse another plate of the same material with but little loss of intensity. Each substance acts as a sieve, and transmits only those rays which are able to penetrate the material of the screen. Thus light which has passed through one plate of red glass will be largely transmitted by a second red glass : so, also, if the nine thermal rays transmitted by a plate of alum be incident on a second plate of alum, ninety per cent., or eight of the rays will be again transmitted. In general any medium is diathermanous for certain rays, and ab- sorbs the greater portion of the remainder. Glass is diathermanous for rays of high refrangibility, but almost, if not quite, athermanous for obscure rays. 342 NA T URA L PHIL OS OP II Y. If iodine be dissolved in bisulphide of earbon, it will form a very dark and opaque solution. If light from any source be transmitted through layers of this iodine solution, about one-tenth of an inch in thick- ness, the luminous rays will be entirely absorbed, but the obscure rays will pass freely. These invisible rays may be concent rated by lenses of rock salt, and made to melt and even ignite solid bodies. The same effect may be produced by concentrating the luminous solar rays with lenses of glass, or even of ice. 607. The following table of diathermancy of fluids was obtained by transmitting the heat of an Argand lamp through layers of fluids thirty-six hundredth* of an inch in thickness, contained in glass cells. It must be borne in mind that the glass employed permitted only the luminous rays to enter the liquid. The table shows the per centage of the incident rays transmitted. Bisulphide of carbon 63 Turpentine 31 Olive oil... 30 Alcohol 15 Solutions of salt and sugar 12 Pure water 11 608. The simple gases, hydrogen, nitrogen, oxygen, and dry air, are almost perfectly diathermanous, but some of the compound gases have great absorptive power, especially for dark heat. This is strikingly shown by the following table of the absorption of heat by various gases, each at the tension of one inch, barometric pressure, in comparison with dry air. Air Oxygen Nitrogen Hydrogen Carbonic oxide .................. 7~>0 Sulphide of hydrogen ......... 2100 Ammonia ......................... 7200 Oletiant gtis ........... Chlorine oO Sulphurous acid. 8800 I-Yoni this it will be seen that minute quantities of these .u;a>e- nui-t have great effect on the diathermancy of tin- atmo-phere. It' our atmo-pheiv were coal gas, only twenty per cent, of the thermal rays from tin- .-mi could reach the earth. With regard to vapors, it may In- said that tln-ir ab-orptive power is in the same order as the liquids from which they are derived. Hence, by reference to the previous table, it will be seen that aqueous vapor is a powerful absorbent. ABSORPTION OF HEAT. 343 609. The absorptive effect of the aqueous vapor in the atmosphere is calculated to be more than one hundred times that of dry air. The absorptive power of aqueous vapor for obscure rays, is many times greater than for luminous rays. The solar rays pass with comparative free- dom to the earth, and are expended in warming the earth. The heated earth radiates only obscure rays, which are absorbed by the atmosphere, and, consequently, its rate of cooling is diminished. In central Asia the nights are very cold and the winters almost unendurable, because of the dryness of the air. 610. If heat falls on a body not diathermanous, the rays that are not reflected are absorbed. Hence, the ab- sorbing power of athermanous bodies is inversely as their reflecting power. That is, good absorbents are bad reflect- ors. As bodies must give out in cooling the heat they have absorbed, so good absorbents are good radiators. The relation between the radiating, reflecting, and absorbent powers will be seen by the following table: Radiation. Absorption. Reflection. Lampblack 100 100 Indian ink 85 96 4 White lead 100 53 47 Isinglass 91 52 48 Gum lac 72 43 57 Polished metal 12 14 86 611. The formation of dew may be explained in accord- ance with these principles. As soon as the sun sinks below the horizon, the heat radiated from the surface is no longer compensated by the solar rays, and, consequently, the tem- perature of the surface is speedily reduced below 7 that of the stratum of air in contact with it. If this stratum is charged with moisture, the dew will be deposited on any good radi- ator, as grass or leaves, but will not ordinarily collect on metallic surfaces. Clouds or overhanging branches of trees prevent the de- position of dew, because they return the heat to objects 344 NATURAL PHILOSOPHY. beneath them. So, also, a fresh breeze, which brings new layers of air in contact with the surface, prevents the reduc- tion of the temperature and the formation of dew. The dew will, therefore, be most abundant on still, cloudless nights. If the temperature sinks below 32 F., the dew is deposited in needles of ice, which constitute white, or hoar frost. 612. All the phenomena of radiant heat show a remark- able analogy to those of light. If, now, we add that heat may be polarized and made to exhibit the phenomena of diffraction and interference, we can hardly resist the con- clusion that heat and light are identical. 613. Applications. The hot beds of the gardeners act by economizing the heat of the sun. The solar rays pass freely through the glass and are absorbed by the earth and the plants. These emit only obscure rays, which can not escape through the glass. The air confined in the bed may thus attain a temperature above that of the exterior atmosphere. The effect is enhanced by coating the wooden sides of the bed with lampblack. Meat roasters are constructed of polished tin, to reflect all the rays of the fire upon the article cooking. Franklin found by placing pieces of cloth of the same texture but of different colors upon newly fallen snow, that the snow melted under the cloth with the greater rapidity the darker the tint. This fact shows that for solar rays clothes of dark color are better absorbents and poorer reflectors than white. Hence, as the object of clothing is to preserve the body from sudden changes in temperature, white garments are preferable to black. Other experiments show that this difference in the ab- sorptive effect of colors entirely fails f.r heat from artificial sources. It so happens that many good reflectors arc white, and nmny good absorbents and radiators arc dark ; but their respective powers are due rather to the molecular condition of their surfaces than to their colors. SOURCES OF HEAT. 614. Recapitulation. 345 Conduction. {^onaucuon. Convection. Radiation. Radiant heat, incident on a body, may be. Reflected. Refracted. Absorbed. Transmitted. THE SOURCES OF HEAT. 615. The sources of heat may be comprised in three classes: (1.) physical, (2.) chemical, (3.) mechanical. Physical sources. The sun is the ultimate source of most of the available heat of the globe. To measure the intensity of the radiant heat of the sun an instrument, called the pyrheliometer, has been devised. It consists of a thermom- eter, d, whose bulb is inclosed in a shallow cylindrical box of silver, A, which is filled with water. The upper surface of the box is coated with lampblack. At the other ex- tremity of the instrument is a disk of the same diameter as the box. The face of the box will be perpen- dicular to the sun's rays when the shadow of the box exactly coincides with the disk. The measurement requires three steps : FI 1. The instrument, sheltered from the sun, is turned toward the clear sky for five minutes. It will lose, by its own radiation, an amount of heat which we may denote by r. 2. The blackened face is turned to the sun for five minutes, and will absorb a certain quantity of heat. Denote the gain in heat by A. 346 NATURAL PHILOSOPHY. ::. While heated, it is again turned to the clear sky for five minutes. and will lose heat equal to r'. Now, since r denotes the loss by radiation into a clear sky before heating, and r' the loss after heating, the radiation during the heat- ing will be the mean between the two, or r -*-. As this radiation is going on even while the blackened face is absorbing the sun's rays, the whole heating effect of the sun, during the five minutes exposure will e 4 ual A + r -*. Now, as the area of the face is known, we may express the effect of the sun's heat on any given surface by stating that it is competent to raise so much water so many degrees in temperature, or to melt a film of ice of proportionate thickness. 616. By these measurements it has been found that the r> lilcal rays of the sun are competent to melt a film of ice .00728 of an inch thick, every minute. The intensity of the rays decreases with their obliquity, and the atmosphere absorbs 0.4 of the entire radiation of the sun received by the eartb. Taking these considerations into account, it is calcu- lated that, if the earth had no atmosphere, the solar beat received by the earth in one year would melt a layer of ice completely enveloping it to the depth of one hundred feet. To compute the total radiation of the sun, imagine a hollow sphere to surround it at the distance of the earth from the sun. Two thousand one hundred and twenty-nine millions of globes, as large as the earth, placed one against the other, would be required to cover this imaginary sphere; hence, the total heat emitted by the sun is two thousand one hundred and twenty-nine million times that which reaches our earth. 617. It has been estimated that the fixed stars annually radiate sufficient heat to the earth to melt an envelope of ice eighty feet in thickness. It is evident that were the supply of either solar or stellar heat cut off. tin- life of the globe would soon be destroyed. 618. The phenomena of volcanoes and hot springs a the existence of intensely heated fluid matter within the CHEMICAL SOURCES. 347 earth itself. The heat received from celestial bodies does not penetrate the earth's surface more than one hundred feet. If thermometers are carried to greater depths in mines and in artesian wells, the temperature is found to rise quite regularly at the average rate of 1 F. for every fifty-four feet of descent. At this rate, depths would soon be reached at which all known rocks would melt, so that it is not probable that the thickness of the solid crust of the earth much exceeds one hundred miles. Neverthe- less, from the imperfect conductibility of this crust, it does not appear that the central heat of the globe affects the annual tempera- ture of the surface more than one-twentieth of a degree. Besides these physical sources of heat, may be mentioned electricity and the heat attending molecular changes, as absorption, capillary action, and the phenomena of liquefaction and solidification. 619. Chemical sources. When any two bodies unite in chemical combination there is usually an evolution of heat. The amount of heat evolved is always the same ; but if the combination takes place slowly, the heat can not be measured for any single moment. Combustion is the rapid combination of two or more sub- stances, attended by the evolution of heat and usually of light. Thus, if water be poured upon quicklime, the two will combine, and may evolve heat sufficient to boil the water. If a grain of iodine be placed upon a slip of phos- phorus they will kindle into a flame, which will afterward be continued by the oxygen of the air. Ordinary combustion is due to the union of the oxygen of the air with the carbon and hydrogen contained in the coals, oils, fats, and gases of our fires and flames. The rusting of iron, the decay of w r ood, the process of fermentation, are examples of slow combustion with oxygen. Animal heat is due to slow combustion. In respiration (1.) oxygen passes through the cell-walls of the lungs by os- mosis, and is absorbed by the blood, which it thereby renders arterial, (2.) This arterial blood is then distributed to the 348 NATURAL PHILOSOPHY. capillaries of the different organs, where a greater or less consumption of carbon takes place, with the evolution of carbonic acid. (3.) The blood charged with this carbonic acid is rendered venous and returned to the lungs, where the carbonic acid is exhaled by osmosis, and a fresh supply of oxygen absorbed. The supply of carbon is furnished by the tissues, which are themselves maintained by the processes of digestion and nutrition. Thus, in one sense, our animal heat is main- tained by the indirect combustion of food and air. The following table shows the total heat of combustion with oxygen of one pound of each of the substances named, expressed in thermal units of one pound of water raised one degree F. : Pounds of oxygen Thermal Compound Symbol. consumed. units. formed. Hydrogen H 8 62032 HO Carbon C \\ 4344 CO Carbon C 2* 14544 CO 2 Carbonic oxide CO i 4376 CO 2 Sulphur S 1 4032 SO 2 Phosphorus P \\ 10344 PO 5 Iron Fe & 2836 Fe 3 O 4 Alcohol C 4 II 6 O 2 3 12929 Olefiantgas C 4 H* 3 21344 Marsh gas C 2 H 4 4 23513 620. It is to be noted that the total heat is the same, whether the oxidation be reached at once or by successive steps. For example, one pound of carbon, in burning imperfectly, forms 2J pounds of carbonic oxide, and evolves 4344 units of heat. If thrse 2J pounds of carbonic oxide be burned they will evolve 10210 units of heat in forming carbonic acid, making 4344 -f 10210 - 14554 units of heat, or the same amount tlint would be obtained by the complete combustion of one pound of carbon. 621. The mechanical sources of heat are percussion, compression, and friction. (1.) If a nail be pounded on an anvil with light, rapid blows, it may be made red hot by MECHANICAL SOURCES. 349 percussion. (2.) The production of heat by the compression of gases may be shown by the pneumatic syringe, Fig. 279. This instrument consists of a thick glass tube, in which a piston works air tight. To use it, a piece of tinder is placed on the bottom of the piston, which is then driven suddenly downward in the tube. Flo. 279. The air in the tube is thus compressed, and liberates so much heat as to set fire to the tinder, which is seen to burn when the piston is withdrawn. The disengagement of heat is found to be proportional to the reduction in volume, and the consequent increase in density. (3.) The friction of two bodies always produces heat, which is the greater the more rapid the motion and the greater the pressure. It is the heat thus produced that ignites the phosphorus on the end of a match, and that causes the axles of car wheels to ignite the wood work in their immediate vicinity. Savages procure fire by revolving the eod of one piece of dry wood in the cavity of another. FIG. 280. An experimental demonstration of the same fact may be strikingly shown by attaching to a whirling-table a brass tube filled with water and corked. Fig. 280. If, when the tube is revolving rapidly, a 350 NATURAL PHILOSOPHY. clamp, P, of two pieces of oak is pressed against the tube, the heat evolved by the friction of the wood against the tube, will be sufficient to boil the water in a very few minutes. THE DYNAMICAL THEORY OF HEAT. 622. The dynamical theory of heat, which assumes that heat is a mode of molecular motion, affords a satisfactory explanation of these various phenomena. In all cases of friction, compression, and percussion, a certain amount of mechanical force is arrested, the energy of its visible motion is spent in producing molecular motion, and is thus trans- formed into heat. The quantity of heat evolved is in proportion to the mechanical force expended. Thus, when air is compressed, the rise in temperature is due to the mechanical effect or work which must be spent in driving the particles of the air nearer together. Conversely, Heat is consumed in effecting mechanical work. Let a cylinder filled with compressed air be cooled to the temperature of surrounding bodies. Its elastic force is competent to produce mechanical work, (1.) by moving a piston, or (2.) in displacing the air in front of the cylinder. If, now this air is allowed to expand into the atmosphere, the air will be chilled, because mechanical work has been performed by the expenditure of the heat to which the elastic force of the air was due. 623, The relation which exists between heat and work, is known as the mechanical equivalent of heat, or, simply, as Joule's equivalent. To determine it for gases, suppose a tall cylindrical vessel, C, whose section is equal to a square foot, and let I' 1' he a piston without weight moving in the cylinder. If the piston he placed so that tiie height, A P is one loot, it will inclose a cubic foot of air. Now, if this air he heated -I'M) F., its volume will he doubled, and will raise the piston Fro. 281. one foot, or to I" 1". In rising it has overcome JOULE'S EQUIVA LEN T. 351 the pressure of the atmosphere above the piston, or has lifted 15 X 144 21GO pounds one foot, and has performed work equal to iMiiO foot-pounds. With the same amount of heat, only about one-fourth as much water would have been raised 490, because the specific heat of air is 0.24 that of water. The weight of a cubic foot of air is .08 pounds, hence the heat imparted to perform the work of the air, would have heated only 0.08 X 0.24 = .0192 pounds of water 490. This is equiv- alent to 9.4 pounds of water heated 1 F. Hence, 9.4 thermal units have been required to raise 2160 pounds one foot high, by the expan- sion of the air. If the piston had been fixed so as to retain the air at a roHxtnnt volume while being heated, the quantity of heat re- quired to raise its temperature 490 would have been less than when expanding under a constant pressure, in the ratio of 1.421 : 1. Hence, the thermal units required to raise the temperature of the cubic foot of air when kept at a constant volume is found to be 9.4 -f- 1.421 =6.6 units. Deducting 6.6 units from 9.4 units, we find that the excess of heat imparted to the air when permitted to expand, is competent to raise 2.8 pounds of water 1 F. This excess has been employed in performing the work of lifting 2160 pounds one foot high. Dividing 2160 by 2.8, we find that the quantity of heat required to raise one pound of water 1 F. is competent to lift 772 pounds a foot high. This is, therefore, the mechan- ical equivalent of one thermal unit. 624. Joule deter- mined the mechanical equivalent of heat by the friction of fluids. A metallic box. Fig. 282, was provided with eight sets of paddles, which were made to revolve be- 352 NATURAL PHILOSOPHY. tween four stationary vanes, V. AVeights were attached to cords passing over the pulley, C, and wrapped around the roller, A. The descent of these weights caused the wheel to rotate. The box was filled with water and the weights allowed to sink. The mechanical work expended in pro- ducing the rotation was measured by the descent of a known weight through a known distance, and the heat was deter- mined by a thermometer at T. After allowing for all sources of error, and repeating the experiment with other liquids, and with iron disks sunk in mercury, Joule found that the quantity of heat produced by the friction of bodies is always proportioned to the work expended. The average of many experiments gave 772 foot-pounds as the mechanical equivalent of the heat required to raise one pound of water 1 F. Hence, heat and mechanical force may be exchanged, one for the other, in the ratio of 772 foot-pounds for one thermal unit. 625. In calculating the relation between mechanical mo- tion and heat, all the possible factors must be found and allowed for, in order to obtain the exact equivalence. When a body falls freely through the air, a portion of its force will be expended by friction of the air, and the heat produced will be dissipated by radiation. If a body, falling through a vacuum, is suddenly arrested by collision with another, the heat generated will be in proportion to the height of the fall. A portion of this heat may bo airain instantly converted into the mechanical motion of the rebound, and the remainder will be divided I. ctwccn the two bodies. Now, since the height through which a body falls is proportioned to the square of the velocity attained (V = 8.02|/H), the heat ible heat. In like manner, the cohesive force which changes a liquid to a solid, performs interior work, and the potential energy becomes actual; that is, the latent heat become.- -en-ihlc. So, also, when two bodies unite by chemical affinity, the molecular motion is transformed to heat. Thus, when -J- of a pound of hydrogen combines with * of a pound of oxviieii -.IK- pound of .-team is produced, and o'S!)2 thermal units are evolved, which are equivalent to ~>:}'2(H\'2\ foot-pounds. The molecular force evolved in chaii^iiiu n mixture of these gases in a pound of ice will therefore be: CONSERVATION OF FORCE. 355 Thermal units. Foot-pounds. 1. The potential energy of combination 6892 5320624 The potential energy of steam 967 746524 :;. The potential energy of water 143 110396 Total energy 8002 6177544 This is equivalent to the force required to raise one ton to a height of 3098 feet, or 3098 tons one foot high. Molecular forces are, therefore, by far the most powerful of any with which we are acquainted. 629. Force may be changed but not annihilated. The sun is the ultimate source of the available forms of force with which we are surrounded. Let us consider a few of the ways in which sunshine may be transmuted and preserved: 1. The mechanical energy of the winds, of falling water, and of running streams, is due to the joint action of gravi- tation and the solar heat. A part of this energy may be made to re-appear as heat by friction. Thus, a large room has been warmed by the friction of two plates, made to revolve by machinery driven by a fall of water. 2. Plants grow by reason of the light and heat of the sunshine, and accumulate a supply of fuel and food. (a). Wood and mineral coal are, therefore, transmuted sunshine. In combustion, the solar energy again appears as heat, or may be applied as a moving force for engines. (6). Food is transmuted by animals into animal heat and muscular energy. Beef and mutton are, therefore, due to solar rays, twice transmuted. 630. Recapitulation, The sources of heat are, /-The sun. 1. Physical J The fixed stars. v The molecular forces. -. ( 'lic'inical Combustion. f Compression. :). Mechanical -I Percussion. (. Friction. 356 .V. 1 T URA L PHIL OSOPJI Y. THE STEAM ENGINE. 631. The steam engine is a machine in which the elastic force of aqueous vapor is the motive power. The essential parts are (1.) the boiler, in which the vapor is formed, and (2.) the cylinder, in which the elastic force is applied. Besides these, there are usually other contrivances for trans- ferring, regulating, and economizing the motion which is produced. Dr. Wollaston's glass model illustrates the action of the atmospheric engine. Fig. 283. To the boiler, B, is attached a cylinder, C, in which a piston, P, works steam tight. The piston rod is hollow, and is closed 1>\ ;i screw at H. The boiler is first partially filled with water, the screw, H, removed, and the piston forced down to the bottom of the cylinder. Heat is then applied, and as soon as the steam begins to escape from the piston rod, the screw is replaced on the top of the rod. The tension of the confined steam will then force the piston to the top of the cylinder. Now, if the cylinder be cooled by pouring upon it a stream of cold water, a partial vacuum will be formed within it, by the condensation of the steam, and the piston will be driven down by the pressure of the atmos- phere. By successively heating and cooling this instrument, ;m alternating, or up and down motion, will be communicated to the piston. If the piston be made to perform work by connecting it with suitable machinery, we shall then have the essential action of Newcomerfs engine. 632. This engine, constructed in 1715, by Thomas Newcomen, was the first in which an FI.;. MS. alternating motion was given to the piston. It was used to raise water from the coal mines in Knirland. Its structure is exhibited in Fig. 284. To one end of :i walking beam, F V, \\:\< attache.] the piston rod, hi', mid to the other the pump rod. W X. Tli.-e parts were so CMimterl.alanced that the weight of the pump rod was capaMe of rai-iiiL' ilie pi-ton to the top of th<- cylinder. Steam was then ad- mitted to the cylinder tlin.u L .|i the valve, /, and the air was allowed to escape through the eduction valve, E. NfJ W CO MEN'S ENGINE. 357 A- -non as the cylinder was filled with steam, the valves E and i were closed, and a jet of cold water was injected through the valve, t, from the reservoir, R. I)y tli is means the steam was condensed, and a partial vacuum produced beneath the piston. The pressure of the atmosphere then forced the piston down and drew up the pump rod at the other end of the beam. The jet of cold water was then shut off, the condensed steam drawn out through E, fresh steam re-admitted, and the pro- cess was continued. Humphrey Potter devised an automatic apparatus by which the engine opened and shut its own valves at the proper mo- ments. A I 633. The safety valve, invented by Denis Papin, in 1690, is a necessary part of every steam boiler. This consists of a valve, V, fitting an opening in the top of a boiler. A lever of the second kind rests above this, and holds it in its place by a load, M. This load, which should never be equal to the full strength of the boiler, is sometimes applied to the lever by means of springs. Any excess of this tension will be shown by the escape of the steam from the valve. In the recent form, shown in Fig. 285, the small orifices at t are filled with an alloy of lead and bismuth. As the relation between the temperature and tension of steam is known, the fusing point of the alloy is made less than the tempera- ture of steam at its greatest allowable tension. At higher tensions, the alloy will melt and the steam escape. Practically, the safety valves are only indicators of high tension, as the openings are never large enough to permit much steam to escape. FIG. 285. 358 NATURAL PHILOSOPHY. 634. The modern steam engine is due to James Watt. In 1 "Go, Watt, while engaged in repairing a model of New- comen's engine, devised a series of contrivances for obvi- ating its defects, and between that time and 1784 invented the single and double acting steam engines. The improve- ments added by others, relate chiefly to the details of the mechanism. The following are the principal of Watt's inventions : 1. The condense)-. This is a chamber (I, Fig. 286), into which the steam from the cylinder and a jet of cold water are admitted at the same time. The vacuum is formed here, and avoids the loss of heat consequent on cooling the cylinder. 2. The jacket. This is simply an exterior casing of wood, to pre- vent the cylinder from losing heat by radiation. 3. The single acting engine. Watt admitted the steam at the top of the cylinder, and thereby depressed the piston by the elastic force of the steam instead of by the weight of the air. 635. These improvements changed the engine from an atmospheric to a steam engine. The piston was still raised by the weight of the pump rod, and consequently the steam acted only intermit- tently. These single acting engines are now used only for pumping water. 4. In 1782, Watt pat- ented the double acting steam engine. In this, the top and bottom of the cyl- inder are alternately con- nected both with the steam pipe and the exhaust pipe. The theoretical action of the condensing engine is shown in !'!_. -JSU. // .-mil I, are the upper and lower valve- of the steam pipe; K, the exhaii-t pipe, with its ', '/; and I the conden.-er, full of cold water. WATT'S STEAM ENGINE. 359 Now, suppose all parts of the cylinder and the connecting pipe to be filled with steam, the valves a and c to be opened, and b and d closed; the steam will pass from below the piston through the ex- haust pipe into the condenser, and thereby a vacuum, more or less perfect, will be formed below the piston. The steam from the boiler will drive the piston to the bottom of the cylinder. When the piston has reached its lowest point the valves are changed; that is, 6 and d are opened, and a and c shut. Now, a vacuum will be formed above the piston, steam will enter below, and the piston will ascend. The non-condensing engine differs from this simply in the tact that the waste steam passes from the exhaust pipe directly into the air or into the smoke stack of the boiler. Fig. 287 is a condensing engine. The locomotive, Fig. 290, is a non-condensing engine. 5. Tlie parallel motion. This was a device to make the piston rod move vertically in its collar, and thus prevent wear and friction. Fig. 287. This was effected by a system of jointed rods, A B, B F, F D, at- tached to the rod, A O, moving about a fixed point, O. The lengths .f these rods are so proportioned that, while the end of the beam describes an arc of a circle, the point, B, moves in a very nearly ver- tical line. This is also true of the center of the link, A D, to which is attached the pump rod of the hot well. In this country, the piston rod is generally attached to a cross piece, which moves in the vertical grooves of a stiff framework. 6. Tlie crank. The motion of the beam was transmitted through the connecting rod, F'M, to the crank, M O', which is attached to the shaft of the engine, and gives motion to the machinery connected with it. This converts the alter- nating motion of the piston to a rotary motion. 7. The fly wheel. When the crank is at its highest or lowest position the steam has no power to move it, and therefore these points are called dead points. To carry the crank beyond these points, a heavy fly wheel, V V, is attached to the shaft. This wheel, having once been set in motion, carries the crank 360 .V. 1 777,'. I /. rillL OSOPIIY. beyond the dead points by its inertia, and brings it into a position where the power again becomes effective. A steamboat or locomotive has no fly wheel, because its momentum is sufficient to prevent arrest of motion at the dead points. 8. The throttle valve, T, is placed in the throat of the steam pipe to regulate the supply nf steam to the cylinder. To make this automatic, Watt applied the already discovered principle of the governor. Fi.;. 287. This consists of a vertical axis, y, which receives from the shaft ;i revolving motion. Attached to this arc- two rods, &,"//, terminat- ing in hravy balls, zz' '; at the points, bl/, arc applied two other n.d-, he, 6 / e / , which are connected with a collar, m, capable of mov- ing up and down on tin vertical axis. When the engine i- at iv-t, the ball- haii'_ r nearly vertical, but when the axis, //, is turned they are thrown outward by centrifugal force. This rai.-e- the collar, m, WATT'S IMTROVEMENTS. 361 which acts upon the throttle valve, by levers, not shown in the figure, so as to admit a greater or less supply of steam. The weight of the balls is adjusted so as to regulate the supply to the required speed of the engine. If the shaft moves too rapidly, the balls are thrown out and the throttle valve closes ; if too slowly, the balls fall, and a greater supply of steam is introduced. 636, Other inventions were added by Watt, which relate to details of construction, and are here omitted. In Fig. 286, the eduction and steam pipes are represented on oppo- site sides of the cylinder. In the actual engine, the cylin- der has but two ports for the alternate admission and ejec- tion of steam. These ports are controlled by valves of vari- ous forms and niuiies. Those shown in Fig. 287, are called the long D valves. The short D valve is the one generally used in land engines. This arrangement for the distribution of steam is shown in Fig. 288. The steam is admitted from the boiler into the valve chest be- hind the valve. Below the valve is the exhaust port, o, which leads sideways to the air or to the condenser. On each side of this are the cylinder ports, which are connected by curved tubes to the top and bottom of the cylinder. The valve is made to close the exhaust port and one of the cylinder ports at the same time, by means of an eccentric rod, d, attached to the shaft of the engine. In Fig. 288 the lower port is open for the admission of steam ; the upper, is connected with the exhaust port to allow the waste steam to escape. In Fig. 289, this condition is reversed, the lower port being closed, and the upper open. Sometimes a second valve, FIG. 2.v>. called a " cut off," is attached to the sliding valve, by which Fw the steam may be shut off from the cylinder at any portion of the stroke of the piston, as one-half or one- third. The expansion of the steam already admitted to the cylinder completes the work of moving the piston. 362 \ATl'/fAL PHILOSOPHY. 637. Steam boilers vary in shape and size with the pur- pose for which they are designed. In locomotives, an abundant supply of steam at high tension is required. For this reason, the boiler is pierced with numerous hori- zontal pipes, which serve as Hues for the fire, and, at the same time, expose a large heating surface to the water. To increase the draft, the exhaust pipe is placed in the smoke stack. Fi.;. 290. 638. The mechanical power of steam may he estimated in foot-poimd> or in horse-powers. A cubic foot of water when converted into steam yields Hi'.Hi eiil.ie li-et at the pre lire of one aliiHisj.ln-rc. Hence, if the steam he formed beneath a pi>t..n of one foot area, it is capable of lifting a weight of fifteen pound- on cadi square inch, to the height <>f I ( '!M; feet. This is equivalent to rai>iiiL! lf>Xl44X Him; :;i;i;:;:;r,ii i;..,t-poimds. Deducting one-iil'th for loss by friction and other CM1M6, the available power of a cubic, POWER OF STEAM. 363 foot of water, when converted into steam at 212, is 2930688 foot-pounds. The horse powers depend on the rapidity of the evapora- tion. If the boiler evaporates a cubic foot of water each minute, its efficiency will be equal to 2930688 -f- 33000 = 88.8 horse powers. In rough calculations, it may be as- sumed that the evaporation of one cubic foot per hour is equal to one horse power. To evaporate one cubic foot of water requires the com- bustion of nearly five pounds of anthracite coal. Hence, for each pound of coal burned per minute, we should have an effect equal to nearly twenty-five horse powers. This is very nearly realized in the Cornish single acting condensing engines. In the United States, it is usual to allow about 6.5 pounds of anthracite coal for each horse power. 639. Recapitulation. The essential parts of a steam engine are : 1. A boiler, for generating the elastic force of steam. A cylinder in which this elastic force is made to produce an alternating motion in a piston. The accessory parts are : 1. An apparatus by which the piston rod is made to move in the same straight line. (Parallel motion). 2. An apparatus by which the alternating motion of the piston may be converted to rotary. (Crank.) 3. Apparatus for regulating and controlling the motion. (Fly wheel, throttle valve, and governor.) 4. Other parts added for the sake of safety, economy, and con- venience. (Safety valve, condenser, jacket, and automatic action.) 364 NATURAL PHILOSOPHY. CHAPTER IX. 640. It has long been known that a certain ore of iron, called the loadstone, has the remarkable property of attract- ing iron filings to itself: also, that amber when rubbed, and tourmaline when heated, acquire temporarily, the property of attracting light bodies, as bits of cotton and straw. Within the past century, philosophers have found that these arc but particular manifestations of a force which is con- stantly evoked in all kinds of molecular changes, and whose phenomena are among the most wonderful and beautiful in nature. This force is electricity. It is convenient to study its phenomena under three divisions: (1.) magnetism, (2.) statical electricity, (3.) dynamical electricity. MAGNETISM. 641. The loadstone is an abundant and widely distributed ore of iron, having the chemical formula Fe 3 O 4 . Because the ore was first found near Magnesia, a city of Asia Minor, loadstones are called nnlnrnl magnets. If a loadstone be rolled in iron filings, the filings will cling to it, but especially at its ends. Ki, ; . i. Fig. 291. These ends are termed the poles of the magnet. The force residing in a magnet is called magnetism. Artificial magnets are bars or needles of hardened steel which have acquired magnetic proper-tie.-. These are at once more convenient and powerful than natural magnet.-. If a magnetic bar or needle be poised at it- center so that it will -win- t'n-ely. one end will always point toward the north and the other toward the south. Hence, one end is MA G NET ISM. 365 called the south and the other the north pole of the magnet. The north pole is the marked end of the magnet. If a sheet of stiff paper be laid upon a bar magnet and iron filings be sifted evenly upon the paper, the particles of iron will arrange themselves in curved lines about the FlO. 292. poles. Fig. 292. These lines are called lines o/ magnetic force. The action of the magnet is not diminished by the interposition of any substance that is not itself magnetic, as paper or glass. 642. Either pole will equally attract magnetic substances; but if two magnets are brought near each other, it will be found that the marked end of one will attract the south pole of the other, but if the two marked ends are brought near each other, a repulsion takes place. Hence, this law : Like poles repel aud unlike poles attract each other. A force which exhibits a combination of equal powers, acting in opposite directions, is called a polar force. 643. If a long steel needle be magnetized, the center FIG. 293. will exhibit no magnetic force, and is said to be neutral. 366 NATURAL PHILOSOPHY. If the needle be broken, each half will be found to be a magnet with two equal and opposite poles. If this division be continued, no portion can be obtained so small that it will not be a perfect magnet. We, therefore, conclude that every magnet is a collection of polarized particles, having their similar poles turned in the same direction. Thus, if N S, Fig. 294, represents a magnet, the alternate black and white spaces will represent the polarity of each particle. All the n" sf' n' sf n s Fio. 294. north poles are disposed in one direction and all the south poles in the opposite. The opposite polarities balance each other at the center, which thus remains neutral, but are strongly manifested at the ends. 644. Induction. If a rod of soft iron, (Fe,) Fig. 295, be brought near one of the poles of a magnet, M, the rod will become a temporary magnet, having two poles, each capable of attracting iron filings. The polarity of the rod will be opposite to that of the magnet; that is, if the rod be near Ki.i. . the marked end of the magnet, the nearer end of the rod will manifest south polarity, and the remote end north. This influence, by virtue of which a magnet can develop magnetism in iron, is called induction. The phenomena <>f induction may be explained by supposing thai, in the omnagnetized condition of the rod, all the molecules are en- dued with magnet i-m, Imt M combined that the opposite forc< trali/e e;ich other. In the presence of a magnet the two halves of itch moh-enle as-miir an opposite magnetic condition, or become pnlari/ed. M -liown in FL'. 'JUl. MAGNETIC SUBSTANCES. 367 645. In any form of induction there is no transfer of :uiy force, but merely a development of polarity among the particles of the body acted upon. The lines of magnetic force, Fig. 292, are due to the fact that the minute particles of iron become temporary magnets, and arrange themselves in accordance with the law of attraction and repulsion. The inductive force is greatest when the magnet is in contact with the iron, but entirely ceases when the two are separated to a sufficient distance. If a steel bar be in contact with a magnet, its particles be- come polarized very slowly ; but, when once acquired, its magnetism is permanent. Magnetism may be sooner induced in steel by rubbing it with one of the poles of a magnet. In this way the ordinary mag- netic needles are prepared ; but the most powerful magnets are pro- duced by means of a voltaic current, as will be described hereafter. (745.) 646. A magnetic battery consists of a number of mag- nets joined together with their similar poles in contact. The most common form is that of the horse-shoe, Fig. 296. When a magnet exerts its inductive power on a piece of soft iron, its own magnetic intensity is increased. For this reason the magnet is provided with a keeper, or arma- ture, K, of soft iron. The weight which the armature will support is more than twice that which either pole would bear. The power of a magnet may be doubled by adding daily a small weight to the ar- mature; but if the contact be once broken only the original load will be sustained. The power of a magnet may be seriously impaired by heating, or by any rough usage. 647. Magnetic substances are those which are attracted by a magnet. Iron, steel, nickel, and cobalt are the only substances in which magnetism can be developed by or- dinary induction. By using very powerful magnets, Fara- day found a small number of other substances to be mag- Fio. 2%. 368 NATURAL PHILOSOPHY. netic. Among these are manganese, chromium, platinum, plumbago, and oxygen. On the other hand, a great number of substances, when suspended between the poles of a strong horse-shoe magnet, take up a position at right angles to the line joining the poles, as if repelled by them. Such substances are called diamagnetic. Among diamagnetic substances are phos- phorus, bismuth, antimony, zinc, tin, resin, hydrogen, and coal gas. TERRESTRIAL MAGNETISM. 648. If a small magnetic needle be suspended by an untwisted thread over a bar magnet, N S, and be slowly carried from one end of the bar to the other, it will assume in succession the positions shown in Fig. 297. At the center of the bar it will be horizontal, with its marked end pointing toward the south pole of the bar magnet. At either side of the center, it dips or inclines; the south pole dips on the north polar side of the center, and the north pole dips on the south side. The dip will increase as tin n, VII 1 VI f v V UL \ II Fio. 297. aeedk approaches the poles, at which points the inclination will be <)0. Now, if a magnetic needle be freely suspended and car- ried to different points on the earth's -nrf'arc, it will not nicrdy le directed toward the north, lmt will also dip more and mure a- it approaches the polar regions. These phenom- ena warrant u> in r.iii^idmnir the earth as a great magnet, who.-e poles are very near the t-m->trial poles. MAGNETIC ELEMENTS. 369 649. The magnetism of the earth is further manifested lv its inductive influence. If a bar of iron be placed in [In- direction which a dipping needle would assume, it im- mediately becomes polarized. This may be shown by moving a small magnetic needle along the bar. The marked end of the needle will be repelled by the lower end of the bar, and attracted by its upper end. If the iron is somewhat hard, its magnetism may sometimes be rendered permanent by strik- ing it a sharp blow with a hammer. This phenomenon is frequently seen in rods which remain at rest for some time in a nearly vertical position, as the poker and tongs. 650. The magnetic elements necessary for the full knowl- edge of the earth's magnetism at any place, are (1.) incli- nation, (2.) declination, (3.) intensity. Inclination. If an unmagnetized steel bar be accurately balanced and then magnetized, it will be found that its bal- ance is lost, and that it now makes a certain angle with the horizon. This angle is called the inclination, or dip, of the needle. A dipping needle, is one by means of which this incli- nation can be measured. The inclination, N cd, shown in Fig. 298, is the same as that of a dipping needle at Rochester, N. Y., or about 75. 651. The magnetic poles are points at which the dipping needle is vertical. Sir James Ross found an inclination of 8959' in Boothia Felix, at 70o' N. lat. and 96 43' W. Ion. This point is taken as the north magnetic pole. The south ma.irm-tic pole is calculated to be in about 7530' S. lat., and 154 E. Ion. Lines connecting places in which N. P. 24. Flo . 370 NATURAL PHILOSOPHY. the needle is of equal dip may be drawn about the mag- netic poles in irregular curves, somewhat resembling those of the parallels of latitude drawn about the terrestrial poles. Most of the United States lies between the lines of 75 dip and 60 dip. The mcujmtir cijmttor of the earth is a line of no dip, or it is a line connecting those places in which the needle remains horizontal. The magnetic equator crosses the earth's equator in the Atlantic and Pacific oceans. making an angle with it of about 12 In the northern hemisphere, the marked end of the needle is afiin's Hay the needle Fig. 299. points due west. 653. A line of no declination, or one that connects places in which the needle points due north and south, passes in nearly a great circle around the globe. In the \\vstcrn hemisphere it runs from the north magnetic pole through Hudson's Pay and Lake Kric, cutting Ohio, Penn- MAGNETIC INTENSITY. 371 svlvania, Virginia, and North Carolina, and enters the Atlantic near Cape Lookout; thence it sweeps eastward of the West Indies, and after passing through the south polar regions, re-appears at tin- south magnetic pole. It then runs northerly through Australia, but beyond this follows an irregular curve through the Caspian sea to the Arctic ocean. In the Atlantic hemisphere, which is included within this line, the deviation is every-where westward. In the Pacific hemisphere, which includes the greater part of the United States, the declination is very generally eastward ; the exception being an oval area in Eastern Asia, which is bounded by a second line of no declination. 654. Intensity. If a magnetic needle be drawn aside from its position of rest, it will recover its equilibrium after a series of oscillations. Since the magnetic force at any given place and time may be regarded as constant, these oscillations of the needle will be governed by laws analogous to those of the pendulum. [41 and 42.] Hence, the intensity of the earth's magnetism in any two places, will be proportioned to the square of the number of vibrations made by the same needle in equal times. The magnetic intensity in Peru has been assumed as the stand- ard of comparison, and is, therefore, taken as unity. A dipping needle, which, in Paris, made 245 vibrations in ten min- utes, when transported to the magnetic equator in Peru, made only 211 vibrations in the same time. The intensity at Paris will, there- fore, be ^ = 1.348. 655. There are four foci of maximum magnetic intensity, of which two are in the northern and two in the southern hemisphere. The strongest, which lies a little south of Australia, may be represented by 2.06. The American focus lies a little north-west of Lake Superior, the intensity being 1.88. The least intensity hitherto found is in South Africa, and aim units to 0.7, or about one-third of the highest intensity. 372 NATURAL PHILOSOPHY. The absolute magnetism of the earth lias been raleulated to be equal to eight thousand lour hundred and sixty-four quadrillion times that of a saturated bar magnet one pound in weight. 656. The magnetic elements are subject to constant changes, some of which are regular, and others irregular. Thus, the inclination in Europe is gradually decreasing, and the declination is at present veering eastward. The rate of these changes is not the same for different places, nor is it constant for the same place. The following list exhibits the secular changes in declination and inclination at London : Table of Secular Magnetic Changes. Y.ar. 1")8() Declination. 11 17 X E Y-ar. 1720 Inclination. 744 >)/ HifiO O 7 1790 7153 X 1815 040.);' w 1818 7034 / 18fi9... ...20 2'W. 1869 .. ...6754' It appears from this, that in 1660 the needle pointed due north, at London; it then varied westward until 1S1.~>. when it pointed farthest from the true north. Since that time it has moved eastward at an annual rate of about 8'. The annual decrease in dip is about 2'.6. 657. These changes show that the magnetic poles are continually shifting their position, and, consequently, that the lines of equal declination and dip are not the same from year to year. The needle has also a daily and annual oscillation, ap- parently connected with changes in temperature. Thus, at Philadelphia it has a maximum westward declination at 1 P. M. and at 2 A. M., and a minimum at ft A. M. and at 10 P. M. The greatest daily change is between April ami September, or during the summer months. 658. The irregular variations an- indicate.! by sudden di-tiirbam-i's >f the magnetic needle, which are x.niet iine> con-iderable, but are of short duration. The appearance of the Aurora l>oreali> is invariably accompanied by these STATICAL ELECTRICITY. 373 fluctuations. Magnetic disturbances often occur simultane- ously in very distant countries, and have received the name of magnetic storm*. These storms, which were once thought to be wholly irregular, are found to be periodical, having epochs of maximum intensity every ten years. These epochs coincide with the maximum recur- rence of the spots on the sun; this appears to show that magnetic storms are connected with changes in the solar atmosphere. 659. The source of the earth's magnetism is now gen- erally attributed to the sun. It is supposed that the solar heat develops electrical currents in the materials of the earth's surface, and that these currents give rise to mag- netic phenomena. This hypothesis is supported by the facts already noticed in regard to magnetic storms, and the daily changes in declination, and receives a strong support from the fact that the lines of equal beat and of equal magnetic intensity on the globe, manifest a marked corre- spondence. 660. Recapitulation. Magnets are ......... { Natural or artificial. I Permanent or temporary. Subst-inces ("Attracted by magnets are .......... Magnetic. I- Repelled by magnets are .......... Diamagnetic. {Inclination. Declination. Intensity. , Daily. The changes of the magnetic ele- f Re 8 ular - Annual. ( Secul:ir ' mentsare ........................... v Periodical, in magnetic storms. STATICAL ELECTRICITY. 661. The fundamental phenomena of statical electricity may be studied by means of the electric pendulum, Fig. 300. This consists of a pith ball attached, by means of a silk thread, to a glass support. 374 NA TURA L PHIL OS OJ'/f } '. Flo. 300. If a stick of sealing wax, or an ebonite ruler be rubbed with dry llainu'l and be brought near the pith ball, the latter is in- stantly attracted but is soon re- pelled. If, now, a warm glass rod lie rubbed with a silk hand- kerchief, and presented to the ball, the same phenomenon of attraction and repulsion will be observed Fig. 300. It will now be found that when the hall has been repelled by tin- glass, it will be attracted by the wax ; and when again repelled by the wax, it will be attracted by the glass. If the glass and wax be placed on opposite sides of the ball, it will vibrate between them by the alternate attraction and repulsion of each. It is, therefore, manifest that the excited glass and wax manifest similar but opposite properties. These properties, thus developed by friction, are due to the force of electricity. 662. Electricity is a polar force which becomes manifest by its peculiar phenomena of attraction and repulsion. It is now regarded as a mode of molecular motion, which is always manifested in two opposite or polarized states. That developed on the glass is called positive (-}-), and that on the wax negative electricity ( ). Formerly, electricity was supposed to be due to the presence of two fluids, called vitreous, or jn^lfii-f, and resinous, or negative. Many of the terms of the older theory are still in common use, because they are convenient for describing most electrical phenomena, al- though the meaning attached to them is taken in a sense different from that originally intended. There is no evidence of the existence of any electrical fluid. 663. In the preceding experiment, we suppose that the wax became negatively elect rii'n-d ly the friction, and, on contact, transferred a portion of this force to the hall. The ball thereby became electrified or rharyvd with negative elec- tricity, and the two lodi<-- >-paruted. On bringing the CONDUCTORS AND INSULATORS. 375 charged ball near the positively electrified glass, the t\vo were attracted because of their different electrical states. The glass then communicated enough of positive electricity to neutralize the negative electricity of the ball, and also to render it positively charged. The ball was then repelled by the glass and attracted by the wax, and so on through a series of attractions and repulsions. From these experi- ments we derive the following law: Two bodies cliarged witii like electric it ir* repel eacJi other; two bodies charged with opposite fl<-Hricitit'4 attract each otJier. 664. Statical electricity may be developed by any cause that tends to disturb the 'molecular condition of bodies, as cleavage, pressure. It may be developed in tourmaline and certain other minerals by heat. The usual source is friction, and hence this form of electrical force is sometimes called J'l'ictional electricity. It is called statical electricity because it may te retained for a time on an excited or charged body. 665. Electricity is transmitted from one body to another with different degrees of rapidity. Those substances that transmit electricity readily are called conductors; those that do not are called non-conductors, or insulators. These classes differ only in degree, for there is no such thing as perfect conduction or perfect insulation. In the following list, the substances named are arranged in the order of their conducting power. Those midway in the list may be term semi-conductors or semi-insulators. Conductors. Semi-conductors. 1. All the metals. 10. Alcohol. 19. Furs. 2. Charcoal. 11. Ether. 20. Silk. 3. Graphite. 12. Flowers of sulphur. 21. Gems. 4. Acids. 13. Dry wood. 22. Glass. o. Water. 14. Paper. 23. Wax. i. Vegetables. 15. Dry ice. 24. Sulphur. 7. Animals. 16. Phosphorus. 25. Resins. 8. Linen. 17. Caoutchouc. 26. Shellac. 9. Cotton. 18. Air and gases. 27. Ebonite. Semi-iiisulators. Insulators. :;TI; NATURAL 666. In order that a charged body may retain its elec- trical force, it must either be a non-conductor or be insulated by being supported on non-conductors. The most common insulators are made of green glass ; ebonite is the best. * Baked wood covered with shellac varnish will answer very well. Dry air is essential for insulation. In a damp room a film of moisture gathers upon the apparatus and forms a conducting surface. The reason why electrical excitement is not more frequently mani- fested by friction is because the electrical force is carried off as fast as it is developed. When the electrical force is sufficient to force its way through a bad conductor, a spark may be produced. In dry, frosty weather, a person, by shuffling about a warm, carpeted room in dry slippers, may develop electricity sufficient to emit a spark from his finger capable of igniting a jet of gas. 667. Both kinds of electricity are always simultaneously produced. If two insulated disks of dry wood, one covered with shellac and the other with silk, are rubbed together and separated, the shellac will manifest positive and the silk negative electricity. Any substance in the following list, when rubbed by any one succeeding it, becomes posi- tively electrified, and by any one preceding it, negatively electrified : + Cat's fur, flannel, smooth glass, cotton, paper, silk, the hand, sealing wax, rough glass, sulphur, ebonite . Thus, paper becomes negatively electrified when rubbed with Haniu-1, and positively electrified when rubbed with silk. 668. An electroscope is an instrument used to detect the pn-.-rnee and determine the kind of electricity in any body. The simplest, is some form of the electrical pendulum, with one or two pith balls. The gold Ira!' eleet ro-e. ,pe. Fi^. .",01, consists of two strips of gold leaf .-uspended in a glass vessel by means of ;i metallic rod. which terminate.-- in a knob, or plate. The upper por- tion of the jar is coated with >hellac and the interior is filled with air kept perfectly dry. Within the ve.-sel are two metallic This i> tin- material ol which hard rubber combs are made. ELECTRICAL INDUCTION. 377 i serve to remove an excess- onnected with the ground whicl ive charge from the k-aves. If the knob be touched with an t/lertrilied glass rod, the leaves will diverge, because they become charged with positive electricity. If, now, any electrified body be brought near the knob, the kind of electricity in the body may be determined by its influence on the leaves ; for if the electricity be of the same kind as that of the leaves, they will diverge farther, lint if of the opposite kind, they will collapse. 669. Induction. Electri- fied bodies influence bodies at a distance in a manner analogous to the action of a FIG. 301. magnet on magnetic sub- stances. This influence is called electrical induction, and the resulting effect induced electricity. Let A B be a conductor of brass or tin, insulated on a glass pillar and furnished with a number of pith ball electroscopes. If this is FIG. 302. brought near an electrified body, C, but without receiving a spark from it, the balls will diverge, as shown in Fig. 302, thereby man- ifesting the presence of uncombined electricity at each end, and 378 NATURAL PHILOSOPHY. of a neutral line near the center. By means of the gold leaf electro- scope, we may ascertain that the nearer end, A, of the conductor contains electricity opposite to that of the electrified luuly, C, and the further end the same kind. If be positively charged, its effect will be to attract negative electricity at the nearer end, A, and to repel positive electricity toward the further end, B. There is no transfer of any electrical force in induction, because the action is only temporary ; for if C be removed or be discharged by touching it with the hand, the balls immediately collapse. 670. The two electrical forces may be separated by induction. Suppose three conductors like A B, placed end to end; or, what is the same thing, suppose the conductor A B to be made of three parts, each insulated and movable, and while the whole is under the influence of a positively electrified body, let the parts be separated by removing the central portion. (1.) This part will yield either no spark, or a very feeble positive one. (2.) The portion B may be discharged by bringing the hand near it, yielding a spark of positive electricity. Its electricity is, therefore, free to diffuse itself. (3.) So long as A and C remain near each other, neither can be discharged by touching them separately, because their electricities are retained by their mutual attractions. Electrical forces in this condition are said to be bound. or disguised. If communication be made between them, they will both be discharged by the union of their opposite forces; or if the two are separated, A will yield negative, and C positive electricity. 671. If the cylinder, A B, while near the positive ball, C, be touched with the hand, the pith balls at A will divert- further the at B will collapse. As the hand and body are conductor.-, the positive electricity will be repelled to the earth, and the neutral line will recede to an indefinite di.-taiicc from A. The negative can not escape, being bound by the attraction of the positive ball. Oil the THE ELECTROPHOROUS. 379 contrary, it will increase, because the inductive force of C is no longer subject to the counter-action of the similar force accumulated in the end, B. If the hand be first re- moved and then the inducing body, the cylinder will remain negatively charged, and will yield all the phenomena of free electricity. Thus, a body may be charged by induction as well as by conduc- tion. In conduction, the electrified body loses a part of its force to impart the .same kind of electricity to an insulated body. In induc- tion, the charging body loses none of its force, but excites the oppo- site kind of electricity in an insulated body, which requires to be uninsulated for a time in the presence of an excited body. 672. The electrophorous illustrates the action of induc- tion, and affords a ready supply of statical electricity. It consists (1.) of a cake of res- inous matter, R, resting on a conducting plate of tin, and (2.) a movable metal cover, T, provided with an insulating handle, G. If the resinous cake be beaten with cat's fur, or rubbed with a warm flannel cloth, it becomes charged with negative electricity. If, now, the cover be placed on the cake, its con- dition is that of a conductor under the influence of an electrified body. Its lower surface becomes positive and its upper negative, by induc- tion. If the cover be uninsulated for a moment, by touching it with the finger, the negative force passes to the ground, while the positive is held bound by the negative electricity of the resin. If, now, the finger be first removed, and then the cover be raised by means of its insulating handle, its positive electricity diffuses itself over the cover, and muy be made to yield a brilliant spark by bringing it near FIG. 303. 380 NATURAL PHILOSOPHY. a conductor. The reason why the cake does not discharge itself into the cover, is due (1.) to the non-conducting power of the resin, and (2.) to the minute inequalities of its sur- face, which do not permit an intimate contact of the cover. As the cake acts only by induction, when once charged it retains its electricity for a long time, and may be made to induce any num- ber of successive charges in the disk. Instead of the resinous cake a sheet of gutta-percha, or a tin plate coated with melted sealing wax. may be used. The disk may be made of a tin plate, with a stick of scaling wax to serve for a handle. This simple contrivance may be made to yield very excellent results. It may be used to charge mov- able conductors of a spherical or cylindrical form, like those shown in Fig. 302, or for performing experiments in which a continuous supply of electricity is not required. 673. Faraday's theory of induction .supposes (1.) that all particles of matter are more or less conductors; (2.) that under the influence of an electrified body, the mole- cules of the surrounding medium become arranged in a polarized form. Thus, if c a 6 c d C represent a positively e_ ^1* charged body, the polari- rm (*(*(* ^- ^K9 zation of the contiguous Flo .jQj molecules of air, and of A B, a distant insulated conductor, may be represented by a series of black :md white hemispheres. (3.) That contiguous particles can communicate their polarity, more or less readily, one to the other. Those that communicate their electrical forces readily, are conductors; those that retain their polarity, or communicate their electrical forces with extreme difficulty, are insulators. (4.) Induction is the action of an electri- fied body upon insulating matter. If the insulated cylinder, A B, be contiguous t<> the polari/ed molecules of air, its particles will also be polari/ed; but, as they are conductors, they will discharge their electric forces one into the other, ami thereby the cylinder it-elf will become polarized, as if it were a huge molecule. INDUCTION. 381 674. Induction is essential in most, if not all, electrical phenomena. 1. In utt met ion. The pith ball of the electrical pendulum is first polarized, like the cylinder, A B, Fig. 304. The side next the excited glass rod becomes negative by induc- tion, and as soon as the attraction of the opposite electrical forces becomes greater than the repulsion of the positive electricity on the further side of the ball, the ball flies to the rod. 2. In charging. In Figs. 302 and 304, suppose C, posi- tively charged, to be brought toward A B. The polarization < >f .V B will rise higher and higher, in proportion as C conies nearer. When C is near enough, AB will become permanently charged with positive electricity, either by spark or by contact. The most probable explanation of this is, that at a high state of polarization the adjoining particles discharge their electrical forces into one another. At spark or at contact an equal amount of both electricities becomes neutralized, and the cylinder becomes charged, not by receiving more positive electricity, but by discharging its negative. As soon as the negative disappears, the posi- tive diffuses itself over the conductor, and is prevented from escape by the insulation of its support and of the air. 3. Discharging. If, now, the hand be brought near the positively charged conductor, the electricity of the hand is polarized. Its positive electricity passes to the ground, and its negative to the fingers. At contact, the negative of the hand and the positive of the cylinder combine, and the molecules of the conductor become unpolarized, or neutral. Hence, we may say that the cylinder was charged by losing its negative electricity, and discharged by losing its positive. These terms express what is true in effect though not in process. 675. Nothing passes from particle to particle but the 382 NATURAL PHILOSOPHY. inductive force. This first develops the two electrical forces in each molecule by polarization, and then, when of sufficient intensity, causes this polarity to disappear by dis- charge into contiguous molecules. The molecules of con- ductors are easily polarized and discharged; the molecules of insulators require a greater force to effect polarization and discharge. Herein consists the analogy between magnetic and electrical induc- tion. The induction of magnetism in soft iron is instantaneous but temporary; that of steel is effected with greater difficulty, but is per- manent. The analogy is not complete in other respects, especially in this, that in magnetic induction the two forces can not be separated. Nevertheless, the polar character of electricity is sustained even in electrical induction, for, although a body may be charged positively or negatively, yet this can only be effected and maintained by the opposite force induced in the insulating molecules which surround it. 676. Electricity is found only on the surface of an insu- lated conductor. This is a direct consequence of the pre- ceding, and may easily be verified. Let a brass ball be suspended by a silk thread, and be covered with two closely Fio. 305. fitting hemispheres of brass, provided with insulating han- dles. If a charge be communicated to the apparatus so compounded, and tin- hemispheres be withdrawn, no elec- tricity whatever will remain on the sphere. Hence, a hollow conductor i- as -.-rvicrable ;i> \\ solid one. ELECTRICAL APPARATUS. 383 677. The charge is distributed uniformly only in the case of the sphere. If the conductor be a cylinder with rounded ends, the intensity will be least at the center and greatest at the ends, as represented by the divergence of the balls in Fig. 302. The more pointed the ends, the greater will be the accumulation of intensity at the extrem- itics. The effect of a point, either on a charged surface, or turned toward a charged surface, is such as to discharge a body with extreme facility, and generally without the passage of a spark. 678. The terms quantity and intensity will be under- stood by reference to the analogous use of the terms with respect to heat; thus, the heat of molten iron is intense, but a hogshead of boiling water contains a greater quantity of heat than a pound of molten iron. In one case, each particle is in very rapid vibration, in the other very many particles are in vibration, and the sum of all the vibrations determines the quantity. Electrical intensity has reference to the amount of force lodged in each particle ; quantity of electricity has reference both to the number of particles affected and to the force lodged in each. Of course, in every electrified body, there is both quantity and intensity, but the charge may be characterized by the predominance of either quality. In statical electricity, the quantity is always small, though its intensity is sometimes enormous. The in- tensity is due to a high state of polarization, and is measured by its power to effect discharge through bad conductors. Thus, a long spark is an evidence of great intensity. ELECTRICAL APPARATUS. 679. An electrical machine is an apparatus by means of which large supplies of statical electricity may be developed in a convenient manner. Fig. 306 represents Winter's plate machine, which is one of the best. This consists of a circular plate of glass, mounted on a glass 384 NATURAL PHILOSOPHY. axis, which is supported by two posts of glass or of dry wood, and made to revolve by a winch. Friction is applied to the glass by means of two rubbers, R, made of stuffed leather, and coated witli an amalgam of mer- cury, tin, and zinc. The rubbers are kept in place by means of a pair of clamps attached to an insulated brass hall, N, called the negative con- ductor. Attached to the rubber are two wings of silk, to prevent the elec- tricity from escaping into the air. The plate also passes between two wooden rings, W, which are at- tached to an insulated brass ball, P, known as the prime conductor. On the side of the wooden rings, next the glass plate, are two rows of brass points, which are connected by means of tin foil to the prime conductor. On turning the plate, negative electricity is developed on the rubbers and conducted to the negative conductor, N, and positive electricity is developed on the glass plate. As the plate revolves, the positive electricity of the glass acts by induction on the prime conductor, attracting its negative electricity. This negative electricity collects on the points inside of the rings, W, and finally attains sufficient inten- -ity t-> pass through the intervening space of air and unite with the positive electricity on the glass, and thcrchv render ttl -urf'acc neutral. The prime conductor, then-Ion-, Drives up its negative and remain-; eh:irged with positive electricity, in the manner described in (674). 680. If both the conductors were insulated, this action FIG. 30f>. WINTER'S MACHINE. 385 would speedily cease, because the positive electricity of the prime conductor would act inductively on the negative of the other conductor, and thus only a feeble charge would be possible. If either conductor be uninsulated, its tension will he reduced to zero, and thereby leave the electric force on the other conductor free. Hence, when the rubbers are connected to the ground by means of a chain, positive elec- tricity is accumulated on the prime conductor. When negative electricity is wanted, the chain is removed from the rubbers and attached to the prime conductor, and the negative electricity accumulates on the negative con- ductor. If the hand is brought near either conductor when charged, a spark follows, which is renewed as the plate is turned. The length of the spark is wonderfully increased by the addition of a large wooden ring, I, surmounting the prime conductor. An iron wire forms the core of this ring, and is in metallic connection with the prime conductor. The wooden ring acts inductively on the prime conductor and prevents discharge until the electric force attains a high tension. Without the ring, which may be removed at the pleasure of the operator, the machine will give a rapid suc- cession of sparks, two inches in length ; with the ring, sparks may be obtained six or seven times as long, but these are proportionally less frequent. The quantity of electricity developed is the same in both cases. There are many other electrical machines having the same action as the one described. Among these are several varieties of the plate machine, and others in which a hollow cylinder of glass is substituted for the glass plate. Electricity may also be generated in enormous quantity by the friction of steam passing through jet pipes of hard wood. A hydro-electric machine, constructed on this principle, yielded sparks twenty-two inches long, and was capable of fully charging a battery of thirty-six large Leyden jars upward of sixty times a minute. ir<- 681. There are other machines which act on the principle of the electrophorous. In Holtz's machine, Fig. 307, elec^ N. P. 25. 386 NA T URA L PHIL OS OP 11 \ '. tricity is developed by the continuous inductive action of a body already electrified. It consists of two circular plates of glass, about one-tenth of an inch apart. The larger one, A, is fixed and insulated ; the smaller, B, turns on a glass axis, which passes through a hole in the center of the fixed plate. In the plate, A, are two openings, each furnished with an ar- mature. These armatures consist of a band of paper terminating in a sort of tongue, which is glued to the glass so that the tongues, //', project into the window. Fm. 307. In front of the armatures, but on the other side of the movable plat.-, B, are two brass combs, P P', supported by two brass rods. Through the rounded ends of these rods arc inserted two smaller rods, terminating in knobs, /// and //, which are called the /W:i-- anuniil tin- m-i-dli-, the deflecting power of the current will be doubled. By coiling the wire se\vral times around the needle, provided that the coils are insulated from each other, the deflecting GAL VANOMETER. 423 power of the current will be so multiplied that the needle may be used to detect the presence of very weak currents, to determine their direction, and even to measure their intensity. An instrument con- structed on this principle is termed a galvanometer. 739. The sensibility of the galvanometer may also be increased by the use of an astatic needle. This consists of two magnetic needles, Fig. 337, fast- ened in the same axis of suspension, but with their poles reversed. If these are suspended by a silk thread, so that one needle swings freely within the coil and the other above it, they constitute the astatic S'- -N' FIG. 337. FIG. 338. galvanometer, shown in Fig. 338. The advantages of this instrument are: (1.) the directive force of the earth on the needle may be almost neutralized, because the poles of the 424 X AT URAL PHILOSOPHY. needles lie in opposite directions. (2.) The force of the coil is exerted in the same direction upon two needles in- stead of one. For, although the upper needle is subject to the action of two opposite currents, yet as that in the upper part of the coil is much the nearer, its action prepon- derates, and, because the needles are reversed, both are deflected in the same direction. The wire used in this, and in other coils, should be carefully insu- lated, by being covered with white silk thread. A coil having a few hundred turns of moderately thick copper wire is well adapted for ordinary experiments ; but, for very delicate investigations, as many as thirty thousand turns of fine wire have been used. 740. If the conducting wire be movable we may obtain results the converse of the preceding. That is, a straight conducting wire will tend to place itself at right angles to a magnet held in its vicinity. De la Rive's floating battery, Fig. 339, will enable us to verify this fact, as well as to exhibit other properties of the current. It consists of a small voltaic ele- ment, which is floated in acidulated water by means of a cork attached to its upper end. The conducting wire may be made straight, rect- angular, or coiled. The spiral coil shown in the figure is technically called a helix. An elongated helix, with its conducting wire returned through the axis of the coil, is a solenoid, Fig. 341. The coil is right-handed, when its spire winds to the right, like a corkscrew, and is left-handed when its spire winds in the opposite direction. 741. By means of this apparatus, it may be shown that when a current is passing through the wire, it exhibits all the properties of a magnet. 1. If a permanent magnet be held near the helix, one f'aee of the coil will l>e attracted by the north pole of the magnet, and the other repelled. 2. Kadi >idc of the helix will attract iron filings. 3. If a helix 01- solenoid he free to move, it will swing so that its axis points north and south. If the coil be SOLENOIDS. 425 right-handed, the south pole will be the end at which the current enters; but if the coil be left-handed, the north pole will be the end at which the current enters. 4. If the conducting wire of the floating battery be straight, and a wire from another circuit be placed parallel to it: (1.) The wires will be mutually attracted if the currents pats in the same direction, but (2.) will be repelled if the cur- rents pass in contrary directions. The attraction of similar currents may be shown by means of a spiral of fine copper wire, connected at its upper end with the positive pole of a battery, and slightly dipping, at its lower extremity, in a cup of mercury, which is in connection with the nega- tive pole. When the current passes, each turn of the spiral attracts the next, thereby shortening the spiral, and breaking the current with a spark. f IG- 340. The weight of the wire then restores the connection, and thus a continuous oscillation is sus- tained. 5. If tw r o solenoids are brought near each other, Fig. FIG. 341. 341, with their similar ends adjacent, they will repel each other, because the currents of the two coils are in opposite 426 NATURAL PHILOSOPHY. FIG. 342. directions. Conversely, the dissimilar ends will attract each other. 742. Electro-magnetic rotation. We have seen that the current acts at right angles to a magnet, and tends to urge the north pole of a magnet always toward the left. Hence, it is pos- sible so to arrange the connecting wire and the magnet, that one shall revolve about the other. There are many contrivances for accomplishing this, one of which is shown in Fig. 342. E and F are two glass cups containing mercury. A B C is a conducting wire, jointed at D, and dipping at each end in the mercury. N S, N x S', are two bar magnets, one fixed and the other attached by a thread to the bottom of its cup. If, now, a current is passed through the mercury and the conducting wire, there will be a mutual repulsion between the ends of the magnets and the conducting wire. The magnet, N S, being free, will revolve about the end, A, of the wire; but in the other cup, as the magnet is fixed and the wire free, the wire will revolve about the magnet, W S'. When the current passes in the direction of the arrows, both rotations will be to the left; but if the current is passed in the opposite direction, the rotations will be to the right. 743. The voltaic current may also induce magnetism in magnetic substances. If a bar of soft iron, N S, be placed in the axis of a helix, so that the current may pass at right angles to its length, the bar will be instantly magnetized, but will lose its magnetism as soon as the cur- rent ceases. If the helix is held vertically while the current is pass- ing, the bar will not fall out. If the bar be pulled down a little way and then let go, it will spring back With a powerful current and a no. MS. to its former position. ELECTS 0-MA GNETS. 427 large coil, a weight of several hundred pounds may be sus- pended from the bar, and the whole sustained without any visible support. A pleasing modification of the same experiment may be had by joining the ends of two semicircular pieces of soft iron, with one pair of the ends within the helix, as shown in Fig. 344. While the current is passing they will adhere with considerable force. 744. Electro-magnets are bars of FlG - 344 - soft iron which become magnets under the influence of the voltaic current. Electro-magnets of surprising power have been made by bending bars of soft iron in the form of a horse-shoe, and surrounding each leg with many coils of insulated copper wire. When a strong current is passed through the wire, the magnetism induced is far greater than is pos- sible in a permanent magnet. Electro-magnets have been made that were capable of sustaining nearly two tons. The polarity of an electro-mag- FlQ net depends upon the direction in which the current moves in the helix. If the direction be reversed the polarity will be reversed. If the current is broken the magnetism almost instantly ceases. 745. Permanent magnets. If the iron employed in elec- tro-magnets is not quite pure, it will retain traces of mag- netism for some time after the circuit is broken. A steel bar placed in the helix, Fig. 343, will become permanently magnetized. It is sufficient to move the bar once nearly through the coil, then backward till it lies in the center of the coil ; the current is then stopped and the bar taken out. A better result will be attained, if 428 NATURAL PHILOSOPHY. the bar be previously armed with short cores of soft iron, which just fit the ends of the helix. This method may also be applied to horse- shoe magnets of steel. Permanent horse-shoe magnets may be made of steel wrought in the proper shape, by connecting their open i-nds with a keeper of soft iron, while an electro-magnet is passed along a few times from the poles to the bend. A better method is that shown in Fig. 346. The steel horse- shoe is applied to the electro- magnet, and a piece of soft iron is drawn, in the direction of the arrow, beyond the curve, and is then replaced and the process repeated. Both magnets are then turned over without separating the poles, and the other side treated in the same way. Magnets have been made in this manner so as to be capable of sustaining twenty- six times their own weight. 746. Ampere's theory of magnetism. In view of these various magnetic properties of the current, Ampere as- sumes that all bodies which exhibit polarity derive this polarity from electrical currents, which are perpetually traversing each molecule of a magnetic substance. Mag- netization consists in giving to these individual currents a parallel direction. When all the currents are parallel, the magnet is said to be saturated. The resultant of these parallel currents is equal to a single current which traverses the outside of a magnet as if it were a solenoid. At the north end of a magnet, the FIG. 317. direction of these current.- is opposite to that of the hands of a watch, and at the south end the direction is the same ELECTRO-MAGNETIC MACHINES. 429 as that of the hands. In this view of the subject, magnet- ism is a branch of dynamic electricity. This theory does not assign a reason for the persistence of currents in permanent magnets, but in other respects affords a satisfactory ex- planation of all magnetic phenomena. For instance, it explains why like poles attract and unlike repel. If two south poles are brought near each other, they have opposite currents on their adjoining sides, and hence repel. A north and south pole have similar currents on their adjoining sides, and attract. ELECTRO-MAGNETIC MACHINES. 747, Various machines have been devised in the hope of employing the prodigious force of electro-magnets as a motive power. All of these take advantage of the facility with which the polarity of an electro-magnet may be an- nulled or reversed, by which attractions and repulsions may be so arranged with another magnet as to produce a rotary or alternating motion. The action of the first class may be illustrated by Page's revolving electro-magnet, Fig. 348. A small electro-magnet, H, is fixed to a vertical shaft so as to revolve between the poles of a permanent horse-shoe magnet. The ends of the wires of the helix are sol- dered to two strips of silver on opposite sides of the shaft, insulated from each other and from the shaft. Two metallic springs, Z, C, connecting with the battery, are so placed that when the shaft makes half a revolution, the silver strips pass from one spring to the other. This reverses the direction of the current in the helix, and thereby causes the poles of the electro-magnet to be changed twice in each revolution. The position of the two magnets is such that, during the first quarter of a revolution, their like poles are adjacent and repel; during the second quarter, their unlike poles approach and attract. The current is then reversed, like poles again face each other and are repelled. The shaft is thus made to rotate, Fio. 348. 430 NATURAL PHILOSOPHY. ami may be made to communicate motion to a train of wheels, so that the rate of motion may be accurately determined. The velocity attained by this machine has reached as high as 2500 revolutions per minute. No electro-magnetic engines have been or can be devised which can compete with steam engines in economy, because the expense of the zinc and the acid consumed in the battery far exceeds that of the coal burned in steam boilers of the same power. Nevertheless, small electro-magnetic engines have been employed successfully in cases where economy is of less consequence than convenience and facility of application. 748. The electric telegraph is by far the most important application of electricity to the practical affairs of life. Very many forms of this telegraph have been invented, but every electric telegraph consists essentially of four parts: (1.) a voltaic battery for generating a current; (2.) a circuit consisting of an insulated metallic connection between two places; (3.) a key, which is an instrument for sending signals from the one station, and (4.) an instrument for receiving signals at the other station. Any constant battery may be used for generating elec- tricity. In this country, Grove's and Daniell's are both in use. Twenty-five Grove's elements are required for a line of one hundred miles. The line circuit. Two stations must be connected by at least one insulated metallic wire. Generally speaking, this is done by passing galvanized iron wires over glass in- sulators attached to a series of tall wooden posts. When the wire is to be laid in the sea, or under ground, it is in- sulated by being coated with gutta-percha. 749. The earth circuit. At the station which sends the dispatch the line is connected with the positive pole of the battery ; but as the current will not pass unless the two pol^s of the. battery are connected, it is necessary to have a second conductor n-timnnpeaker are easily recognized. On long lines, however, the sound transmitted is too feeble to be audible, and is, betides, liable to become confused by currents in adjacent wires. To obvi- ate these difficulties a battery is used, and a special transmitter more or less resembling one of tin- two following instruments. 759 a. The Microphone is an instrument capable of trans- mitting distinctly very i' 1>K- sounds. THE MICROPHONE. 4356 Hughes's Microphone, Fig. 351 a, consists essentially of two carbon sockets S and S', each of which is connected with one of the wires in a galvanic circuit, and of a carbon spindle, C, placed vertically so as to rest in the lower socket and play loosely in the upper. Now, if while the current is passing, a noise be made in front of the spindle C, it will so jar the spindle as to produce a greater or less surface contact between the ends of the spindle and its sockets. In consequence of this, the current transmitted by the battery will vary in like proportion. These variations will represent the sound waves, and may be made to reproduce audible sounds if a receiving instrument such as a Bell's telephone be interposed in the circuit. Xow, as the spindle is set in motion by very feeble sounds, such as the ticking of a watch, it receives the original impulse strongly, and also impresses the receiving in- strument strongly, and, it is said, that when a powerful battery is used the intensity of the sound is increased. Fig. 351 b shows the interior of the Blake transmitting telephone, which is extensively used to send audible messages. It contains a diaphragm which vi- brates in answer to the voice against a small platinum disk, which is thereby forced against a movable carbon cylinder C. The disk and carbon are connected with a battery, and the current will not pass except when these are in contact. The amount of surface contact between them will of course vary with the condensation and rarefac- tion of the sound waves, and conse- quently there will be a variation in the resistance of the primary circuit which may be reproduced as sound waves in a distant telephone receiver. The receiving telephone is placed in connection with an induction coil, I, and is worked by the secondary cur- rent. [The words primary and sec- ondary are defined in the next article.] Usually each station has a call, arranged on the principle of fire alarms. (756.) There are other forms of this instrument; some of which have rendered conversation distinctly over 250 miles of wire. FIG. 351 a. FIG. 351 6. 436 NATURAL PHILOSOPHY. ELECTRO-DYNAMIC INDUCTION. 760. The phenomena of current induction may be shown by the apparatus represented in Fig. 352. Let P and I be two helices of insulated wire, the first connected with a voltaic battery, and the other with a galvanometer. If, when the current is passing through P, it be brought near FIG. 352. the helix, I, a momentary current, in the opposite direction, will be induced in I, and will be manifested by the deflec- tion of the needle in the galvanometer. The first current is called the primary, or inducing, current, and the other, the secondary, or induced, current. A current in the same direction as the primary, is said to be direct; but if in the opposite direction, inverse. If the two helices are held in the same relative position, the induced current soon ceases, and the needle falls back to its old position. If the primary coil is placed within the other, another momenta! y inverse current is produced. This will also be the ca.se, if the intensity of the battery be in- creased.' If, however, the primary current be weakened, the circuit broken, or the coil withdrawn, a momentary current will be induced, which in i-ach of these cases will be direct. INDUCED CURRENTS. 437 Hence, (1.) An inverse momentary cut-rent will be induced in u lu'ujhboriinj circuit by a primary current on starting, ap- proaching, or inci-eatfiny in intuisity. (2.) A direct moment- ary current will be induced by a primary current which decreases in intensity, or ichich is removed or stopped; but (3.) A continuous and constant current does not induce any current in a neighboring conductor. 761. The induced currents are, therefore, but momentary in their action; nevertheless, they have all the properties of the primary currents. For instance, they may induce other currents on adjacent circuits, and thus currents of the third, fourth, and even of the seventh orders have been obtained. The direct induced and the inverse induced currents of the same order are equal in quantity, and, therefore, have the same effect on the galvanometer. The direct induced current has greater intensity than the inverse, and will, therefore, give rise to a more powerful shock. The direct induced current also magnetizes to saturation, while the inverse does not magnetize. The intensity of the direct induced current is always high, even when excited by a feeble primary current, but increases with the in- tensity of the primary. The more rapid its action, the greater will be its intensity, and hence the more instantaneously the primary cir- cuit is demagnetized, the more intense will be the induced current. 762. A primary current may also act inductively on itself, and thus give rise to what is called the extra current. It is this which produces the spark on breaking the circuit. This is particularly observable when the conducting wire has the form of a helix, because then each spire acts inductively on the next succeed- ing one. The effect of the extra current is to prolong the duration of the primary current when the circuit is broken, and it, therefore, reduces the tension of the induced currents, by retarding the sud- denness of the change. 763. Magneto-electrical induction. Since a helix, through which a current is passing, is essentially a magnet, we ought to expect that a permanent magnet would, like it, induce electrical currents. In fact, if we substitute for the 438 NATURAL PHILOSOPHY. FIG. 353. primary coil, P, in Fig. 352, a permanent magnet, we shall obtain almost identical effects. The same phenomenon may be studied by placing a bar of soft iron within a helix, as shown in Fig. 353, and bringing above it a strong perma- nent magnet. The core of soft iron becomes magnet- ized by induction, and in- duces an electrical current in the helix, by reason of which the needle of the galvanometer is deflected for a moment, and then returns to its normal posi- tion. On removing the magnet, the needle is de- flected in the opposite di- rection. The direction of the currents depends upon the pole of the magnet presented, and is in accordance with Am- pere's law, (738). 764. The magneto- electrical machine is constructed on this principle. Fig. 354. This consists of a per- manent magnetic battery, A B, in front of which two helices of fine copper wire, carefully insulated, are made to revolve on an axis,/, by means of a wheel and winch. The cores of the helices are made of two pieces of soft iron, joined by a soft iron, ttf. The same wire is coiled about the two core-, hut in dif- ferent directions, in order that the currents induced hv the opposite INDUCTION COILS. 439 poles may be in the same direction. The two ends of this wire ter- minate in two metallic plates insulated from the axis and from each other by ivory, and are connected alternately with the springs, S S'. On turning the wheel, a current of electricity is induced in each helix, the direction of which changes twice at each revolution. 765. This instrument is capable of producing sparks, decomposing water, and igniting wires, and of producing other effects of dynamical electricity. If a break piece, not shown in the figure, be added, an extra current of great tension will be induced, which is capable of producing very powerful shocks, if the handles, P P', be grasped with the hands slightly moistened. With a good apparatus, the muscles contract with such force that they no longer obey the will, and the handles can not be dropped. From its convenience and neatness, this is a very common apparatus for applying the effects of induced currents in therapeutical operations. 766. Other magneto-electrical machines of remarkable power have been constructed on the same principle. They have been used for all the practical operations of electricity, such as electroplating, telegraphing, and more recently for the electric light. The machines are driven by a steam engine. Wilde's machine yields a light of surpassing brilliancy, and evolves sufficient heat to melt iron rods 15 inches long and \ inch thick. The Gramme machine, and Brush's modification of it have been successfully used to light the interior of large buildings and also for street lamps, using some form of the electric arc. Fig. 332. 767. Induction coils are instruments which employ both magnetic and electric induction. One form in which the helices are separable is shown in Fig. 355. The primary coil, P, is, of coarse, insulated copper wire, connected by the screw cups, -f and , with the battery. I is the secondary coil, of very fine, insulated copper wire, to which handles may be attached. M is a bundle of iron wires, which are sufficiently insulated from each other by the rust which soon gathers on them. The primary current is made to open and close by its own action. This is effected 440 NATURAL PHILOSOPHY. by a small electro-magnet, B, the spring of whose armature is made to open and close the circuit. As soon as the coil of B receives the current, the armature is drawn down and the circuit is broken. At every interruption of the pri- mary current, the iron wires, M, become magnetized and demagnetized, FIG. 353. and react upon the secondary coil. The intensity of the induced currents is thereby much increased, and may even become of so high tension as to produce all the effects of statical electricity. The form shown in Fig. 355 is frequently used for giving shocks, and for medical purposes. 768. Ruhmkorff's coil is made on the same principle as that already described. The utmost care is taken in insu- lating the wire used. The secondary helix contains from three to thirty miles of fine wire. To avoid the effect of the extra current of the primary coil, a condenser of tin foil is placed in the base of the instrument and is connected with the interrupter. This is ordinarily a ratchet wheel, turned by the hand, which breaks and closes the current every time its spring passes from one tootli to another. With three or four Bunsen's . elements and a lurge coil the induced current becomes of ama/ing tension, although of inconsiderable quantity. Some of the eU'eets ,,f die coil follow.- : THERMO-ELECTRICITY. 441 1. Physiological. The shocks are so violent as to be dan- gerous, and incautious experimenters have been prostrated by them. 2. Calorific. Fine iron wires brought between the ends of the induced wire are melted and burned. 3. Luminous. Sparks have been obtained nineteen inches in length. When the discharge is passed into rarefied air or gases, the phenomena of auroral light is produced in a most beautiful and varied manner. FIG. 356. These experiments are performed with sealed glass tubes, known as Geisler's tubes, one of w r hich is show r n in Fig. 356. The color of the light varies with the vapor inclosed in the tube, and is frequently arranged in bands, giving the ap- pearance of stratified light. To produce these effects with the primary current would require a battery of over fifty elements. 4. Leyden jars may be charged and discharged by means of the coil with an almost continuous spark, of great bril- liancy and accompanied by an almost deafening sound. These, as well as the mechanical and chemical effects of the coil, are similar to those produced by statical electricity. THERMO-ELECTRICITY. 769. If any two metals are soldered together and heated at their junction, an electrical current is evolved which is capable of deflecting the needle of the galvanometer. On 442 NATURAL PHILOSOPHY. the other hand, if their junction be cooled, the needle will be deflected in the opposite direction. These currents are called thermo-electric currents, but they differ in no respect . from those already studied. 770. The direction of the current within the pair will depend on the metals which are associated together. The following thermo-electric se- ries is so arranged that if any two of the substances named are soldered together, and heated at the soldering, the current will pass from the first named to that succeeding it. FIG. 357. t-t 3 ~ - - ft -~ c " c ^ 771. The most efficient electro-thermal couple is said to be formed of artificial sulphide of copper and metallic copper. Fig. 357. The usual combination is bars of anti- mony and bismuth. Fig. 358 shows a section of a thermal battery made up of these metals. The greater the number of pairs, the greater will be the force of the current. Although the electro-motive force of a thermal battery is always low, it may be used to attain the same results as the voltaic battery. Since in combining the pairs it is necessary to join both ends of all except the outer bars, the effect of the current will be due to the difference in the temperature of the two ends. Fio. 358. This fact is utilized in the thermo-multiplier shown at T in Fig. 359. This consist < <>\' thirty pairs of bismuth and ;mtimony, inclosed in a non-conducting frame, and con- ANIMAL ELECTRICITY. 443 nected with a galvanometer which has only a few turns of tolerably thick wire. This apparatus is so sensitive that FIG. 359. even the radiant heat emitted by insects may be estimated by it. It is therefore used in all delicate investigations on the subject of radiant heat. ANIMAL ELECTRICITY. 772. We have already seen that electricity produces peculiar phenomena in living animals, and that one of the most sensitive galvanoscopes may be had in the legs of a recently killed frog. Matteuci has reversed this last ex- periment, and has succeeded in evolving a current by means of a battery formed of the muscles of frogs. 773. Several species of fish have the power of giving, when touched, shocks like those of the Leyden jar. Among these are the torpedo, the gymnotus, and the silurus. Each of these fish has special organs for the production of elec- tricity. This electrical apparatus is under the control of the animal, and may be made to serve as a means of offense and defense. It is thought by some philosophers that electrical currents are evolved and consumed in all animals during the various vital proc- esses, like secretion, digestion, and the like. None of these theories are sufficiently well established to be introduced here. 444 NATURAL PHILOSOPHY. 774. Becapitulation. I. The science of electricity includes the phenomena of 1. Electricity that may be insulated Statical. 2. Electricity continually discharged in currents Dynamical. Dynamical electricity investigates the phenomena I. Within the path of the current : 1. Due to chemical action Galvanism. 2. Due to heat Thermo-electricity. 3. Due to vital action Animal electricity. 4. Due to Amperean currents Magnetism. II. External to the path of the current : 1. Inducing magnetism in iron and steel...Electro-magnetism. 2. Inducing currents in adjacent circuits. ...Electro-dynamics. III. Of currents induced by permanent magnets Magneto-electricity. Induced currents are applied 1. For physiological and therapeutical purposes. 2. For evolving light and heat of great intensity. 3. For effecting chemical changes. 4. For making temporary and permanent magnets, which are employed to produce mechanical action in engines, tele- graphs, clocks, etc. PROBLEMS. THE object sought in these problems is rather to enforce the principles of Physics than to afford practice in arith- metic. They are therefore as easy as circumstances will permit. In their solution it will not be necessary, as a gen- eral thing, to employ more than two places of decimals. The student will understand that they are to be solved only in view of the principle involved, and that circum- stances modifying the application of the theory in actual practice are excluded. The solutions should be preserved for reference and comparison. USEFUL FACTORS. 77 = 3.1416 7T2 = 9.87. Circumference of a circle 2?rr = -rrd = 3.1416d. Area of a circle *r* = frd 2 = .7854d 2 . Surface of a sphere *r z = vd 2 = 3.1416d 2 . Volume of a sphere f*r 3 = frd 3 =0.5236d 3 . SOMATOLOGY. Art. 17. 1. How many metres in an English mile? How many mile? in a kilometre? What part of an inch is a millimetre? How many inches in 776 millimetres? 2. The radius of the earth is 3963 miles ; find its circumference. 3. The distance of the earth from the sun is 91430000 miles ; find the circumference of its orbit, supposing it to be an exact circle. 4. If the radii of two circles are given, what is the ratio between their circumferences? Between their areas? 5. Find the area of a circle whose radius is 1 inch; 10 inches; T \y of an inch. (445) 446 NATURAL PHILOSOPHY. 6. How much more water will flow through a 2 inch pipe than through a 1 inch pipe? 7. What is the ratio between the surfaces of two spheres whose radii are given? Between their volumes? 8. Find the spherical surface of an inch ball ; a 10 inch ball ; j- s of an inch ball. 9. Find the volume of an inch ball ; a 10 inch ball ; a T V of an inch ball. 10. Find the cubic inches in a pint. Find the litres in a gallon. How many gallons in a cubic foot? How many cubic feet in 10 gallons? How many litres in a cubic foot? Art. 19. 11. How many grammes in a pound? 12. What is the volume of a pound of water? What is the weight of a pint of water ? What is the weight of a cubic inch of mercury ? How many grains in a cubic foot of hydrogen ? What is the volume of a pound of hydrogen? Art, 24. 13. Calculate, from Example 2, the velocity per minute of a point on the equator. 14. Calculate, from Example 3, the velocity per minute of the earth in its orbit. 15. Find the time required for electricity to pass around the equator. For sound to traverse the same distance. 16. Find the space that light will traverse in 8 minutes and 13 seconds. How far will a rifle ball go in 3 seconds? 17. How long would it take a railway train to reach the sun? Art. 29. 18. An ounce of water contains 360 drops : if a grain of nitrate of copper be dissolved in a gallon of water, how much nitrate of copper will there be in a single drop ? Art. 30. 19. Suppose a grain of water be blown into a soap bubble 10 inches in diameter, what will be the weight of the water in each square inch of the film? Art. 38. 20. Find the weight of a cubic foot of cork ; of ice ; of a ball of silver 10 inches in diameter. Of a pint of alcohol. 21. Find the weight of a gallon of ammonia in both the liquid and :i- rit'orm states. 22. How many times heavier is a cubic inch of platinum than i.f hydrogen ? PROBLEMS ON MECHANICS. 447 Art. 42. 23. How deep must water be at 39.2F. to equal the pressure of one atmosphere ? at 62 ? 24. What is the pressure in pounds indicated by a column of mer- cury at 62 F. and eighteen inches high ? 25. How many feet of air are required to produce the same press- ure as 30 inches of mercury at 32 F. 26. Suppose a boy has a surface of 8| square feet, what is the atmospheric pressure he sustains? Art. 62. 27. How much will a rod of steel, 1 inch in section and 10 feet long, be stretched by a weight of 100000 pounds? 28. How much force is required to crush a cubic foot of oak ? Of cast iron? 29. How much force is required to overcome the tenacity of a steel wire y 1 ^ of an inch in diameter? Art. 74. 30. What is the weight of the finest platinum wire a mile long ? What is the weight of a square inch of finest gold leaf? Art. 93. 31. How many gallons of ammonia may be absorbed by a pint of water ? What will the solution weigh ? Art. 95. 32. How many gallons of ammonia may be absorbed by a cubic foot of charcoal? 33. What weight of carbonic acid may be absorbed by a cubic foot of charcoal ? MECHANICS. Art. 114. 34. Find the momentum of a glacier 300 feet high, 5 miles long, and 1 mile wide, moving at the rate of 1 mile a month. 35. Find the momentum of a locomotive weighing 25 tons, and having a velocity of 30 miles per hour. 36. Find the velocity of a cannon ball weighing 60 pounds, and having a momentum of 30000 pounds. Find the weight of a ball that has the same momentum and a velocity of 1200 feet per second. Art. 120. 37. Two forces, A and B, act on the same point; A with a force of 90 pounds, B with 120; what will be their resultant if they lie in the same direction? If in opposite directions? If at right angles to each other? Art. 123. 38. The resultant of two forces acting at right angles is 10 ; one of the forces is 8 ; what is the other ? N. P. 29. 448 NATURAL PHILOSOPHY. Art. 125. 39. Suppose two equal forces act at an angle of 60 de- grees; what will be the direction and force of their resultant? If one force be double that of the other? Apply the method by construction. Art. 128. 40. If two inelastic bodies A having a weight of 3 pounds and a velocity of 5 feet per second, B having a weight of 4 pounds and a velocity of 3 feet per second collide from opposite di- rections, what will be the resulting momentum, velocity, and direction ? If they move in the same direction, and A strikes against B, what will be the resulting momentum and velocity ? Art. 129. 41. In the last example, what would have been the result if the bodies had been perfectly elastic ? Art. 134. 42. Calculate the striking force in examples 34 and 35. 43. If light were matter, and one-millionth part of a grain entered the eye in a second, what would be its striking force as compared with an ounce rifle ball with a velocity of 1200 feet per second? 44. How fast must a battering ram weighing 3 tons be propelled in order to have the same striking force as a 30 pound cannon ball with a velocity of 1200 feet per second? With equal vis viva, how would their momenta compare? Art. 143. 45. If two cannon balls, weighing respectively 30 and 80 pounds, be connected by a rigid bar, where will the common center of gravity be? 46. If the mass of the moon is ? T that of the earth, where is their common center of gravity ? Art. 154. 47. What is the work, expressed in foot-pounds, that is required to raise 193 pounds 4 feet high? To raise 10000 gallons of water from the bottom of a mine 600 feet deep? Art. 155. 48. How many horse powers are required to fill every day a reservoir, having a capacity of a million cubic feet, with water from a lake 400 feet below the reservoir? Art. 157. 49. Suppose a power of 50 pounds moves throuirh a ver- tical distance of 10 feet, how high can it lift a load of 250 pounds? How great a load can it lift 100 fret high? In each case, what will be the relative velocities .f the power :md the load? Art. 162. ."iO. A power of 7") pound- i- applied at one end of a lever 12 feet long, to move a load at the other end; what will he the load when the fulcrum i- at the center <>\' the lever'/ When tin- ful- crum is 3 feet from the load? 1 loot from the load? PROBLEMS ON MECHANICS. 449 51. When the same bar is employed as a lever of the second kind, what will be the load when it is sustained at the center? At 3 feet from the fulcrum ? At one foot ? VJ. If, with the same bar, the load and the fulcrum be placed at the ends, and the power applied between them, what will be the load when the power is at the center? At 3 feet from the fulcrum ? At 1 foot? 53. If, with the same bar, a power of 30 pounds balances a load of 180 pounds, how far from the load will the fulcrum be when it is used as a lever of the first kind? As a lever of the second kind ? Art. 166. 54. If A and B carry between them, on a pole 9 feet long, a load of 150 pounds, how much will A bear when the load is 3 feet from him ? 6 feet ? Art. 167. 55. In the compound lever, shown in Fig. 47, A F is 6 feet long, A' B' 4 feet, A" F" 5 feet, and the distances, F B, F x B', F" B /x , each 1 foot ; what is the relation between the power and the load? What load may be sustained by a power of 60 pounds? How far from B must a power of 10 pounds be placed to balance a load of 300 pounds at L. Art. 171. 56. In a false balance, a bundle weighs 16 pounds in one scale pan and 9 pounds in the other ; what is the true weight ? What is the relative length of the arms ? Prove the answers obtained. Art. 175. 57. In a wheel and axle, the radius of the wheel is 10 feet and that of the axle 6 inches; required, the load that may be sustained by a power of 1 pound ? By 100 pounds ? Art. 176. 58. With the same machine, what will be the length of the rope unwound from the wheel, when the load has been lifted 10 feet? Art. 177. 59. A capstan has an axle 1 foot in diameter, and is fur- nished with 5 handspikes, each 6 feet long; how much power must be applied at each handspike to lift an anchor weighing 4000 pounds? Art. 178. 60. In a differential wheel and axle, the two parts of the axle are respectively 8 and 10 inches in diameter; what is the load that may be lifted by this machine by a power of 100 pounds, ap- plied at a winch of 2 feet radius? Art. 179. 61. In a train of three wheels, the number of teeth in each wheel is 64, the number of leaves on each pinion 16; when a power of 10 pounds is applied at the circumference of the first wheel, what load will be sustained at the third pinion? How many times must the first wheel revolve, in order that the third pinion may be turned around once? 450 NATURAL PHILOSOPHY. 62. In Fig. 176, the cord, D, passes from the wheel, A, 5 feet in diameter, to the axle of the second wheel, B, 2 inches in diameter ; how many times faster will B revolve than A? B has 100 teeth which strike against a card, E; how many teeth will strike the card when A has revolved once? Art. 185. 63. In a system of 2 movable pulleys, with a continuous cord, the power is 100 pounds ; required the load. 64. What power will be required to raise 2000 pounds with a sys- tem of 4 movable pulleys? Art. 187. 65. In the Spanish burton, shown in Fig. 64, what power will be required to lift one ton? Art. 189. 66. On a road rising 1 foot in 25, what power will be re- quired to sustain a wagon weighing 1000 pounds? 67. A plank 16 feet long extends from the ground to a wagon 4 feet high ; required the power necessary to roll a cask weighing 500 pounds into the wagon. What would be the power required if applied par- allel with the ground ? 68. Apply the method by construction to find the power required when applied at an angle of 40. Art. 198. 69. In a book-binder's press the lever is 6 feet long, and the threads of the screw 0.5 inch apart ; what pressure may be applied by a power of 100 pounds? 70. In the differential screw, the threads of the two screws are re- spectively \ and of an inch apart; through what space will the plate move when the lever is turned 90? Art. 201. 71. In the crane, Fig. 75, the axle at G is 6 inches in diameter, and the winch 3 feet in radius, with one movable pulley ; what will be the relation between the power and the load? The wheel and axle remaining the same, what advantage may be gained by the use of a system containing 4 movable pulleys? Art. 202. 72. In Fig. 76, suppose the muscle to be applied 1 inch from the joint, and the length of the fore-arm to be 15 inches; required the power necessary to raise a weight of 10 pounds. Art. 207. 73. Suppose an oak block weighing 100 pounds rest upon an oak plank, with their fibers parallel. What will be the force required (1.) to start and (2.) to keep the block in motion, if no unguents are used? PROBLEMS ON MECHANICS. 451 Art. 208. 74. A wagon weighs 2000 pounds. What will be the power required to draw it over a well paved, level road? Over a dry highway? Suppose the road to rise 1 foot in 30, what will be the power necessary in each case? Art. 210. 75. What force will be required to draw a scow with blunt bow, having a submerged area of 8 feet broad and 2 deep, through water at the rate of 1 foot per second? Of 1 foot per minute? Art. 211. 76. In the problems already detailed for machines, what allowance must be made for friction ? Art. 219. 77. A body falls freely through the air. What will be the space described in the fifth second? The velocity at the end of the sixth second ? The total space described in 8 seconds ? Art. 220. 78. What will be the velocity attained by a body falling from a vertical cliff 784 feet high? In what time will it fall? Art. 221. 79. Suppose a smooth plane to extend 10000 feet up a mountain side, with an inclination of 1 foot in 10, and that a smooth ball rolls from the top to the bottom. What will be the time required for the descent? What will be the velocity attained? Art. 223. 80. In the case supposed, what will be the space passed over in 5 seconds if the ball is started with a velocity of 100 feet per second ? Art. 224. 81. With what velocity must a ball be thrown to strike the top of a flag-staff 257.32 feet high ? What will be the time re- quired for its flight? Art. 226. 82. Suppose a rifle ball is shot horizontally, with a velocity of 1200 feet per second. What will be its range if shot from a rest 4 feet high? From a rest 64 feet high? Art. 229. 83. Suppose the radius of the moon were the same as that of the earth, what would be the weight of a terrestrial pound when taken to its surface? Assuming the lunar radius to be \ that of the earth, what would be the weight of a terrestrial pound taken to the surface of the moon if its mass were the same as that of the earth ? 84. If the moon's mass be assumed as .0128 and its radius as .24, what would be the weight of a terrestrial pound taken to its surface? 452 NATURAL PHILOSOPHY. 85. If the mass of the sun be 314760 and its radius 110 times that of the earth, what would be the weight of a terrestrial pound on its surface? What would be the space passed over in the first second by a falling body ? Art. 230, 86. If a body were dropped from a distance of 12000 miles from the earth's center, how far would it fall in 10 seconds? Art. 232. 87. What would be the weight of a cubic foot of iron 500 miles below the surface of the earth ? Art. 238. 88. What is the length of a pendulum at New York that vibrates in of a second? In 3 seconds? What is the ratio between the lengths of these two pendulums? How long should a pendulum be to vibrate 100000 times in a day ? Art. 239. 89. Find the increment of velocity due to gravity at Spitzbergen from the length of the seconds pendulum 39.21614 inches. Art. 257. 90. What will be the centrifugal force of a wheel 10 feet in radius, whose weight may be considered as concentrated in a rim weighing 1000 pounds, when the wheel makes 1 revolution in a second ? 5 revolutions in a second ? 91. With what speed must a pail of water be whirled over the head to prevent the water from falling out, granting that the radius of the circle in which the pail revolves is 3 feet? HYDROSTATICS. Art. 274. 92. Find the pressure on the bottom of a reservoir 120 feet long and 40 feet wide, when the water is at a depth of 10 feet. 93. A pipe leading from the reservoir descends 100 feet into a valley. What is the pressure on each square foot at the bottom of the valley? Art. 275. 94. What is the pressure on each side of the reservoir? What is the total pressure at the sides and the bottom ? What is the weight of the water contained in the reservoir? Art. 276. 95. What is the pressure on a cubic foot of iron sunk in water to the depth of a mile? Art. 277. 96. In Pascal's experiment, suppose the pipe to have had an area of 5 square inches, what would have been the weight of water in the tube? What would have been the pressure on each square inch ? PROBLEMS ON HYDROSTATICS. 453 Art. 278. 97. If the upper board of the hydrostatic bellows has an area of 100 square inches, and a boy standing upon it raises water in the pipe to the height of 30 inches, what is the weight of the boy? Art. 280. 98. In Bramah's press, suppose a power of 1000 pounds to be applied at one end of a lever of the second class 10 feet long, whose weight is 3 inches from the other end, and suppose the larger cylinder to have 1000 times the area of the smaller: what will be the pressure on the ram? 99. If the larger cylinder have an area of 200 inches, what will be the pressure on each square inch? How high a column of water would this pressure support? Art. 284. 100. If the discharge pipe of an Artesian well is 200 feet above the surface, what is the least elevation possible for its distant source? Art. 286. 101. At what distance can a mountain 5 miles high be seen from the sea-level ? Art. 289. 102. What will be the buoyant effort of water on a cubic foot of iron immersed in it? How much weight will a cubic foot of iron lose when immersed in water? Of lead? Art. 291. 103. What is the volume of water displaced by a cubic foot of cork? Of ice? Art. 293. 104. How many cubic feet of water must an iron boat weighing 480 pounds displace in order that it may float? If it dis- places twice this volume, how many pounds will it carry ? Art. 301. 105. From the table on page 16 calculate the specific gravity of iron : of copper. From the tables on pages 24 and 25 find the weight of a cubic inch of oak : of glass : of lead. 106. How much weight will a pound of iron lose when immersed in water? How much will a pound of lead lose? 107. Find the volume of a pound of lead. Of a pound of iron. 108. If a pound of lead be in a cubical shape, what will be the length of each side? Art. 302. 109. A mass of iron pyrites weighs 6 ounces in air and 4.8 ounces in water. What is its specific gravity? Art 303. 110. The same mass attached to an ounce of cork weighs in water 4.7 ounces. What is the specific gravity of the cork ? 454 NATURAL PHILOSOPHY. Art. 304. 111. 480 grains of carbonate of potassa weighs in alcohol 270 grains. The specific gravity of the alcohol being .85, required the specific gravity of the carbonate of potassa. Art. 305. 112. A small flask contains 900 grains of water, 800 grains of alcohol, or 1350 grains of sulphuric acid. Required the specific gravity of the alcohol and sulphuric acid. 113. A boy's marble weighs in air 450 grains, in water 300 grains, in naphtha 350 grains. Required the specific gravity of the naphtha. Art. 306. 114. If 1500 grains are required to sink a Nicholson's hydrometer to the mark on the stem, what will be the specific gravity of a solid that requires 1000 grains to be added to the pan when the body is on the scale pan, and 1100 grains when the body is in the basket ? Art. 308. 115. What is the specific gravity of a liquid correspond- ing to 30 Beaume? For heavier liquids? For lighter liquids? Art. 309. 116. A flask full of air weighs 131 grains ; when full of carbonic acid, 146 grains ; the flask weighs 100 grains. What is the specific gravity of the carbonic acid ? Art. 311. 117. A nugget of quartz and gold weighs in air 10 ounces, and loses 2 ounces in water ; the specific gravity of the quartz being 2.5. How much gold does the nugget contain ? HYDRODYNAMICS. Art. 314. 118. With what velocity will water flow from an orifice 25 feet below the surface? What will be the relative velocities of two streams respectively 9 and 16 feet below the surface? Art. 315. 119. What will be the range of a stream escaping from the center of a reservoir 72 feet high ? Art. 316. 120. What will be the theoretical volume discharged per minute from each orifice, in the above examples, supposing the head to be constant, and the diameter of the stream 1 inch ? Art. 318. 121. What will be the volume if allowance is made for the vena contracts without adjutage? What with a good adjutage? Art. 322. 122. If the flow of the Mississippi were not retarded by the shape of its bed, etc., what would be its velocity at its mouth, which is 1572 feet below its source? PROBLEMS ON PNEUMATICS. 455 Art. 323. 123. What i.s the gross power of a stream flowing through a weir having a section of 4 square feet and a fall of 9 feet ? Art. 326. 124. What will be the eflective power of the same stream when applied to an overshot wheel ? To a turbine ? PNEUMATICS. Art. 338. 125. How high must a barometer tube be if filled with sulphuric acid, having a density of 1.84? Art. 339. 126. How heavy a brick may be raised by a boy's sucker, whose effective diameter is 2 inches ? Art. 340- 127. What is the pressure on each square inch required to condense air to T V of its original volume ? Art. 344. 128. If an air pump exhausts y^ of the air from a receiver at each stroke, what will be the tension of the air remain- ing at the fifth stroke? Art 345. 129. What will be the pressure on a pair of Magdeburg hemispheres 2 inches in diameter when the gauge of the pump stands at 24 inches? 130. How heavy a load may be raised by a weight lifter whose diameter is 3 inches? 131. How much weight will be gained respectively by 10 pounds of lead and of cork when transferred to a vacuum ? 132. What is the ascensional power of a spherical balloon 100 feet in diameter, and filled with coal gas of a specific gravity of 0.5? Art. 346. 133. Tf the cylinder of a condensing pump is T a 7 the volume of its receiver, what will be the tension of the condensed air after 50 strokes of the piston? Art. 351. 134. What will be the variations in atmospheric pressure due to a range of 3 inches in the barometer? Art. 354. 135. What will be the difference in pressure on the body of an average sized man ? Art. 355. 136. On the same man, when he has descended in a diving bell 17 feet ? Art. 359. 137. W r hat is the pressure required to force a stream of water 75 feet high ? Art. 361. 138. What is the greatest vertical height possible for a siphon used for transferring alcohol? 456 NATURAL PHILOSOPHY. ACOUSTICS. Art. 397. 139. What is the relative intensity of two sounds from the same source heard at the distances of 10 and 250 feet? Art. 406. 140. With air at 32 F., how long will it take sound to travel 1 mile? How long with air at 90 F.? 141. A stone dropped into a deep well returns the sound in 3 sec- onds ; required the depth of the well. Art. 409. 142. An iron gas pipe is 5 miles long; required the time for a blow struck at one end to be heard at the other, through the iron and through the air. (The velocity of sound in iron may be taken as the same as in steel.) Art. 421. 143. A string which sounds C l is 2 feet long ; what must be the length of the same string to sound C_ l} A 2 , G 3 ? 144. If the same string is made 8 inches long, what will be the sound that may be emitted by it? With what relative force must the original string be stretched to sound G 2 ? 145. Suppose a string of the same material, but of quadruple the relative weight, sounds C^ what is its length ? Art. 422. 146. What is the absolute number of vibrations corre- sponding to G_ 2 , G 5 ? Art. 423. 147. What is the length of the sonorous wave corre- sponding to G , G" 2 ? Art. 428. 148. What is the relative number of vibrations corre- sponding to F 1? F^, G^, G? The absolute number? Art 429. 149. In the key of A what notes are sharped? Art. 434. 150. What is the length of the sonorous wave corre- sponding to C 2 when made in carbonic acid gas? (Compare 408.) OPTICS. Art. 441. 151. It is calculated that the light from the polar star requires :\\ years t<> reach the earth; what is its distance? Art. 446. 152. What are the rehuive intensities <) Convection of heat 336 of electricity 392 Crane 98 Crank 359 Culinary paradox 323 Current, electrical 402 direction of 403 primary and induced . . .436 extra 437 thermo-electric . . 442 INDEX. 461 Daniell's battery 411 Dead points 359 Declination of the needle ... 370 Dt- la Rive's floating battery . . 424 Density 23 Drw point 321 \h-\\-. formation of 343 Dialysis 49 Diamagnetic substances .... 368 Diathermancy 341 Diffraction 279 Diffusion of liquids 46 of gases 47 Dioptrics 257 Direction, line of 66 Discharge of liquids, rate of . . 162 Discharging rod 388 Distances, how estimated . . . 245 of lightning estimated ... 398 Distillation 327 Divisibility 19 Ductility 35 Dynamics, denned 51 considered 106 Earth, variation of gravity on . 116 found by pendulum . . 120 attraction of 116 curvature of 116 cause of present form . . . 132 diurnal revolution proved . 125 magnetism of 369 Ebullition, defined 319 how influenced 322 Echo 223 Elastic bodies, collision of ... 60 Elasticity, defined 29 kinds of, classified .... 30 table of 32 Electricity 364 defined 374 statical electricity 373 law of 375 transmission of .... 375 distribution of 382 quantity and intensity of 383 charge by cascade ... 390 phenomena of 391 kinds of discharge of . .392 points and flames . . . 392 effects of 393 recapitulation of . . . .400 atmospheric electricity . . . 397 Electricity, dynamical . . . .401 current 402 direction of .... 403 energy of 405 quantity of 405 intensity of .... 406 conductors of . . . .406 effects of 412 negative plate, how pro- tected 404 current induction 421 recapitulation 444 thermo 441 animal 443 Electric spark 393 duration and velocity of . .394 light 414 alarms 434 clocks 435 Electrical induction 377 apparatus 383 battery 388 pendulum 374 hail 391 pistol 396 Electrodes 405 Electrolysis 416 Electrophorous 379 Electroscope 376 Electro-chemical series, table of 417 Electro-metallurgy 418 Electro-motive series, table of . 404 Electroplating 419 Elect-retyping 420 Electro-magnets 427 Electro-magnetism 422 Oersted's discovery . , . . 422 Ampere 'slaw 422 Electro-magnetic rotation ... 426 machines 429 Elements, number known ... 8 Engine, fire 193 steam 356 electro-magnetic 429 magneto-electrical .... 438 Equilateral hyperbola .... 40 Equilibrium 68 relation of solids to gravity . 69 of liquids 144 of floating bodies 151 Evaporation, laws of 319 cold produced by 329 water frozen by 330 462 NATURAL PHILOSOPHY. Kxchanges, theory of heat . . 338 Kxpansibility 25 Expansion, an effect of heat . . 305 cubical and linear ;>OG unequal, of solids . . . . . 307 used to measure heat ... 308 co-efficient of 310 force in 311 in solidi lying 317 Extension 14 Eye, structure of 285 accommodation of .... 287 shape of 288 Faraday's theory of induction . 380 Far-sightedness 289 Field of view of lenses .... 290 Fire alarms, electric 434 Fire engines 193 Flame, cause of 273 Flexibility 31 Floating bodies, laws of . . . .149 Fluids, defined 8 manner of action 135 transmission of pressure in . 136 diathermancy of 342 Fluorescence 278 Fly wheel 359 Foot pound, defined 74 Force, defined 7 how applied 29 impulsive and continuous . 51 constant and variable ... 52 manner of action 54 striking 62 elastic, of gases 171 of expansion 311 not annihilated 355 Forces, classified 9 resolution of 57 centripetal and centrifugal . 128 Foucault's pendulum 125 Franklin's electrical experiment 397 Fraunhofer's lines 271 Freezing point 316 Feezing mixtures 318 Friction, manner of action . . 27 classified 101 laws of 101 Fusion W Galvanism .... Galvani's experiment 401 Galvanometer 423 Gamut 226 Gases, defined 8 classified 172 diathermancy of 342 Gassiot's water battery . . . .414 Gauge for tension of aeriform bodies 177 Geisler's tubes 441 Gravesande's ring 306 Gravitation, terrestrial ... 63 universal 114 recapitulation of 116 Gravity 64 center of 65 how found 65 direction of 64 poi nt of application of . . . 65 intensity of 106 Gravity, specific, defined ... 23 tables of 24 how found 152 Grove's battery 410 gas battery 412 Gyroscope 133 Hardening 36 Hardness 35 Harmony in music 230 Harmonics 234 Hearing, defined 212 limits of 218 Heat, defined 307 effect in expansion .... 305 fusion 315 vaporization 319 incandescence 239 distribution of by conduction 332 by convection 336 by radiation 338 dynamical theory of . . . .350 reflection of 339 refraction of 340 absorption of 340 transmission of 340 sources of 345 solar, estimated 346 animal 347 (.1 combustion, estimated . . 348 Heat litfhtnini,' 398 Meinlit ol the ainn-|.here ... 187 Heights measured by tlu- barom- eter 188 INDEX. 463 Heights measured by the ther- mometer Helix Holtz's electrical machine . . . Horse power, defined of steam boilers Hydraulics, defined Hydraulic press Hydraulic ram Hydrodynamics, defined . . . considered Hydro-electric machine . . . . Hydrometers of constant vol- ume of constant weight . . . . Hydrostatics Hydrostatic bellows Images, virtual real multiple formed by direct light . . . by plane mirrors .... by concave mirrors . . . by convex mirrors . . . by convex lenses .... by concave lenses . . . by mirrors and lenses, re- capitulated in the eye Impenetrability Incandescence Inclination of the needle . . . Inclined plane laws of examples of bodies rolling down .... Indestructibility Induction, of magnetism . . . of statical electricity .... Faraday's theory of . . . .380 essential in electrical phe- nomena 381 of dynamical electricity . . 421 of secondary currents . . . 436 magneto-electrical . . . .4:37 coils 439 Inertia 18 law of 54 Instruments, musical 234 Insulators 375 .350 It] Joule's equivalent. N. P. 30. Kaleidoscope 250 Key, signal 431 Lantern, magic 292 Latent heat 317 table of, for liquids . . . . 318 of vapors 328 of vapors, applied 331 effect of water in nature 318, 330 Lenses, classified 262 convex, foci of 263 axis of 263 secondary axis 264 formation of images by . 265 concave, foci of 266 formation of images by . 267 magnifying 289 illuminating power of . 290 crystalline 286 Level surface defined 145 spirit 146 Levers 77 illustrations of 78 bent 79 compound 81 applications of 81 Leyden jar 387 theory of 388 Light, wave theory of 238 sources of 239 velocity of 240 pencils and beams of . . . .241 intensity of 243 compared by shadows . 244 disposition of incident . . .246 absorption of 246 reflection of 247 diffused 247 intensity of reflected ... 248 refraction of 2-57 atmospheric refraction ... 259 total reflection 259 refraction by regular surfaces 261 by prisms 262 by lenses 262 decomposition of 268 dispersion of 271 homogeneous 273 properties of 277 interference of 278 length of waves 279 double refraction of .... 297 polarized 298 464 NATURAL PHILOSOPHY. Li-lit, electric 414 Lightning 398 conductors 399 Liquids, defined 8 compressible 135 transmission of pressure by . 136 effect of gravity on .... 138 pressure of 139 in motion 163 equilibrium of 144 buoyancy of 147 in motion 160 range of flowing 161 volume discharged . . . .162 velocity of discharge . . . .162 waves in 198 as conductors of heat ... 333 diathermancy of 342 as conductors of electricity . 406 Liquefaction of vapors .... 327 Load, defined 74 Loadstone 364 Luminous tube 393 Luminous bodies 238 Luminous effects of statical elec- tricity 393 Machine, defined 74 advantages of 76 Machines, simple 77 compound 98 recapitulated 100 useful effect of 105 for water power 166 for raising water 190 electrical 383 magneto-electrical .... 438 Magnetism 364 induction of 366 terrestrial 368 source of 373 Ampere's theory of . . . . 428 Ma-nets 364 how prepared 427 When saturated 428 Magnetic battery 367 Magnetic substances :;I;T Magnetic force, lines of .... Magnetic elements 369 changes of ,T72 Magnetic poles, terrestrial . . . :\i\'.t intensity 371 to-electrical induction . I.;: Magneto-electrical machine . . 438 Magic lantern 292 Magnitude 14 Malleability 35 Manometers 177 Marcet's globe 324 Mariotte's law 177 Matter, defined 7 properties of, classified . . . 11 Mechanics 51 Mechanism, human 99 Mechanical equivalent of heat . 350 Medium, for sound 217 for light 238 Melody 230 Melting points, table of . . . .316 Meniscus 262 Microphone 435,6 Microscopes, simple 289 compound 293 solar 292 Mirage 260 Mirrors 248 formation of images by plane 249 curved 251 concave spherical 251 formation of image of lu- minous point .... 251 formation of images by . 253 convex spherical 255 aberration of sphericity of . 250 Mobility 17 Molecules, defined 7 Molecular forces 9 energy of 354 Momentum 53 Monochord 225 Morse's telegraph 431 receiver 432 alphabet 4&S Motion, absolute and relative . 17 rate of 17 uniform and varied .... 52 Newton 'slaws of 54 simple and compound . . . 55 recapitulated 73 impediments to 100 circular 128 of waves 1!I7 Music, the pleasure in 2: ill major and minor modes . . 12-'!1 transposition in _':;:; Musical sounds . .225 INDEX. 465 Musical rate of vibration deter- mined 225 absolute number of vibra- tions in 228 interval 228 scales 229 instruments 23-1 Natural philosophy, defined . . 11 Near-sightedness 288 Needle, magnetic ; astatic Newcomen's engine 356 Newton's laws of motion ... 54 wheel 270 rings 278 telescope 296 Nodes 200 in pipes 236 Nodal lines 202 Octave in music 226 Oersted's discovery 422 Opera glass 296 Optics 238 Optic nerve, structure of ... 287 Optical instruments 284 Oscillation, center of 121 Osmose 48 Parallel motion 359 Pascal's experiment on pressure of liquids 141 with barometer 173 Pendulum 117 employed to determine grav- ity 120 compound 121 compensating 123 applied to clocks 124 Foucault's 125 ballistic 127 Penumbra 242 Percussion, center of 126 Phonograph, Edison's 214 Phosphorescence 239 Physics, defined 12 Pitch of sound 215 Pneumatics 172 Pneumatic paradox 19o Poles, of magnets 365 magnetic, of earth .... 369 of voltaic element . . .405 Polar force, defined 365 Polarized light, explanation of . 299 mused by double refraction . 298 by absorption 300 by reflection 301 by refraction 302 rotatory 303 applications of 304 Porosity 21 Power, defined 74 Pressure, transmission of in liq- uids 136 Problems 445 Projectiles 112 Pulley 89 Pump, lifting 191 air 164, 179 forcing 192 Pyrometer 306 Pyrheliometer 345 Quantity of electricity defined . 383 Radiant heat, disposition of . . 339 applications of 344 Radiation of light 241 of heat 338 Rainbow, formation of primary 281 of secondary 283 Range of projectiles 112 of spouting liquids . . . .161 Reaction in hard bodies .... 58 in soft bodies 62 Reaction wheels 168 Receiver, Morse's 432 Reflection, of solids 61 of waves 209 of sound 222 of light 247 total 259 of heat 339 Refraction, of sound 224 of light 257 index of 258 laws of 259 atmospheric 259 by regular surfaces . . . 261 by prisms 262 by lenses 262 double 297 of heat 340 Relay 433 Resistance, defined 64 466 NATURAL PHILOSOPHY. Resistance of fluids 103 Resolution of forces 57 Refinance 1224 Resonant bodies 216 Rest 17 Retina, duration of impression on 287 Rigidity of cords 103 Rivers, velocity of 165 Ruhmkorfs coil 440 Safety, position of, in thunder storms 398 Safety valve 357 Scale, chromatic . . 232 diatonic 226 natural, in music 233 thermometric 309 Screw 96 law of 96 differential 97 applications of 98 endless 98 Shadows 241 used to measure intensity of light 244 Sight to what due 287 Siphon 193 Size of objects, how estimated . 245 Smee's battery 409 Soft ruing of steel 3fi Solenoid 424 Solution 42 Solvent powers 43 Sound, deflued 212, 214 conditions requisite for . . 213 quality of 214 intensity of 215 distance of audibility . . .218 velocity of 219 co-existence <>f 221 combination and interfer- ence of 222 reflection of -222 refraction of 224 Sounds, musical 225 laws of L'_7 rate determined 22S Speaking trumpet 219 Specific heat :;i.; how a>c.-rt ained 313 tables of 314 effect of, in nature 315 Specific gravity, defined. ... 23 tables of 24 standard of 152 how ascertained 152 for heavy solids .... 153 for light sol ids 154 for soluble solids .... 154 for liquids 154 for gases 158 practical applications of . .158 Spectrum, solar 269 dark lines in 271 explanation of 276 reversed 276 properties of 277 Spectrum analysis 273 Spheroidal state 325 Spirit level 146 Statics, defined 51 considered 74 Statics and dynamics, general . 51 Stability of solids 70 applications of 72 of floating bodies 152 Steam, mechanical power of . .362 temperature of 324 superheated 325 Steam engine 356 Steam boilers 362 Steel, how tempered 37 how magnetized 427 Steelyard 81 Strength, ultimate and proof . . 31 on what dependent .... 32 Strength of materials 31 Stereoscope 291 Sublimation 319 Tables, of weights 16 velocities 18 specific gravity 24 units of pressure 26 direction of strain 29 ultimate strength 32 elasticity 32 hardness of minerals ... 35 relative malleability, etc. . . 36 solubility of uases 44 absorption of gases .... 45 co-efficients of friction . . . 103 friction of wagons on roads . 103 useful i-H'ert of machines . . 105 atmospheric pressure ... 187 INDEX. 467 Tables, of velocity of sound . . 22u indices of refraction .... 258 wave lengths of colors . . .279 expansion by heat .... 311 specific heat 314 melting points 316 latent heat of liquids . . .318 boiling points 322 at different pressures . . 324 at different levels . . .324 latent heat of vapors ... 329 volume of different vapors . 331 thermal conductivity ... 333 reflecting powers 339 diathermancy of solids . . 341 of liquids 342 of gases 342 radiating, reflecting, and ab- sorbent powers 343 heat of combustion .... 348 secular magnetic changes . 372 conductors and insulators . 375 electrics . 376 electro-motive series .... 404 powers of current conduction 406 electro-chemical series . . .417 Telegraph, electric 430 Wheatstone's 431 Morse's 431 House's and Hughes 's ... 435 Telescope 293 astronomical 294 terrestrial 295 Galileo's 295 reflecting 296 Herschel's 296 Newton's 296 equatorial 294 Tempering 37 Temperature 308 Tenacity, defined 31 how increased 34 Tension of aeriform bodies . . 171 how ascertained 176 Thermo-electricity 411 Thermo-multiplier 442 | Thermometer 308 ' Thermal unit 313 Throttle valve 360 Thunder 398 Tone, musical 215 ! major and minor 230 semitone 230 i Torricelli, theorem of 161 barometer 173 Tourmaline pincette 300 Transposition in music .... 233 Turbines 168 Umbra 241 Undulations 196 formation of 197 progressive 198 of solids 198 of liquids, surface 198 stationary 199 progressive changed to sta- tionary 200 in fluids 202 in aeriform bodies .... 205 of light 278 Units of weight and measure . 15 pressure 26 velocity and time 52 thermal 313 Vapors, defined 171 Vaporization 319 Velocity, defined 17, 52 table of 18 of uniformly varied motion 53 of falling bodies . . *. . .106 increment of 109 laws of 110 of bodies thrown upward . .112 of liquids 161 Vena contracta 163 Vesicular condition 45 Vibrations, of pendulums . . .118 of cords 198 simple and complete .... 199 of elastic solids 201 simultaneous 211 recapitulation 212 sympathetic 217 of sonorous cords 225 absolute rate of 228 of light 238 Vision, to what due 287 limits of distinct 288 anomalies of 289 Voltaic element, simple .... 401 batteries 407 arc 415 Voltameter 417 Volume 14 468 NATURAL PHILOSOPHY. Warmth, sensation of .... 305 Water, expansion of 312 specific gravity 152 a standard for temperature . 308 specific heat 313 latent heat 317 effect on climate . . . 315, 318 evaporation of 320 tables of boiling points of . 324 frozen by its own evapora- tion 330 Water power 166 Water wheels 166 Watt's steam engine 358 Wave motion described .... 197 surface of fluids 198 combination and interfer- ence of 203 Waves, of the sea 204 of condensation and rarefac- tion 205 velocity of 208 intensity of 208 combination and inter- ference of 208 reflection of 209 Waves, co-existence of sono- rous 21 length of sonorous .... 228 length of luminous . . . .279 Wedge, law of 95 applications of 95 Weight, absolute 15 specific "23 Weighing, modes of 81 method of double 84 Wheatstone's telegraph . . . .431 Wheel and axle 84 law of 85 differential 86 WlK-rls, train of 86 how connected 88 water 106 Wilde's magneto-electrical ma- chine 439 Windlass 85 Winds 337 Winter's electrical machine . .383 Work, defined 74 how calculated 75 relation between, and heat . 350 interior 353 ECLECTIC EDUCATIONAL SERIES. Published by VAN ANTWERP, BRAGG & CO., Cincinnati and New York. ECLECTIC MANUAL OF METHODS FOR THE ASSISTANCE OF TEACHERS. How to teach Language. How to teach Grammar. How to teach Composition. How to teach Geography. How to teach Reading. How to teach History. How to teach Arithmetic. How to teach Penmanship. How to teach Physiology. Especially adapted to assist the many teachers using the text-books of the Eclectic Series. This Manual is the outgrowth of numerous requests from young and inexperienced teachers of country schools in nearly every part of the United States, for assistance in their work. While it is, therefore, addressed particularly to this class, it is hoped that it contains many suggestions which will prove useful also to teachers generally. During the past few years there has been a strenuous effort made in many States to evolve some degree of symmetry and order out of the chaos in which the ungraded schools have heretofore existed. Superintendents have held meetings, and discussed methods and the proper use of text-books ; they have also, in many cases, issued manu- als to their teachers, setting forth the results of the conferences, and making many valuable suggestions as to the future conduct of the schools. These manuals, although frequently differing in unessential details, agree in recommending a definite and uniform course of study, and, as far as practicable, a uniformity of text-books in classes. Wherever these suggestions of the superintendents have been fol- lowed, the schools, without exception, have been improved in char- acter. But many difficulties confront the inexperienced teacher, regarding which he receives no aid from the Superintendents' Manual. Not the least of these, perhaps, is owing to the fact that he does not understand how to use his text-books to the best advantage. It has been the endeavor to show, in the Eclectic Manual, what the method is for each subject, and how it should be applied. Bound in full cloth ; 262 pages. Single specimen copy for examination with a view to first introduction, 60 cents. " The Eclectic Manual is a safe and reliable guide for the teacher, whether in the graded or ungraded school." J. M. GREENWOOD, Supt. ScJiools, Kansas City. " I have examined the Eclectic Manual of Methods and think it well adapted to secure the results aimed at." H. K. EDSON, Ch. of Didactics, Iowa College. "I congratulate you on the Eclectic Manual of Methods. It ought to have a wide sale, and will doubtless be of vast benefit to all classes of teachers, but especially to those who struggle against the heavy odds of unclassified schools." H. C. SPEEK, late State Supt. Kansas. Eclectic Educational Series. Duffefs New French Method, BY F. BUFFET, PARIS, FRANCE. Revised by ALFRED HENNEQUIN, A. M., University of Michigan. 12mo., cloth, 394 pp. From the Preface : THIS revised edition of Professor Buffet's FRENCH METHOD does not differ in the main from the original work, which lias, in a very short time, become so favorably known in Europe and in this country. It is still an eminently "Progressive and Practical Method for the Study of the French Language." The object to be obtained in studying a foreign language is certainly to understand it, to speak it, and to write it at the earliest possible moment. With this in view, Professor Buffet introduces the student to the language itself in its most useful and practical forms from the very beginning. It is, in fact, a colloquial grammar, simple, but thorough, short, and complete. We do not claim, as reviser, to have added much to the intrinsic value of the work. Our object has been to adapt the book to the re- quirements of American schools and colleges. Most of the important changes that have been made occur in Part First, in which have been introduced numerous tables and diagrams, explaining the parts of speech in a more systematic form than Professor Buffet had attempted. Short rules have also been given where deemed advisable, and many of the original rules have been re-worded. PART SECOND has called for very few changes aside from the intro- duction of Tables and Biagrams. The order of the Rules of Syntax has been maintained. The verbs have also been left in the order given by Professor Buffet, and the same classification retained. We have, however, given an enlarged formation of the tenses, adding numerous references to the same, thereby doing away, to a very great extent, with the mechani- cal memorizing of the irregular verbs. Various other minor changes have also been made in the verbs, mostly through the introduction of Tables and Biagrams. University of Michigan, Ann Arbor. ALFREB HENNEQUIN. KEY TO DUFFETS FRENCH METHOD. Duffei* s French Literature, Brief Extracts in Prose and Poetry from the writings of Fifty of the best French writers. I2mo., cloth, 168 pp. PUBLISHED BY VAN ANTWERP, BRAGG & CO., Cincinnati and New York. ECLECTIC EDUCATIONAL SERIES. Published by VAN ANTWERP, BRAGG & CO., Cincinnati and New York. ENGLISH LANGUAGE. HARVEY'S LANGUAGE COURSE. By THOMAS W. HARVEY, A. M. HARVEY'S REVISED ELEMENTARY GRAMMAR AND COMPOSITION. I2mo., cloth, 160 pp. HARVEY'S REVISED ENGLISH GRAMMAR, larno., half roan, 264 pp. A practical course in Oral and Written Language Lessons, Com- position and English Grammar. The Golden Mean between the too labored attempt at simplification, and thescientific technical gram- mar. HOLBROOK'S NORMAL SERIES. By A. HOLBROOK, Principal National Normal University. HOLBROOK'S TRAINING LESSONS, lamo., 135 pp. HOLBROOK'S COMPLETE ENGLISH GRAMMAR, I2mo., cloth, 204 pp. PINNEO'S GUIDE TO COMPOSITION A Series of Practical Lessons designed to simplify the Art of Writing Composition, By T. S. PINNEO, A. M., M. D. i2mo, cloth, 162 pp. Designed for those who desire a concise but comprehensive course of Instruction in Composition. PINNEO'S EXERCISES IN FALSE SYNTAX. izmo., 104 pp. Systematically arranged ; contains, also, promiscuous examples of correct and incorrect syntax. PINNEO'S EXERCISES IN PARSING AND ANALYSIS. i2mo., 120 pp. A brief review of the leading principles of Grammar, conveniently arranged for reference ; followed by a well-arranged series of selections from the besl authors, with explanatory notes and references. WILLIAMS'S PARSER'S MANUAL. The Parser's Manual, embracing classified examples in nearly every variety of English construction. By JOHN WILLIAMS, A. M. izmo., cloth, 264 pp. OBJECT LESSONS AND COMPOSITION. Things Taught : Systematic Instruction in Composition and Object Lessons. By Dr. M. E. LILIENTHAL and ROBT. ALLYN, M. A. Prepared by order of the Cin- cinnati School Board. i6mo., 96 pp. LANGUAGE EXERCISES. For Primary Classses. By J. MICKLEBOROUGH, Prin. Cincinnati Normal School, and C. C. LONG, Prin. 2oth District School, Cincinnati. PART I. For First and Second Reader classes, i2mo., 48 pp. Part II. For Third and Fourth Reader classes, 12010- , 96 pp TEACHER'S EDITION, i2mo., 187 pp. Contains Parts I and II ; Course of Study in Language Lessons for Cincinnati Schools ; plans for developing the Exercises and methods for presenting them; and much valuable information and many suggestive hints for the successful teaching of Language. These Exercises follow the Language Course lately adopted by the Cincinnati Peda- gogical Association. ECLECTIC EDUCATIONAL SERIES. VAN ANTWERP, BRAGG & CO., Publishers, Cincinnati and New York. NORTON'S CHEMISTRY. THE ELEMENTS OF CHEMISTRY. BY SIDNEY A. NORTON, A.M., M. D. I2mo, cloth, 504 pages. The present edition has been thoroughly revised and has also been enlarged by the introduction of a dozen chapters treating of OKC.AMC CHEMISTRY. This work is intended as a text-book, not as a manual for reference. The author has endeavored to select such chemical phenomena as represent the cardinal principles of the science, giving preference to those which are easily reproduced by the student, and which enter into the affairs of common life. To attain this end, he has omitted many excellent experiments which require the use of expensive apparatus, and has substituted others which, if less " classical," are of easier application. The engravings represent well-fashioned apparatus; but no one ought to be deterred from attempting an experiment because he has not the exact shaped figure. Any drug-store or kitchen will afford bottles and tumblers, which may be used in place of flasks and beakers. In some way, the experiments ought to be tried. As regards nomenclature, the author has endeavored to follow as closely as possible, in a work of this size, the rules of the London Chemical Society. Old and well-known names have been retained because of their common use. As regards notation, it must be born in mind that all formula" are alike subject to change. No greater mistake can be made than that any formula (except a binary) tells the whole truth about a molecule, or that any formula which correctly represents the percent- age composition of a substance may not be, at times, available in fixing in the mind of the student the fact to be remembered. The author has, therefore, used the formula that appeared convenient at the time ; and feels that an experience of twenty years' teaching war- rants him in advising his fellow-teachers hot to attempt to place theory above practice. 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