ECLECTIC EDUCATIONAL SERIES. THE ELEMENTS OF PHYSICS A TEXT-BOOK FOR ACADEMIES AND COMMON SCHOOLS BY SIDNEY A. NORTON, A. M. WILSON, HINKLE & CO. 137 WALNUT STREET 28 BOND STREET CINCINNATI ,NEW YORK TO PjU'AA COPYRIGHT, 1875, BY WILSON, HINKLE & CO. ELECTROTVPED AT FRANKLIN TYPE FOUNDRY, CINCINNATI. ECLECTIC PRESS : WILSON, HINKLE & CO. CINCINNATI. PREFACE. This volume lias been prepared, at the request of many teachers, for the use of pupils in academies and common schools. The topics considered have been selected with ref- erence both to the average age of such pupils and to the time usually allotted to the study of Physics. The object of this book is not merely to give a system- atic and symmetrical epitome of the Science, but so to pre- sent each topic that the pupil shall receive, from the first, clear, accurate, and scientific ideas. In no other way can the study of any science be made a means of mental dis- cipline. No pains have been spared to attain this result; and it is hoped that, however much has been omitted that many teachers would desire to have presented, the pupil will, at least, have nothing to unlearn. 869010 TABLE OF CONTENTS. CHAPTER I. GKKERAL NOTIONS OF MATTER AND FORCE . CHAPTER II. PHENOMENA CONNECTED WITH COHESION 27 . CHAPTER III. PHENOMENA CONNECTED WITH ADHESION 33 CHAPTER IV. THE LAWS OP MOTION 41 CHAPTER V. PHENOMENA CONNECTED WITH GRAVITATION 50 CHAPTER VI. THE LAWS OP FALLING BODIES 5? CHAPTER VII. THE PENDULUM 65 vi CONTENTS. CHAPTER VIII. PAGX SIMPLE MACHINES 72 CHAPTER IX. FLUIDS AT REST . .91 CHAPTER X. FLUIDS IN MOTION 103 CHAPTER XI. THE PHENOMENA OP AERIFORM FLUIDS 108 CHAPTER XII. , THE MODES OF MOLECULAR MOTION 128 CHAPTER XIII. ACOUSTICS, OR THE PHENOMENA OF SOUND 135 CHAPTER XIV. OPTICS, OR THE PHENOMENA OF LIGHT 153 CHAPTER XV. THE PHENOMENA OF HEAT, OR PYRONOMICS 196 CHAPTER XVI. ELECTRICITY . 228 THE ELEMENTS OF PHYSIOS. CHAPTER I. GENERAL NOTIONS OF MATTER AND FORCE. 1. Matter is any thing that is capable of affecting our senses. The objects that surround us, the food we eat, the water we drink, the air we breathe, are different forms of matter. 2. A body is any separate portion of matter, whether large or small: thus a mountain, a pebble, or a dew-drop, is a body. The different materials of which bodies are composed are called substances: thus iron, wood, and sugar are substances. 3. Some substances contain but one kind of matter. These are called simple substances, or the ELEMENTS. There are sixty-three elements now known. The most abundant of these are oxygen, silicon, aluminium, iron, calcium, mag- nesium, sodium, potassium, nitrogen, hydrogen, and carbon. 4. Compound substances are composed of at least two elements, so firmly united that they can not be separated except by chemical processes. These compound substances make up the bulk of the globe : thus water is composed of (7) 8 ELEMENTS OF PHYSICS. oxygen and hydrogen ; quartz and white sand, of silicon and oxygen; clay, mainly of silicon, oxygen, and aluminium. * X ,5. Many^odies are mixtures of several substances: thus , gunpowder is a mixture of niter, carbon, and sulphur. The ^ahvfe al&o "a mixture. The most important of its constituents are oxygen, nitrogen, carbonic acid, and the vapor of water. 6. Many substances can exist at different times in three different states: thus water can exist as ice, as water, or as steam. A body is in the solid state when its particles are held firmly together, and retain the shape that has been given them by nature or art. Ice, wood, and tallow are solids. A body is in the liquid state when its particles easily change their relative positions. When a liquid is poured into an open vessel, it adapts itself to the shape of the vessel, except that its upper surface is horizontal. Water, alcohol, and oil are liquids. A body is in the aeriform state when its particles tend to separate from each other, and to occupy a greater volume. Bodies in this state are called aeriform bodies, gases, or vapors. Aeriform bodies can not be retained in an open vessel ; and when shut in on all sides, completely fill the vessel in which they are placed. Steam, the air, and illuminating gas are aeriform bodies. The term fluid is applied both to liquids and aeriform bodies : thus we may speak of water as a liquid or as a fluid; or of air as an aeriform body or as fluid. 7. No one can conceive of a body which does not possess length, breadth, and thickness. Even the fine particles of dust which are seen only in the path of the sunbeam must have a certain shape or figure, and occupy a certain amount of space. The amount of space that a body occupies is called its bulk or volume. MEASURES. 9 The ordinary measures in the United States are derived from an arbitrary unit called the yard ; although we may use any one of its divisions or multiples as a unit as the inch, foot, or mile. The square inch, square yard, etc., are units of sur- face. The cubic inch, cubic foot, etc., are units of volume. The wine gallon of the United States contains 231 cubic inches. The imperial gallon of England contains 277.274 cubic inches. The French unit of length is the metre, which is equal to 39.3685 of our inches. All the French measures increase or de- crease in decimal proportion. For the increase the Greek prefixes deca (10), hecto (100), and kilo (1000), are used; for the decrease the Latin prefixes deci ( T L), centi (y^j-), and milli (^Vir)' are used. A decimetre is drawn in Figure 1, in comparison with a scale of inches. One inch is very nearly 25.4 millimetres. The French unit of volume is a cubic decimetre, and is called the litre. It contains 61.022 cubic inches, or 2.113 wine pints. 8. All bodies may be divided into very minute particles: thus stones may be crushed to powder; the hardest steel may be broken; and even the diamond may be reduced to dust. Wonderful ex- amples of minute divisibility are afforded by odors and coloring matters. Odors can be caused only by particles of matter FIG. i. in the air; and yet how small must those be that enable a hound to follow his game ! A grain of musk has perfumed 10 ELEMENTS OF PHYSICS. a large apartment for several years without perceptibly los- ing in Aveight. An ounce of aniline is capable of coloring two hundred ounces of silk thread. We may separate this thread into 3,000,000,000,000 parts and discern the red color of the aniline in each one of them. Many chemical tests reveal the presence of exceedingly small quantities of matter. If a grain of iron or of copper be dissolved in nitric acid, and then added to a tumblerful of water, the presence of either metal may be detected in every part of the mixture. This may be done by placing a drop of the solution on a watch-glass and then adding a solu- tion of ferrocyanide of potassium, when the iron solution will be turned blue, and the copper solution will be reddened. Even by mechanical means we may obtain particles so small that it is difficult to form just conceptions of their size. Gold leaf is sometimes so thin that fifteen hundred leaves placed one above another will not equal the thickness of ordinary paper. One square inch of this leaf weighs less than one twenty-thousandth part of an ounce ; and we can divide this into ten-thousand parts, each one of which is distinctly visible to the eye, though weighing less than one two-hundred-millionth part of an ounce. 9. There are many reasons for believing that there is a limit to the divisibility of matter. The smallest eonceiv- able particle of water, or of any compound body, is called a molecule. A molecule is so small that no microscope -will ever enable us to see it. It is the smallest particle into which a body may be divided without losing its identity. 10. By chemical means a molecule of water may be still further divided into its components oxygen and hydrogen, and thus particles obtained which are the smallest conceiv- able. These are called atoms. An atom is the smallest particle of matter capable of entering into a molecule. POROSITY. 11 11. How the atoms are arranged to form molecules, or how the molecules are arranged in bodies, is unknown. We know that all bodies expand when heated, and contract when cooled. # Thus, if an empty flask is inverted in a vessel of water, and heat is applied (Fig. 2), the air will expand so much that a portion will be expelled. On cooling, the air remaining in the flask will resume its original volume. We know also that all bodies are made smaller by pressure : thus a bottle of ' ' soda water " contains several times its volume of compressed gas, which expands to its original volume when the cork is removed. All bodies are expansible and compressible. Gases FIG. 2. show these properties very readily, but they are also exhi- bited by solids and liquids. These and similar phenomena render it probable (1) that the molecules of a body do not touch each other, but are sep- arated by vacant spaces or pores ; and (2) that the molecules are free to move even in the most rigid bodies. When bodies expand, the molecules separate, and the pores become larger ; when bodies contract, the molecules approach, and the pores become smaller. 12. The pores of bodies are of two kinds. (1) Those which exist between molecules are called physical pores. These are so small that they can not be seen even by the aid. of a microscope. (2) Sensible pores are cavities that may be seen, as the pores in bread, or in some kinds of wood. If water is heated in a glass vessel, bubbles of air sep- *When clay is heated, it contracts permanently, because its par- ticles suffer a chemical change. 12 ELEMENTS OF PHYSICS. arate out and cling for a time to the sides of the vessel. These must have come from the physical pores of the water. So also, if a cup be filled to the brim with hot water, two or three spoonfuls of pulverized sugar may be gradually added before the cup overflows. The molecules of the sugar find sufficient space in the pores of the water. Sometimes an actual contraction of volume occurs on mixing two liquids. Thus, if a long and slender test-tube be half filled with water, and strong alcohol be poured carefully in, so as not to mix the two liquids until the tube is quite filled, and then the tube be tightly closed and inverted, the liquids will mix and no longer fill the tube. The explanation of this phenomenon is that the molecules of the alcohol and the water are mutually so arranged as partially to fill the pores previously existing in the two bodies. 13. We do not believe it possible that any two particles of matter can occupy the same place at the same time. In other words, we believe that matter is impenetrable. If a pebble be dropped into a tumblerful of water, enough water will overflow to equal the bulk of the pebble. The ex- amples given in the preceding section are only apparent exceptions to the property of impenetrability. There are other apparent exceptions, which can be even more readily explained. 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 fill the tube because of the impenetrability of the air inclosed in the tube. Nevertheless it will be seen that the water will rise a little way in the tube; but this is because the air is compressed, and so allows space for the water to enter. An easy experiment, which illustrates the same fact, may be made by wrapping moistened paper around the tube of a DENSITY. 13 funnel, so that it may be made to fit air-tight in the neck of a bottle, as shown in Fig. 3. Now, if water be quickly poured into the funnel, only so much will enter the bottle as corresponds to the compressed or displaced air. 14. Space which contains no matter is called a vacuum. 15. Bodies vary greatly with respect to the pores which they contain. Those that contain FlG - 3 - large pores are called rare bodies ; those that have small pores are called dense bodies. Density is, therefore, a term which expresses the relative amount of matter which equal volumes of different substances contain. Iron, for example, is denser than stone, but is less dense than gold. In com- paring the relative density of bodies, it is convenient to select some substance which shall be taken as the standard of comparison, and reckoned as unity, or 1. Thus the air is a standard of density for all aeriform bodies, and water is a standard of density for liquids and solids. It is also nec- essary to select some temperature at which the comparison shall be made. The temperature usually taken is 32 F. for all bodies excepting water, which is unity when at 39. 2 F. In the case of gases, it is also necessary that they should be compared when under the same pressure. The pressure as- sumed is the average pressure of the atmosphere at the level of the sea, which is 14.7 pounds to the square inch, and which equals a column of mercury 29.92 inches high.* These are called the normal conditions of temperature and pressure. 16. The ratio which shows how many times heavier any given substance is than an equal volume of water or of air, *Sec Section 31. 14 ELEMENTS OF PHYSICS. under the normal conditions, is the specific gravity of the sub- stance. The specific gravity of chlorine gas is 2.47, which means that a given bulk of chlorine, as a pint or a gallon, is 2.47 times heavier than the same bulk of air. The specific gravity of silver is 10.5, which means that a given bulk of silver, as a cubic inch, weighs 10.5 times more than the same bulk of water. Weights of the Standards. One cubic inch of air weighs, at 32 F., 0.32712 grains. at 60 F., 0.30954 grains. One cubic in. of water weighs, at 32 F., 252.875 grains. at 60 F., 252.456 grains. Specific Gravities Compared. at 32 F. at 62 F. Katio of air to water, 1 to 773.2 1 to 816.8 Ratio of water to air, 1 to .00129363 1 to .0012243 Table of Specific Gravities. Air, 1. Cork, 0.24 Steam, .622 Ice, 0.93 Hydrogen, .069 White Oak, 0.86 Oxygen, 1.106 Ebony, 1.33 LIQUIDS. Glass, 3. Pure Water, 1. Iron, 7.78 Sea Water, 1.026 Copper, 8.85 Olive Oil, 0.915 Lead, 11.35 Sulphuric Acid, 1.84 Gold, 19.26 Saturated Brine, 1.205 Platinum, 21.53 17. Matter is every- where subject to change. When the smith heats a bar of steel, it expands ; when he beats it on his anvil, he is changing its form; when he hurls it from MOTION. 15 him, he is changing its position. If the steel be rubbed on a magnet, it acquires the property of attracting iron filings. It may be melted to a fluid state and cast into any shape. Such changes as these are called physical changes. Physical changes are those by which the substance is not altered so as to lose its identity. On the other hand, in chemical changes the identity of the substance is entirely lost. Thus, when steel rusts, the red powder which forms is due to a chemical change in which water has been decomposed into oxygen and hydrogen ; the oxygen has united with the iron in the steel, to form a new kind of substance, and the hydrogen has escaped into the air. So, also, the decay of leaves, the burning of wood, the souring of cider, are chemical changes. 18. Force is that which causes any change in the form or condition of matter. All the phenomena of the visible universe are caused by the action of force upon matter. The simplest change in matter is that of position. We determine the motion or rest of a body by its relation to some given point ; but as this point may be itself fixed or moving, motion or rest is either (1) absolute, or (2) relative. 19. Absolute motion is change of place with regard to a fixed point : relative motion is change of place with regard to a point in motion. The motion of the heavenly bodies with reference to ideal fixed points in space are examples of absolute motion. Strictly speaking, no bodies are in a state of absolute rest. Every particle on the earth's surface partakes of all the daily and annual motions of the earth; and, therefore, the terms absolute motion and rest, when applied to bodies on the earth's surface, have reference to objects that appear fixed. A person seated on a steamboat in motion is in absolute motion with respect to the harbor he has left, or to the har- 16 ELEMENTS OF PHYSICS. bor he is approaching, and is in a state of relative rest with regard to the parts of the vessel. If he walks toward the stern of the boat as fast as the vessel moves forward, he is in a state of relative motion with regard to the parts of the vessel, but is in absolute rest with regard to the harbors. 20. Velocity is the rate of motion. It may be found by dividing the space passed over by the time occupied in the transit. Thus, if a locomotive is five hours in going one hundred miles, its velocity is twenty miles an hour. The formula, v = s -f- 1 Expresses the relation between space, time, and velocity. 21. A natural unit of time is the day, but any of its subdivisions hour, minute, or second may be assumed as convenience dictates. Table of Velocities. MILES PER HOUR. FEET PER SECOND. Man walking, 3 4.4 Man running, 10 14.66 Swift trotting horse, 27 40. A rifle ball, 1,000 1,466.66 Sound, 762 1,117.6 22. Motion and rest are equally natural to a body. When the forces that are acting upon matter exactly balance each other, it is at rest, and is in motion when they do not. We say, then, that matter has the property of inertia, by which we mean that it tends to retain its present state, whether of motion or of rest. It requires some force to set a body in motion, and when it is in motion, it requires force to stop it. The inertia of the air becomes manifest by the resistance it offers to a body moving through it. If we endeavor to run with an open umbrella, we need to employ considerable force to overcome FORCES IN NATURE. 17 the resistance of the air, because we shall have to displace or set in motion the air which is in front of us. The heavier a body is, the greater will be its inertia ; that is, it will require more force than a lighter body to set it in motion, or to stop it when it is moving. Thus, a small boy will easily "dodge" a larger, because the heavier boy will be unable to -change his course at once. A person standing in a wagon partakes of its condition of motion or rest. If it is suddenly set in motion, he is thrown backward, because his feet are drawn along by the friction against the bottom, before his head can acquire the motion, forward. If the wagon is suddenly stopped when in rapid motion, he is thrown forward. 23. There are many forces in Nature, and it is conven- ient to divide them into three classes. (1) Those which act only upon the molecules of matter, and at distances which are inappreciable to our senses. These are named Cohesion, Adhesion, and Affinity. Taken collect- ively, they are called the molecular forces. (2) Those which act also upon bodies taken as a whole, and at both sensible and insensible distances. These are Gravitation, Light, Heat, and Electricity. (3) Those which take part in the phenomena of living plants and animals by controlling or modifying the forces of inanimate nature. These are called the vital forces. 24. Cohesion causes like molecules to unite in one mass. It keeps the particles of a body together. It is strongly ex- erted in solids, feebly in liquids, and not at all in aeriform bodies. Thus a dew-drop is spheroidal because of the co- hesive force. When the drop is very large it becomes flat- tened, because the force of cohesion is partly overcome by the force of gravitation. The following pretty experiment illustrates the tendency PHYS. 2. 18 ELEMENTS OF PHYSICS. of liquids to assume the spheroidal form : Take a wine-glass half full of water, and carefully fill it with alcohol so as not to mix the two liquids ; then drop a very little olive oil through the alcohol. It will come to rest in the middle of the glass, and, if the quantity taken is not too great, will as- sume the shape of a ball. When the cohesion of solids has been once destroyed, it is difficult to cause the particles to reunite. If a bar of lead be cut in two, the several parts may be made to cohere by so cutting their faces that they will present a bright and even surface, and then pressing them tightly together with a slight twisting motion. Two plates of polished glass will cohere, under pressure, so firmly that they may be worked as a single piece. 25. Adhesion causes the molecules of different kinds of matter to cling together. Thus, adhesion causes the dust to cling to any thing it falls upon ; chalk to cling to black- boards, and dew-drops to leaves. Under the name of Friction it diminishes the work of moving force, (1) by stiffening the joints of machines, (2) by increasing the resistance to be overcome. Friction often acts as a mechanical advantage, as in retaining nails and screws in their sockets, in preventing our feet from slipping when - standing or walking, and in en- abling us to take firm hold upon objects. 26. Affinity causes the atoms of unlike substances to unite and form new kinds of matter. All chemical phe- nomena are due to affinity. When iron dissolves in nitric acid a new kind of matter (the nitrate of iron), differing both from the iron and the acid, is formed. 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 acted upon. They differ from each other in this, that adhesion acts between unlike par- GRAVITATION. 19 tides, and cohesion between like particles. They all agree in this, that their energy increases with the number of mole- cules that are acted upon. This statement, when applied to solids, may be expressed in these words : the energy of molecular forces increases with the extent of surface exposed to their action. 27. Gravitation is a force by virtue of which every par- ticle of matter attracts every other particle of matter toward itself. The term mass is used to- denote the amount of matter in a body, and it has been established that gravity is propor- tional to mass. If a stone were dropped from a balloon it would fall to- ward the earth by reason of the attraction of the earth, or terrestrial gravitation. The earth also tends to fall toward the stone, but its mass is so much the greater that its motion is inconceivably small. But gravitation does not always produce motion. A stone resting on the top of a table is not free to fall, and, in such a case, the force of the earth's attraction is expended in pressure against its support. This pressure is called the ab- solute weight of the body. Hence, weight is the measure of the earth's attraction. 28. Gravity is also influenced by distance, as will be shown hereafter. An iron ball which weighs one hundred and ninety-four pounds at the equator will weigh one hundred and ninety-five pounds at the poles. Hence, weight does not always mean the same as mass, for a body will always contain the same amount of matter in every conceivable place. Nevertheless, as weight is always proportional to mass, we may use weight as a means of estimating mass, or, in most instances, use the two terms interchangeably without sensible error. 20 ELEMENTS OF PHYSICS. 29. Universal gravitation is the same force applied to the heavenly bodies. It is by reason of this force that the earth and other planets move round the sun. 30. 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 equals 15.434 grains; a kilogramme equals 15434 grains, or 2.2046 avoirdupois pounds. Weight in pounds of one cubic foot at 62 F. Air, . 0.080728 Water, 62.418 Mercury, 848.75 Potassium, 53. Wrought Iron, 480. Copper, 556. Lead, 712. Gold, 1224. Gravitation is made serviceable to man in the force of running water, and in machinery moved by weights, as well as in giving stability to buildings and other structures. 31. The unit of pressure in most frequent use is the pressure of one at- mosphere. This pressure is due to the attraction of gravitation. We may ascertain its amount by the experiment of Torricelli. Fill a glass tube, thirty-two inches long, with mercury, close the open end firmly with the finger, and then invert it in a cistern of mercury, Fig. 4. On removing the finger, the mercury will fall a little way in the tube and leave a vacuum above it. Now, as the FlG - 4 - weight of the mercury tends to make it flow out of the EXPANSION BY HEAT. 21 tube, the column must be sustained by an equal and oppo- site force. This force can be nothing else than the pressure of the atmosphere; and, hence, this pressure may be meas- ured by the mercurial column. This apparatus is called a Barometer, and is used to measure the pressure of the air. At the level of the sea, and at 32 F., the average height of the mercurial column is 29.922 inches, or 760 millimetres. A column of this height, a square inch in section, weighs 14.73 pounds. We are accustomed to say that the pressure of the at- mosphere is nearly fifteen pounds to every square inch of surface. Table of Pressures. POUNDS ON THE SQUARE FOOT. POUNDS ON THE SQUARE INCH. One atmosphere, 2121.12 14.73 One foot of water, at 39.2 R, 62.425 0.4335 One inch of mercury, at 32 F., 70.73 0.4912 32. Heat tends to make the molecules of matter re- cede from each other. When a body is warmed, it becomes larger; when it is cooled, it contracts. The apparatus shown in Fig. 5 illus- trates the expansion of solids. This consists of a brass ball, so made that, at ordinary temperatures, it will pass easily through the ring, m. On heat- ing the ball, it will no longer pass through the ring. This increase of volume of a heated body must be due to a motion among the molecules, which tends continually to separate them. When this motion increases in intensity, the body be- comes warmer; when this motion decreases in intensity, the FIG. 5. 22 ELEMENTS OF PHYSICS. body becomes cooler. Hence, we may measure the intensity of the heat, or tfie temperature of a body, by the degree of the molecular motion, or by the expansion of bodies. 33. The Thermometer is an instrument which measures temperatures. The ordinary mercurial thermometer consists of a very small glass tube (Fig. 6), at one end of which is blown a bulb the bulb and part of the tube are filled with mercury. When the thermometer is placed near a source of heat, the column of mercury rises, and falls when it is removed, because of the expansion and contraction of the mercury. The glass also expands and contracts, but only one-seventh as much as the mercury; and so we have only to notice the apparent expansion of the mercury. In order to compare temperatures, we assume as standards the temperatures of melting ice and of water boiling, under the pressure of one atmosphere. These standards are called, respectively, the freezing and the boiling points. For greater convenience, arbitrary scales have been devised to designate small variations in the mercurial column. The freezing and boiling points are first determined, and the height of the column in each case is marked on the tube, or on the scale attached to it. The space between these is then divided into any number of equal parts, called degrees, and parts of the same length set off above and below the boil- ing points. The Centigrade scale marks the freezing point by 0, and the boiling by 100. Reaumer's scale marks the freezing point by 0, and the boiling by 80. FahrenJieit's scale marks the freezing point by 32, and the boiling by 212. MEASUREMENT OF HEAT. 23 These scales are distinguished by the letters C, K, and F. The divisions below zero are indicated by the negative sign. Thus, 10 signifies ten degrees below zero; 10, or +10, signifies ten degrees above zero. To compare these scales, we first notice the interval be- tween the freezing and boiling point, and find C = 100, R=80, F=180; hence, these are equal, or 1 C = 4 R 1 F. Now, if we remember that the zero of Fahrenheit's scale is 32 below the freezing point, we may convert one scale into another, thus: F = J R -f- 32 R= (F 32) f R = iC _ 34. The amount of heat in a body must not be con- founded with its temperature. It is evident that a pint of boiling water would have the same temperature as a gallon of boiling water, and would equally affect a thermometer. The relative amount of heat present in a body is measured by the thermal unit. This is the quantity of heat required to raise a pound of water from 32 F. to 33 F. Hence, a gallon of boiling water would contain eight times as many thermal units as a pint, and would be competent to melt eight times as much ice or snow. 35. The force of light is closely related to that of heat. It may seem strange that it is reckoned as a force ; but it is easy to show that it may produce change in matter. Thus, if the gases hydrogen and chlorine are mixed in equal quan- tities in the dark, they will not combine; but if exposed to the free sunlight, they will unite with explosive violence. The photographer's art depends on the force of light. Soak a strip of white newspaper in common salt brine and let it dry; when dry, again moisten it in a darkened room with a 24 ELEMENTS OF PHYSICS. sponge dipped in a solution of silver nitrate, and again dry it. This process covers the paper with white silver chloride. Now if this coated paper be placed in the sunlight, it will darken, showing that the light effects a change in the silver chloride. Moreover, in the grand laboratory of nature, light is an essential force. To define it, we select one of its prop- erties and say that "light is that mode of motion which ex- cites in us the sensation of vision." 36. The force of electricity is familiar to all, in its ap- plications to the telegraph, in the magnet, and in the flash of lightning. Its simplest effects may be shown by rubbing a glass rod briskly upon the coat-sleeve, and then presenting the rubbed end to small and dry pieces of paper. If the air is not too damp, the paper will be attracted to the rod, cling to it for a little while, and then fly off. Instead of the bits of paper, we may employ a light pith ball, suspended by a silk thread, Fig. 7. The ball will be first attracted and then repelled by the excited rod. We may use this phenomenon to define electricity as a force which becomes manifest by its peculiar phenomena of attraction and repulsion. 37. These are the only forces of inanimate nature of which we have any certain knowledge. They produce, by their action upon matter, secondary forces, which are employed by man in machines. Thus, the strength and elasticity of springs is mainly due to cohesion ; the action of glues and cements, to adhesion; the elastic FIG. 7. CONSERVATION OF FORCE. 25 force of steam, to heat; the power of running water, or of falling weights, to gravitation; the muscular strength of men, to cohesion, affinity, etc., modified by the vital forces. 38. However forces act upon bodies, the matter of which they are composed is not lost. When gunpowder is exploded, it disappears, leaving only for a moment a trace of smoke. It has, however, only undergone a chemical change, by which a part of its ingredients have been converted into gases. If the explosion is made in a sealed vessel, suffi- ciently strong to stand the shock, the vessel and its contents will not change in weight by the operation. Matter is in- destructible by any force that man can employ upon it. We are also justified in asserting that force is indestruct- ible. Affinity, electricity, heat, arid light, are so closely allied that the action of any one may induce the action of any other : thus a candle burns by reason of affinity, and gives out heat and light. For this reason these four are called correlative forces. NATURAL PHILOSOPHY OR PHYSICS treats of the physical changes which are produced by the action of force upon matter. RECAPITULATION. Bodies are classified f Solid, as ice. I. With regard to state as < Liquid, as water. (. Aeriform, as steam. TT iTT-i.i- f Simple, as oxygen. II. With regard to composition, < ( Compound, as water. Forces act I. Only on molecules, II. Also, on bodies, C Cohesion, -j Adhesion. (. Affinity. Gravitation. PHYS. 3. Also, on OOQL / Electricity. I Light. j Heat. ' Gravitation. 26 ELEMENTS OF PHYSICS. ' The general properties of matter are magnitude, weight, impene- trability, mobility, inertia, divisibility, porosity, compressibility, ex- pansibility. We estimate the action of forces by certain units. Among these are units of measure, units of volume, units of time, units of weight, units of pressure, units of heat. PROBLEMS. 1. How many centimetres are there in 29.922 inches? 2. How many inches are there in 0.994 metres? 3. How many square inches are there in a circle of one inch radius? of two inches radius? What is the ratio between the two areas? How many square centimetres are there in each circle ? ^4, How many cubic inches are there in one pint? How many cubic centimetres? How many litres? "N^ How many litres are there in a sphere of six inches radius? of one foot radius? What is the. ratio between the two volumes? How many gallons are there in each sphere ? 6. What will be the weight of each sphere if made of air? of water? of gold? Reckon each in pounds and also in grammes. 7. What will be the edge of a cube containing ten pounds of water? the radius of a sphere containing an equal weight of water? 8. From the table of specific gravities calculate the weight of a gallon of oxygen, of sulphuric acid, of cork, of silver. 9. What does a litre of dry air weigh in grammes? 10. What is the average velocity per minute of a locomotive that passes over 138 miles in six hours? 11. What will be the atmospheric pressure on a surface of six square inches in pounds? in grammes? On a surface of six inches square, in pounds? in kilogrammes? 12. What is the atmospheric pressure on one square centimetre in kilogrammes ? 13. Convert 25 C. to F. ; 50 C. to F. Can you say that 50 C. is twice as hot as 25 C. ? 14. Convert 62 F. to C. ; 39.2 F. to C. 15. If a gallon of boiling water will melt ten pounds of ice, how mucfc will be squired to melt one cubic foot ? CHAPTER II. PHENOMENA CONNECTED WITH COHESION. 39. The cohesion of solids may be estimated by the resistance which they offer to forces which tend to separate their particles. There are many ways by which the strength of a body may be tried. Among these are : (1) By a stretching force. We may hang a rubber tube from a hook, and pull it downward by a weight. The rubber will stretch, and, with a weight sufficiently heavy, will be torn in pieces. The strength which a body offers to a stretch- ing force is called its tenacity. The tenacity of metals is in- creased by drawing them into wires. A cable made of wires twisted together is far stronger than a chain of equal weight. Wire cables are used in suspension bridges for this reason. The suspension bridge at Cincinnati has a span of one thou- sand feet. (2) By a compressing force. If we place a weight on a small bar of wood, it will compress its particles and tend to crush the bar. When the bar is not allowed to bend, it offers the same resistance to pressure that it would to a stretching force. (3) By a bending force. If we fasten one end of a lath, placed horizontally in a vice, and apply a weight at the other end, it will bend and tend to break. The strength which the substance exhibits depends not only on the material but also on the manner in which the strain is applied. A sudden shock causes a much greater strain than a gradually increas- ing force of greater amount. So, also, the lath will support (27) 28 ELEMENTS OF PHYSICS. a greater weight when its broad side is placed vertically than when it is horizontal; then, also, the longer it is the less weight it will support. Finally, if both ends are supported, it will sustain half the weight, when it is concentrated at the center, that it will when distributed along its whole length. What is true of the lath, is also true of the beams used in houses, they are placed so as to receive the strain on their edges. The bones of animals, and the stalks of grain, are hollow. This is the most economical arrangement of a given weight of material. We may illustrate this fact by resting the ends of a flat sheet of paper on bricks, and ascertaining the force neces- sary to break it down ; then re- peat the test with a similar sheet of paper after having coiled it into a tube, Fig. 8. If a broad FlG> 8- strap is used to hang the weight from, a closely coiled tube of this sort will support three or four times as much weight as before.* (4) By a twisting strain. Suppose, when the lath is in the vice, we attempt to twist it. The force will tend to wrench the particles asunder; and it is possible that we may ac- complish this with a long and thin lath. The kind of strength that resists a twisting strain is called resistance to torsion. 40. The effective strength of any structure is that which is not employed in supporting the weight of the structure itself. It would be impossible to build such roofs and bridges of iron as have been built of wood, because the strength of the material would not be sufficient to support its own weight. Pine, which has nearly half the tenacity, has only one-tenth ANNEALING. 29 the weight of iron ; so that, for equal weights, pine has more than_ four times the tenacity of cast-iron. Steel has the greatest tenacity known. A rod of steel, one foot long and a square inch in area, will support a weight of 130,000 pounds. 41. If a body does not give way on the application of a strain, it is frequently permanently changed in shape. A stretching force may draw some bodies into a wire-shape. Such bodies are ductile. (Glass is very ductile when at a red heat, and may be drawn into very delicate threads. A com* pressing force flattens some bodies into thin sheets. Such bodies are malkable. Most metals are both malleable and ductile, though not in equal degrees. Gold is the most malleable, and platinum the most ductile of metals. 42. A sudden blow often breaks many bodies that in other respects are quite strong. Such bodies are brittle. Glass is a good example. A bottle that will resist a great pressure is broken by a gentle blow from some hard sub- stance. A hard substance is frequently also brittle. We measure the hardness of a body by the readiness with which it is scratched by another substance. The diamond is the hardest body-v known. Quartz is hard enough to scratch glass. y/J?/? / JrfY ? 43. When steel is strongly heated, and then suddenly cooled, it becomes very hard, and so brittle that it is suit- able only for the dies used in coining, and for the hardest files. On the other hand, if it is cooled slowly, it becomes softer, more ductile, and tenacious. This process of slow cooling is called annealing. Steel is tempered by first harden- ing it, and then a portion of its hardness is removed by reheating the steel to a lower temperature than at first, and then cooling it gradually. The temper required depends on the use to which the steel is to be applied. Surgical instru- 30 ELEMENTS OF PHYSICS. ments require a hard, keen edge ; table knives require more flexibility ; and springs require both flexibility and tenacity. The effect x>f rapid or slow cooling in glass is about the same as in steel. Melted glass dropped into water solidifies into the curious toy known as Prince Rupert's drops, Fig. 9. 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. This brittleness is pre- vented in glass utensils by carefully annealing. As soon as the glass vessels are blown, they are drawn through a long furnace in which the heat gradually FlG> 9 * diminishes from one end to the other. The thicker the glass, the longer the time required in annealing." 44. The phenomena just considered involve a perma- nent displacement of the particles of a body. If the strain does not exceed a certain limit, the body will resume its previous shape, when the force has ceased to act. The en- ergy with which the particles resume their original position is due to their elasticity. Up to the limit of elasticity, the elastic force is exactly equal to the strain, and the elasticity is therefore perfect. Beyond this limit, brittle bodies break : the molecules of most other solids are permanently displaced, or set-, with new relations to elasticity, exactly similar to the first. Thus : when a wire has been permanently lengthened by a great strain, it is still enabled to manifest perfect elas- ticity by recovering from a smaller strain. Flexibility should not be confounded with elasticity. A \vire of soft iron is very flexible, though but slightly elastic ; that is, it may be readily bent, but does not recover its posi- tion when the force is removed. A steel spring is both flex- ible and elastic. 45. The elasticity developed by compression belongs to all bodies, whether solids, liquids, or gases. All fluids are per- ELASTICITY. 31 fectfy elastic. Liquids are but slightly reduced in volume under ordinary pressures. Gases decrease in volume as the pressure exerted upon them increases; if the pressure be. doubled, the volume will be one-half, etc. When the pressure is removed, both liquids and gases resume their original volume. The elasticity of aeriform bodies is exemplified by a boy's pop-gun. The air between the wad and the piston increases in elastic force as it decreases in volume, until the elasticity is sufficient to expel the wad. The elasticity of such solids as India rubber, ivory, and steel, is very great. 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 covered 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 this experiment, it will be seen that the size of the spot on the slab and on the ball increases with the height from which it falls. It appears, therefore, (1) that the ball was compressed at the moment of the shock ; (2) that the rebound was caused by the effort to regain its shape ; (3) that the elastic force increases with the strain. Lead, clay, and the fats receive a set with only a moderate compressing force, and, therefore, have but little elasticity. 46. The elasticity of musical strings is developed by stretching. The tendency that twisted strings have to un- twist exemplifies the elasticity developed by torsion. The elasticity, developed by bending, is splendidly shown in glass threads : in them it is perfect, as they never receive a set, but break when the limit of elasticity is passed. 47. The practical applications of elasticity are innu- merable. The elasticity of solids is applied in the springs used in watches, clocks, carriages, bows, spring-balances, etc. 32 ELEMENTS OF PHYSICS. The elasticity of air is turned to account in foot-balls, air- cushions, air-springs, etc. RECAPITULATION. The properties which have been considered in this chapter are called the specific properties of bodies. They fall into two classes : Tenacity, I. Those involving strain of particles, Resistance to pressure, Resistance to bending, Resistance to torsion, Elasticity. (Ductility, Malleability, Hardness, Brittleness. CHAPTEK III. PHENOMENA CONNECTED WITH ADHESION. 48. The force of adhesion gives value to cements : thus glue is used for wood ; gum mastic and shellac for glass ; dex- trine for paper; etc. This choice of cements for different objects shows that adhesion varies with the kind of matter. Some of the phenomena of adhesion have received specific names, and are of great importance. Among these are the following : 49. Capillary action. If a clean glass plate is dipped vertically in water, the liquid will rise on each side to the height of nearly one-sixth of an inch, Fig. 10. It must be evident that the weight of this liquid column is sup- ported by the adhesion of the water to the glass. A second plate will sup- port an equal weight; and, hence, if two parallel plates are brought so near ^ each other that both may act on the i same molecules of the liquid, the Fia 10> column of the water will rise higher. The nearer the plates, the higher will the liquid rise, Fig. 11. Two plates, one- hundredth of an inch apart, will sup- port a column of water two inches high. When two plates are inclined to- ward each other, as in Fig. 12, the FIG. 11. water takes the shape of the curve known as the equilateral hyperbola. (33) 34 ELEMENTS OF PHYSICS. Finally, if a tube is substituted for the plates, the molecules of the liquid will be attracted on all sides, and the water will rise to twice the height produced by two plates, separated by a space equal to the diameter of the tube. If the tube has a diameter of one- hundredth of an inch, the column of water will be four inches high. FIG. 12. 50. The adhesion which causes liquids to rise on solids is called capillary attraction, because it is best exhibited in very small hair-like tubes. Liquids do not rise in tubes unless they wet them ; if they do not wet them, they are depressed. A needle, slightly greased, can be made to float on water, because, not being wet by the liquid, it produces a depression in which it is supported. For the same reason mercury is depressed by a glass plate, but rises freely on lead and some other metals. The amount of ascent and depression varies with the sub- stances used: thus, in a glass tube, alcohol will rise about one-half as much as water mercury is depressed in a glass tube, and its surface is convex, while water exhibits a con- cave surface. 51. Familiar illustrations of capillary attraction are seen in the action of lamp-wicks. Blotting paper readily draws ink into its pores, which resemble short capillary tubes. The pores in writing paper are closed by sizing. If One end of a towel is dipped in a basin of water, and the other left hanging over the edge, the Avhole towel will be- come wet. Water can not be poured out of a full tumbler without running down the outside because of the adhesion of the water to the glass. SOLUTION. 35 In the droughts of summer the water necessary to the support of vegetation is drawn toward the surface of the ground by capillary action. It is also one of the principal causes of the ascent of sap in plants, and plays an essential part in the circulation of liquids in animal tissues. 52. Solution. If a lump of sugar is dipped in water, the liquid will rise by capillary attraction until the whole is moistened. If enough water is present, the sugar will entirely disappear in the liquid, thus forming a solution. This shows that the adhesive force is sometimes sufficient to overcome the cohesion of solids. Each drop of the solution is sweet like sugar, and fluid like water, showing that the adhesion is perfect, because it is shared by every molecule. A solution is said to be saturated when no more of the solid will dissolve in it. 53. The solvent powers of liquids vary exceedingly. An ounce of cold water will dissolve two ounces of sugar, although it can dissolve hardly a grain of sulphate of lime. Fats dissolve in ether, benzine, and bisulphide of carbon; resins dissolve in alcohol ; lead and gold in mercury. When a metal disappears in an acid, as copper in nitric acid, the action has two stages: (1) a chemical action by which the solid and liquid unite to form a substance differ- ent from either, as nitrate of copper; (2) a simple solution by which the compound thus formed dissolves in the liquid. 54. Gases also dissolve in liquids. The rapidity with which water absorbs ammonia may be prettily shown by the following experiment : having fitted 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 in water, Fig. 13. After a little time the water will absorb so much of the gas as to leave a partial vacuum in the bottle; the pressure of 36 ELEMENTS OF PHYSICS. FIG. 13. the atmosphere will then force the water up the tube and form a small fountain. One volume of water absorbs 1049 volumes of ammonia, 506 volumes of hydrochloric acid, and nearly twice its volume of carbonic acid. 55. The weight of any gas absorbed by a liquid varies with the pressure; that is, if the pressure be doubled or tripled, the weight of the gas absorbed will be doubled or tripled. The effect of pressure on a gas is to diminish its volume and increase its weight in propor- tion to the pressure. Therefore the volume of the gas absorbed is the same for all pressures. If the pressure is removed, the gas resumes its original density, and escapes with effervescence. The "soda water" of the confectioner is water charged with carbonic acid gas, absorbed under pressure. \x 56. Porous solids like charcoal, dry clay, and metals in a state of fine division, often absorb large amounts of gases. One volume of charcoal will absorb 35 volumes of carbonic acid, and 90 of ammonia. A piece of freshly burned char- coal, exposed to the air for a few days, will often increase one-fifth in weight. This phenomenon can be explained by the supposition that the solid, by reason of its porous condi- tion, offers a very large extent of surface, to which the gases adhere, and become condensed. Finely divided platinum absorbs 250 times its volume of oxygen. 57. The absorptive power of charcoal is of great eco- nomic value. The variety known as bone-black is used for clarifying sugar. The brown sirups are filtered through a layer of bone-black twelve or fourteen feet in thickness, and are thus obtained perfectly clear, all the coloring matters, whether solid or liquid, being perfectly absorbed. Ale and DIFFUSION. 37 porter filtered through animal charcoal lose much of their bitterness, and all of their gases. All varieties of charcoal are efficacious in absorbing the gaseous products of decaying animal matters, and, thereby removing noxious effluvia from the air. 58. Solids also adhere to gases. The transportation of dust by the winds is a proof of this. This action, if continued for a long series of years, may effect great physical changes, as is seen in the shifting sands of the deserts, and in the sandy hills, called dunes, that are formed on the coasts of France. 59. When fluids mix with each other without entering into chemical union, it is because of the mutual adhesion of their. molecules. Some liquids, like water and alcohol, or glycerine, are miscible in all proportions. If equal volumes of water and ether are shaken together, and then allowed to stand, they will, in great measure, separate, each liquid dissolving about one-tenth of the other. The adhesion of oil and water is so feeble that they can not be made to mix per- manently by any amount of shaking and stirring. Any two gases will form a permanent mixture when they are placed in the same vessel, if they do not enter into chemical combination. 60. The tendency of fluids to mix with each other is called diffusion. Diffusion may take place without stirring or shaking, and even in apparent opposition to the attraction of gravitation. Thus, if a tall jar is partially filled with a solution of blue litmus, or water in which a red cabbage has been boiled, and sul- FIG. n. phuric acid is carefully poured through a long funnel (Fig. 14), reaching to the bottom of the jar, the line of separation between the two liquids will be, at first, distinctly marked. 38 ELEMENTS OF PHYSICS. Soon the acid will rise and the water will sink, until the two are perfectly mixed. This will, however, require some time, and the progress of diffusion may be traced from hour to hour by watching the gradual change from blue to red. This may be repeated with any two miscible fluids, as cab- bage water and a solution of caustic soda. 61. The diffusion of gases may be illustrated by the apparatus shown in Fig. 15, which con- sists 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. The greenish color of the chlorine enables us to trace its gradual ascent. In a few hours the two gases will mix perfectly and perma- nently. This experiment should be performed only in a darkened room so as to avoid an explosion. 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, -_., i= ^_J and would arrange themselves with the FIG. 15. heaviest at the bottom if it were not for this beneficent law of nature. The carbonic acid, a product of decay and com- bustion, would be found at the surface of the earth, and destroy all animal life. As it is, the noxious gases are rapidly diluted when formed, and soon are so perfectly dis- seminated through the air, that chemical analysis fails to find any essential difference in the air of mountain, plain, or valley. 62. Osmose is a term used to denote the diffusion of OSMOSE. 39 fluids when they are separated by a porous partition or septum. The presence of the septum greatly modifies the phenomena of diffusion. Tie a glass tube to the mouth of a bladder, Fig. 16, fill the bladder with strong brine, su- gar 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 substance that was in the interior. Hence, a cur- rent has been produced in two directions. The one passing in- to the bladder is called endos- mose; the one passing out, exos- mose. The rate of diffusion is greater in osmose than in simple diffusion. Instead of the bladder, an inverted funnel, having its mouth closed by a strip of any animal membrane, or by parchment paper, may be used. 63. Dialysis is the application of osmose to the separa- tion of mixed solutions. If a solution contains alcohol, hydrochloric acid, or crystallizable bodies like sugar, they will pass through the septum ; but gum-arabic, gelatine, and other substances that do not crystallize, will not. 64. The osmose of gases may be shown by a striking experiment. Close the mouth of a long glass funnel with 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 FIG. 16. 40 ELEMENTS OF PHYSICS. the mouth of the funnel therein, and then suffering the plaster to harden. After drying the septum, place the tube in colored water, and invert over the closed mouth a jar filled with hydrogen, Fig. 17. The endosmose of the hydrogen will soon become manifest by the escape of bub- bles through the water. Remove the jar, and the hydrogen will escape from the funnel in a contrary direction, as may be seen by the rise of the water in the funnel tube. Although the nature of osmose has not been satisfactorily determined, it is manifest from the porous nature of animal and vegetable membranes, that it must play an important part in the operations of life. In breathing, the lungs give out carbonic acid by exosmose, and absorb oxygen by en- dosmose. It is probable that the ascent of sap in plants, and the various pro- FIG. 17. cesses of secretion in animals are either controlled or essen- tially modified by osmotic action. RECAPITULATION. The force of adhesion is shown in I. Cements and Friction - IT. Capillary action III. Solution of solids IV. Solution of gases V. Absorption of gases VI. Shifting sands - VII. Diffusion of liquids VIII. Diffusion of gases IX. Osmose - - Solids to solids. Liquids to solids. - Solids to liquids. Gases to liquids. - Gases to solids. Solids to gases. - Liquids to liquids. Gases to gases. - Diffusion through septa. CHAPTER IV. THE LAWS OF MOTION. 65. A body at rest remains at rest; a body in motion will continue moving with uniform velocity in a straight line, unless it is acted upon by some external force. This statement is known as the law of inertia, or as the first law of motion. It is difficult to furnish examples which will perfectly illustrate this law. Our experience teaches us that a body will not move unless some force acts upon it; but that a moving body will continue in motion, is not so self-evident. Now let us roll a ball along the ground, then on a smooth floor, then on the ice : the fewer the obstacles in the way, the more direct will be its course, the longer will it continue in motion, and the more uniform will be its velocity. So, also, if we spin a heavy top in the air, and then in a vacuum, it will continue moving much longer in the latter case than in the former. All moving bodies on the earth's surface meet with opposing forces, such as gravity, friction, and the resist- ance of the air. The examples given above show that the more we can reduce these opposing forces, the nearer will the motion correspond to the law. If we could conceive of a body set in motion by a single impulse, and then left to itself, its motion would be in exact conformity to the law. 66. To comprehend the action of a force, three things must be known. (1) The energy with which it acts in a unit of time: this may be expressed by the pressure it exerts, or by its power of doing work, and may be repre- sented' by a straight line. (2) The direction, or the line along PHYS. 4. (41) 42 ELEMENTS OF PHYSICS. which it acts; and (3) the point of application, or the point upon which it exerts its action. In stating the theoretical action of forces, such external forces as friction, and the resistance of the air, are generally left out of account. This fact must be borne in mind when experiments are made intended to illustrate the action of forces. 67. A force which acts for an instant and then ceases to act is called an impulsive force. Projectiles, like bullets and arrows, are set in motion by impulsive forces. A con- stant force acts with the same energy without ceasing. It is convenient for us to consider a constant force as due to an in- finite number of equal successive impulses, each one of which acts through -a very brief interval of time. Gravity is a con- stant force. A locomotive under head of steam that is kept constant is another. A constant force tends to produce a velocity that increases at each successive instant. Thus, a locomotive starts slowly, and rapidly increases its rate of motion ; but after awhile it moves with uniform velocity, because the friction and the resistance of the air also increase so that they are exactly equal to the motive power of the engine. 68. Simple motion is produced by the action of a single force. Compound motion is produced by the joint action of two or more forces. A ball falling in a perfect vacuum is an example of simple motion. A ball falling in the open air is an example of compound motion. It is well to consider some other examples of compound motion. Suppose a boat, impelled by oars on quiet water at the rate of four miles an hour, enters a river whose current is three miles an hour, then, (1) if the boat go down the river, its speed will be seven miles an hour ; (2) if the boat go up the river, its speed will be one mile an hour; (3) if the boat is rowed directly across the river, its speed will be COMPOUND MOTION. 43 five miles an hour. Let AB be the direction of the boat, and AC the direction of the current ; that is, let these two lines represent the motion that would be produced if only one force were acting at a time. If both are acting at the same time, ^ K ' the actual direction of the boat will be the D line AD, which is the diagonal of the paral- lelogram ABCD. This line also represents the intensity of the joint action of the two FlG - 18 - forces ; and the boat will move as if impelled only by a single force in the direction of the line AD. A single force that represents the effect of two forces taken together is called their resultant. When the forces, as in the third case, are at right angles to each other, the find- ing of their resultant is the problem of finding the hypotenuse when two sides of a right-angled triangle are given. Thus, 3 2 + 4 2 = 5 2 . 69. Illustrations of compound motion. When a steamboat is in motion, all the objects on it partake of the onward motion of the boat. Balls may be thrown and caught with the same certainty as on shore. But the direc- tions which these balls take when referred to the ground beneath the boat will be the resultants of the motion of the boat, and the motions which the players give to the balls. So, also, an acrobat as easily goes through his feats of skill on the back of a horse in rapid motion as he would on the ground. Conversely, when we have the resultant of two or more forces, we may find its components. As an illustration, take the sailing of a sloop under a wind oblique to the course of the boat. Represent the direction of the wind by the line Vm. Its force may be resolved into two components : the one, iff, tangent to the sail, and producing no effect; the 44 ELEMENTS OF PHYSICS. other, mn, perpendicular 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 leeway. Therefore, this force is again decomposed by the keel and the rudder, and the re- sultant impels the boat on its course. These are examples of the second law of motion, which is : If two or more forces act together on a bodij, each force pro- duces the same effect as if it were acting alone. FIG. 19. 70. The measure of force. We can now understand that if a given force, acting for one second upon a mass, .will generate a certain velocity ; a double force, acting for one second, will generate twice the velocity. So, also, if it re- quires a given force to impart a certain velocity to a mass, it will require double the force to produce the same velocity in twice the mass ; for if the double mass were halved, and half the force applied to each ? placed side by side, the ve- locity 'would be the same. Hence, the product of the mass by the velocity is one measure of force. This product is called momentum. CIRCULAR MOTION. 45 Thus, the momentum of a body weighing five pounds, and moving with a velocity of four feet per second, is twenty. That is, it would require twenty units of force, acting in the opposite direction for one second, to produce pressure enough to bring the body to rest. The momenta of< large bodies, moving very slowly, are sometimes enormous. The momenta of icebergs are irresistible by any human power, even though their motion be so slow as to be almost imperceptible. There is also another measure of force* which is termed energy, or the power of doing work, which we shall consider hereafter. 71. The unit of work is the force required to raise one pound one foot high. This is called the foot-pound. Tfie unit of power is the force required to raise one foot-pound in one second of time. A horse-power is the mechanical value of a force capable of raising five hundred and fifty pounds one foot high in one second. Its work is, therefore, five hundred and fifty foot-pounds in one second. 72. Circular motion. It follows from the first law of motion that a single force will produce motion in a straight line. It follows from the second law that if a moving body deviates from its original direction, a .second force must be acting upon it. If a body moves in a circle, which is a con- stant series of deviations from a straight FIG. 20!" line, it must be acted upon by a constant force, in addition to the impulse which urges it in a straight line. If a ball be whirled in a circle by means of a rubber cord held by the hand, we feel the cord stretched by a sensible force pulling outward the hand resists this by pulling in- ward. If the cord is cut, the outward force will carry the ball in the direction of the tangent to the circle, as AT; 46 ELEMENTS OF PHYSICS. but when the two forces are equal, the curve is that of a circle. Circular motion is produced by the action of two forces, one of which, at least, is a constant force. The force that tends to draw bodies to the center, is called the centri- petal force; that which tends to drive bodies from the center, is called the centrifugal force. 73. The tendency of revolving bodies to fly off at a tangent is easily illustrated. A stone let go from a sling, the mud flying off from the wheels of a carriage in rapid motion, are examples. If a glass globe, containing a little colored water and some mercury, is swiftly revolved by a twisted string, both fluids will be whirled away from the axis; the mercury, having the greater relative weight, will occupy the equator, with a belt of water on each side, Fig. 21. In laundries clothes are dried by placing them in a wire basket which is then revolved many hundred times in a minute. The centrifugal force may be made to counteract gravity: thus, if a cup of water be balanced on the inner face of a hoop, by beginning with a series of short swings, the cup and its contents may be whirled over the head with- out spilling the water. 74. Newton proved that the shape of the earth is pre- cisely that which a globe of plastic material would take by virtue of centrifugal force. The cause of the flattening of the earth at the poles may be illustrated by passing an axis through two thin hoops of tin, and then twirling them FIG. 21. FIG. 22. ACTION AND REACTION. 47 round with moderate velocity ; they will take the shape shown in Fig. 22. Of course, the upper part of the hoop must be free to slide up and down on the axis. 75. The third law of motion asserts that action and re- action are always equal, and are in opposite directions. When a weight rests upon a table, the table resists the pressure with an equal force. When a ball is fired from a cannon, the cannon recoils with a momentum equal to that of the ball, but its backward velocity is much less because of its greater weight. 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. If we could imagine the bird beating its wings in a vacuum, there could be no reaction, and the bird could not move. So, in walking, we are assisted by the reaction of the ground to the pressure we exert. 76. The reaction of solids may be shown by balls hung from a frame so that their diameters shall lie in the same straight line. Suspend two equal ivory balls from the frame, in Fig. 23, and let 6 fall from D upon b'. If both balls were perfectly elastic, b will lose half its velocity in com- FIG. 23. pressing b', and the body b' will destroy an equal amount in regaining its shape ; therefore, b will lose all its velocity and 48 ELEMENTS OF PHYSICS. remain at rest. The other ball, b', will acquire all the ve- locity of b, and move to C, a distance, on the other side, equal to D. If the experiment is repeated with non-elastic balls of clay, both will move forward : the momentum of the falling body will be communicated to the one at rest, and the united momenta will be equal to that of the falling ball. They will therefore rise to a less distance than C. 77. When bodies strike a fixed plane they rebound by reason of the reaction of the plane. Suppose a perfectly elastic ball falls from P, Fig. 24, upon a perfectly elastic plane, AB. It will r*ebound to the height from which it fell. Now suppose it thrown in the direc- tion of IN, the force of the col- A ~ lision at N will be resolved into two components : the one, NE, j^ parallel to the plane AB, which FIG. 24. represents its velocity, in the direction of the plane ; the other component, ND, perpendicular to AB, represents the elastic force tending to urge the ball in the line NG. By reason of these two components the ball will take the direction NR, which is the diagonal of the parallelogram NERG. The angle INP is called the angle of incidence; the angle PNR is called the angle of reflection. In the reflection of perfectly elastic bodies, the angle of incidence is always equal to the angle of reflection. When either body is not perfectly elastic, the component NG will be proportionally smaller; hence, the body will proceed, after reflection, in a line nearer the plane than NR, and the angle of reflection will be greater than the angle of incidence. These facts may be illustrated REACTION IN SOFT BODIES. 49 by bounding balls of rubber, ivory, clay, putty, etc. , upon a hard floor. 78. The reaction in soft bodies is not instantaneous, and the destructive effect is less. Thus, if a man leaps from a height into deep water, the reaction is the same as though he alighted on a solid plane, but it is diffused through a sufficient interval of time to render it comparatively harm- less. Even soft bodies require some time for the displace- ment of their particles. If the surface of water be struck sharply with the open palm, the blow is met by considerable resistance. The sport of "skipping stones" on water ex- emplifies this power of resistance for the moment. KECAPITULATION. There are three laws of motion. The first declares that the appli- cation of force is necessary to move a body from a state of rest; the second, that if two forces act upon a body at the same time, each acts as if it were acting alone ; the third, that the application of "a force requires the agency of some external body. PROBLEMS. 1. Find the resultant of two forces that may be represented by 7 and 11: (a) When they act in the same direction. (&) When they act in opposite directions, (c) When they act at right angles to each other. 2. Find the momentum of a body whose weight is 5 tons, and whose velocity is 5 "feet per minute. With what velocity must a second body, whose weight is 5 pounds, move in order that it may have a momentum equal to that of the first body? 3. How many units of work are required to raise 10 cubic feet of water 34 feet high? 4. How many horse -powers are required to raise 6 cubic feet of water each minute to the height of 100 feet? PHYS. 5. CHAPTER V. PHENOMENA CONNECTED WITH GRAVITATION. 79. Weight has been defined as a measure of the earth's attraction. If a lead ball be suspended by a string, it con- stitutes what is called a plumb line. If a plummet hangs so that its point touches the surface of a vessel of water, the line and the surface of the water will be at right angles to each other, Fig. 25. The direc- tion of the line at any place is called the vertical, and a line at right angles to it is called a horizontal line. If vertical lines are drawn at different places on the earth, they will all be directed toward the earth's center. Xw- 25 - Hence, the direction of ter- restrial gravity is toward a point at or near the center of the earth, Fig. 26. At places near each other these verticals may be ^"considered as parallel. 80. The center of gravity is the point about which all the parts of a body balance each other. Each particle of a body is drawn toward the earth's center by gravity, and, hence, the effect of gravity on a body, taken as a whole, will be the same as the resultant of (50) EQUILIBRIUM. 51 an infinite number of equal and parallel forces. If we sus- pend a body so that it will hang freely from a point, a plumb line attached to the same point will show the direc- tion of this resultant. Now, on repeating this experiment, after suspending the body from another point, a second resultant will be found, and the center of gravity will be the common point of intersection of any two resultants. 81. When the center of gravity is supported, the body will remain at rest. Hence, (1) the weight of a body may be considered as concentrated in the center of gravity ; or (2) the center of gravity may be regarded as the point of application of the force of gravity, since it is the only point common to all the resultants. The line of direction of a body will be the vertical passing through the center of gravity, Fig. 27. 82. Although a body will remain at rest, or in equilibrium, when its center of gravity is supported, this equilibrium may be one of three kinds : (1) A body is in stable equilibrium if it tends to return to its original position after it has been somewhat displaced. Fl &- 27. This will always be the case when any change of position elevates the center of gravity. A plumb line, when disturbed, finally comes to rest in its original position. (2) 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 wheel is suspended on its axle. (3) A body is in unstable equilibrium when it tends to depart further from its original position after it has oeen 52 ELEMENTS OF PHYSICS. slightly displaced. This will be the case when the point of support is below the center of gravity. Thus, in Fig. 28, the cone B is in unstable equilibrium. It may be balanced in this position, but the least displacement will throw the FIG. 28. line of direction beyond the point of support, and the cone, will topple over. The cone A is in stable equilibrium, be- cause its center of gravity is as low as it can be. The cone C is in neutral equilibrium, because if it is rolled around the center of gravity will not be raised or lowered. The toy shown in Fig. 29 is in stable equilibrium, although the fig- ure withdut the balls would be un- stable. The addition of the balls has the effect of throwing the center of gravity below the point of sup- port. The same principle is illus- trated in Fig. 30. A pail is sus- pended from a stick lying on the edge of a table, and a second stick, EG, is placed with one end against the corner of the pail, and the other in a notch cut in the horizontal stick CD. By this contrivance the center of gravity of the connected bodies is brought under the edge of the table, and the whole is in stable equilibrium. FIG. 29. STABILITY. 53 The pail may now be filled with water without changing the equilibrium. FIG. 30. 83. The relation which gravity bears to equilibrium may be shown by the apparatus represented in Fig. 31. It consists of a cork, through which have been thrust, at right angles to each other, two half knitting needles arid one whole one, and sup- ported by two wine-glasses placed under one of the shorter needles. By push- ing the vertical needle up and down, the position of FIG. si. the center of gravity can be altered at pleasure, and the apparatus brought into either stable or unstable equilibrium. This is a case of a body resting on two points. A man on stilts is another when at rest, he can be only in a state of unstable equilibrium. A man walking on a tight rope uses a long pole, which he thrusts from side to side to assist 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. 84. The stability of a body depends on the relation which the center of gravity bears to at least three points not in the same straight line, and on which it is supported. 54 ELEMENTS OF PHYSICS. The base of a body is the polygon formed by connecting the points of support; as, for example, the legs of a table. A body resting upon a base is stable, when the line of direction falls within the base. The stability of bodies may be estimated by the force required to overturn them. This will be the force required to raise the entire body to the height that the center of gravity would be elevated in order to bring the line of direction beyond the base. The diagrams in Fig. 32 represent sections of different solids drawn through the center of gravity, G. To turn FIG. 32. any of these bodies over the edge E, the center of gravity must be raised through the height HT. A careful study of these figures leads to the following deductions: (1) The stability of bodies of the same height is increased by widening the base. The legs of chairs are inclined out- ward. A child's high chair has a very wide base. Candle- sticks and inkstands have broad bases. (2) The stability of bodies is increased by bringing the center of gravity to the lowest possible position. In load- ing a wagon or a ship the heaviest articles are placed at the bottom. A load of hay is easier overturned than a load of stone. (3) Of bodies having the same height and base, but of dissimilar figure, the pyramid is the most stable. Now compare the sections of the inclined figures in Fig. 33, and, we may add, (4) The stability of a body is the greatest when the line of direction passes through the center of the base. MOVEMENTS OF MEN. 55 (5) When the line of direction falls without the base, the body will fall, because the center of gravity is unsupported. The leaning towers in Pisa and Bologna incline far from a perpendicular position. In these the line of direction still FIG. 33. falls within the base; but the visitor who sees them for the first time can not help thinking that they are likely to fall. 85. Practical applications. 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 about are the results of instinctive efforts to keep the line of direction within the base. A man stand- ing with his heels against a vertical wall finds it difficult to stoop to the floor without falling forward. In running, or in climbing a hill, the body is thrown forward, so that its weight may be carried with less effort. In descending a hill, a man leans backward, so that his weight shall not cause him to fall forward. When a person carries a load, he endeavors to preserve the line of direction, common to himself and the load, with- in the base. If a heavy load is in the right hand, the body is inclined to the left, and the left hand thrown out. If the load is equally divided between his hands, or placed on his head, there is no tendency to lean to either side. If the load is on his back, he leans forward; if carried in his arms, he leans backward. 56 ELEMENTS OF PHYSICS. RECAPITULATION. The center of gravity is the point in which the weight of the body may be considered as concentrated. Equilibrium is stable, neutral, or unstable, according to the posi- tion of the center of gravity. Stability depends on the relation which the center of gravity bears to the base. CHAPTER VI THE LAWS OF FALLING BODIES. 86. Gravitation has been shown to produce pressure; we are now to study how it acts in producing the motion of falling bodies. If we attempt to experiment by dropping different balls from a height, we shall meet with many difficulties. (1) The resistance of the air. Light bodies, as feathers and leaves, almost float in the air ; but if any two bodies whatever, as a coin and a feather, be made to fall through a perfect vacuum, they will reach the ground in exactly the same time. If two bodies have the same weight, but are of different material, as a lead bullet and a cork, the difference in bulk will make so great a difference in the resistance of the air as to make the cork fall perceptibly slower. If the bodies were of the same material, but of different size, the resistance of the air would be slightly in favor of the larger ball, although they would reach the ground in J very nearly the same time. / ^ (2) If we catch equal balls, dropped from dif- FIG. 34. ferent heights, we shall not only find that the swiftest balls are those which have fallen through the greatest heights, but that the velocity increases so rapidly that we can not readily measure the rate of increase in a free fall. There are several methods by which we may render the initial velocity so slow that it can be accurately measured. The simplest of these methods is that of Galileo, who first deter- (57) 58 ELEMENTS OF PHYSICS. mined the law of falling bodies by rolling smooth balls down a polished groove cut in a plane which he inclined at different angles of elevation. When a body rests upon an inclined plane, its weight or gravity is resolvable into two portions, one producing pressure on the surface, and the other tending to produce motion down the plane. This latter portion bears the same ratio to the whole force of gravity as the height of the plane does to its length ; and, hence, we may diminish the velocity of the ball at pleasure by lowering the height. Nevertheless, only the absolute motion will be changed ; the body will pass, in successive moments, through spaces bearing the same ratio to each other as if it fell freely through the air. 87. To repeat the experiment of Galileo, stretch two parallel wires between the walls of a room, at any conven- FlG. 35. ient angle, as in Fig. 35. On the lower wire hang a weight to a pulley, so that it will move with little friction, and on the other fasten a convenient index, as a bell or a slip of paper, so that it may be struck by the top of the pulley 6. Suppose that the inclination of the wire is such that, in the first second, the pulley passes over the space ^s; in the second, over the space ss'; in the third, over s's"; and so on. LAWS OF FALLING BODIES. 59 If we measure these spaces, taking that of the first second as unity, we shall find that they increase in the series of odd numbers 1, 3, 5, 7, etc. or at the rate of two spaces for each second. This proves that increase of velocity is uniform ; and that for bodies near the surface of the earth gravity is a constant force. Let us now see what we have gained by our experiment. (1) The spaces described by a falling body increase in the series of odd numbers 1, 3, 5, 7. Any term of this series is equal to twice the number of seconds, minus one. FIRST LAW. The space described by any falling body, in any given second, is equal to the product of twice the number of seconds, minus one, into the space described the first second. (2) The velocity is all the time increasing at the rate of two spaces for each second ; therefore we have the SECOND LAW. The velocity acquired by a falling body at the G&d of any given second is equal to the product of the number of seconds into twice the space described the first second. This product, it must be borne in mind, is the space a body would describe in the next second were gravity to cease to act, and not the space it actually describes. (3) The total space passed through at the end of the first seeond is 1 ; at the end of the second second, 1 -j- 3 4 ; at the end of the third second, 1 -f 3 -f 5 = 9. This series in- creases in the order of the squares of the number of seconds ; therefore we have the THIRD LAW. Tlie tojal space described by a falling body at the end of any given second is equal to the product of the square of the number of seconds into the space described the first second. It is evident that these laws are true, not only for any in- clination of the plane, but also for a free fall. If in the experiment the height of the plane had been one foot and 60 ELEMENTS OF PHYSICS. the length sixteen feet, the pulley would have traveled 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. 88. It has been determined by careful experiment that, at 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 in- crement* of velocity due to gravity, and is generally represented by = 32.16. The space passed over during the first second is %g = 16.08.* 89. The velocity increases every second by the quan- tity 32.16 feet. The velocity at the end of the first second is 32.16 ; at the end of the second, 64.32 ; at the end of the third, 96.48, and so on. Now, the total space fallen through at the end of the first second is 16.08 feet; at the end of the second, 64.32 feet; at the end of the third, 144.72 feet, etc. If we compare these two series we shall find that the velocity vanies as the square root of the height fallen through ; for 32.16 : 96.48 :: 1/16.08 : T/144.72. This is an important law. The velocity which is acquired % We may employ formulae to express these laws by representing the space passed over during any second by s; velocity by v; the total height of the fall at the end of any given second by S, and the num- ber of seconds by t. First law Second law Third law On combining these formulae v = Y2yS, t = V2S + g, or f ' S -+ 16.08, etc. PROJECTILES. 61 by a body falling through any given height may be found by multiplying the square root of the height by \g, or by 8.02. Thus, a velocity due to a fall of four seconds, or to a fall of (4 2 X 16.08) =257.28 feet is 8.02 1/257.28 = 128.64 feet. 90. 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 # = 32.16. Hence, the time of ascent is the same as that of a falling body which attains a final velocity equal to the initial velocity of the ascending body. Further, if a body be projected upward, the height to which it ascends is such that when it falls again, the body will have acquired under gravity during its descent a velocity equal to that with which it started upward. ^91. Examples of this law. Suppose an iron ball is thrown upward with a velocity of 32.16 feet per second. At the end of one second it will come to rest and begin to fall. It will have moved in this second with an average velocity of (32.16 -f 0) ~ 2 = 16.08 feet, and hence will rise to the height of 16.08 feet. Now, suppose the initial velocity be doubled, or 64.32 feet. It will rise two seconds with the average velocity of (64.32 -f 0) -r- 2 = 32.16, and will describe during the two seconds 32.16 X 2 = 64.32 feet. If the initial velocity be tripled, its average velocity will be (96.48 -f 0) ~ 2 = 48.24, and the total ascent 48.24 X 3 = 144.62 feet. Hence, with a double velocity of projection it will rise four times as high, with a triple velocity, nine times as high, and so on. That is, the heights to which a body will rise are as the squares of the velocities of projection. In these examples the force has been doing work, for it 62 ELEMENTS OF PHYSICS. has carried the body through space in opposition to the constant force of -gravity. Hence, the energy of the force is proportional to the square of the velocity. The energy is also proportional to the mass of the body, for it is evident that it requires twice the energy to raise two pounds that it does to raise one pound. Therefore, the energy is propor- tional to the mass multiplied by the square of the velocity. To compute the work done by a projectile force in oppo- sition to gravity, it is sufficient to multiply the weight of the body expressed in pounds by the number of feet through which it is lifted. The fyeight to which the body will rise is equal to v 2 -~ 64.32, or to the square of the velocity divided by 2g. Hence, the work of the force, expressed in foot- pounds, equals mv 2 -=- 64.32. In general, the energy of a force is equal to one-half the product of the mass into the square of the velocity, or E = Jrav 2 . The factor %mv 2 is also called vis viva, or living force. It expresses the work that a moving body can perform before it is brought to rest, if no additional force is added to it ; as for instance, the power ==3 .4___ B which different cannon balls would have to pen- etrate obstacles, like planks, clay, etc. 92. If a projectile be fired in a horizontal direction, its path will be due (1) to the force of the gunpowder, and (2) to the constant force of gravity. In Fig. 36, FlG - 3G - suppose the velocity due to the powder to remain uniform during four seconds, and to be represented by equal spaces 6\ UNIVERSAL GRAVITATION. 63 on the line AB, and represent the accelerating velocity due to gravity by the unequal spaces 1, 3, 5, 7. The resultant of these two forces will be the curve Aahcd, which is called a parabola. 93. Universal gravitation. Thus far we have considered gravity as acting only upon bodies near the earth's surface, and have found that for such bodies gravitation is a constant force proportional to mass. When we consider the earth's at- traction upon remote bodies, as the moon, or the universal gravitation acting between the heavenly bodies, we must take into account not only (1) the mass of each body, but also (2) the distance between the centers of gravity of the two bodies. The law of gravitation, discovered in 1666 by Sir Isaac Newton, is usually stated as follows: Every particle of matter attracts every other particle, with a force (1) directly proportional to its mass, and (2) in- versely proportional to the square of its distance. Whenever the distance between any two bodies is consid- erable, gravity must be considered as a variable force which diminishes as the square of the distance increases. Thus, suppose a body taken one thousand miles above the earth's surface, it is five thousand miles from its center. The force of gravity will, therefore, decrease in the ratio of (-f$$$) 2 = |f. At this distance a body will weigh J-f of its surface weight, and during a fall of one second will acquire a velocity of f| of 32.16 feet = 20.6 feet per second. At the distance of the moon, which is about sixty times the earth's radius, the attraction of the earth becomes (g^) 2 = -g-gW an ^ capable of supporting a column _^ of water only 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 j 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, con- nects the working -barrel to the surface of the ground. The at- Flo 106 mospheric pressure forces the water from the well into the working -barrel ; the force applied to the piston lifts the water from the working-barrel to the top of the discharge- pipe. 182. In the forcing-pump, the piston is made solid, and the upper valve, u, is placed in a lateral discharge-pipe, d, connected with the bottom of the barrel. 124 ELEMENTS OF PHYSICS. FIG. 107. 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 -barrel. 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 pis- ton, the upper valve closes, and prevents the water in the discharge-pipe from re- turning ; the lower valve opens to admit more water into the barrel. At each de- pression of the piston, more water is driven into the discharge-pipe, until it is elevated to the required height. 183. 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 Fig. 108. When the piston descends, it forces the water through the valve, i, into the air-chamber, A ; the water partially fills the chamber, and thus compresses the air. The tension of the compressed air increases as its bulk is diminished, and soon becomes sufficient to force the water in the chamber out through the tube, T, in a constant stream. 184. 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 dischar'ging-pipe. \ 185. The siphon is employed for transferring liquids FIG. 108. THE SIPHON FOUNTAIN. 125 from a higher to a lower levelj It consists of a bent tube with two unequal arms, Fig. 109. 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 D M 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. "5 After the suction is stopped, tne 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, CMF, by a force equal to the excess of the weight of M K over that of ML 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. 186. These facts may be pret- tily shown by the siphon foun- tain. Close the mouth of a tall flask, J?, with a cork, and insert two glass tubes, as shown in Fig. 110. The shorter arm should be drawn out at the upper end to a very fine bore. On exhausting the air from the tube, the ordi- nary flow of the siphon will commence. If, now, the longer FIG. 110. 126 ELEMENTS OF PHYSICS. 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 differ- ence in the length of the two arms. FRICTION OF FLUIDS AGAINST EACH OTHER. 187. The atomizing tube is a contrivance for breaking up the particles of a liquid into spray. A common form is shown in Fig. 111. It consists of two open tubes, so inclined to each other that a jet of fluid driven through one shall issue over or near the mouth of the FIG. in. other. The blast tube, A, is usually contracted at its mouth, so as to increase the velocity of the stream. The lower end of the suction tube, J5, is plunged in any liquid, as cologne. If a stream of air is driven forcibly through the blast tube, it will, on issuing from the mouth, drag the contiguous par- ticles of air along with it, and thus produce a rarefaction behind it. As the air is rarefied in the suction tube, B, the atmospheric pressure on the liquid will force a column up- ward in the tube, and, if the tube be not too long, the par- ticles will rise to the top. At this point, the jet of air will drag the liquid molecules along with it, and the two streams will be mingled in one of excessively fine spray. The same principle is sometimes employed in producing a draft in chimneys and locomotives. In locomotives the waste steam is driven through a blast pipe in the smoke stack, and carries the smoke along with it, and thus increases the draft of the fire. THE PNEUMATIC PARADOX. 127 188. The pneumatic paradox affords another illustration of the same sort. It may be made by taking two small disks of card board, and fitting to one a small tube. Now, if the other disk is placed above the tube, and a pin passed through the center to keep it from sliding, it can not be blown off by any ordinary cur- rent of air driven through the tube. Because, as the air is driven between FIG. 112. the disks, a rarefaction will be produced at the center of the iipper disk ; the air above it will crowd it toward the orifice and hold it the more firmly as the blast is made stronger. While the current of air is passing, the tube may be held in any position. The force requisite to blow away the upper disk must exceed the atmospheric pressure holding it down. KECAPITULATION. 1. Aeriform fluids are governed by the same laws as liquids, except that, by reason of their compressibility, their volume is inversely, their density and tension directly, as the pressure to which they are subjected. 2. All gases, like air, may be shown to possess the universal proper- ties of matter ; but, except air, none are necessary to the support of animal life, and few are concerned in ordinary combustion. 3. The barometer measures the pressure of the atmosphere, and may be used : (1.) To calculate the altitude of a place. (2.) To predict changes in the weather. 4. The pressure of the atmosphere is employed in pumps and siphons. 5. The friction of fluids against each other is employed in blast- pipes. CHAPTER XII. THE MODES OF MOLECULAR MOTION. 189. The topics considered in the last eight chapters natu- rally fall into two groups. (1) Phenomena which relate to bodies in equilibrium ; these belong to the science of statics. (2) Phenomena which relate to bodies in motion ; these be- long to the science of dynamics. Statics and dynamics taken together constitute the science of MECHANICS, which treats of bodies in equilibrium and in motion. Now, it will be noticed that in these chapters we have studied the effect which force produces upon a body taken as a whole. It is true that the force of gravity acts upon every molecule of a body, but we have always assumed that the motion or rest of the body did not alter the relative position of these molecules. Thus, in falling bodies, and in the pendulum, we considered only the motion that was com- mon to the entire mass. The molecules which made up the moving body did not change their relative positions, and were, therefore, at rest with respect to each other. 190. The following chapters relate to motion among the molecules of a body, but which involve the entire mass of the body. These molecular movements sometimes cause a visible change in the position of the body, but more fre- quently do not produce any motion in the body taken as a whole that we are able to detect by our senses. We know that these molecular motions exist by the results of the motion, just as we know that the hour-hand of a clock, or a rifle bullet, has moved by the result of the gross motion ; for our senses do not enable us to detect very slow nor very (128) UNDULATIONS OF SOLIDS. 129 swift motions. When a body expands by heat, we are con- vinced that the result is due somehow to a motiort among the molecules of the body. It would be difficult to keep any body at the same temperature all the time ; and if the tem- perature varies, the rate of molecular motion is increased or diminished, and the body is growing larger or smaller. It would be still more difficult to find a body that did not have some motion among its molecules due to the energy of heat, that is, that was in a state of absolute cold. Hence, on this consideration alone, it is probable that the molecules of even the most rigid bodies are constantly in motion even while the body, as a whole, appears to be in a state of rest. 191. A pendulum vibrates as a whole. The times of its vibrations are said to be isochronous ; that is, they -g are performed in equal times. If an elastic body / is bent, its molecules must have changed their rela- j tive positions, because the shape of the body is al- E\- - D tered. If, now, it is let go, the molecules will tend \ to assume their original positions, and, by reason of \ their elastic force, a series of vibrations will follow, AQ> which are also isochronous. To show this, suspend FlG - 113 - a rubber tube from a hook, and stretch it taut by the hand. Now, if the cord be plucked at the center, it will vibrate in the dotted lines shown in the figure, and pass from D to E in precisely equal times, until it finally comes to rest. Such vibrations are called transverse vibrations. The greater the disturbing force, the greater will be the distance ED. This distance is called the amplitude of the vibration. The greater the amplitude, the greater will be the energy of the vibra- tion, but the time required for a vibration is unchanged. If, now, the cord be stretched by a weight, A, and the weight be pulled down and then suddenly let go, the cord will perform a series of longitudinal vibrations, which are also 130 ELEMENTS OF PHYSICS. isochronous. That is, the weight, A, will oscillate alter- nately above and below its normal position, while the cord becomes alternately shorter and longer. So, if we twist the weight around, it will turn backward and forward in a series of isochronous torsional vibrations. 192. All elastic bodies may be thrown into alternating motions of some sort, which are due to the nature of the disturbing force and the elasticity of the body. If we con- sider the motion of only one particle, as A or E, these motions are called vibrations or oscillations. If we consider the motions of a line of particles, they are called waves or undulations. 193. How undulations are formed may be shown by stretching a heavy rubber cord from a fixed point, as X, by means of A- x the hand at the other end, as at % A. If the hand be jerked up- ^^N\^ ^ ward, an apparent movement will be transmitted along the cord like the waves on the sea. If the hand be jerked but once, its effect will be to produce the crest, A E N; the elastic force of the cord will cause the corresponding hollow, ND 0. The curve, A END 0, will advance along the cord, as- suming successively the positions /, II, III, until it reaches the end, X, and then return in an inverted curve, IF, F, FJ, to the hand. The curve, A E N D 0, is called a wave. 194. The particles of the cord appear to move from one end of the cord to the other. This, however, is irapos* FORMATION OF UNDULATIONS. 131 sible; each particle has moved only up and down, and the wave is due to a series of particles which are passing in suc- cession from the highest to the lowest point of the wave. Such a wave is called a progressive undulation. A is the length of the wave. H E is the height of the wave. D P is the depth of the wave. HE-\- D P is the amplitude of the wave. FlG - 115 - A E N is called the phase of elevation of the wave. N D is called the phase of depression of the wave. If a pebble be dropped in a placid pool, progressive undu- lations will be formed. The waves will spread in widening circles around the pebble, and decrease in amplitude as they increase in diameter, until they finally become inappreciable. As in the case of the cord, the motion of each particle is only up and down, as is proved by the rise and fall of bodies floating upon the surface. A progressive undulation is, therefore, only an advancing form, and any apparent pro- gression of the particles in the wave is merely an optical illusion. 195. The surface waves of fluids are propagated by gravity. All other waves are dependent, mainly, on the elastic force developed in a body by some disturbing force. Undulations may be confined to the body in which they are formed, or they may be formed in one body and transmitted through several others. So the vibrations of solids may cause waves to be transmitted to other solids, to the atmos- phere, or to water. Any body through which waves are transmitted is called a medium. 196. Surface waves have a crest and hollow, or an up and down motion, but there are also waves in which the motion of the particle is in the same line as that of the 132 ELEMENTS OF PHYSICS. direction in which the wave is transmitted. Thus, if the piston in the weight-lifter, Fig. 102, is pulled down and the pressure suddenly removed, the elasticity of the air will FIG. lie. cause the piston to vibrate up and down. This must be due to the alternate condensation and rarefaction of the air above and below the piston. The undulations in aeriform bodies are chiefly due to similar waves of condensation and rarefaction, in which the same particle may be considered as moving backward and forward instead of up and down. 197. Let a soap-bubble containing a mixture of oxygen and hydrogen be exploded by the flame of a candle. The vapor formed by the union of these elements forms a sphere many times greater than the soap-bubble, and thus a rare- faction will be produced at the center of disturbance. The pressure of the surrounding air will then cause the vapor AERIAL UNDULATIONS. 133 sphere to contract, its elasticity will again impel it outward, and thus it will continue to oscillate by alternate refraction and condensation for some time. 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 aerial shell ; it, in turn, upon a third, and so on. These movements are analogous to the waves upon the surface of liquids, in that they increase in circumference from the center ; only instead of a crest we have condensa- tion, and, instead of a hollow, a rarefaction. While a sur- face wave consists of a crest and a hollow ; an aerial wave consists of a condensation and a rarefaction. Fig. 116 is an attempt to represent to the eye four aerial waves : the darker parts represent condensations, the lighter the rarefactions. 198. Surface waves, starting from a center of disturb- ance, decrease in intensity, because, as the circles widen, there are more particles to be moved, and each will move with a less amplitude. Aerial waves form spherical sur- faces, and, as they expand, the number of particles to be set in motion will increase as the squares of their radii; hence their intensity will decrease in the same ratio or, the inten- sity of an aerial wave diminishes as tlie square of the distance from the center of propagation increases. 199. It will be easily understood that the greater the intensity of an aerial wave, the greater will be the amount of condensation and of rarefaction. The amplitude of an aerial wave is the space through which any particle passes from a state of condensation to a state of rarefaction, and hence the amplitude will increase with the intensity of the wave. On the other hand, the length of the wave will de- 134 ELEMENTS OF PHYSICS. pend on the number of particles Avhich constitute one con- densation plus one rarefaction. Hence the amplitude of a vibration may be only a small fraction of an inch, while the length of an undulation may be many feet. 200. Suppose an impulse to be communicated through one thousand feet in one second by means of waves. This will express the velocity of the wave motion. Now, the greater the amplitude the greater will be the resistance to be overcome ; the less the amplitude the less the resistance, and, hence, all the waves will move over equal spaces with equal velocities. The length of the wave depends on the rapidity with which the waves succeed each other; that is, on the rapidity of the vibrations or impulses which produce the waves. The more rapid the vibrations, the greater the number of waves and the shorter the wave length ; the slower the vibrations, the smaller the number of waves and the greater the wave length. Hence we may determine a wave length by dividing its velocity of transmission by the number of vibrations performed in the same time. EECAPITULATION. There are two varieties of waves : I. Waves of crests and hollows, in which the direction of displace- ment is perpendicular to that of transmission. This is exemplified by waves of water, the undulations of light and heat. II. Waves of condensation and rarefaction, in which the direction of displacement coincides with that of transmission. The vibrations of musical instruments are transmitted through the air by waves of this sort to the ear. These are, therefore, called sonorous ivaves. The intensity of a wave is dependent on the energy of the disturb- ing force. The initial amplitude is dependent on the intensity. The velocity of a wave is the rapidity with which it is propagated in a medium. The length of a wave is dependent both on the velocity and the number of vibrations in one second. CHAPTER XIII. ACOUSTICS, OR THE PHENOMENA OF SOUND. 201. Three conditions are necessary for the sensation of sound : Every species of sound may be traced to the vibra- tions of some elastic body. When a tuning-fork sounds, its vibrations may be felt by placing one of its prongs lightly upon the teeth. If a knife- blade be placed against the edge of a bell that is ringing, it will be made to rattle. The tremors produced in the ex- ternal air by the vibrations of an organ-pipe are distinctly perceptible. Bodies capable of producing sound are called sonorous. ^$Q An elastic medium is requisite for the transmission of sound. The ordinary medium is the atmosphere. The vibrations of sonorous bodies produce in the air, waves of condensation and rarefaction, which correspond in rapidity and amplitude to the rapidity and amplitude of the vibra- tions. These waves succeed each other in ever increasing spheres, until at last they reach the ear. Two or more media may be employed in transmitting the same sonorous wave ; thus persons in a close room are sensible of distant sounds. In such a case, the undulations of the external air cause vibrations in the windows and walls, which produce corresponding undulations in the air within the room. If a bell, kept in constant vibration by clock-work, is supported on a thick layer of loose cotton, under the re- ceiver of an air-pump, the sound, at first distinct, grows (135) 136 ELEMENTS OF PHYSICS. more feeble as the air is exhausted, and finally ceases to be heard when a vacuum is obtained. Fig. 117. In like manner sound is quenched by the interpo- sition of any body having feeble elasticity. Thus, a partition filled with sawdust, or covered by a thick carpet, will prevent the transmission of sound from one room to another. ^&) The auditory nerve is neces- sary to the sensation of sound. If "Jie experimenter is deaf, or if a bell rings when there are no hearing organs capable of per- ceiving the vibrations, they ex- ist merely as such, without pro- ducing sensation. (Nevertheless, in studying these vibrations it is convenient to dis- FIG. in. regard the sensation, and define sound as a mode of motion which is capable of affecting the auditory nerve.) / ' / 202. \A musical sound is produced by vibrations which succeed each other at short and equal intervals.] If the vibrations are rapid, the ear recognizes the sound as high or acute ; but, if slow, as low or grave. ^ These facts may be shown by pressing a card against a toothed wheel in motion. Fig. 118 represents Savart's wheel. If the card, E, strikes against less than 16 teeth per second, only a succession of taps will be heard. If the number exceeds 16 per second, the impulses blend together in a clear musical sound. \A.s the velocity is increased, the sound is more and more acute. ; Therefore///^ pitch or tone depends on tiie rapidity of the vibrations. ^Savart's wheel has SAVAET'S WHEEL. 137 at H an apparatus which indicates the number of revolu- tions in the toothed wheel by which we can easily calculate the number of vibrations per second that are required to FIG. 118. produce any given tone. / Sounds are in unison when the rates of vibration are the same, j We may determine the rate of vibration in tuning-forks and other musical instru- ments by making the wheel sound in unison with them, and then noting the rapidity of the vibrations produced by it. If the vibrations are less than 16 per second, the ear is affected by each impulse separately, and only a noise, or a suc- cession of noises, is heard, j ^ 203. The quality of sound depends on the elasticity and form of the sounding body. Steel, glass, silver, brass, and cat-gut, are sonorous, because these substances are highly elastic, and possess sufficient strength for rapid vibrations. The fibers of wool and cotton are elastic, but are not sonor- ous, because their elasticity is so feeble that their vibrations are slow and inaudible. Hence, all elastic bodies are not sonorous, although all sonorous bodies are elastic.} 204. If a tuning-fork be struck by a sharp blow, its sound will be at first loud, and then gradually die away. PHY*. l-_'. 138 ELEMENTS OF PHYSICS. The blow causes vibrations in its prongs that have consid- erable amplitude; the greater this amplitude, the greater will be the condensation which it produces in the aerial wave. As the amplitude decreases the condensation is less, until finally the condensation is not sufficient to affect the ear. QrEence, the intensity or loudness of the sound depends on the amplitude of the vibrations.) It must not be forgotten that the loudness has nothing to do with the pitch of a tone; thus, the same tuning-fork always vibrates with the same rapidity and yields the same tone, whether that tone be loud or soft. \he amplitude of sonorous waves rapidly decreases, be- cause they are propagated in spherical surfaces ; hence, the intensity of sound varies inversely as tJie square of the distance of the sounding body. J A drum at a distance of one hundred feet sounds four times louder than at two hundred feet, and one hundred times louder than at one thousand feet. 205. When a string vibrates in free air, it emits but a feeble sound ; but if it is fastened to a violin or a suitable sounding-box, the sound is louder. This arises from the fact that the thin plates of the box and the air within them vibrate in unison with the string, and the united effect is to produce a wave of greater intensity. We may illustrate this by holding a vibrating tuning-fork over the mouth of a tall jar, and carefully pouring water into the jar. Fig. 119. When it has reached a certain level, the sound of the fork will be greatly increased by the vibration of the column of air within the jar. The best effect will be produced when the length of the air column is such that a wave of condensa- tion or of rarefaction will go down and back while the tuning-fork is making a single vibration. That is, the length of the column* should be one-fourth of the length of the sonorous wave produced by the fork. We learn from INTENSITY OF SOUND. 139 these experiments iha,t(jsound is increased in intensity by the proximity of a resonant body.} 206. These experiments show that a vibrating body is capable of exciting undu- lations in bodies whose rate of vibration is the same as its own. When the voice utters a prolonged loud tone near a piano, that wire will be set in vibration whose sound is in unison with the voice. Such vibrations are termed sympathetic. ( Only that wire answers to the voice that is capable of emit- ting tfie same tone when it is struck. N FIG. 119. 207. The intensity of sound depends on the density of the medium in which it is generated. The experiment of the bell in vacuo shows that the more the air is rarefied, the weaker is the sound. On the tops of mountains the sound of a pistol resembles the report of a fire-cracker ; while a whisper sounds painfully loud to the occupants of a diving- bell. The energy with which solids and liquids transmit sound exceeds that of the atmosphere. The scratch of a pin at the end of a long stick of timber is distinct to a person whose ear is at the other end. 208. The intensity of sound is weakened in passing from one medium to another. A noise made under water is feebly heard in the air, and vice versa. If the lungs are filled with hydrogen, the voice is weak and piping. The 140 ELEMENTS OF PHYSICS. reason why sounds are more distinct by night than by day is because the air is more homogeneous. In the day- time the air contains layers of different densities, and the sound is weakened both as it enters and as it leaves one of these layers. 209. The distance at which sound is audible varies with the conditions that determine its intensity. Still air of great density and uniform temperature is favorable to the transmission of sound. In the Arctic regions, Lieuten- ant Foster conversed with a sailor at the distance of a mile and a quarter. The earth transmits sound further than air. The cannonading at Antwerp in 1832 was heard in the mines of Saxony, 320 miles distant. 210. The velocity of sound. Every one must have no- ticed that the flash of a distant gun is seen before the report is heard. If the distance and the time between the flash and the report are known, the velocity of sound may be computed. The velocity of sound in still air at 32 F. is 1090 feet per second. 211. The velocity varies with the temperature, increas- ing, as the temperature rises, at the rate of 1.12 feet for every degree Fahrenheit. At 60 F. sound has a velocity of 1121 feet per second. 212. These facts enable us to compute the distance of a sounding body when the time of transmission is known. Thus : suppose, on dropping a stone from a cliff, eight sec- onds elapse before the stone is heard to strike the base. A part of the time, x, was occupied by the falling body, the rest, 8 x, by the sound. By the law of falling bodies x i x 16^ equals the height of the cliff; by the law of the transmission of sound (8 x) 1090 also equals the height. Hence, x 2 X 16 T V (8 x) 1090. x~-= 7.23; 8 x = 0.77. The height of the cliff is, therefore, 839.7 feet. THE VELOCITY OF SOUND. 141 213. All sounds are transmitted with the same velocity in the same medium. If this were not true, the different notes simultaneously produced by the instruments of an orchestra would reach the ear of a distant auditor one after another, and so pro- duce discord. 214. The velocity of sound varies with the medium. In gases denser than air, it moves with less velocity ; and in those rarer, with greater velocity : in carbonic acid, the rate is 858 feet, and in hydrogen 4,164 feet per second. In solids and liquids, the velocity is greater than in air; in water, the rate, per second, is 4,700 feet; in lead, 4,030 feet; in steel and glass, 16,600 feet ; in ash, 15,314 feet. The difference of velocity in solids and in air may be demonstrated by placing the ear at one end of a long beam 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 approach of a railway train may be soonest heard by applying the ear to the rail. 215. If the sonorous wave is not permitted to expand, its intensity can be maintained for a great distance. The speaking-tubes employed in large buildings for transmitting .messages from one story to another illustrate this fact. The hearing trumpet concentrates sound, because the condensa- tion and rarefaction of the sonorous wave which enters it is communicated to portions of air which are smaller and smaller, and thereby the intensity is increased. 142 ELEMENTS OF PHYSICS. SONOROUS WAVES. 216. Many sounds may be transmitted at the same time in the same medium without modifying each other. A cultivated ear can readily distinguish the sound of each different kind of instrument in a large orchestra. If, how- ever, there are many instruments of the same kind perfectly in unison, their sounds will unite to produce a resultant wave of increased intensity. So, also, many feeble sounds, separately inaudible, may unite to produce a sort of mur- mur, as is exemplified by the rustle of leaves, or the hum of a whispering school. 217. If two sonorous waves of equal intensity combine, FIG. 120. the effect may be either to increase or diminish their inten- sity. We can readily illustrate this effect by means of a long, narrow canal, with glass sides, partially filled with water. On tilting one end, a wave will pass to the other end, and be there reflected. If new waves are formed by fresh impulses, we may so time the motion that the direct and reflected waves may be made to meet at any phase of their undulation. If crest combine with crest and hollow with hollow, the amplitude of the resultant wave will be doubled ; but if crest combine with hollow, both waves will disappear, and the surface become horizontal. This phenomenon is called the interference of waves. In like manner, if two sonorous waves of equal intensity meet in opposite phases, so that the condensation of one INTERFERENCE OF WAVES. 143 corresponds with the rarefaction of the other, both are de- stroyed, and silence results. The feeble sound of a tuning- fork, held in the hand, is partially due to the fact that the prongs are vibrating in opposite directions, and produce a partial interference of their waves. If a tuning-fork, when vibrating, is turned slowly around 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 sec- ond, 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 con- densation, 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 com- plete opposition, 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 again com- bine. At every even number of half seconds the sound will be doubled in intensity, and at every odd number destroyed. 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 hundred and fifty arid the other vibrates two hundred and fifty-six times in a second, the number of beats will be six. 218. Echoes are produced by the reflection of sound from distant surfaces. Let a circular wave emanate from the center, 0, and strike the plane surface, S B, with a velocity sufficient to 144 ELEMENTS OF PHYSICS. have carried it in the next moment to S P B. The parti- cles in the perpendicular ray, 0', will first strike the sur- face, and will be reflected in the direction, 0' P. When any diverging rays, as D' and 01 reach the surface, they will be reflected on the other side of the perpendiculars, MK and M' E, in the lines, O'D and 0' I, making the s ~ angles of reflection equal to the angles of incidence. Now, as the velocities of the direct and the reflected waves are the same, the reflected wave will reach the points, DPI, in the same time that the direct wave would have reached D' P T, and the same is true of all intermediate points. Hence, the reflected wave proceeds as if from a center, 0', on the opposite side of the surface, SB, and at a distance from the surface equal to that of the center, 0, of the incident wave. When the origin of the wave is far distant from the re- flecting surface, the waves will be arcs of very large circles. In such cases, the diverging rays which fall upon a small surface will be nearly parallel. Parallel rays, incident upon a plane surface, will also be parallel after reflection. Echo. The voice can not utter, nor the ear hear, more than five syllables in a second ; therefore, a distinct echo of articulate sounds will require the reflecting surface to be at least 1090 -r- (5 X 2) = 109 feet distant, as the sound has both to go from and return to the speaker. At a greater distance, two or more syllables may be perfectly repeated by the echo ; but, at less distances, the direct and reflected waves will be more or less commingled, and the echo will not be distinct. RESONANCE. 145 219. The increased intensity produced by the com- mingling of direct and reflected waves is termed resonance. Resonance is specially noticeable in empty rooms with bare, smooth walls. If the echoing walls are not distant more than thirty-five feet from the speaker, the reflected wave will reach the ear one-sixteenth of a second after the direct wave. This very short interval will not be noticed by the ear, and the voice will be strengthened without a loss of clearness. If the walls are at a greater distance the words are less distinct, unless the echoes are quenched by the fur- niture, or by the presence of an audience. 220. The echo may be heard when the direct sound is inaudi- > ble. Thus, if two concave mir- ' rors are placed opposite to each other, the ticking of a watch placed in the focus of one mirror will be so reflected that it may be heard in the focus of the other, FlG - 122 - even when placed at a considerable distance. Fig. 122. The same effect may be produced in circular rooms. In such a chamber, a whisper at one focus will be heard at the other focus, although inaudible at any other place. ' Such whispering galleries are not uncommon. The dome of St. Paul's Cathedral, London, and of the Capitol at Washing- ton, are fine examples. 221. Sound may be bent out of its course or refracted in passing from one medium to another. The laws of refracted sound are the same as those of light, and will be studied hereafter. PHYS. 13. 146 ELEMENTS OF PHYSICS. KECAPITULATION. 10 1. The quality of souncl depends on the elasticity and form of the sonorous body. 2. The pitch of sound depends on the rate of vibrations. 3. The intensity of sound increases: (1.) With the amplitude of the vibrations. (2.) With the density of the generating medium. (3.) By the proximity of a resonant body. The intensity of sound decreases: (1.) As the square of the dis- tance increases. (2.) In passing from one medium to another. The intensity 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 { (2) may combine and interfere. i (3) may be reflected or refracted. MUSICAL SOUNDS. 222. The appreciation of musical sounds varies in different persons. Some can hardly distinguish variations in pitch, although they are sensible to variations in inten- sity. All ears are deaf to some vibrations. The gravest sound is produced by 16 vibrations per second, the highest sound by 38,000 vibrations per second ; but there are many persons who can not hear very high notes like the note of a cricket, although they can distinguish very feeble sounds, as the lowest whisper. 223. More than 38,000 sound waves are possible, each one of which will, by itself, produce a pure tone. No ear is capable of recognizing, as distinct tones, one-hundredth part of these. Two tones, whose rates of vibration are nearly the same, can be distinguished from unison only by the for- MUSICAL SOUNDS. 147 mation of beats. If these beats are not readily perceptible, the ear recognizes the sound as the same. 224. Suppose a guitar string to be stretched across a sounding box, as in Fig. 123. When the whole length of FIG. 123. the string vibrates, it produces a sound called the funda- mental tone of the string. Suppose this tone to be that due to 128 vibrations in one second, as measured by Savart's wheel. If, now, the bridge, B, be placed at half the length of the string, it will make 256 vibrations per second, or twice as many as the fundamental. If the string be again halved, the number of vibrations will be again doubled, and so on. The ratio between any two tones is called an interval, and indicates how much one sound is higher than another. The interval 1 : 2 is called an octave, because, between any two tones bearing this ratio, other tones may be placed, so as to form, with the two extremes, a series of eight sounds hav- ing agreeable relations to each other. 225. These eight tones constitute the diatonic scale or gamut. They are designated by the first seven letters of the alphabet. If the length of the string which sounds the fun- damental be assumed as 1, the relative length required to produce the other tones are : 148 ELEMENTS OF PHYSICS. Tones CDEFGABC Relative length of cord. . . 1 I | | | f A i Relative number of vibrations. 1 f f f f -f V 5 2 The laws which govern the vibrations of strings are : (1) The number of vibrations per second is inversely pro- portional to the length of the string. (2) The number of vibrations per second varies as the square root of the weight by which the string is stretched. (3) The number of vibrations per second varies inversely as the square root of the weight of a given length of string. All these laws are applied in the construction of stringed instruments. The high notes on a piano 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. 226. Musicians have agreed to designate the tone due to 128 vibrations per second as C. It corresponds to C in the second space of the base clef. The number of vibrations corresponding to any other tone may be found by multiply- ing this number by the fractions -f, f, etc., which express the relative number. The actual number employed by orches- tras in different cities is not the same. For this reason a new scale of vibrations has been proposed, which give all the tones of the lower octave of the treble in whole num- bers, C 2 being 264. 227. The length of a sonorous wave is found by divid- ing the velocity with which sound travels in a second by the number of vibrations per second. In air, at 60 F., the length of the wave, C, is 1,121 -f- 128 = 8.7 feet. 228. Musical intervals are named by the order of their position with respect to the fundamental, as seconds, thirds, fourths, etc. The interval of the fifth, as CG or G Z> 2 , is MUSICAL SCALE. 149 expressed by the ratio 3 : 2. The following table gives a condensed summary of the relations of two octaves of the diatonic scale : s-m e- Hi MM! < ! M'TT" im- r4iJi-4 co .& o" * o S> O /%-. 3 .-, N ^ H- co cs g si 5 O :o (N I fa fa' -l- C " !>- O O w S ta" ^H H ~ = ' ' ^ J or %' In optics, the word dense signifies of great refractive power, and rare, of little refractive power without reference to the specific gravity of the substance. The essential oils and alcohol are in this sense denser than water, although their specific gravity is less. 262. When a ray of light passes perpendicularly from one medium to another, it is not refracted. If, in the ex- periment, on p. 166, the eye is directly above the coin, the coin is seen in its true direction, but there is also a curious effect produced of making the coin appear nearer than it really is. This is due to the fact that the rays which reach the eye from the edge of the coin are not perpendicular to the surface of the water, and hence suffer a refraction. When light passes obliquely from a rarer to a denser medium, it is refracted toward the perpendicular. When a star is near the horizon it appears to -be higher than it really is, because, as its light passes through successive strata of the atmosphere, it is refracted more and more, and appears in the direction which the ray has when it enters the eye. When light passes obliquely from a denser to a rarer me- dium, it is refracted from the perpendicular. In this case the angle of refraction is always greater than the angle of incidence. Suppose light to pass from water into air. Fig. 142. As the angle of the incident rays I T I" ', etc., increases, the angle of the refracted ray, JKR 1 R 2 , etc., also increases. There will be found some ray, as L, whose angle of refrac- REFRACTION. 169 tion is a right angle, and the ray, if refracted, would coincide with the surface. If the incident angle is increased beyond this limit, say to TON, the ray can not suffer refraction, but will be totally reflected in the angle, N T '. This result may be shown by filling a goblet with water, and placing in it a spoon. When the eye is a little below the sur- face of the water, it will see a bright image of the part of the spoon immersed, reflected from the surface of the water. REFRACTION BY REGULAR SURFACES. 263. If a transparent body is entirely surrounded by air, a ray of light, on entering it, will be refracted toward the perpendicular, and, on emerging from the body, will be refracted from the perpendicular. (1) When the two surfaces of the medium are parallel, the incident and emergent rays are also parallel; because the ray is refracted an equal amount at each surface, and in the opposite direction. The two refractions do not cause any change in the general direction of the ray, but produce a slight lateral displacement, whose amount increases with the thickness of the medium and the obliquity of the in- cident ray. Fig. 143. A pane of glass occasions no distortion of the objects seen through it when its sides FIG. 143. are perfectly parallel; if they are not parallel, the objects will appear more or less dis- torted. PHYS. 15. 170 ELEMENTS OF PHYSICS. (2) A prism is a transparent medium having two plane surfaces not parallel. A prism may be a solid wedge of glass or crystal, or may consist of liquids inclosed in hollow prisms with sides of plane glass. The path of light through a prism is exhibited in Fig. 144. Suppose the light to come from 0. As the incident ray, D, enters the prism, it is refracted towards / ?' the perpendicular, P P, because it enters a denser medium, and will FlG - 144> 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 line K H. The light is thus twice refracted toward the base of the prism, and the eye which receives the emergent ray, K H, sees the object at O f nearer the summit of the prism than the real position of the point, 0. (3) A lens is a transparent medium, having at least one curved surface. The curved surface is usually spherical. ABC D E F FlG. 145. There are six . varieties of spherical lenses, viz. : A is a double convex, B a plano-convex, C is a meniscus, concave on one side and convex on the other, the convex surface hav- ing the shorter radius. These three are thickest at the center, and are converging lenses. D is a double concave, E is a plano-concave, and F is a concavo-convex, the concave sur- face having the shorter radius. These three are thinnest at the center, and are diverging lenses. Fig. 145. DOUBLE CONVEX LENSES. Ill The line, MN, which passes through a lens perpendicular to both surfaces, is called the axis of the lens. 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. Hence, as a prism refracts light toward its base, a convex lens will re- fract the light toward its axis, and tend to converge the rays ; a concave lens will refract light away from its axis, or tend to disperse the rays. We shall study only the double convex and the double concave lenses, because the properties of these lenses are similar to the others of the same group. 264. If parallel rays fall upon a convex lens, the rays will converge to one point, which is called the princi- pal focus of the lens. This focus is real, for all the rays of the sun may be collected at this point. The ordinary burning- glass is simply a large double convex lens. Fig. 146. 265. If the rays diverge from the principal focus they will be rendered parallel. A lamp so placed will illuminate objects at a great distance. Fig. 146. 8 FIG. 146. FIG. 147. 266. If the rays diverge from a point beyond the prin- 172 ELEMENTS OF PHYSICS. cipal focus, as at I, they will converge on refraction to some point, as L, also at a greater distance than the principal focus ; and conversely if they diverge from L they will converge at L Both these foci are real ; one is less than twice the principal focal distance and the other greater. 267. Real images are formed when the object is at a finite distance beyond the principal focus. Suppose A B to be at more than twice the principal focal distance. A ray diverging from A will converge on refraction at a ; diverging FIG. 148. from B, at b. Hence, the image of A B will be a b, real, inverted and smaller than its object. Conversely, if a b were a luminous object at less than twice the principal focal distance, but beyond the focus, its image would be A B, real, inverted, and larger than the object. If the rays diverge from a point nearer the lens than ...-n FIG. 149. the principal focal distance they will be less divergent on refraction, but will form no real focus, nor even be rendered parallel. Thus, the rays from L will appear to come from a virtual focus at I, which is on the same side of the lens as DOUBLE CONCAVE LENSES. 173 the luminous point. If a small object, as A E, (Fig. 150), were so placed, a virtual image would be formed at a 6, A FIG. 150. which would be erect, and larger than the object. This is the ordinary way of using a lens as a magnifying glass. 268. The foci of concave lenses are always virtual, and the images formed by them are also virtual. Let A B be an object in front of a con- cave lens. The rays from the point, A, will be so re- fracted as to appear to come from its virtual focus, a, and the rays from the point, J?, will appear to diverge from FIG - ia - its focus, b. Therefore, the eye sees at a b an image of A B, which is always virtual, erect, and smaller than the object. FIG. 152. 269, If a crystal of Iceland spar be placed upon an object, as in Fig. 152, a double image will be perceived. 174 ELEMENTS OF PHYSICS. This phenomenon is called double refraction. Most transpar- ent bodies have the same property of refracting light in two separate pencils, but not to so great a degree. These doubly refracted rays have properties which dis- tinguish them from ordinary rays, and are said to be polar- ized. Light is also polarized by absorption, single refraction, and reflection. The subject of polarized light is so abstruse that it can not be taken up with profit in an elementary course. It must suffice us to say that when a ray has been polarized, it will neither be reflected, refracted, nor absorbed in precisely the same manner as common light, although the eye can not, unaided, distinguish one from the other. RECAPITULATION. I. Light is not refracted : 1. In passing through a uniform medium, nor 2. When passing perpendicularly from one medium to another. II. 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. III. Lenses are either converging or diverging. IV. The effects of concave mirrors and of convex lenses are simi- lar : 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. CAMERA OBSCURA. 175 5. At a finite distance, more than twice the principal focal distance, The image is real, inverted, and diminished. 6. At an infinite distance, There is concentration of light at the principal focus. V. The effects of convex mirrors and of concave lenses are also similar, forming images which are always virtual, erect, and smaller than the object. OPTICAL INSTRUMENTS, AND VISION. 270. If luminous rays are transmitted through a small aperture, and there received on a white screen, they form in- FlG. 153. verted images of external objects. The luminous rays pro- ceed in straight lines ; those from the top of the object, (Fig. 153), 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 must, therefore, cross each other without inter- fering. A darkened room so arranged is one form of the camera obscura. 176 ELEMENTS OF PHYSICS. The photographer's camera, Fig. 154, differs from this only A FIG. 154. in having a convex lens in the tube, A. The effect of the lens is to converge the rays so as to produce a small image of the object, which is, at the same time, clear and well defined. 271. The mechanical action of the eye is very similar to that of the photographer's camera. The human eye is very FIG. 155. nearly spherical, and is about an inch in diameter. It con- sists essentially of (1) three enveloping coats and (2) three refracting bodies. Fig. 155 presents these parts in hori- zontal section. THE HUMAN EYE. 177 (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 cov- ered, on its inner face, by a dark, velvety substance, called the black pigment. The inner coat is the retina, m, which is mainly an expan- sion of the optic nerve, n, with the addition of terminal 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 liwnor. 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. 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 cut off by the iris, 178 ELEMENTS OF PHYSICS. and only those that are nearly parallel are admitted through the pupil. These are transmitted through the crystalline and the vitreous humor, arid finally fall upon the retina. The effect of these refracting bodies is to form at, or very near, the retina an image of the luminous point. The same being true of all diverging pencils proceeding from an object, there will be formed on the retina a small inverted image of the object. 272. 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 a layer next the black pigment, and consist of a great num- ber of very minute bodies, arranged side by side, and re- sembling 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 vibra- tions, which are conducted by the nerve fibers in such a way to the brain that it is excited and acknowledges the recep- tion of the luminous image on the retina. 273. 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 Thaurnatrope, Fig. 156, con- sists of a card which is made to revolve by means of strings G. isc. attached to its sides. A horse may be so painted on one VISION. 179 side and a rider on the other, that a rapid revolution of the card will cause the rider to appear seated on the horse. 274. The accommodation of the eye to different dis- tances is effected by the action of the ciliary muscle upon the crystalline lens. When the eye is turned toward a dis- tant object, the muscle relaxes and the lens is flattened ; but, for near objects, the muscle contracts and the lens becomes more convex. In this way the conjugate focus of the object is made always to fall upon the retina. The power of ac- commodation 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 the letters on this page, are seen most distinctly. This distance, which, for ordinary eyes, varies from five to ten inches, is called the distance of distinct vision. 275. Par-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 a short dis- tance, varying from three inches to twenty feet. For normal eyes, the farthest point of distinct vision is infinitely distant, the nearest point more than three inches. 276. An object will not appear distinct to the normal eye unless the rays which proceed from it enter the eye nearly parallel. This will be the case for a luminous point when it is distant more than eighteen inches. If a printed page be brought too close to the eye, the letters appear more or less blurred, because the rays are too divergent to focus on the retina. Now, place between the eye and the page a thin card in which a pin-hole has been pricked. The card will exclude the outer divergent rays, and the eye will be able to converge the few nearly parallel rays which pass through the pin-hole upon the retina, and thereby form a 180 ELEMENTS OF PHYSICS. faint, but distinct, image. At the same time, the letters will appear magnified, because the visual angle is increased. 277. A convex lens placed a little nearer an object than its focal distance will converge all its rays upon the retina, thus preserving all the light while it magnifies the object by increasing its visual angle. With a powerful lens the object must be very near the lens, and, consequently, the field of view will be very small. The magnifying glasses used for viewing pictures magnify but little, because their radius of curvature is very large, but they afford a large field of view. Pocket microscopes usually contain two or three convex lenses, acting as a single thick lens. They seldom magnify more than five diameters. 278. The compound microscope consists of an object- glass, M, of short focus, and an eye-glass, N, of less magni^ fying power. The object, A B, is placed a little beyond the M focus of the object-glass, and its real image, a 6, inverted and magnified, is formed a little within the focus of the eye-glass. By this glass the real image is viewed as with a simple microscope, and, hence, forms another image, a' b', which is still more magnified, and is virtual. The advantage of this form of microscope is that a high magnifying power is ob- tained with a comparatively large field of view. The difference between the simple and compound micro- scopes consists in this, that in the simple microscope the object is viewed directly, and in the compound microscope a real magnified image of the object is viewed with a common magnifier. THE TELESCOPE. 181 279. The telescope is used for viewing distant objects. In refracting telescopes a real image is formed by an object- glass of small convexity ; in reflecting telescopes a real image is formed by a concave mirror ; these images are, in both cases, very small, but very bright. They are then viewed by an eye-glass of high magnifying power. 280. The astronomical refracting telescope consists of the object-glass, M, and the eye-glass, N. Fig. 158. The object-glass forms an inverted image, b a, of a distant object, FIG. 158. A B, in its principal focus, F. This image is then viewed by the eye-glass, JV, which is so placed as to receive the image at a distance a little less than its own focal length. The image is inverted. This occasions little inconvenience in viewing heavenly bodies, but would be a serious defect if employed for terrestrial objects. 281. The terrestrial telescope has, therefore, two addi- tional lenses for rendering the image erect. Fig. 159. The A M, FIG. 159. action of these glasses, P and Q, will be understood by tracing the rays from the luminous point, A. P renders them parallel, and gives them a new direction. Q converges them in the focus of the eye-glass, so as to form a real image which has the same position as the object. This second 182 ELEMENTS OF PHYSICS. image is then viewed in the ordinary way by the eye-glass, R. 282. Reflecting telescopes have several different forms. Herschel's telescope is represented in Fig. 160. It consists ,. o FIG. 160. of a concave reflector, M, and a convex lens, 0. The reflector is so inclined to the axis of the tube that the image of the star is formed near the side of the tube, in front of the eye-piece, 0, and is then magnified by the lens and received by the eye. Lord Rosse's telescope has a mirror six feet in diameter. The amount of available light received at the eye-piece exceeds 250,000 times as much light as commonly enters the eye. This enormous illuminating power enables the observer to use eye-glasses whose magnifying power is 6,000 diameters. This would render an object as large as the capitol at Washington visible at the distance of the moon. Alvan Clarke, of Boston, has lately succeeded in making a refracting telescope for the Washington observatory, whose object-glass is 26 inches in diameter. 283. The magic lantern is an instrument by which translucent objects are magnified and thrown on a screen. Fig. 161. A lamp is placed in the common focus of a reflector, M N, and of a convex lens, A, so that a strong beam of light is thrown on the object which is inserted in THE STEREOSCOPE. 183 the slit, CD. A magnifying lens at B forms an image of the object on the screen, EF. The objects are usually painted on glass, but the instrument may also be used to magnify any translucent object. FIG. id. The solar microscope is essentially a magic lantern illumi- nated by the sun. 284. 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. 162. the two images formed on the retina will not be exactly alike. Fig. 162 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. 163, is contrived to assist the eye in blending two slightly different pictures of the same object, taken 184 ELEMENTS OF PHYSICS. from points of view related to each other in the same man- ner 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 dia- phragm, D, (Fig. 164), prevents each eye B FIG. 1G4. FIG. 163. 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 0, and the rays from the lens, N, also appear to come from C. Thus, the two pictures are blended in one, and appear to come from a solid object at C. RECAPITULATION. Enveloping coats. C Sclerotic, j Choroid. (. Retina. Refracting bodies. ( Aqueous humor I Crystalline lens. ( Vitreous humor. I. The human eye consists of II. The sensation of sight is produced by luminous vibrations passing through the cornea, aqueous humor, pupil, crystalline lens, 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. III. All optical instruments are combinations of either prisms, lenses, or mirrors. CHROMATICS. 185 IV- Microscopes are used for magnifying near objects. Telescopes are used for magnifying distant objects. V. Microscopes are simple, and compound. Telescopes are refracting, and reflecting. CHROMATICS, OR COLORS. 285. 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. 165). If, now, a prism be placed in the path of the pencil, it will form on a screen an elongated band of colors, which FIG. 165. is called the solar spectrum. That is, the prism not merely refracts the rays, but refracts them unequally, and produces what is called the dispersion of light. Newton distinguished seven of these colors as primary, which are, beginning with the least refracted, red, orange, yellow, green, blue, indigo, violet. 286. White solar light is, therefore, composed of differ- ent colored rays. An additional proof of this is found in the PHYS. 16. 186 ELEMENTS OF PHYSICS. fact that, when all the colors of the spectrum are recono- bined, they will reproduce white light. Thus, if all the FIG. 166. rays of the spectrum are received on a convex lens or on a concave mirror, a white image will be formed in the focus. If a circular card be painted with the seven colors and revolved 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 spectrum. Fig. 166. 287. If the solar light be admitted through a very A JJ. f , G J.IJ J OAKK HEAT KAYS CHEM/CAL KAYS FIG. 167. narrow slit and received on a good flint-glass prism, it will FRAUNHOFEES LINES. .187 be found that the colors of the spectrum are not continuous, but that they are interrupted by numerous dark spaces, known as Fraunhofer's lines. On viewing the spectrum with a telescope two thousand of these lines are visible. Seven are more distinct than the rest, and are designated by the letters B, C, D, E, F, G, H, to serve as means of reference. Fig. 167. 288. The index of refraction for the different colors is fixed with precision by ascertaining the position of Fraun- hofer's lines, B, C, etc. The table on p. 167 gives the index of refraction for the line E in the yellowish -green rays, which is assumed as the mean of all the rays. If similar prisms are made of different substances the mean refraction may be very nearly the same, and yet the spectra they fur- nish be of very unequal lengths. The dispersive power of a medium indicates the amount of separation it produces in the extreme rays compared with the amount of refraction in the mean rays. Table of Dispersive Powers. Bisulphide of Carbon 0.130 Crown-glass . . . 0.036 Flint-glass .... 0.052 Water .... 0.035 Diamond .... 0.038 Quartz crystal . . 0.026 289. If two prisms, exactly alike, are placed near each other, with their bases turned in a contrary direction, the one will ex- actly neutralize the other, and the light will emerge from the second as if from a medium with parallel faces. Now, suppose two unequal prisms, one of flint and the other of crown-glass,* be placed together, as in Fig. 168. The dispersive power of flint-glass is almost double that of crown-glass, while 188 ELEMENTS OF PHYSICS. its refractive power is but little greater ; hence, if the refract- ing angle of the former is made so much smaller than the latter that their dispersive powers are equal, only white light will emerge, but it will be refracted with about half the refracting power of a single prism of crown-glass. An achromatic lens is made on the same principle by combining a double convex lens of crown-glass with a concavo-convex lens of flint-glass. Fig. 169. Such a lens transmits un colored light. In any single lens, the image is fringed with colored rays, which are due to the dispersive power of the lens. 290. The spectra formed by artificial lights are usually wanting in several colors, but yield the remainder with the same refrangibility as the corresponding colors of the solar spectrum. An almost colorless flame may be produced by burning pure alcohol, or by burning gas in a Bunsen's burner. If a platinum wire be dipped in common salt, or in any sodium compound, and held in a colorless flame, the sodium will vaporize and emit a very pure yellow light. Lithium yields a pure red. Several other substances yield characteristic colored flames: thus, strontium gives a red color ; potassium, purple ; copper, green. 291. The spectroscope is an instrument used for analyz- ing flames. Fig. 170. The substance which colors the flame is placed on platinum wires in a Bunsen's burner at E, and vaporized. The light which it emits is received through a narrow slit in the end of the tube, A, where it is condensed by lenses and thrown on the prism, P. The refracted rays fall on the object-glass of a small telescope, B, and pass through it to the eye. The tube, C, is not neces- sary, but is added for the sake of convenience. It contains a transparent scale which is divided into equal parts. When THE SPECTROSCOPE. 189 a candle is placed in front of C, it casts a bright image of the scale on the prism, which is reflected into the tube, B, FIG. 170. so that the observer sees at once the refracted rays and the lines of the scale to which they correspond. Sodium gives a bright line, identical in refrangibility with the dark line, D, in the solar spectrum. Thallium gives a green line near the dark line, E. The light emitted .by these substances is monochromatic ; that is, of only one color. Potassium gives a red line near A, and a violet ray near H. Strontium gives several red lines between B and D, and a blue line between F and G. The light emitted by these substances is, therefore, not homogeneous, but contains two colors. Any substance which can be volatilized will furnish a spectrum of a few bright lines which have a constant degree of refrangibility. This is also true of incandescent 190 ELEMENTS OF PHYSICS. gases : hydrogen yields three bright lines, which are iden- tical in position with C, F, G. If several substances are mixed, each will give its own system of lines as if it were burned separately. This property has been turned to account in chemistry in detecting the presence of sub- stances that are easily volatilized. For these bodies, it is an exceedingly sensitive test. It is, in fact, difficult to obtain a flame that does not show the presence of sodium, as ToWnro f a grain of sodium will yield its yellow line. Since the year 1860 four new metals have been discovered by the aid of the spectroscope. Two of these, caesium and rubidium, are widely distributed, being found in many min- eral waters, and in the ashes of tobacco, but in such small quantities that the usual chemical tests failed to detect them. 292. If light, which would give a continuous spectrum, is passed through certain almost transparent and colorless solutions and then examined, dark lines are found, which are owing to the fact that the solution has absorbed some of the rays. Thus, solutions of didymium give two dark lines, one in the yellow and the other in the green. The gases also produce absorption bands; the 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 Fraunhofer's lines are, undoubtedly, due to the air, but the larger portion must have another cause. 293. If two sodium flames are placed before the spec- troscope, so that one must pass through the other, no spectrum is produced. In other words, sodium vapor absorbs the same rays that it emits. So, also, if the lime-light which gives a continuous spectrum is passed SPECTR UM ANAL YSIS. 191 through a sodium flame, a dark line is found in the place where the yellow sodium ray should be, and the spectrum is said to be reversed. These phenomena are exhibited by so many substances that we may group the effects produced in two general statements. (1) Every substance, when rendered luminous, gives out rays of a definite degree of refrangibility. (2) Every substance has the power of absorbing the same kind of rays that it emits. 294. In view of these facts, Kirchhoff supposes (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 elements, each of which would, by itself, give its system of bright lines ; (3) that when the light from the nucleus is transmitted through this luminous atmosphere, the bright lines that would have been produced by the atmosphere are reversed ; and (4) that Fraunhofer's lines are these reversed lines. Since the bright lines of the elements coincide with very many of Fraunhofer's lines, it is fair to suppose that these elements exist in the sun. Iron gives four hundred bright lines which coincide with Fraunhofer's lines. Eighteen dif- ferent metals give similar coincidences. Hence, we are led to suppose that the sun contains iron, manganese, nickel, calcium, copper, sodium, hydrogen, and some other ele- ments. Hitherto no evidence has been given of the presence of gold, silver, mercury, and many other elements. The fixed stars also show similar coincidences ; thus Sirius and Aldebaran are thought to contain sodium, magnesium, and hydrogen. The comets and nebulae give spectra with bright lines, which seem to show that these bodies are incandescent gases. 192 ELEMENTS OF PHYSICS. 295. When a sunbeam falls on a film of oil floating on water, or on a soap-bubble, we notice a very brilliant dis- play of colors. The light is reflected to our eyes both from the outer and inner surface of the film, and produces the phenomena of interference and combination. This is a con- firmation of the wave theory of light. We may obtain similar phenomena in various ways. One of the simplest methods is the following : Press together a convex lens, A B, of long radius of curvature, upon a plate of plane glass, D E. If a beam of monochromatic light falls ^* J? fr perpendicularly on the lens, a F *G. 171. portion of it will be reflected from the convex surface, ACB, and another portion from the plane surface, D E. These two systems of waves will intersect in crests and hollows according as their paths differ by an even number of semi-undulations, or by an odd number. At a certain distance FIG. 172. from 0, as at F, the two waves will meet in opposite phases and destroy each other, and, hence there will be a black ring at F. At a greater distance, as at G, the waves will meet in the same phase and increase the amplitude of vibrations, and there will be a bright ring of the same color as the light. Other points will be found beyond G, in which the waves will meet in opposite or in sim- ilar phases, and, consequently, a series of black and colored rings will be found about the center, C. If the solar light be employed, each ring contains all the colors of the spectrum, because the colors have different refrangibilities, and the rings are not exactly superimposed. 296. These rings are known as Newton's rings. Now, as we can calculate exactly the distance between the two surfaces, we have a means of determining the wave length COLOR OF LIGHT. 193 due to various colors. The following table has been con- structed in accordance with these data : Colors. Lengths of waves in parts of an inch. Number of waves in an inch. Number of waves in a second. Extreme red . . . Red .0000266 .0000256 37640 39180 442000000000000 458000000000000 .0000240 41610 489000000000000 Yellow .0000227 44000 517000000000000 .0000211 47460 558000000000000 Blue .0000196 51110 599000000000000 .0000185 54070 634000000000000 Violet .0000174 57490 675000000000000 Extreme violet . .0000167 59750 702000000000000 297. The color of light is determined by the frequency of its vibration, or by the length of its wave. Light and sound are somewhat similar. We found that the low tones have a slow rate of vibration and a great wave length. So the luminous rays that are the least refracted are longer and slower than those that are more refracted. But the student will not fail to notice how very small and how very rapid are light waves when compared with sound waves. 298. It is usual to classify the properties of the spec- trum in three groups : Luminous, Heating, and Chemical. Every ray possesses, it is probable, all of these properties, but not in equal intensity. Thus the maximum chemical effect is found in the rays of high refrangibility ; the maxi- mum heating effect in the rays of low refrangibility; the maximum luminous effect in the rays of nearly mean refran- gibility, viz. : the yellow. The curves in Fig. 167, show the relative intensity of each property in a spectrum pro- duced by flint-glass. It will be noticed that the spectrum PlIYS. 17. 194 ELEMENTS OF PHYSICS. is drawn as if extending beyond the colored rays ; that is to say, there are heat rays that the eye can not perceive because their rate of vibration is too slow, and there are chemical rays which it can not perceive because their rate of vibration is too great. These invisible rays do not differ in kind from the visible rays. Some persons are color-blind, and can not distinguish colors at all, although in every other respect their sight is perfect. The most common defect of this sort is an in- ability to distinguish red colors. A person "red-blind" believes that ripe cherries are of the same color as the leaves which hang near them. 299. The natural color of a body is due to the power it has of extinguishing certain vibrations, and of reflecting or transmitting others. A red cloth reflects the red rays and absorbs the rest ; red glass transmits only the red rays. A body that reflects all the rays of the solar spectrum is white ; a body that reflects but very little light is black. A curious experiment illustrates that the color of a body is not inherent. Darken a room, and then set on fire a cup of alcohol which has been saturated with common salt: every object will be illuminated by the yellow light of sodium, and appear of a yellow color. As this light falls on the faces of those near the cup, it gives them a ghastly appearance, which is quite wonderful to those who see the effect for the first time. RECAPITULATION. When solar light is examined with 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 spectrum in many particulars. All spectra have luminous, thermal, and chemical properties, but not in equal intensity. COLORS. 195 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 reflection and refraction. Colors are dependent on the frequency of the luminous vibrations. PEOBLEMS. 1. It is calculated that the light from the polar star requires 3 years to reach the earth ; what is its distance ? 2. What are the relative intensities of two lights that cast equal shadows at distances from an opaque rod respectively 6 inches and 6 feet? 3. A wax candle is fixed at 10 inches from the opaque rod ; what must be the distance of a gas-light from the same rod to cast an equal shadow when the gas burns with "12 candle power?" 4. What will be the index of refraction when light passes from crown-glass into bisulphide of carbon? When it passes 'in the other direction? 5. What will be the relative lengths of two solar spectra produced under the same circumstances by prisms of quartz and of bisulphide of carbon? 6. With red taken as unity, find the ratio between the relative number of vibrations in the colors of the spectrum, and compare with the relative number of sonorus waves in an octave. Will the comparison warrant any analogy between vibrations of light and of sound? CHAPTER XV. THE PHENOMENA OF HEAT, OR PYRONOMICS. 300. The phenomena of heat are so generally manifest that we have had frequent occasion to refer to them, and have explained the methods by which heat may be meas- ured. It may be noticed that our sensations of warmth and cold are only relative, and are sometimes utterly untrust- worthy as a means of measuring heat. If we place the right hand in iced water and the left in hot, and then transfer both to ordinary cistern water, the left hand will pronounce the cistern water cold and the right hand pro- nounce it warm. So, also, if we pass from the outer air of a winter's day into a heated room, our sensations may lead us to declare it overheated, even while the occupants of the room are somewhat chilly. We have also noticed that one effect of heat is to render bodies incandescent, and that the solar rays have their maxi- mum heating effect near the red rays. These phenomena, as well as others that we shall have occasion to study, so connect heat with light that we are almost justified in assum- ing that their phenomena are due to the same force. Both are certainly forms of energy by which molecules of matter are thrown into vibrations and give rise to waves of crests and hollows. They differ in the fact, that the eye recognizes as light only those waves which have certain limits of rapidity of motion, and which are, at best, very small, while waves of heat can be recognized that are, in comparison, large and of slow rate of motion; although it is not meant to be (196) EFFECT OF HEAT. 197 stated by this that heat waves may not also accompany, or be identical with, the most refrangible luminous waves. Besides these phenomena, heat produces certain effects within the bodies upon which it acts, which we shall now proceed to consider. 301. The first effect of heat on any body, solid, liquid, or aeriform, that is not destroyed by it, is to expand it. The expansion of gases may be shown by the air- ther- mometer. Fig. 173. This consists of a bulb of glass with a long stem, which dips into a colored fluid. ^. If the bulb be warmed by the hand, the air inclosed will so expand that a portion will be expelled and rise in bubbles through the fluid. On cooling, that portion of the air which remains will contract to its former volume, and the fluid will rise to take the place of the air expelled. On repeating this experiment with other gases, it will be found that att aeriform bodies expand equally and regularly for equal successive incitements of temperature. The ex- pansion is T | T for each degree F., or for each degree C. The expansion of liquids may be shown by a flask having a long narrow tube fitted to its neck by a cork. Fig. 174. If the flask be filled with alcohol and plunged in boiling water, the expansion of the alcohol will be shown by its rise in the tube. Coal oil expands more than alcohol, but most other liquids less, showing that different liquids expand unequally for the same increments of temperature. FIG. 174. ]y[ ore accurate experiments show that each liquid also expands irregularly. On being raised from 32 F. to FIG. 173. 198 ELEMENTS OF PHYSICS. 212 F. alcohol expands ^ of its volume, water about ^ T , and mercury -%-%. The expansion of solids may be illustrated by the ap- paratus given in Fig. 5. * These 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. Fig. 175 represents the pyrometer, an instrument which shows the linear expansion of solids, and which is sometimes FIG. 175. used to measure very high temperatures. A metallic rod, A, fixed at one end, B, presses at the other end the short arm of the index, K. When the rod is heated it expands and drives the index along the scale. 302. Different solids expand unequally for equal in- crements of temperature. If two thin bars of iron and brass are riveted together at different points along their whole length, and boiling water is poured on them, it will FIG. 176. FIG. 177. bend so that the brass will be on the convex side of the curve. If it is then plunged in cold water, it will curve in the opposite direction. The reason of this is, that the brass expands and contracts more than the iron, and the bar curves, so that the longest bar shall be on the convex side. EXPANSION. ' 199 Tabk of Expansion from 32 F. to 212 F. Linear. Cubical. Linear. Cubical. Flint-glass . ^ s ^ Brass . . . . -gfa Platinum . . y^ ^ Silver .... -5^4 Steel .... ^ 3^ Tin ..... ?) -L- ^ Iron .... -^ ^k ZinC 1*7 TT3 The fractions in the above table of linear expansion show what proportion of its length a body will increase in being raised from 32 F. to 212 F. It will be noticed that the cubical expansion is expressed by a fraction three times as large. With very few exceptions, all bodies contract on cooling to their original dimensions. 303. When water is heated from 32 F. to 212 F. it expands .0466 of its volume ; it is compressed by a pressure of one atmosphere .000044 of its volume. Therefore, it would require a pressure of over 1000 atmospheres to restore boil- ing water to its bulk when at the freezing point, or to pre- vent its expansion on being heated 180. We see from this that the amount of force exerted in expansion or contrac- tion by heat is enormous. The expansive force of water for each degree F. is nearly y% / = 6 atmospheres, or 90 pounds per square inch. A bar of wrought iron expands for each degree F. with a force of nearly two hundred pounds per square inch. Hence, it is often necessary to take into account the changes in length which are produced by variations in temperature. Iron beams built into masonry should be left free at one end. We have an application of the same principle in the method by which tires are secured on wheels. The tire, made a little smaller than the wheel, is heated red-hot, and, 200 ELEMENTS OF PHYSICS. while expanded, placed in position. On cooling, it not only secures itself on the rim, but holds all the other parts of the wheel in position. Brittle substances, as glass or cast-iron, often crack when heated suddenly ; because the outside is heated sooner than the inside, and thereby causes an unequal expansion. The thicker the plate, the greater the liability to fracture. A sudden cooling by producing an unequal contraction, has the same tendency to fracture. 304. Water presents an exception to the general law of expansion and contraction by heat. If a flask with a long and very slender neck, Fig. 174, be filled with boiling water and allowed to cool, the water will contract 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 occu- pies the same space that it did at 48 F. The maximum density of water is, therefore, 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, expan- sion begins at the surface, and the lighter, though colder, particles float on the warmer particles below. Hence, the freezing takes place only at the surface. At the moment of freezing, water, in becoming solid ice, undergoes a sudden increase of about ten per cent in volume. The ice, once formed, covers the water like a blanket, and renders the freezing process very slow. If the ice had a greater specific gravity than water, it would sink to the bottom, and in time our lakes would become solid. 305. The second effect of heat on a solid is to melt it. Some solids, as paper, wood, wool, do not melt, but are de- composed. The temperature at which any solid melts is FUSION. 201 invariable for the same substance, if the pressure is the same. This temperature is called the melting point. Table of Melting Points, in Degrees Fcdirenlieit. Mercury" .... -37.9 Bismuth .... 512. Bromine .... -f- 9.5 Lead 620. Ice 32. Zinc 680. Phosphorus .... 111.5 Silver .... 1832. Potassium .... 136. Gold ..... 2282. Tin 451. Wrought Iron . . 2912. Certain bodies, as iron, platinum, glass, and wax, soften before they fuse and become plastic. It is in this plastic state that glass is worked and iron or platinum forged. The melting point of alloys is often lower than that of either of its components. Rose's metal, which consists of four parts of bismuth, one of lead, and one of tin, fuses at 201 F. 306. If a liquid is cooled sufficiently it generally solidifies at the melting point, but the freezing point may be lowered by various means. If water is boiled to expel the air and then allowed to cool very slowly and without agitation, it sometimes reaches 10 F. before it freezes. When in this condition, any dis- turbance, as a jolt or the addition of a bit of ice, will cause immediate congelation throughout the entire mass. The temperature will rise to 32 F. In fine capillary tubes, water has been lowered to 4 F. without solidifying. This probably explains why sap is not frozen in plants. The presence of salts in solution lowers the freezing point of water. Saturated brine freezes at 4 F. Sea-water freezes at 27. 4 F. In such cases, nearly pure ice is formed. The water appears to crystallize out, leaving the salt behind. Weak alcoholic mixtures, like wine and cider, may be con- '202 ELEMENTS OF PHYSICS. centrated by exposing them to cold and removing the layers of ice as they form. 307. Water expands with enormous force at the mo- ment of freezing. Bomb-shells an inch thick, filled with water, have been burst by the freezing of the water. On a smaller scale, the fact is familiar to northern housekeep- ers in the breaking of utensils in which water has been allowed to freeze. Cast-iron, bismuth, antimony, and type- metal also expand on solidifying. These substances give sharp casts, because, when the metal gets, the expansion forces it into the minute lines of the mold. Most sub- stances contract on solidifying. Coins of copper, silver, and gold are not cast, but stamped. 308. The third effect of heat is vaporization. Some solids, as iodine, arsenic, and camphor, vaporize without becoming liquids ; but, generally, vapors are formed from liquids, as liquids are from solids. If the vaporization takes place quietly, it is termed evaporation; but, if the liquid is agitated by the formation of bubbles of its own vapor, the process is termed boiling. 309. The evaporation of water is going on constantly in nature, and is one of the means by which the earth is rendered fit for the maintenance of life. The principal cir- cumstances which influence the evaporation of water are the following : (1) The temperature. Evaporation may go on at very low temperatures. Snow and ice disappear from the ground even when there has been no thawing. Clothes are dried on a winter's day when the thermometer shows a tempera- ture below freezing. Increase of temperature favors evap- oration. In summer, the roads are soon dry after a shower, "because the evaporation is rapid. EVAPORATION. 203 (2) Tlie amount of surface exposed; because evaporation proceeds only from the surface. (3) Tlie condition of the air. The air can hold only a limited amount of aqueous vapor. At 32 F. one cubic foot of air can hold only 2.37 grains of aqueous vapor, which is ^-s-Q part of its weight. For every increase of 20 F. the capacity of air for moisture is nearly doubled ; at 52 F. it can absorb T ^-- part of its weight ; at 72 F. about part, and so on. When air contains as much moisture as it can hold, it is said to be saturated, and evaporation must cease. Therefore, evaporation is most rapid in dry air. Now, if the air above a liquid is not changed, it becomes saturated. Hence, evaporation is more rapid in a breeze than in still air. For this reason a warm, sultry day is less favorable to evaporation than a cold day with a brisk wind. 310. Suppose air at 72 F. to be saturated with moist- ure, and then to cool gradually. As the temperature low- ers, its capacity for moisture decreases, and a portion of the moisture present will be deposited as dew. If the tempera- ture falls to 52 F. half of the original quantity will have been deposited. Now, suppose the air at 72 F. to have been nearly but not quite saturated ; as the temperature is lowered, a point will be reached at which the air is satu- rated, and then a temperature at which the dew will begin to form. This last temperature is called the dew-point. The dew-point may be determined with sufficient accuracy for ordinary purposes by placing ice in a tin cup containing water, and noting, by a thermometer, the temperature of the water when the dew begins to form on the outside of the vessel. The " sweating" of pitchers is an indication of rain, because it shows that the air is nearly saturated with moist- ure, which will fall if the temperature of the air is lowered below the dew-point. 204 ELEMENTS OF PHYSICS. Our comfort depends largely on the amount of moisture present in the atmosphere. If the air is saturated, the per- spiration is not carried off from our bodies ; if it is, at the same time, warm, we perspire more, and the air is said to be sultry. If the air is too dry, the moisture is carried off too rapidly from our lips and eyelids, and they become dry. 311. The temperature at which liquids boil is con- stant for the same substance, under like conditions. Sev- eral conditions influence the boiling point: 1. The nature of the liquid. The boiling point of several liquids under the pressure of one atmosphere is given below. Table of Soiling Points. Nitrous oxide . 157 F. Bromine . . 145.4 F. Carbonic acid . 108.4 Alcohol . . . 173.1 Sulphurous acid -f 17.6 Water . . . 212. Ether 94.8 Mercury . . . 662. 2. The adhesion of the liquid to the vessel that contains it. Water sometimes boils in a glass vessel at 214 F. ; espe- cially is this apt to be the case if the water has been deprived of air by previous boiling. 3. Salts in solution increase the boiling point. A satu- rated solution of common salt boils at 227 F.; of calcium chloride at 355 F. Substances mechanically suspended, like sawdust, do not influence the boiling point. The steam which forms in the last two conditions assumes almost imme- diately the temperature of 212 F. 4. Variations of pressure. A liquid boils when the tension of its vapor is equal to the pressure which it supports. If a cup containing 'ether be placed under the receiver of an air-pump, the ether will boil when the receiver is partially exhausted. So, also, tepid water may easily be made to boil in an exhausted receiver. BOILING POINT. 205 FIG. 178. The culinary paradox illustrates the same principle. A flask containing boiling water is tightly corked while the steam is escaping, and in- verted. If, now, cold water be poured on the bottom of the flask, the boiling will be renewed. The reason of this is, the cold water condenses the steam above the water, produces a partial vacuum, and thus diminishes the pres- sure on the liquid. The sirup of sugar and of vegetable extracts are concen- trated in closed vessels, called vacuum pans. A powerful air-pump constantly removes the pressure from the pan, and, consequently, the evaporation proceeds at a temperature so low that it secures the sirup or the extract from injury by heat. 312. A variation of an inch in the barometric column makes a difference of about 2 F. in the boiling point of water. The atmospheric pressure is lowered on ascending mountains; hence, water boils at lower temperatures on mountains than at the sea level. A difference of 600 feet of ascent makes a variation of about 1 F. in the boiling point. Under increased pressures the boiling point is raised. If \vater be placed in a small boiler, Fig. 179, furnished with a thermometer, a manometer, and a stop-cock, and boiled, it will be found that so long as the stop-cock is open the tem- perature of boiling will remain steadily at 212 F. On closing the cock the boiling point will rise, because the steam which continues to form increases in elastic force, and produces pressure on the water. When the manometer 206 ELEMENTS OF PHYSICS. shows a pressure of thirty inches of mercury, the boiling point will equal 249. 5 F. This is the boiling point due to two atmospheres : one shown by the manometer ; the other, the atmospheric pressure present before closing the cock. If steam is formed in a boiler and then conducted through red-hot tubes, it follows the general law for expansion of gases, and is then called superheated steam. Such steam is applied to the rendering of fats. 313. Every one must have noticed that when drops of water are thrown on a heated stove they roll about, becoming gradually smaller, and finally disappear in a sort of explosion. The explanation of this phenom- enon is, that as soon as the drop reaches the F IG . 179. surface a portion of it is converted into vapor, which sup- ports the liquid and prevents it from touching the heated metal. The drop assumes what is called the spheroidal state, and evaporates at a temper- ature lower than its boiling point. If a copper flask be intensely heated, and a small quantity of water poured in, the water will assume the spheroidal condition, and, for a time, all will appear quiet. Fig. 180. Now cork the flask and remove the source of heat. When the flask has sufficiently cooled, the water will come in con- tact with its surface, and so much steam will be formed FIG. 180. LIQUEFACTION OF VAPORS. 207 suddenly that the cork will be ejected with violence. It is probable that boiler explosions are sometimes caused in a similar manner. There are some curious phenomena which are due to the spheroidal state. Thus, if sulphurous acid is thrown into a capsule heated white hot, it assumes a spheroidal state, and remains at a temperature of 13 F. Water thrown into it will instantly freeze. So, also, a hand moistened with water may be drawn without injury through molten iron as it runs from the furnace. The moisture forms a non-conducting envelope which sufficiently protects the hand during the short period of its immersion. 314. A saturated vapor condenses into a liquid at its boiling point. The process of distillation illustrates this m^. | f^ si II ^.-^ ~j~ '___ 1 FIG. 181. fact. It is used to separate volatile liquids from mix- tures. Fig. 181 represents a common still : the boiler, a, contains the liquid to be evaporated; the spiral tube, del, 208 ELEMENTS OF PHYSICS. which is called a worm, receives the vapors from the boiler. The worm is kept cool by being surrounded with cold water, and the vapors condense within it and run into a suitable receptacle. KECAPITULATION. 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. SPECIFIC AND LATENT HEAT. 315. Let us now consider some facts relative to the amount of heat which is required to produce changes of tem- perature in known weights of different substances. We as- sume as a relative measure of the quantity of heat that may be gained or lost by a body the thermal unit, which is the amount of heat required to raise one pound of water from 32 F. to 33 F. Suppose, now, that we have a uniform source of heat, as an alcohol lamp that consumes a pint of alcohol an hour, and suppose that in our experiments no heat is wasted in heating the apparatus, or the surrounding objects. If we em- ploy this heat in warming different substances, we should find two sets of phenomena: those of specific, and of latent heat. SPECIFIC HEAT. If one pound of water were raised from 32 F. to 33 F. in a given time, the same amount of heat would be competent to raise five pounds of sulphur or SPECIFIC HEAT. 209 thirty pounds of mercury from 32 to 33 F., or would raise one pound of sulphur five degrees F. and one pound of mer- cury thirty degrees F. The heat required to raise one pound of any substance through 1 F., compared with the thermal unit, is called the Specific Heat of the substance. 316. We may determine the specific heat of bodies by reversing this experiment. Suppose equal weights of differ- ent bodies be heated to the same temperature in a bath of boiling water or oil, and then placed in cavities in a cake of ice. In comparison with water, sulphur will melt i, iron J, and mercury ^ as much ice. These fractions express the spe- cific heats of these substances, because the heat given out in cooling is precisely equivalent to that required to raise the same body through the same number of degrees. 317. The specific heat of aeriform bodies may be de- termined by passing a heated gas through the worm of a distilling apparatus, and noting the rise in temperature produced in the water when a given weight of gas has been cooled to a known temperature. 318. The specific heat of a substance increases slightly with a rise in the temperature, and is generally much greater in the liquid state than in either the solid or the aeriform condition. These facts are shown in the annexed tables. Tables of Specific Heat. Between Between 32 F. and 212 F. 32 F. and 572 F. Mercury 0330 .0350 Silver 0557 .0611 Iron 1098 .1218 Glass 1770 .1900 PHYS. 18. 210 ELEMENTS OF PHYSICS. Aeriform. Liquid. Solid. Water 4805 1.0000 .5050 Bromine 0555 .1060 .0843 Lead .0482 .0314 Alcohol 4534 .5050 Equal volumes. Equal weights. Air 2375 .2375 Oxygen 2405 .2175 Hydrogen 2539 3.4090 Turpentine 2.3776 .5061 319. With the exception of hydrogen, water possesses the highest specific heat known. The presence of large bodies of water has, for this reason, a marked effect on the climate, owing to the large amounts of heat which seas absorb and emit in accommodating themselves to changes in external temperatures. An oceanic climate is, therefore, more equable than an inland climate ; its summers are cooler and its winters warmer. On the islands of Lake Erie, water does not freeze until the water of the lake has cooled to 40 F., thus prolonging the season sufficiently to ripen grapes. A daily effect is witnessed in tropical islands in the land and sea-breezes. While the sun shines, the land becomes warmer than the ocean, and, by consequence, the air above the land becomes rarefied by the heat, and is displaced by the cold air which presses in from the ocean, and a sea-breeze is produced ; in the night, the land is sooner cooled, the air above it becomes more dense and flows out to the ocean in a land-breeze. LATENT HEAT. These facts show that different bodies require different quantities of heat in order to increase their temperature. Suppose, now, that we employ heat sufficient LATENT HEAT. 211 to melt them or to vaporize them. If a thermometer be placed in a basin filled with melting ice, it will remain at 32 F. until the whole is melted. The temperature will then rise to 212 F., and then again become constant until all the water is changed to steam. So, generally, a body in the ad of changing its state in melting or in vaporizing maintains a constant temperature. Now, it is manifest that a considerable amount of heat is required to effect these changes, although it is not sensible to the thermometer. It performs work by overcoming the cohesion of the molecules, and disappears as heat. It is, however, capable of re-appearing as heat; for, when the vapors change to liquids or the liquids to solids, the force of cohesion performs work, and a ^corresponding amount of heat is given out. The heat which a body absorbs or gives out in changing its molecular condition is termed latent heat. 320. The latent heat of fusion may be determined by the method of mixtures. Suppose a pound of water at 212 F. be mixed with a pound of water at 32 F., it will give 212 ..I S2 two pounds of water at - ^p - = 122 F. ; but, if a pound of water at 212 F. be mixed with a pound of ice at 32 F., we shall have two pounds of water at 51 F. In this case the water has lost 212 51 = 161 F., while the ice has gained 51 32 =19 F. ; so that 161 19 = 142 F. have disappeared in changing ice to water; or, in other words, 142 thermal units are required to change a pound of ice into water. Latent Seat of Fusion. Water 142.65 F. Sulphur 16.85 Lead 9.65 Mercury 5.11 212 ELEMENTS OF PHYSICS. The latent heat of water is of the greatest value in nature, because (1) it retards the melting of snows. If it were not for this provision, the inhabitants of northern valleys would be subject to terrific inundations at every approach of spring. (2) The melting of ice withdraws heat from surrounding ob- jects. Near the Great Lakes, 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 heat. Hence, it is a common remark that the weather moderates on a fall of snow. 321. Freezing mixtures depend on the latent heat which is absorbed in dissolving solids. If one part of common salt and two of snow are mixed together, the salt causes the snow to melt and the water dissolves the salt, so that both become liquid and absorb a large amount of heat from sur- rounding objects. The temperature may be lowered to 4 F. This is the mixture used in freezing ice-creams. If crystallized calcium chloride be mixed with snow, a cold of 50 F. may be produced. This is more than sufficient to freeze mercury. 322. The latent heat of vapors may be determined by distilling them and noting the rise of temperature caused in the water surrounding the worm on condensing a known weight of vapor. The following experiment is a convenient method of illustrating the latent heat of water. Arrange a glass flask and beaker, as in Fig. 182. Pour one ounce of water at 32 F. into the flask, and 5J ounces at the same temperature into the beaker. Now, note (1) the time required to raise the water in the flask to boiling and that required to change the boiling water into steam. The latter will be 5 J times longer than the former. (2) When LATENT HEAT OF VAPORS. 213 the water in the flask has been expelled, that in the beaker be raised to 212 F., showing that an ounce of steam FIG. 182. is competent to raise 5J ounces of steam through 180 F. Therefore, the latent heat of steam is 180 X &i = 960. Latent Seat of Vapors. Water ..... 966.6F. Ether .... 162.8 F. Alcohol. . . . 374.9 Bisulphide of Carbon 156. Acetic acid . . 183.4 Bromine ... 82. 323. When liquids are evaporated they absorb heat from surrounding objects and produce cold. A shower of rain cools the air by its evaporation. The more rapid the evaporation the greater will be the effect produced. 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 rapidly ex- hausting the receiver, the sulphuric acid absorbs the aqueous vapor, and allows a very rapid evaporation of the water, which effects the freezing of a portion of it. If a volatile liquid like ether or bisulphide of carbon be poured in a watch-glass which rests on a drop of water placed on a board, and a rapid current of air be blown 214 ELEMENTS OF PHYSICS. over it, the cold produced by the evaporation will freeze the watch-glass to the board. 324. When vapors are condensed they give out their latent heat. Water may be boiled in a wooden tank by forcing steam into it. Buildings are warmed by the heat of steam generated in a boiler placed in the basement. To this end, the steam is conveyed to the several apartments by coils of iron pipes. RECAPITULATION. The measurement of heat may regard, 1. The relative intensity Temperature. 2. The relative quantity Specific heat. 3. The amount absorbed or emitted during molecular changes Latent heat. THE DISTRIBUTION OF HEAT. 325. The effects of heat thus far considered have refer- ence only to the molecular motions which take place within a heated body ; we are now to consider how heat may be transferred to other bodies. In the first place, we remark that no body is known to exist at a temperature of absolute zero; that is, at a temperature in which its molecules are absolutely at rest with respect to each other. Hence, all bodies possess some heat. In the second place, we notice that any body assumes, sooner or later, the temperature of surrounding bodies. Now, this can occur only by a con- tinued exchange of molecular motions, by virtue of w r hich every body emits thermal waves or vibrations of some degree of intensity, while, at the same time, it receives other ther- mal waves from surrounding bodies. If the sum of the TRANSFER OF HEAT. 215 motions received is less than that emitted, the body becomes colder; but, if greater, the body becomes warmer. If it receives back just as much heat as it gives out, it remains at a uniform temperature. 326. 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 molecules moving in currents. 3. By radiation, or by thermal undulations through space. 327. The conductibility of solids may be shown by equal -sized rods, along which a number of marbles are fastened, at equal distances, with wax. Fig. 183. If one end of the rod be in contact with a heated body, the mar- bles will drop off one after the other as the different sec- tions of the rod attain the FlG - 183 - temperature of the fusing point of wax. Different sub- stances will show different conducting power, but in all cases it will be found that the transference of heat by con- duction is a process comparatively slow. Porous solids are poor conductors; liquids and gases almost non-conductors; many of the metals are good conductors. Relative Thermal Conductivity. Silver 100. Iron 11.9 Copper 73.6 Lead 8.5 Gold 53.2 Platinum 8.4 Brass 23.6 Bismuth 1.8 328. That liquids are poor conductors may be shown by passing the tube of an air-thermometer through a funnel, 216 ELEMENTS OF PHYSICS. so that the bulb shall be just below the surface when the funnel is nearly filled with water. Fig. 184. Now, if ether be poured on the water and ignited, the thermometer will be but slightly affected. 329. The conducting power of a body may be roughly estimated by the touch. An iron rod heated above 120 F. will burn the hand, because it conveys its heat rapidly to the skin, and if cooled below F. it will blister the lips, because it con- veys their heat away so rapidly. An oil-cloth feels warmer or cooler than a carpet in the same room accord- ing as their common temperature is greater or less than that of the skin. So, also, a person clad in woolen gar- ments may enter an oven heated to 300 F. without incon- venience, because both his garments and the air are poor conductors. Water is sooner heated in a tin cup than in one of por- celain, because the metal is a better conductor of heat. Porous bodies, like ashes and plaster of Paris, are such poor conductors that if the hand be protected by a thin layer of either, it may carry live coals without danger. 330. Non-conductors are used (1) to prevent the escape of heat, or (2) to exclude heat. 1. Double doors and windows, which inclose a layer of air, prevent the escape of heat from our apartments. Cloth- ing prevents the escape of heat from our bodies. The con- ducting power of the ordinary materials used is in this order: linen, cotton, silk, wool, furs. Hence, with equal FIG. 184. CONVECTION. 217 texture, a woolen garment is warmer than one of silk, cotton, or linen. 2. Furnace men wear thick woolen garments to exclude heat, because that to which they are exposed is greater than the heat of their bodies. Ice may be kept from melting by wrapping about it a thick blanket. Ice-houses have double walls, inclosing a thick layer of straw, sawdust, or charcoal. Water-coolers are constructed in the same manner. 331. Convection. If heat be applied to the bottom of a flask of water, (Fig. 185), con- taining matter in suspension, as sawdust, up and down currents will be formed. The particles of the liquid w T hich become heated ex- pand and rise, because the colder and heavier particles descend and force them upward. This process of circulation among molecules is termed convection. 332. The convection of gases is more energetic than that of liquids, because their expansion by heat is much greater. If "touch- paper" containing potassium chlo- rate be burned in the vicinity of a heated body, the cur- rents of air arising from it may be traced in the smoke. The air which thus rises is heated by convection. 333. In all cases of convection there must be two cur- rents in opposite directions. 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 from the heated room will drive the flame outward, if held at the PHYS. 19. 218 ELEMENTS OF PHYSICS. top of the door ; and a current of cold air will drive the flame inward, if held at the bottom of the door. The winds are primarily due to interchange of air between localities unequally heated. Only the lower current admits of being accurately traced, but we have ample evidence that there are also upper currents. It frequently happens that clouds are seen moving in different directions the lower clouds in the direction of the surface-winds, and the upper clouds in the opposite direction. 334. The heat of the sun can not reach the earth by conduction nor by convection, since heat is propagated by either of these methods very slowly. In our study of the solar spectrum we learned that the least refracted end of the spectrum contained invisible rays which had the power of affecting the thermometer. These dark rays must reach us in the same way that light reaches us; that is, by ther- mal waves, which are transmitted by the aether and other media. Heated bodies have the same power of emitting thermal waves in all directions that luminous bodies have of emitting luminous waves. This emission of heat is termed radiation. The phenomena of radiant heat and light are, in all respects, similar ; and, with the necessary change of terms, their laws are identical. The law r s of radiant heat are: 1. Heat radiates in straight lines in all directions. 2. The intensity of radiant Jieat is inversely as the square of the distance from its source. 3. The intemity of radiant heat is proportional to m the temper- ature of its source. 335. Radiant heat, incident on a surface, may be (1) reflected, (2) refracted, (3) absorbed, or (4) transmitted. 336. Substances which reflect light well are also good REFRACTION. 219 reflectors of heat. The polished metals are all good reflect- ors- of heat. Archimedes is said to have burned the Roman fleet at Syracuse by concentrating upon the ships the solar rays by means of concave mirrors. 337. When a solar beam is transmitted through a prism of rock-salt, and the spectrum is examined by a thermom- eter, we have the result sketched in Fig. 167, showing : 1. That the thermal spectrum extends through and be- yond the visible spectrum. Thermal waves must, therefore, be of different refrangibility and wave length. 2. The maximum heating effect lies beyond the red, in rays of great wave length, but invisible to the eye. The thermal waves which accompany light are called luminous thermal waves, and the dark rays are called obscure thermal waves. When a platinum wire is heated it emits, at first, only obscure rays ; when it becomes incandescent, it not only emits luminous rays, but adds to the intensity of the obscure vibrations. 338. 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. On the other hand, there are bodies that are opaque to light which transmit the dark rays of heat almost perfectly ; such, for example, is a solution of iodine in bisulphide of carbon. A sub- stance which transmits heat is called diathermanous ; one that is opaque to heat is called athermanous. Rock-salt is one of the most diathermanous substances known. A lens made of rock-salt will so concentrate the obscure thermal rays that they may be made to melt and even ignite solid bodies. 220 ELEMENTS OF PHYSICS. The incident rays of heat which are not reflected or transmitted are absorbed. Only the rays which are ab- sorbed have any effect in warming the body on which they fall. Dry air is almost perfectly diathermanous, but air containing moisture has far less power of transmitting lumi- nous thermal rays, and is almost athermanous for obscure thermal rays. The solar rays pass with comparative ease to the earth, and are expended in warming its surface. 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 air is very dry, and the radiation from the earth is so rapid that the nights are very cold and the winters almost unendurable. The hot-beds of gardeners act by economizing the heat of the sun. The solar rays p'ass 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 attains a temperature above that of the exterior atmosphere. 339. If a body is athermanous all the rays of heat which fall upon it that are not reflected are absorbed. Hence, bad reflectors are good absorbents and are readily warmed. As bodies must give out, in cooling, the heat which they have absorbed, so good absorbents are good radi- ators. The relation between the radiating, reflecting, and absorbent powers will be seen by the following table : Reflection. Absorption. Radiation. Lamp-black 100 100 Indian ink 4 96 85 White lead 47 53 100 Isinglass 48 52 91 Gum lac 57 43 72 Polished metal . 86 14 12 RADIATING POWER. 221 The radiating power of a body is dependent more on the nature of its surface than of its substance. If a tin can- ister have one of its sides coated with lamp-black, another with paper, a third scratched or tarnished, and the fourth polished, and be filled with boiling water, its sides will, of course, have the same temperature; but they will differently affect a thermometer placed in succession near each face, according to the difference in their radiating power. Lamp-black has the highest emissive power known; the polished metals are the poorest radiators. Hence, a bright silver tea-pot filled with hot water will retain its tempera- ture longer than one of earthenware. 340. 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 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. Other experiments show that this difference in the absorptive effect of colors entirely fails for heat from artificial sources. It so happens that many good reflectors are white, and many good absorbents and radiators are dark ; but their respective powers are due rather to the molecular condition of their surfaces than to their colors. RECAPITULATION. f Conduction. Heat may be transferred by I Convection. ( Radiation. {Reflected. Absorbed. Refracted. Transmitted. 222 ELEMENTS OF PHYSICS. THE SOURCES OF HEAT. 341. The sources of heat may be comprised in three classes: (1) physical, (2) chemical, (3) mechanical. The principal physical sources are the sun and the fixed stars. It has been calculated that, if the earth had no atmosphere, the solar heat received by the earth in one year would melt a layer of ice, completely enveloping it, to the depth of one hundred feet. It has also been estimated that the earth receives from the fixed stars about four-fifths of this amount. These are the ultimate sources of most of the available heat of the globe. Were either of these cut off, the life of the globe would soon be destroyed. 342. When any two bodies unite in chemical combina- tion heat is usually evolved. Combustion is the rapid com- bination of two or more substances, attended by the evolu- tion of heat, and generally of light. If a grain of iodine l)e placed on a slip of phosphorus they will kindle into a flame, which will afterward be continued by the oxygen of the air. 343. Ordinary combustion is due to the union of the oxygen of the air with the carbon and hydrogen contained in the coals, oils, and gases of our fires and flames. The rusting of iron and the decay of wood, are examples of slow combustion with oxygen. A log of wood in decaying evolves the same amount of heat that it does in burning, although the combustion takes place so slowly that no in- crease in temperature is perceptible. Animal heat is due to slow combustion. In respiration (1) oxygen passes by osmosis through the cell walls of the lungs, and is absorbed by the blood ; (2) this blood is then carried MECHANICAL SOURCES OF HEAT. 223 to the capillaries of the different organs, where the oxygen unites with the carbon of the tissues and forms carbonic acid ; (3) the blood then returns to the lungs charged with this carbonic acid; (4) the carbonic acid is then exhaled by osmosis, and a fresh supply of oxygen absorbed. The supply of carbon in the tissues is maintained by the processes of digestion and nutrition. Thus, in one sense, our animal heat is maintained by the indirect combustion of food and air. 344. The mechanical sources of heat are percussion, compression, and friction. (1) If a nail be pounded on an anvil with rapid blows, it may be made red-hot by percus- sion. (2) The production of heat by the compression of gases may be shown by the pneumatic syringe, Fig. 186. FIG. 186. This instrument consists of a stout 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 down the tube. The air in the tube is compressed, and liberates so much heat as to set fire to the tinder, which is seen to burn when the piston is withdrawn. (3) The friction of two bodies always produces heat. It is the heat produced by friction that ignites the phosphorus on the end of a match, and that causes the axles of car- wheels to become hot. Savages procure fire by revolving the end of one piece of wood in the cavity of another. An experimental demonstration of the same fact n Ay be shown by attaching to a whirling table a brass tube filled with water, and corked. Fig. 187. If, when the tube is revolving rapidly, a clamp, P, of two pieces of oak is 224 ELEMENTS OF PHYSICS. pressed against the tube, the heat evolved by the friction of the clamp will be sufficient to boil the water in a few minutes. FIG. 187. 345. These facts are in accordance with the dynamical theory of heat, which assumes that heat is a kind of energy which produces molecular motion. In all cases of percus- sion, compression, and friction, a certain amount of mechan- ical energy is arrested, and its visible motion is destroyed. At the same time heat is produced. That is, the energy of visible motion is transformed into the energy of molecular motion, which is heat. 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 com- petent to perform mechanical work (1) by moving a pis- ton, and (2) by displacing the air in front of the piston. If the air be allowed to expand so as to perform work, it will be, at the same time, chilled, because its molecular energy is transformed into the energy of visible motion. JOULE'S EQUIVALENT. 225 346. There is a constant numerical relation between the energy of visible motion and the energy of molecular motion, which is known as Joule's equivalent, and is thus expressed : The amount of heat required to raise one pound of water 1 F. is competent to lift 772 pounds one foot high. The converse is also true ; if 772 pounds be dropped one foot it will develop sufficient heat to raise one pound of water 1 F. 347. If we know the weight and velocity of any moving body, we can calculate the amount of heat which would be generated by suddenly stopping it. It has been calculated that if the earth were stopped in its orbit, it would develop heat equal to that derived from the com- bustion of fourteen equal -sized globes of coal. If, then, it should fall into the sun, it would generate by the collision heat equal to that evolved by the combustion of 5,600 equal worlds of solid carbon. These considerations have led some philosophers to the conclusion that the solar heat is maintained by the falling of meteoric masses into the body of the sun. If the earth should strike the sun, the heat developed by the shock would be sufficient to equal the solar radiation for a century. 348. The dynamical theory of heat also explains the phenomena of expansion and of latent heat. Thus, when heat enters a body, its actual energy is employed (1) in increasing the intensity of molecular motion, which is shown by a rise in the temperature ; (2) this also separates the molecules and produces expansion ; (3) a sufficient heat melts or vaporizes the body. The latent heat required is the energy necessary to overcome cohesion ; that is, it per- forms work in separating and re-arranging the position of the molecules. The latent heat which disappears is not lost, 226 ELEMENTS OF PHYSICS. but has been employed in giving the molecules new posi- tions. If the vapor returns to the liquid state, or a liquid to the solid state, an equal amount of heat will be given out, because interior work has been performed by cohesion, which draws the molecules closer together, and is trans- formed into sensible heat. We may roughly compare latent heat with mechanical energy. If I throw a stone to a roof sixteen feet high, I shall need to give to it a velocity of thirty-two feet per second. While the stone rests on the roof it produces only pressure, but it is evident that should it fall, it will again attain a velocity of thirty-two feet per second before it strikes the ground. Therefore, the stone, while on the roof, has a possible energy due to its position. So, also, if I melt a body I shall require to expend a certain amount of sensi- ble heat; but, in so doing, I shall confer upon the mole- cules a possible or potential energy of position, which will be again transformed into the sensible energy of heat when the melted body solidifies. 349. Force may be changed but not annihilated. The sun is the ultimate source of the available forms of energy with which we are surrounded. Let us consider a few of the ways by 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 of 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 re- volve 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 of food. (a.) Wood and mineral coal are, therefore, transmuted CONSERVATION OF FORCE. 227 sunshine. In combustion, the heat re-appears as heat, or it may be applied as a moving force for engines. (6.) Food is transmuted by animals into animal heat and muscular energy, or stored up as flesh. Beef and mutton are, therefore, due to solar rays twice transmuted. RECAPITULATION. The sources of heat are 1. Physical j The sun. ( The fixed stars. 2. Chemical Combustion. C Compression. 3. Mechanical < Percussion. (. Friction. PROBLEMS. 1. How much will a railway track 100 miles long expand on being heated from 32 F. to 96 F. ? 2. How many thermal units are required to raise 80 pounds of water from 32 F. to 212 F.? Suppose a pound of coal, if econom- ically burned, to have this thermal power, how many pounds of mercury can it raise through the same temperature? 3. How many pounds of ice at 32 F. would the same fuel melt? How many pounds of water at 212 F. would it change into steam? 4. From the table on page 199 calculate the relative lengths of silver and platinum which should be taken to construct a gridiron pendulum. CHAPTER XVI. ELECTRICITY. 350. One of the earliest physical facts recorded in the history of science, is that when amber is rubbed with silk, it acquires the property of attracting to itself light bodies, and then of repelling them. Within the past century, phi- losophers have found that these are but particular manifesta- tions of a force which is constantly evoked in all kinds of molecular changes, and whose phenomena are among the most wonderful in nature. This force is electricity. It is convenient to study its phenomena under three divisions : (1) Magnetism, (2) Statical Electricity, (3) Dynamical Electricity. THE PHENOMENA OF MAGNETISM. 351. It has long been known that a certain ore of iron, called the loadstone, has the property of attracting iron filings. Because this ore was first found near Magnesia, a city of Asia Minor, loadstones are called natural magnets. Bars of hardened steel may be converted into artificial mag- nets far more powerful than natural magnets. 352. If a magnet be rolled in iron filings, the filings will cling to it, but especially at the ends. Fig. 188. These ends are termed the poles of the mag- net. The force residing in a magnet is called magnetism. FIG- 188. If a sheet of stiff paper be laid upon a bar magnet, and iron filings be sifted evenly upon (228) MAGNETISM. 229 the paper, the particles of iron will arrange themselves in curved lines about the poles. Fig. 189. If a magnetic bar or needle be poised at its center so that it will swing freely, FIG. 189. one end will point toward the north and the other toward the south ; hence, one end is called the south and the other the north pole of the magnet. 353. Either pole will equally attract iron filings; but if two magnets are brought near each other, it will be found that the north pole of one will attract the south pole of the other. If, however, two sim- ilar poles are brought near each other, a repulsion takes place. Fig. 190. Hence, this law : Like poles repel and unlike poles attract eacJi other. 354. If a long steel needle be magnetized, the center will exhibit no magnetic force and is said to be neutral. If the needle be broken, each half will be found to be a magnet with two equal and opposite poles. If this division be con- tinued, no portion can be obtained so small that it will not be a perfect magnet. We, therefore, conclude that every FIG. 190. 230 ELEMENTS OF PHYSICS. magnet is a collection of polarized particles having their similar poles turned in the same direction. We may represent this state of polarity in a magnet by Fig. 191, in which the alternate black and white spaces FIG. 191. represent the polarity of each particle. All the north poles are disposed in one direction (the black spaces) and all the south poles (the white spaces) in the opposite. The opposite polarities balance each other at the center, which thus re- mains neutral, but are strongly manifested at the ends. 355. If a rod of soft iron, Fe, Fig. 192, be brought near one of the poles of a magnet, M, the two ends of the N>_Fe_& N M S FIG. 192. rod will also be able to attract iron filings. The rod becomes a temporary magnet, but it will lose its magnetic properties soon after it is taken away from the presence of the magnet. The influence by virtue of which a magnet can develop magnetism in iron is called induction. We may suppose that, in its ordinary state, the molecules of the iron rod are all indued with magnetism, but that they are so arranged that the opposite forces neutralize each other ; and that the presence of the magnet in some way so modifies the sur- rounding region that the molecules of the iron assume the polarized state of the magnet as represented in Fig. 191. The inductive force is greatest when the magnet is in con- tact with the iron. If a steel bar be in contact with a magnet, its particles become polarized very slowly; but MAGNETS. 231 when once acquired, its magnetism is permanent. Magnet- ism 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 more powerful magnets are produced by means of the voltaic current, as will be described hereafter. It is important to notice that in in- duction there is no transfer of any force, but merely a devel- opment of polarity among the particles of the body acted upon. A magnetic battery consists of a number of magnets joined together with their similar poles in contact. The common form is that of a horse-shoe. Fig. 193. When a magnet exerts its inductive power on a piece of soft iron, its own magnetic intensity is tem- porarily increased. Fer this reason the mag- net is provided with a keeper or armature, K, of soft iron. 356. Iron, steel, nickel, and cobalt are the only substances in which magnetism can be developed by ordinary induction. Man- ganese and a few other substances are also attracted by very powerful magnets. All these are called magnetic substances. If a FIG. 193. magnetic substance is suspended by a string between the poles of a horse-shoe magnet it will take a position in the direction of the line which joins the two poles of the magnet. On the other hand, there are a great number of sub- stances which, if similarly suspended, will assume 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 phosphorus, bismuth, antimony. The diamagnetism is not permanent. 232 ELEMENTS OF PHYSICS. 357. The earth, acts as a magnet. The magnetic needle, which is of almost priceless value to mariners, points toward the magnetic poles of the earth. These magnetic poles are near, but do not coincide with the geographical poles of the earth. Hence, the needle will point in a due north and south line only when the magnetic meridian coin- cides with the geographical meridian. This is very nearly the case at Cleveland, O., but in New York the needle points west of north and in Chicago east of north. More- over, the magnetic poles are slowly shifting their position westward, so that the magnetic meridian does not remain constant. The deviation of the needle from the geograph- ical meridian is called the decimation of the needle. RECAPITULATION. f Natural or artificial. Magnets are . . ] ( Permanent or temporary. f Attracted by magnets are . . Magnetic. Substances ... < _ , , I Repelled by magnets are . . Diamagnetic. THE PHENOMENA OF STATICAL ELECTRICITY. 358. An electric pendulum is a pith ball attached, by a silk thread, to a glass support. If a stick of sealing-wax be rubbed with dry flannel and brought near the pith ball, Fig. 194, the latter is instantly attracted, but is soon repelled. If, now, a warm glass rod be rubbed with a silk handkerchief and presented to the ball, the same phe- nomena of attraction and repulsion will be observed. It will now be found that when the ball has been re- STATICAL ELECTRICITY. 233 FIG. 194. pelled by the 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, evi- dent that the glass and wax manifest similar and yet op- posed properties. These prop- erties, thus excited by fric- tion, are due to electricity. 359. Electricity is a force which becomes manifest by its peculiar phenomena of at- traction 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 or absence of a single electrical fluid, or to the presence of two electrical fluids. There is, however, no evidence of the existence of any electrical fluid. Nevertheless, many of the terms of the fluid theory are still in common use, and are convenient for describing most electrical phenomena, although the meaning attached to them is taken in a sense different from that originally intended. 360. In the preceding experiment we suppose that the wax became negatively electrified by friction, and, on con- tact, transferred a portion of this force to the ball. The ball thereby became electrified or charged with negative electricity and the two bodies separated. On bringing the charged ball near the positively electrified glass the two PHVS. 20. 234 ELEMENTS OF PHYSICS. 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 charged ivith like electricities repel each other; two bodies charged with opposite electricities attract each other. 361. Electricity is transmitted from one body to an- other with different degrees of rapidity. Those substances that transmit electricity readily are called conductors; those that do not, are called non-conductors or insulators. In the following list the substances named are arranged in the order of their conducting power. Those midway in the list may be termed semi-conductors or semi-insulators. Conductors. Semi-conductors. 1. The metals, 7. Ether, 13. Furs, '2. Charcoal, 3. Graphite, 4. Acids, 5. Water, 8. Dry wood, 9. Paper, 10. Dry ice, 11. Caoutchouc, 14. Silk, 15. Glass, 16. Wax, 17. Shellac, 6. Linen, 12. Air and gases, 18. Ebonite. Semi-iusulators. Insulators. 362. In order that a charged body may retain its electrical force, it must either be a non-conductor, or be imulated by being supported on non-conductors. The most common insulators are made of glass. Baked wood covered with shellac varnish will answer very well. Dry air is necessary for insulation. In a damp room a film of moist- ure gathers upon the apparatus and forms a conducting surface. ELECTROSCOPE. 235 363. Electricity is produced whenever two dissimilar substances are rubbed together. The reason why it is not more frequently manifest is because it 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, may develop electricity suffi- cient to emit a spark from his finger capable of igniting a jet of gas. 364. Both kinds of electricity are always simultane- ously 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, be- comes positively electrified, and by any one preceding it, negatively electrified : -f- Cat's-fur, flannel, smooth glass, cotton, paper, silk, the hand, sealing-wax, rough glass, sulphur, ebonite, . Thus paper becomes positively electrified when rubbed with silk and negatively electrified when rubbed with flannel. 385. The electricity which is produced by friction is called frictional electricity. There are, however, other modes of producing the same electrical phenomena. It is also called statical electricity, because it may be retained for a time upon an insulated body. An electroscope is an instrument used to detect the presence arid determine the kind of electricity in any body. The simplest is some form of the electric pendulum. The gold-leaf electroscope, Fig. 195, consists of two strips of gold-leaf, suspended in a glass vessel by means of a metallic rod which terminates in a knob or a plate. Within the 236 ELEMENTS OF PHYSICS. vessel are two metallic posts connected with the ground, which serve to remove an excessive charge from the leaves. If the knob be touched with an electrified glass rod, the leaves will diverge, because they become charged with pos- itive 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 gold-leaves ; for, if the electricity be positive, the leaves will diverge farther, but, if negative, they will collapse. FIG . 195 . 366. Electrified bodies influence bodies at a distance in a manner similar to the action of a magnet on magnetic substances. This influence is called electrical induction; and the resulting effect, induced electricity. A. Jfl B FIG. 196. Let A B be a conductor of brass, insulated on a glass pillar and furnished with a number of pith ball electroscopes. If this is brought near an electrified body, C, but not so INDUCTION. 237 near as to receive a spark from it, the balls will diverge as shown in Fig. 196. By means of the gold-leaf electroscope we may ascertain that the nearer end, A, of the conductor contains electricity opposite to that of the electrified body, C, and the further end, B, the same kind. If C be posi- tively charged, its effect will be to repel the positive elec- tricity toward the end, B, and to attract negative electricity to the end, A. 367. The two electrical forces may be separated by in- duction. Suppose the conductor, AB, 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 central portion be removed. (1) This part will either yield 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 will be completely discharged on touch- ing it separately, because their mutual attractions tend to retain their opposite electricities. Electrical forces in this condition are said to be bound or disguised. If the two are separated, A will yield negative and C positive electricity. If communication is made between them, both will be dis- charged by the union of their opposite, forces. If the cylinder, AB, while near the positive ball, C, be touched by the hand, the pith balls at A will diverge fur- ther those at B will collapse. As the hand and body are conductors, the positive electricity will be repelled to the earth. The negative can not escape being bound by the attraction of the positive ball, C. On the contrary, it will increase, because the inductive force of C was previously opposed by the positive electricity accumulated in the end, B. If the hand be first removed from the cylinder and 238 ELEMENTS OF PHYSICS. ifieii the inducing body, the cylinder will remain negatively charged. Therefore, a body may be charged by induction, or by conduction. In conduction there is a transfer of either force from an electrified body to another body. In induc- tion there is no transfer of force; but an excited body induces both kinds of electricity in an insulated body, which remains charged with the opposite electricity if uninsulated, for a time, in the presence of the excited body. 368. The electrophorus, Fig. 197, consists (l) v of a cake of resinous matter, R, resting on a conducting plate of tin, and (2) a movable metallic cover, T, provided with an in- sulating handle, G. If the re- sinous cake be beaten with cat's fur it becomes charged with neg- ative electricity. If, now, the cover be placed on the cake, its condition is that of an insu- lated conductor in the presence of an electrified body. Its lower surface becomes positive and its upper negative by induc- tion. The cake does not discharge itself into the cover, because (1) of the inequalities of its surface and (2) because of its non-conducting power. 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. Now, if the finger be first removed, and then the cover raised by its insulating handle, G, its positive electricity diffuses itself over its surface, and the cover will yield a positive spark when it is brought near a conductor. As the cake acts only by induction, when once charged it FIG. 197. INDUCTION. 239 retains its electricity for a long time, and may be made to induce any number of successive charges in the disk. 369. To explain the action of induction we may sup- pose that whenever a body is electrified, the molecules of the surrounding medium become polarized. Thus, if C represent a charged body, the adjacent molecules of air, as a, b, c, d, will become polar- a b c d ized. Fig. 198. The mole- fe ^^m fo C. Wf\ cules of any insulated con- ^^ O d O O ^^B^ ductor, as A B, within their FIG. i9f sparks Avill be ob- tained, which, when exhibited in a darkened room, yield a brilliant display. The luminous tube may be used for this purpose. Fig. 210. It con- sists of a glass tube on which are pasted in a spiral form bits of tin-foil. When the discharge passes off from the thin edge of a plate, a number of feeble sparks are obtained, which assume the form of a brush. If the discharge is effected in rarefied gases the effect is very beautiful. For this ex- periment a receiver called the aurora tube is used. Fig. 211. In rarefied air the light has a bluish color; in nitrogen, more of a purple; FIG. 210. in hydrogen, a fine crimson. 386. The duration of the spark is less than one -mil- lionth part of a second. If Newton's wheel, Fig. 166, be set in very rapid rotation in a dark room and be illumi- nated by an electric spark, the wheel will appear stationary. 387. The velocity of the discharge in copper wire is estimated at 288,000 miles in a second. This was measured by transmitting the discharge of a Leyden jar through a very long copper wire. The circuit was broken at three points, one at the middle of the wire and one near each coating. In this way three sparks were formed, which, to the eye, seemed instantaneous. When they were viewed by means of a revolving mirror, they presented the appearance 2 ii. 250 ELEMENTS OF PHYSICS. of three arcs of equal length, the middle one rather behind the others, as in Fig. 212. The velocity with which the mirror revolved was known, and from this the retardation was calculated which gave the velocity of trans- mission. The velocity is found to vary both with the nature of the conducting medium and the intensity of the charge. 388. Calorific effects. Any combustible substance, as ether, is readily inflamed by the spark. Very thin wires may be melted by a discharge from a Leyden battery. Fig. 213. Those wires are heated most, which are the worst conductors. In using this battery the apparatus, U, on the FIG. 213. right of the figure, is convenient. It consists of three glass posts, two of which carry jointed rods, while the center bears on its top a glass plate. A thin gold wire, a b, sup- ported on this by a paper card, c, is instantly volatilized by a powerful discharge. Chemical effects. The peculiar odor which always accom- panies the electrical discharge is due to the formation of ozone, an allotropic modification of the oxygen of the air. ATMOSPHERIC ELECTRICITY. 251 A succession of sparks passed through ammonia decomposes it. The spark may also effect chemical combination. Thus, if two volumes of hydrogen and one of oxygen be mixed in the electrical pistol, Fig. 214, a single spark will cause them to combine with a loud explosion. 389. The mechanical effects are shown when a discharge passes through a poor conductor. If a discharge is passed through a card of thick paper, a burr will be pro- duced in both directions. A glass plate maybe perforated by a moderately strong FIG. 214. ^ charge. The mechanical effects of lightning are well known. It rends and tears every obstacle which hinders its free transmission, with amazing force. The noise which accom- panies the spark is due to the sudden expansion of the surrounding air, followed by a sudden collapse, thereby pro- ducing a sonorous wave of condensation and rarefaction. 390. Physiological effects. Quite a number of persons may receive the electric spark simultaneously. For this purpose, all must join hands, the first touching the knob of a Leyden jar, and the last the outside. Electricity has also been found of service in the treatment of some diseases. For this purpose, as well as for producing chemical decomposition and magnetic effects, which require quantity rather than intensity, some form of dynamical elec- tricity is generally employed. ATMOSPHERIC ELECTRICITY. Franklin demonstrated, in 1752, that a flash of lightning is simply an enormous spark of electricity. He raised a silk kite at the approach of a storm, and as soon as the rain had wetted his hempen kite string, thereby rendering it a 252 ELEMENTS OF PHYSICS. good conductor, he succeeded in drawing sparks from a key hung on the string and in charging a Leyden jar. 391. The principal source of atmospheric electricity is supposed to be the evaporation and subsequent condensation of water. A cloud becomes positively electrified by the accumulation of the electricity which, before its formation, was disseminated through its particles. It is probable that negative clouds are mostly due to the inductive action of other positively charged clouds. The earth beneath a cloud is subject to the same inductive action and becomes, by consequence, charged with electric- ity opposite to that of the cloud. 392. A flash of lightning is produced when the air between two adjacent bodies oppositely charged becomes highly polarized. The light is due to the intense heat of the discharge which renders the particles of the air incan- descent. The thunder is due to the violent commotion pro- duced in the air by its sudden expansion along the path of the flash, and is prolonged by echoes. Heat lightning is the name applied to bright flashes of light observed in the horizon on summer evenings. This is generally due to the reflection by the atmosphere of ordi- nary lightning so distant that the thunder is inaudible. 393. Lightning conductors are metallic rods used to protect buildings from the effects of lightning. (1.) They offer to the discharge the line of smallest resistance. Hence, the rod should be a good conductor, continuous from top to bottom, and should terminate in earth which is permanently moist. (2.) They may prevent the discharge. If the rods are tipped with points, the discharge may be effected silently and the polarization of the air particles never rise high enough to produce the flash. AURORA BOREALIS. 253 394. There are other phenomena of atmospheric elec- tricity among which may be mentioned the Aurora Borealis, or northern lights, and St. Elmo's fire. It has been noticed that during the auroras the telegraph lines have been dis- turbed so as to prevent sending intelligible dispatches, and, also, that telegraphs may be worked without the aid of a battery when the auroras are very bright, as was the case in 1869. KECAPITULATION. I. The phenomena of statical electricity are : By friction. 1. Excitation , By other molecular disturbances. 2. Attraction of bodies charged with unlike electricities. 3. Repulsion of bodies charged with like electricities. f On the surface of insulated conductors. 4. Distribution 4 ( Accumulated at pointed extremities. f Readily in conductors. By conduction < Slowly in insulators. 5. Transference ( By convection in moving particles. f Spark. By Eruption ( ^^ 6. Induction . . By a charged body on insulating matter. II. The effects of statical electricity are : 1. Mechanical . By producing fracture. 2. Luminous . In the electric spark. 3. Calorific . . By evolving heat. f By effecting combination. 4. Chemical . ] . ( By decomposing compounds. 5. Physiological . In producing electric shocks. 254 ELEMENTS OF PHYSICS. DYNAMICAL ELECTRICITY. 395. All chemical actions are attended with the devel- opment of electrical force. This force is identical with that produced by friction ; but because its discharge is continu- ous that department of electrical science which treats of electricity produced by chemical action is called dynamical electricity. It is also called Galvanism and Voltaic electricity in honor of Galvani and Volta, who were among the first to study its phenomena. The fundamental phenomena of dynamical electricity may be exhibited by means of the simple Voltaic element. Fig. 215. This usu- ally consists of a glass vessel contain- ing a plate of amalgamated * zinc and a plate of copper, partially immersed in water to which a little sulphuric acid has been added. A chemical action takes place, by which (1) the water is decomposed ; its hydrogen is FIG. 215. liberated and its oxygen combines with the zinc to form zinc oxide. With water alone this action is very feeble, because the zinc oxide soon forms a coating on the zinc plate, which does not dissolve in water. (2) The sulphuric acid prevents the formation of this coating. This it does by uniting with the oxide to form zinc sulphate, which readily dissolves in the liquid and leaves the plate clean. The copper is not chemically acted upon and serves merely as a conductor of the electricity. *To amalgamate zinc, it is first cleaned -by immersion in dilute sulphuric acid and then mercury is rubbed over its surface. ELECTRICAL CIRCUIT. 255 As soon as the plates are immersed, there is a slight dis- engagement of hydrogen and both plates become feebly charged with electricity. If the plates are kept from touching, no further action will be perceived. The whole arrangement is in a polarized condition, which may be re- presented by Fig. 216, in which the positive molecules are shaded. The outer end of the zinc is nega- tive, and the portion in contact with the liquid is positive. The negative molecules of the liquid are turned toward the zinc and the pos- itive toward the copper plate. The copper thus becomes polarized in a sense opposite to that of the zinc. If, now, the plates are brought in contact either directly or by means of a metallic wire, a discharge will take place through the whole combination or circuit. At the same time, the chemical action increases and gives rise to a series of charges and discharges in such rapid succession, that the dis- charge appears continuous and the circuit is said to be trav- ersed by an electrical current. The current continues so long as the contact is maintained, but ceases w T hen the plates are disconnected. The operation of connecting the plates is called closing the circuit, and the separating of them is called breaking the circuit. 396. It is to be noted that when the circuit is closed, the hydrogen rises only from the surface of the copper. In explanation of this, it is supposed that when the oxygen and zinc combine, a molecule of hydrogen is set free, and unites with the oppositely electrified oxygen in the neigh- boring molecule of water, and displaces its hydrogen. This molecule of hydrogen is transferred to the adjacent molecule of water, and, in like manner, the same transference takes place throughout the whole series until the hydrogen of the 256 ELEMENTS OF PHYSICS. molecule of water next to the copper is displaced. This hydrogen can not combine with the copper, but discharges its free positive electricity into it and escapes in a gaseous state. Each successive transfer of the hydrogen may be assumed to be accompanied by a separation and recombination of the opposite electricities. The current itself must be considered as due to a constant series of polarization and discharge among all the molecules of the Voltaic element, both liquid and solid, by reason of which there is a transmission of both electrical forces throughout the circuit, the positive going one way and the negative the other. To avoid confusion, only the direction of the positive cur- rent is usually given in speaking of the current. The direc- tion of the positive current (1) within the liquid is from the zinc to the copper, and (2) without the liquid, from the copper to the zinc. 397. The current always sets out from the metal most easily acted upon by the liquid, which is therefore called the generating or positive plate. The other metal is called the conducting or negative plate. In most Voltaic elements, the liquid used is dilute sulphuric acid; that is, acid to which has been added from ten to twenty times its bulk of water. The electric deportment of several substances with reference to this acid is given in the following Electro-motive series: -j-Zinc. Lead. Iron. Nickel. Bismuth. Antimony. Copper. Silver. Platinum . In this list, the metals named are positive with reference to those that follow them, and are negative with reference to those that precede. Poles. The current passes without the liquid, from the negative plate back to the positive plate ; hence, if the con- necting wire be cut, the positive electricity will tend to ELECTRO -MOTIVE FORCE. 257 accumulate at the end of the wire attached to the negative or copper plate and the negative electricity to the positive or zinc plate. These ends are called the poles or electrodes t)f the circuit. In most combinations, zinc is used for the positive plate ; the wire attached to it is called the negative pole or electrode. The wire attached to the negative plate is the positive electrode or pole. 398. The electro-motive force, or that which causes or tends to cause a transfer of electricity, is dependent on the relation which the metals bear to the liquid. It is greater the farther apart the metals are in the series. Dilute sul- phuric acid acts, upon copper when taken by itself; hence, it tends to produce on 'the copper plate a current acting con- trary to that developed on the zinc. The electro-motive force of the Voltaic element is, therefore, due to the differ- ence of these two opposing forces. Now, as dilute sulphuric acid does not act upon platinum at all, a stronger current may be established between zinc and platinum than between any other two metals in the series. 399. The quantity of electricity produced by a Voltaic element is proportional to the chemical activity. The work which the current can do is, therefore, proportional to the amount of zinc consumed in a given time. The quantity is at all times enormous. It has been calculated that an ele- ment which might be contained in a lady's thimble is capa- ble of evolving a greater quantity of electricity than the largest electrical machine ever constructed. 400. The intensity of the current depends both on the electro-motive force and the resistance which is to be over- come. The greater the electro-motive force, the greater will be the intensity ; the greater the resistance, the less will be the intensity. This relation, then, may be expressed by Ohm's law : PHYS. 22. 258 ELEMENTS OF PHYSICS. Electro-motive force Intensity of current = resistance. 401. The resistance is inversely as the conducting power of the substance through which the current passes. The conducting power of different substances of equal dimensions is shown relatively by the following table: Solids. Liquids. Silver . . 100. Mercury 1.6 Copper . . 99.9 Dilute sulphuric acid . . .00009907 Zinc ... 29. Strong nitric acid . . . .00008808 Platinum . . 18. Common salt, saturated solution .00003152 Iron . . . 16.8 Sulphate of copper " " .00000542 Carbon . . .04 Distilled water 00000001 It is manifest that the resistance will increase with the lepgth of the conductor, and also that it will decrease as {he area of its cross section increases. Hence, the shorter and thicker the connecting wire, the less will be the resist- ance. So, also, the nearer the plates are together and the larger their area, the less will be the resistance offered to the current by the liquid layer between them. The table shows that the resistances offered by liquids are enormous when compared with solids. Hence, the resistance caused by the liquid between the plates is far greater than in a short conducting wire. When the conducting wires are very long, as in telegraphs, the external resistance may exceed the internal. 402. A Voltaic Battery consists of several Voltaic ele- n tyt FIG. 217. ments so connected that the current has the same direction in all. The efficiency of the battery will vary with the VOLTAIC CIRCUIT. 259 manner of grouping the elements. For the sake of illus- tration, take six elements, each containing a square inch of zinc, separated from a copper plate by a liquid layer an inch in thickness. If all the similar plates are connected, as represented in Fig. 217, the effect will be the same as that of a single element having a zinc plate of six square inches, one inch .distant from the copper plate. Either arrangement is called a simple Voltaic circuit. In the compound Voltaic circuit the positive plate of each FIG. 218. element is connected with the negative plate of the adjoin- ing element, as shown in Fig. 218. The simple circuit is sometimes called a quantity battery. It is used when the external resistance is very small. It is adapted for producing thermal effects, such as melting wires. The compound circuit is sometimes called an intensity bat- tery. It is used when the external resistance is very great. It is adapted for telegraphs, for the electric light, and for producing chemical decomposition. 403. Numerous batteries have been constructed on the principle of the Voltaic element already described, but most of them have gone out of use, because of the rapid enfee- blement of the current. This may occur (1) from the gradual consumption of the acid and the zinc, and (2) from local action. By local action is meant the production of small closed circuits on the posi- tive plate, which are due to impurities on the zinc plate. This is remedied by amalgamating the zinc. (3) Besides these defects, the older batteries were liable to what is called the galvanic polarization of the plate. In the action of the 260 ELEMENTS OF PHYSICS. simple element, the hydrogen is apparently evolved from the copper. In the process of time, the copper becomes coated with a layer of positive hydrogen, which, of itself, would weaken the current, but which acts the more injuriously because it reduces the zinc sulphate, and thereby forms a layer of metallic zinc on the copper. 4O4. Constant batteries obviate this last defect by pre- venting the permanent deposition of the hydrogen on the neg- ative plate. There are over fifty forms of constant batteries ; among the best of them are the following two-fluid batteries : Grove's battery consists of (1) a glass cup containing a hollow cylindrical zinc plate and weak sulphuric acid; (2) of a porous cup made of unglazed earthenware, containing strong nitric acid and a strip of platinum. The porous cup and its contents are placed inside the zinc cylinder. Fig. 219. The hydrogen which is liberated by the action of the zinc passes by osmosis through the porous cup, and on meeting FIG. 219. the nitric acid unites with a part of its oxygen to form water, and reduces the acid to nitric oxide. This oxide is either dissolved in the liquid or escapes in red fumes. Bunsen's battery (Fig. 220) is sim- ply a large Grove's battery in which the platinum slip is replaced by a carbon cylinder. The chemical action is the same as the preceding, but as the ele- ments are larger, for the same amount of zinc consumed, Bunsen's battery gives a greater quantity of electricity, but less intensity, than Grove's. FIG. 220. CONSTANT BATTERIES. 261 In this form the nitric acid is sometimes advantageously replaced by a mixture of one part of potassium bichromate, two of sulphuric acid, and ten of water. DanieWs battery (Fig. 224) may readily be constructed by the student by placing within the porous cup a zinc plate and dilute sulphuric acid, and in the outer vessel a thin roll of copper with a saturated solution of sulphate of copper. The hydrogen, liberated by the action of the zinc, enters the solution of the sulphate of copper and reduces it, forming (1) metallic copper, which is deposited on the neg- ative plate; and (2) sulphuric acid, which passes by osmosis into the porous cup, and replaces the acid which was neutralized by the zinc. KECAPITULATION. I. A Voltaic element may consist of, 1. Two metals and one fluid .... Voltaic. T Grove's. 2. Two metals and two fluids . . . 4 Bunsen's. (. Daniell's. II. The Voltaic current is due, 1. To the polarization of the metallic and liquid particles, composing the circuit. 2. To the contact of two dissimilar metals. "3. To a chemical action on one metal. 4. To a transfer of the fluid molecules. III. The Voltaic current depends, 1. On the electro-motive force. 2. On the chemical action. 3. On the resistance, both internal and external. IV. The Voltaic circuit may be . j Dimple. ( Compound. 262 ELEMENTS OF PHYSICS. THE PHENOMENA OF DYNAMICAL ELECTRICITY. 405. The effects of the current are manifested either (1) within its path, or (2) external to its path. The for- mer will be first considered. Physiological effects. The science of dynamical electric- ity is said to owe its origin to an experiment of Galvani in 1790, which may be repeated in the following manner : Let a strip of 2inc be passed below the crural nerve of a frog, recently killed, and a copper wire be made to touch the muscles of the legs, as shown in Fig. 221. Each time the ends of the metals are brought together at A, the legs are thrown out in the direction of the dotted lines. The same convulsive movements take place when one pole of a battery touches the nerve and the other the muscles. The muscles contract as F IG . 221. often as the circuit is opened and closed, but remain quiet when the current is passing. Hence, the more frequently and abruptly the circuit is broken and closed, the greater will be the physiological effect. If the electrodes of a strong compound circuit be grasped with the hands, previously moistened, a shock will be expe- rienced; but, unless the number of elements is considerable, the sensation is hardly perceptible. The nerves of the pal- ate and of sight are easily affected. If a strip of zinc be EFFECTS OF THE CURRENT. 263 placed above the tongue and a strip of silver between the gums and the cheek, as often as the metals are made to touch, a peculiar taste will be experienced, and a flash of light will seem to pass before the eye. 406. Calorific effects. If a current be passed through a thin metallic wire, the wire will be heated in proportion to- the quantity of electricity and the resistance offered by the wire. The wire may become incandescent, may fuse, or even be dissipated in vapor. With the same current, the worst conductors will be the most readily heated. Thus, if a suitable current be passed through a chain made of alter- nate links of platinum and silver, it may render the platinum incandescent, while the silver remains dark. On the same principle, if a platinum wire be interposed in any part of the cir- cuit, it may be made to ignite gunpowder. This has been turned to account in blast- ing rocks and exploding torpedoes. 407. Luminous effects. No spark is ob- tained unless the poles are brought in con- tact, or nearly so. With a moderately strong battery, sparks may be obtained at the moment the circuit is broken and closed. A most brilliant electric light is obtained by connecting the terminal wires with carbon points, as shown in Fig. 222. The carbon points are first brought in contact, and the heat developed is such as to render their ends incandescent. They may then be re- moved to a short distance without interrupting the current, which forces its way through the air and produces a lumi- nous arc of great intensity. With 48 Bunsen's elements, the arc is about one-fourth of an inch long. The light is of FIG. 222. 264 ELEMENTS OF PHYSICS. far greater intensity than that obtained by the oxyhydro- gen blow-pipe, being equal to that of 572 wax candles. With 600 elements, the arc is nearly eight inches long, and may be said to rival the brilliancy of the sun. The light is not due to combustion, but to the transfer- ence of the intensely heated particles of carbon from the positive to the negative electrode. In consequence of this, the positive electrode gradually wears away and the negative electrode receives a deposit. The effect of this is to increase the distance between the electrodes; and, hence, some ar- rangement is necessary to bring them together in proportion as the distance alters. This may be done by the hand, or more conveniently by clock-work. The electric light is admirably adapted for illumination in theaters and lecture-rooms, but is not well adapted for gen- eral purposes of illumination. Besides the cost of its pro- duction and the skill required in its management, the very intensity of the light is a source of difficulty, as it acts inju- riously on the eye and throws shadows into too strong relief. The most refractory substances, as platinum, quartz, and lime, when introduced into the arc are fused. The color of the light varies with the substances placed between the terminals. Gold emits a bluish light ; silver, an emerald- green ; lead, a purple, etc. 408. Chemical effects. If a chemical compound, in a liquid state, be made to form a part of the external voltaic circuit, a series of decompositions will take place like those already described as occurring within the simple voltaic element. This process is called electrolysis. Fig. 223 represents a convenient apparatus to show the decomposition of water. It consists of a glass vessel, through the bottom of which are passed two wires terminating in platinum electrodes. The vessel being filled with acidulated ELECTROLYSIS. 265 H FIG. 223. water, two glass tubes also filled with water are inverted over the electrodes, and the outer wires are connected with a battery. Five of Grove's elements will cause a rapid decomposition of the water ; bub- bles of gas will collect in the tube above each pole. Hydro- gen rises from the negative pole and oxygen from the positive. The volume of the hydrogen lib- erated is double that of the oxygen. As the gases evolved are in proportion to the amount of zinc consumed, a modification of this apparatus, called a vol- tameter, is used to measure the strength of a battery. 409. The decompositions of other compounds may be effected by a similar apparatus. If the electrodes are plunged in solutions of binary compounds, like chloride of copper, iodide of potassium, cyanide of silver, the metals collect at the negative pole and the non-metals at the posi- tive. On the principle that bodies dissimilarly charged attract each other, the metals are called electro-positive substances and the non-metals electro-negative. 410. Ternary salts are also decomposed by the current, the metal going to the negative pole, and the acid, on the body which is chemically equivalent to it, going to the positive. Ordinarily, a single voltaic element will suffice for the decomposition of a salt. The condition in which the metal is deposited on the negative electrode, depends somewhat on the strength of the current. When the action is rapid, PHYS. 23. 266 ELEMENTS OF PHYSICS. most metals are deposited as loose, flocculent powders ; but if it is slow, copper, silver, gold, and some others are de- posited in firm, coherent layers, which exactly fit the surface of the electrode. 411. Electro - metallurgy is the art of depositing the metals from solutions of their salts by means of the electric current. The solution is decomposed in the manner just described, and the pure metal is deposited on the negative electrode. This may consist of any article whatever that FIG. 224. If the material is non-conduct- has a conducting surface, ing, the surface may be rendered conducting by covering it with finely powered graphite. The positive electrode, C, Fig. 224, should be a plate of the same metal as that to be deposited in order that the acid which is liberated may dissolve it, and thus maintain the strength of the solution. 412. The processes of electro-metallurgy may be ar- ranged in two divisions : (1) those in which the deposit remains permanently fixed on the electrode, and (2) those in which the deposit is intended to be removed. The first may be represented by electroplating and the second by eledrotyping. ELECTROTYPING. 267 The apparatus employed in electroplating is represented in Fig. 224. The bath consists of a weak solution of cya- nide of silver. The articles to be silvered are first carefully cleaned, then attached to the negative pole of the battery and immersed in the bath. A coating of pure silver begins to form at once, and may be obtained of any thickness desired. When the articles are first taken from the bath, their surfaces appear dull and white. The metallic luster of silver is then communicated to them by burnishing. By a similar process articles may be electro-gilded, 01 coated with other metals, as copper and nickel. 413. In electrotyping, it is usual (1) to form a mold of the object to be copied, and then (2) to deposit within this a coating of some metal sufficiently thick to be stripped off whole. Thus, suppose we desire to copy a medal in cop- per. The medal is first rubbed over with graphite and the excess of graphite blown off; (2) an impression of the medal is taken in wax and the wav: coated with graphite, as before ; (3) a copper wire is now thrust through the wax and made to connect with the layer of graphite; finally, (4), the wax mold is made the negative electrode in a bath of sulphate of copper. A tough coat of copper will gradually be deposited on the surface of the graphite, and, after a day or two, will be sufficiently thick to be removed. The plates from which this book was printed FlG . 225. w r ere electrotyped in this \vay. The student may easily copy small articles like coins and seals by the simple means shown in Fig. 225. A is a glass 268 ELEMENTS OF PHYSICS. vessel containing a saturated solution of sulphate of cop- per. B is a lamp-chimney closed below with a piece of bladder, and containing very dilute sulphuric acid. The apparatus is completed by putting a roll of amalga- mated zinc in the sulphuric acid, and connecting it by a wire to the object to be copied which is laid below the bladder. The connecting wire and any part of the object which it is not desired to copy must be carefully coated with wax or a resin varnish. KECAPITULATION. The effects of the current within its path are: 1. Physiological . . . Applied in some diseases. 2. Calorific .... Applied in firing mines. 3. Luminous .... Applied in the electric light. 4. Chemical .... Applied in electro-metallurgy. PHENOMENA EXTERNAL TO THE PATH OF THE CURRENT. 414. The voltaic current also acts inductively upon conductors external to its path, and thereby causes phenom- ena which closely ally its action to magnetism. These phenomena may be grouped in two divisions : 1. Electro-magnetism considers the phenomena in which magnetic attraction and repulsion are caused by the voltaic current. 2. Electro-dynamic induction considers the production of other currents in the vicinity of closed circuits. ELECTRO -MAGNETISM. 269 Conversely, permanent magnets act inductively on con- ducting wires, and thereby give rise to electrical currents without the aid of a battery. (3) Magneto -electricity considers the production of elec- trical currents by means of permanent magnets. ELECTRO-MAGNETISM. 415. Oersted discovered, in 1819, that a magnetic needle held in the vicinity of a voltaic current tends to place itself at right angles to the conducting wire. FIG. 226. To repeat his experiment, a magnetic needle is allowed to assume its natural position, pointing north and south. If, now, the wire conducting a voltaic current be held parallel to the needle, the needle will be deflected. Fig. 226. The direction in which the needle should turn may be remembered by the following rule : Suppose a diminutive figure of a man to be so placed in the circuit that the current shall enter by his feet and leave by his head: then if his face be turned toward the needle, its north pole will be deflected toward his left. In accordance with this rule, if the current passes above 270 ELEMENTS OF PHYSICS. the needle and goes from south to north, the north pole of the needle will turn toward the west. It will also turn westward, if the current passes below the needle from north to south. Hence, if the wires NS, N'S' be joined so that the current shall- pass around the needle, the deflecting FIG. 227. power will be doubled. By coiling insulated wire many times around the needle the deflecting power is so increased that it may be used to detect the presence of very weak currents, to determine their direction, and even to measure their intensity. An instrument constructed on this principle is called a galvanometer. The Astatic galvanometer, represented in Fig. 227, derives its name from the fact that it employs two magnetic needles fastened to the same axis of suspension, but with FLOATING BATTERY. 271 their poles reversed. The directive force of the earth on the needles is nearly or quite neutralized. 416. 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. 228) enables us to verify this fact. It consists of a small voltaic element which is floated in acidulated water by means of a cork. The conducting wire may be made straight or coiled. The spiral coil shown in the figure is called a Mix. An elongated helix with its conducting wire returned through the axis of the coil is a solenoid. Fig. 229. 417. When the current is passing through the wire it exhibits all the properties of a magnet. 1. If a permanent magnet is held near the floating helix, FlG. 229. one face of the coil will be attracted by the north pole of the magnet and the other repelled. 2. Each side of the helix will attract iron filings. 272 ELEMENTS OF PHYSICS. 3. The axis of the helix will point north and south. 4. If two solenoids (Fig. 229) are brought near each other, their similar ends will repel each other ; their dissimilar ends will attract each other. 5. If the conducting wire of a 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 pass in the same direction, but (2) will be repelled if the currents pass in opposite directions. 418. The voltaic current may also induce magnetism in magnetic substances. If a bar of soft iron, NS, be placed in the axis of a helix, the bar will ~ be instantly magnetized on closing the circuit. Fig. 230. If the helix is held vertically the bar will not fall out. If the bar be pulled down a little way and then let go, it will spring back to its former position. It will also attract bits of iron to itself, and act in every respect like a magnet. When the circuit is broken it loses its magnetism almost instantly. A pleasing modification of the same experiment may be had by passing the ends of two semicircular pieces of soft iron within a helix, as shown in Fig. 231. On closing the circuit, they will adhere with considerable force. FIG. 230. FIG. 231. 419. Electro-magnets are bars of 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 turns of insulated copper wire. Fig. 232. PERMANENT MAGNETS. 273 When a strong current is passing, the magnetism induced is far greater than is possible in a permanent magnet. Electro -magnets have been made that were capable of sustaining nearly two tons. Permanent magnets. When the current is broken, the magnetism - ceases instantly if the iron is quite pure ; but, otherwise, traces of the magnetism will remain for some time. A steel bar placed in the FIG. 232. helix (Fig. 230) will become permanently magnetized. 420. An excellent method of making permanent mag- nets is shown in Fig. 233. The steel horse-shoe is applied to an 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 proc- ess frequently repeated. Both magnets are then turned over without separating them, and the other side treated in the same way. 421. Various machines have been devised in the hope of employing the prodigious force of electro-magnets. The electric telegraph is by far the most important application of electricity. 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 one station ; (4) an instrument for receiving signals at the other station. 1. Any constant battery may be used for generating elec- 274 ELEMENTS OF PHYSICS. tricity. In this country, some modification of Daniell's bat- tery is generally used. 2. The two stations must be connected by at least one insulated wire. Generally this is done by passing galvanized iron wire over glass insulators attached to a series of tall wooden posts. At the station which sends the dispatch, the line is con- nected with the positive pole of the battery, but as the cur- rent will not pass unless the two poles of the battery are connected, it is also necessary to have a second conductor returning in the opposite direction to the negative pole of the battery. In 1837, Stein heil discovered that the earth might be used for the return conductor. To effect this, large metallic plates are buried in the ground at each station, and are connected at the sending station with the negative pole of the battery and at the receiving station with the line wire. The earth really dissipates the electricity, but the effect is the same as if it were an infinitely large return conductor offering an infinitely small resistance. 422. Morse's telegraph, which is more extensively used than any other, requires at least two distinct parts, the signal key and the receiver. Beside these, a third part, called a relay, is necessary on long circuits as adjunct to the receiver. These parts are all shown in Fig. 236. If messages are to be received and answered, each station will require a full set of apparatus. The signal key is used for breaking and closing the circuit at the transmitting station. It usually consists of a brass lever, ad, which works on an axis, K, supported on an insu- lated base. The middle of the lever is always in connection with the line wire. At the ends are two metallic points by which the line wire may be brought in connection either with the receiver or with the positive pole of a battery. MORSE'S TELEGRAPH. 275 (1) When the lever is left to itself, a spring, n, forces the end, a, down, so that a receiver at R' (not drawn in the figure) is in condition to receive a dispatch from a distant station. (2) When a dispatch is to be sent, the end, d, is depressed by applying the finger to an ebonite button, /. The current passes from the battery up the point d, through the lever to K, along the wire to the receiving instrument, or relay, at the distant station, and thence returns by the earth, making the circuit complete. When the finger is removed, the current ceases, and hence the operator can close the circuit for a longer or shorter time, at his pleasure, by depressing or elevating the point d. 423. The receiver, Fig. 234, consists (1) of an electro- magnet whose helices form part of the line circuit, and (2) FIG. 234. a lever which is worked by the joint action of the electro- magnet and an adjustable spring, S. One end of the coil, L, is connected with the line wire from the sending station, and the other, E, with the earth. When the circuit is closed, the electro-magnet draws down the armature A, which is so attached to a horizontal lever that when the end A is depressed, the other end, P, is 276 ELEMENTS OF PHYSICS. forced up. This end carries a steel point, or style, which writes the signals. For this purpose, a narrow slip of paper is drawn by clock-work between the style and a revolving cylinder, and is indented by the pressure of the style. When the circuit is broken, the style is pulled down by the spring, and the paper is left blank. Hence, by varying the time of contact at the sending station, a series of signals consisting of dots and lines is produced at the receiving station. The following is the modified Morse's alphabet : a b c d e f g h i j k I m n o p q r s t u v w x y z & 12 34567 89 _._ _._ __ __ _____ FIG. 235. 424. The clicking sound of the armature and the style indicates to the ear the same distinction of long and short signals that are indicated to the eye upon the paper. A skillful operator seldom looks at the paper when he is receiv- ing a message. In most cases, the paper and clock-work are dispensed with, and the dispatch is read only by sound. The relay. The intensity of the current is so weakened after it has traversed a few miles, that the recording instru- ment can be worked directly by the line current only on short circuits. In circuits exceeding fifty miles, the actual receiving instrument is the relay. This is simply an electro- magnet whose only duty is to open and close a local circuit in which the recording instrument is included. The manner in which this is done will be rendered evi- dent by an inspection of Fig. 236. The line current passes THE RELAY. 277 from the positive pole of the battery, B, through the key and the line wire to the relay, thence around the helices of the relay and down to the earth plate, X. The earth con- nection is then said to return the current to the ground plate, X', and thus finally completes the circuit to the negative pole of the battery. Each time the line current passes into the relay, the electro-magnet attracts its armature, A, which is fixed at the bottom of a vertical lever, L. At the same moment, the upper end of the lever strikes against the screw, P. At this instant, a current from a local battery, B', enters at Earth Circuit - FIG. 236. the axis of the lever, ascends to the screw, P', thence passes to the electro -magnet of the recording instrument, and finally returns to the local battery from which it started. When the line current ceases, the lever is drawn back by the spring $', and the local circuit is broken. By this means, the local current is made to act in unison with the line current, and may be used either to print a legible dis- patch or to transmit a fresh current to a station further on. 425. The electrical fire-alarms, now extensively used in large cities for indicating the localities of fires, are modi- 278 ELEMENTS OF PHYSICS. fications of the Morse instrument. The properties of th0 electro-magnet have also been practically applied to variou? purposes. Among these are electric pendulums, electric clocks, and chronographs. The chronograph is an instru- ment for recording the time at which any phenomenon occurs. Several forms of this instrument have been devised which have been used to register automatically the fluctua- tions of barometers, thermometers, and the winds. 426. Hitherto the attempts to use the electro-magnet as a motive power have not been altogether successful. Nevertheless, small electro-magnetic machines have been employed in cases where economy is of less consequence than convenience and facility of application, as in running sew- ing machines. We can not hope that they will ever be able to compete with steam-engines in point of economy. 427. There are various other forms of the telegraph, among which Wheatstone's needle telegraph is the most important. Its receiving instrument consists essentially of a delicate galvanometer. A modification of this instrument is used with the Atlantic submarine cable. CURRENT INDUCTION. 428. The phenomena of electro - dynamic induction may be shown by the apparatus represented in Fig. 237. Let P be a helix of insulated wire through which a primary current is passing from the battery ; and I a second helix connected with the galvanometer. When the primary cur- rent is brought near J, a secondary or induced current will be set up in I and will cause the deflection of the needle in the galvanometer. If the two helices are kept in the same relative position, the induced current soon ceases, and the needle returns to its old position. It will, however, be again set in motion if CURRENT INDUCTION. 279 the primary current is in any way changed ; that is, if the coil be removed, or if the current be broken or increased in strength. An induced current is, therefore, but momentary in its FIG. 237. action ; but, nevertheless, it has all the properties of the primary current. For instance, it may induce other CUP- FIG. 238. rents on adjacent circuits, and give rise to induced currents of the third, fourth, and even the seventh, order. 280 ELEMENTS OF PHYSICS. 429. Magneto-electrical induction is like the preced- ing, except that it is caused by a permanent magnet. If in Fig. 238 we employ a permanent magnet instead of the primary coil, we shall obtain almost identical effects. This is as we should be led to expect, because we have learned that a helix during the passage of a current is essentially a magnet. 430. The magneto - electrical machine is constructed on this principle. Fig. 239. This consists of a permanent magnet, AB, in front of FIG. 239. which two helices of insulated copper wire are made to revolve on an axis, /, by means of a winch. The cores of the helices are made of two pieces of soft iron joined by an armature, it' . The same wire is coiled about the two cores, but in different directions, in order that the currents induced by the opposite magnetic poles should be in the same direction. The two ends of the wire terminate in two metallic plates insulated from the axis and from each other by ivory, and are alternately connected by the springs, INDUCTION COILS. 281 SS f . On turning the wheel, a current of electricity is induced in the coil each time the core is brought before the magnet. It, therefore, gives rise to a rapid succession of momentary currents. 431. This instrument is capable of producing sparks, decomposing water, igniting wires, and other effects of dynamical electricity. If a break piece, not shown in the figure, be added, an extra current of great tension will be produced. If the handles, PP f , be grasped with the hands slightly moistened, the muscles contract with such force that they no longer obey the will, and the handles can not be dropped. From its convenience, this apparatus is gener- ally used for applying the effects of induced currents in therapeutical operations. 432. Other magneto - electrical machines have been constructed on the same principle. Some of these are of remarkable power, and are used for electroplating, for tele- graphing, and other practical applications of electricity. Wilde has constructed a machine driven by steam power which yields an electric light of surpassing brilliancy, and evolves sufficient heat to melt iron rods fifteen inches long and a quarter of an inch thick. 433. Induction coils are instruments which employ both electric and magnetic induction. One form in which the helices are separable is shown in Fig. 240. The primary coil, P, of coarse insulated copper wire, is connected by the screw cups -j- and with the battery. 1 is the secondary coil of fine insulated copper wire to which the handles are 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 by a PHYS. 24. 282 ELEMENTS OF PHYSICS. 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 arma- ture is drawn down and the circuit is broken. This re- leases the armature and the circuit is again closed. At every interruption of the primary current the iron wires become magnetized and demagnetized, and act inductively on the secondary coil. The primary current also acts in- ductively on the secondary coil, and by this joint action the M FIG. 240. intensity of the induced currents become much increased, and may even become of so high tension as to produce all the effects of statical electricity. 434. Ruhmkorflf'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 copper wire. With three Bun- sen's elements and a large coil the induced current becomes of amazing intensity. Some of the effects of the coil are as follows : 1. Physiological. The shocks are so violent as to be THERMO-ELECTRICITY. 283 dangerous, and incautious experimenters have been pros- trated by them. 2. Calorific. Fine iron wires brought between the ends of the induced wire are melted and vaporized. 3. Luminous. Sparks have been obtained nineteen inches in length. When the discharge is passed into rarefied gases the phenomena of auroral light is produced in a most beau- tiful and varied manner. These experiments are performed in sealed glass tubes, known as Geisler's tubes, one of which is shown in Fig. 241. The color of the light varies with FIG. 241. the vapor inclosed in the tube, and is frequently arranged in bands giving the appearance of stratified light. 4. Mecfianieal Plates of glass over an inch in thickness may be pierced by the discharge. 5. Leyden jars may be charged and discharged by means of the coil, with an almost continuous spark of great brilliancy. THERMO-ELECTRICITY. 435. If any two metals are soldered together and heated at their junction, an electrical current is evolved. On the other hand, if their junction be cooled, an electrical current in the opposite direction will be produced. These currents are called thermo-electric currents, but they differ in no respect from those already studied. 284 ELEMENTS OF PHYSICS. The direction of the current within the pair will depend on the metals which are associated together. The following thermo-electric series 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. 3 ri I * I + 1 4 11 T3 I, -s . . J ;a | iiif j iiiiii j pqo^HHHOPUoQcsjM^IaQ The most efficient electro-thermal couple is said to be formed of artificial sulphide of copper and metallic copper. Fig. 242. The usual combina- tion is bars of antimony and bismuth. Fig. 243 shows a section of a thermal battery made up of these metals. The greater the number of " FIG. 242. 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 obtain the same results FIG. 243. as the voltaic battery. In combining the bars, it is necessary to join both ends of all the bars except the two extremes. Hence, the effect of the current will be due to the difference of temperature in the two ends. This fact is utilized in the thermo-multi- plier, shown at T in Fig. 244. It consists of thirty pairs of bismuth and antimony, inclosed in a non-conducting frame, and connected with a galvanometer which has only a few turns of moderately thick wire. The slightest differ- ANIMAL ELECTRICITY. 285 ence in the temperature of the two ends of the thermo- multiplier will instantly be manifested by the deflection of FIG. 244. the needle of the galvanometer. The apparatus is used in all delicate investigations on the subject of radiant heat. ANIMAL ELECTRICITY. We have already learned that electricity produces peculiar phenomena in living animals, and that one of the most sen- sitive galvanoscopes may be had in the legs of a recently killed frog. Matteuci has reversed this last experiment and has succeeded in evolving a current by means of a battery formed of the muscles of frogs. 436. 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. 286 ELEMENTS OF PHYSICS. KECAPITULATION. 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 magnetic 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 intense light and heat. 3. For effecting chemical changes. 4. For making permanent and temporary magnets. THE END. 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. JUN9-196637 1 I RECEIVED BY JUKI- G8 2 RCO JUN 18 1385 IRCULATION DEPT* MAR 2 3 1977 8 - LD 21A-60m-10,'65 (F7763slO)476B General Library University of Californis Berkeley GENERAL LIBRARY - U.C. BERKELEY BDOQ77MEM8