John 3"ffett " ' '" : ' tir . Courst oi NATURAL PHILOSOPHY, FOR HIGH SCHOOLS AND ACADEMIES. BY W. J. ROLFE, FORMERLY HEAD MASTER OF THE HIGH SCHOOL, CAMBRIDGE, MASS., AND J. A. GILLET, PROFESSOR OF MATHEMATICS AND PHYSICS IN THE FEMALE NORMAL AND HIGH SCHOOL OF THE CITY OF NEW YORK. POTTER, AINSWORTH, AND COMPANY, NEW YORK AND CHICAGO. Entered according to Act of Congress, in the year 1874, by WOOLWORTH, AINSWORTH, AND COMPANY, In the Office of the Librarian of Congress, at Washington. EDUCATION DEPT, By the same Authors. CHEMISTRY, ASTRONOMY. These books are on the same plan as this Natural Philosophy^ and the three volumes form the Cambridge Course of Physics. Also, HANDBOOK OF NATURAL PHILOSOPHY. HANDBOOK OF CHEMISTRY. HANDBOOK OF THE STARS. These are brief, elementary manuals of Natural Philosophy, Chemistry, and Astronomy, and form a Shorter Course in Physics. PRESS OF RAND, AVERY & FRVE, BOSTON MASS. PREFACE. THE authors were led to prepare this series mainly that they might provide themselves with text-books containing an ele- mentary view of the present state of the Physical Sciences. The general plan and method of the Course were worked out by Mr. Gillet, and thoroughly tested in the class-room by oral teaching, before there was any thought of publishing the books. The authors felt, from- experience, that the elementary text- books on Physics now in use are, as a class, deficient in two important particulars. First, they are sadly behind the times ; and, secondly, they fail to give any systematic development of leading principles. A great revolution has taken place during the last twenty-five years in the departments of Chemistry, Elec- tricity, and Heat. In Chemistry this revolution has been so complete that the present theories of the science are currently known as "Modern Chemistry." The hypothesis of electric fluids has been swept away, and Heat has been shown to be a mode of molecular motion. It is but recently that Helmholtz has given the correct explanation of the formation of the vowel sounds, of resultants, and of dissonance ; and that Tyndall and others have investigated the subject of sounding and sensitive flames. In Optics, too, the cause of long and short sightedness, and the way in which the eye adjusts itself for near and distant objects, have been correctly understood only within a few years. In Astronomy, also, the analysis of solar and stellar light by means of the spectroscope has led to discoveries of the highest interest ; while recent investigation has thrown much light upon the nature of the photosphere and spots of the sun. As the principles of physical science are all established by facts of observation, the method has been adopted in this Course of first establishing the fact by experiment, when this is possi- 54! ?f2 IV PREFACE, ^ble, and <5 tjijsht drawing out the principle. The summaries 'always* coW it thVenjl of a topic, not at the beginning. *t Tbe'aUt^^ 8 Relieve ihat the simplest experiments, and those ' which* rfeqirife* the* 'simplest apparatus, are usually the best, and they have therefore sought to give such experiments in all cases. From their experience in teaching, the authors strongly rec- ommend that each lesson be explained and illustrated with the class before being given out to be studied. In preparing the present volume, the material for the SOUND has been drawn almost wholly from Tyndall's " Lectures." This valuable work is now brought within the reach of all teachers by the neat reprint of the Appletons (New York, 1867). Much of the material for the LIGHT has been taken from Ganot (Traite fildmentaire de Physique, I2 e e'dit, Paris, 1866), Herschel (Familiar Lectures on Scientific Subjects, London, 1867), and Potter (Physical Optics, London, 1856). In treating of HEAT, we have drawn mainly from Tyndall's "Lectures" and papers, and from Stewart (Heat, Clarendon Press Series, London, 1867). In ELECTRICITY we have been greatly indebted to Faraday's " Researches," to Noad's " Manual of Electricity, to Dr. Fergu- son's " Electricity " in Chambers's Educational Course (Edin- burgh, 1866), and to Professor Cooke's " First Principles of Chemical Philosophy" (Cambridge, 1868). The chapter on the PHYSICS OF THE ATMOSPHERE is main- ly condensed from Buchan's " Handy Book of Meteorology " (second edition, Edinburgh, 1868). The teacher will do well to get this book, and also Professor Loomis's excellent " Treatise on Meteorology " (recently published by the Harpers), to which we have once or twice referred. CAMBRIDGE, November 15, 1868. TABLE OF PART FIRST. MECHANICS. PAGE PRESSURE . . . 1; T V- . . . .. . 3 WEIGHT i '$ t. ' : 4 CENTRE OF GRAVITY . V V .' 'v^ ... 6 SUMMARY . ' . " 12 PRESSURE OF LIQUIDS . . *. . . 13 SPECIFIC GRAVITY . " . ' . . x .... 22 SUMMARY 24 PROBLEMS 25 PRESSURE OF GASES 29 SUMMARY 44 PROBLEMS . .45 MOTION 47 FIRST LAW OF MOTION 47 SECOND LAW OF MOTION 50 FALLING BODIES 53 PROBLEMS 55 THIRD LAW OF MOTION 58 SUMMARY 62 PROBLEMS .64 THE PENDULUM 65 SUMMARY 70 PROBLEMS 71 MACHINES AND SOURCES OF MECHANICAL POWER 73 THE LEVER 73 THE WHEEL AND AXLE 77 THE PULLEY 83 THE INCLINED PLANE . . . . . . .85 THE WEDGE & THE SCREW 87 SUMMARY . . . 89 TABLE OF CONTENTS. : 91 kfct 92 HORSE -PcwE. ^ . * \ 94 F/O ^Vft^D Pbtv,EJ J *-- V" 95 WATER POWER 9 6 STEAM POWER ......... 100 SUMMARY no PART SECOND. SOUND. PAGE NATURE AND PROPAGATION OF SOUND. . . 3 SOUND-WAVES 3 SUMMARY . 16 MUSICAL SOUNDS 17 SUMMARY 32 THE SUPERPOSITION AND INTERFERENCE OF SOUND- WAVES 33 SUMMARY 43 CHORDS AND DISCORDS 44 SUMMARY 5 MUSICAL INSTRUMENTS 51 TRANSVERSE VIBRATION OF STRINGS AND STRINGED IN- STRUMENTS .' . . 51 SUMMARY '.' . . 54 LONGITUDINAL VIBRATION OF STRINGS, RODS, AND COL- UMNS OF AIR; AND WIND INSTRUMENTS . . 55 SUMMARY 72 SOUNDING FLAMES . \ . . v . . 74 SUMMARY - . .* 'i- ;r ' r V' . 79 THE HUMAN VOICE . . 80 SUMMARY 82 THE HUMAN EAR. ... . . . . .83 SUMMARY 86 CONCLUSION . . . . .... . . .87 LIGHT. NATURE AND PROPAGATION OF LIGHT . . . 91 RADIATION . . 91 SUMMARY ; 96 TABLE OF CONTENTS. Vll REFLECTION AND REFRACTION . . \ 11^1.1^ % 96 , SUMMARY . . . . . . j ." J J .' J ' . * ^. 105 ; DISPERSION j . A. j , J 1 JJ J j . l > ip^ j SUMMARY *"* 4 f* j ***;/ ..?tSl6w : j ABSORPTION .... v . . . . in SUMMARY 116 INTERFERENCE AND THE UNDULATORY THEORY OF LIGHT 116 SUMMARY . . . . . '." " "'. "' . . . 127 DOUBLE REFRACTION AND POLARIZATION . ; . I2 8 SUMMARY . " . 143 THE RAINBOW . . * . . , . . . . 144 SUMMARY v . . . 147 OPTICAL INSTRUMENTS ." * . . ^ , . . 148 LENSES . . 148 SUMMARY ... 152 THE EYE 152 SUMMARY 168 THE MICROSCOPE AND THE TELESCOPE. . . . 170 THE MAGIC LANTERN 174 SUMMARY . . 176 MIRRORS 177 SUMMARY 182 PHOTOGRAPHY 182 SUMMARY 187 CONCLUSION 187 HEAT. NATURE AND PROPAGATION OF HEAT . . .193 RADIATION 193 SUMMARY 201 ABSORPTION 202 SUMMARY 212 EFFECTS OF HEAT ON BODIES 213 CONDUCTION -213 SUMMARY 215 TEMPERATURE . 215 SUMMARY . 222 CHANGE OF STATE 223 SUMMARY 233 Vlll TABLE OF CONTENTS. ......... 234 SUMMARY:' **,.; ....... 240 '. . ; ........ 240 *!"*." ....... 242 THE RELATION OF WATER TO HEAT .... 243 SUMMARY .......... 244 THERMAL INSTRUMENTS ...... 245 SUMMARY ......... 253 CONCLUSION .......... 254 ELECTRICITY. MAGNETISM ......... 257 SUMMARY .......... 262 NATURE AND SOURCES OF ELECTRICITY . 263 VOLTAIC ELECTRICITY ....... 263 SUMMARY .......... 276 RELATIONS OF ELECTRICITY TO MAGNETISM . . . 277 SUMMARY ......... 280 THE RELATION OF ELECTRICITY TO HEAT . . . 280 SUMMARY ....... ... 284 FRICTIONAL ELECTRICITY ....... 285 SUMMARY ......... 293 ELECTRICAL MACHINES AND APPLICATIONS OF ELECTRICITY ........ 293 * MACHINES FOR DEVELOPING ELECTRICITY . . . 293 SUMMARY . . . . . . . ". . . . 303 APPLICATIONS OF ELECTRICITY . . . . . 304 SUMMARY . . * . . . ..' ' ... .' . " .318 CONCLUSION ....... r \ ' . 318 APPENDIX . . . i. . ,. . . . .319 PHYSICS OF THE ATMOSPHERE 321 SOURCES AND CONVERSION OF ENERGY .... 358 NOTES . . 37 QUESTIONS FOR REVIEW AND EXAMINATION . . .381 INDEX 399 THE ELEMENTS OF NATURAL PHILOSOPHY. THE ELEMENTS OF NATURAL PHILOSOPHY. I. PRESSURE. 1. Solids. If we take hold of any part of a stone and lift it up, the whole stone comes up. The parts of the stone hold together firmly, so that when one part is moved they all move in a piece. Wood, iron, lead, and many other bodies, are like stone in this respect. Such bodies are called solids. 2. Liquids. If a goblet be filled with water and slowly tipped, the water runs out, not all together, but a part at a time. The parts of the water do not hold together so firmly as those of the stone. When the water is poured from the goblet, all its parts do not move in a piece, as those of a solid would do were it tipped from the same goblet. Alco- hol, quicksilver, and many other substances, resemble water in this respect. Such substances, whose parts move easily among themselves, are called liquids. 3. Gases. If water be poured into a goblet from above, it readily fills. If, however, a goblet be inverted and pressed down upon water, it does not fill with water. The reason it does not fill is, that it is already full of air. When it is inverted and pressed down upon the water, there is no chance for this air to escape ; but when the water is poured in from above, the air readily escapes from the mouth of the goblet. NATURAL PHILOSOPHY. ait m: tkfc goHet is quite unlike either a solid or a liquid. Air and other substances like it are called gases. All substances are called matter. There are, as we have seen, three states of matter, the solid, the liquid, and the gaseous. 4. Matter is acted upon by Gravity. When a stone is held in the hand, it is felt to press downward. There is some force drawing it towards the earth. This force is called gravity. WEIGHT. 5. The downward pressure which gravity causes a body to exert is called its weight. When different bodies, as iron and wood, are taken in the hand, it is easy to feel that some are heavier than others, but it is not so easy to tell exactly how much heavier one is than another. 6. The Spring Balance. But the weight of a body may be made to bend a spring, and, when different bodies are made to bend the same spring, we can readily tell how much heavier one is than another by seeing how much Fig. i. more it bends the spring. If it bends the spring twice as much, it is twice as heavy ; = ^ =1 - - an d if three times as much, it is thrice as heavy. An instrument for finding the weight of a body by seeing how much it can bend a spring, is called a spring balance. One form of this balance is shown in Figure i. Ii consists of a steel spring wound into a coil One end of this coil is fastened to a ring, and the other to a hook. The body to be weighed is fastened to the hook, and the whole raised by the ring. The weight of the body straightens or draws out the spring. A pointer moving over a plate in front, which is divided into equal NATURAL PHILOSOPHY. ',/ i '*- Fig. 2. parts, shows how much the spring A body which will straighten the spring a certain amount is said to weigh a pound ; one which will straighten it half as much, half a pound ; one fourth as much, a quarter of a pound ; twice as much, two pounds ; and so on. 7. The Balance. If a straight rod be supported on a pivot, in the centre, so that it can turn freely, as shown in Figure 2, it will remain level or horizontal. If now a pound of lead be hung from each end of this rod, it will still re- main horizontal. The two pieces of lead will just balance each other. If a second pound of lead be hung from one end of the rod, it will require a second pound at the other end to balance it. If then we have a number of pieces of lead of different sizes, whose weight is known, we can readily rind the weight of any other body by hanging it to one end of the rod, and adding the pieces of lead to th e other end till they balance it. If one pound of lead will balance it, its weight is one pound ; if a quarter ol a pound of lead will balance it, its weight is a quarter of a pound ; and so on. An instrument for finding the weight of a body in this way is called a balance, and the pieces of lead or iron used in weighing it are called weights. A common form of the balance is shown in Figure 3. It consists of a bar turning on a pivot in the centre, and having pans hung from each end for holding the weights and the body to be weighed. 8. The Steelyard.- If we have a straight rod balanced like the one above, with one arm considerably longer than NATURAL PHILOSOPHY. ?! an&& weight of a quarter of a pound is arranged so that it can slide along the longer arm, it will be found, on hanging a weight of a quarter of a pound to the end of the shorter arm, that the weight on the long arm must be placed just the length of the short arm from the pivot, in order to balance the weight on the short arm. If a half- pound weight be hung to the short arm, the weight on ths long arm will have to be placed twice the length of the short arm from the pivot, in order to balance it. If the weight on the short arm is three quarters of a pound, then the weight on the long arm must be placed three times the length of the short arm from the pivot, to balance it ; and so on. We can then find the weight of a body by hanging it to the short arm, and seeing how far the weight on the long arm must be placed from the pivot, to balance it. An instrument for finding the weight of a body by this method is called a steelyard. A common form of the steel- yard is shown in Figure 4. THE CENTRE OF GRAVITY. 9. Centre of Gravity. In the case of the bar whose arms are of the same size and of equal length, it has been seen that, when its centre is supported, the force of gravity acting upon each arm just balances that acting upon the other. The same is true when one arm of the bar is twice as long as the other, provided the shorter arm is twice as heavy as the longer. If a circular disc of wood (Figure 5) be pierced at the centre and supported upon a wire, it will remain at rest in whatever way it may be turned. In this case, then, NATURAL PHILOSOPHY. 7 the force of gravity acting upon the part of the disc to the right of the support always exactly balances that acting upon the part to the left of the support. If, however, one part of the disc be loaded with lead or other heavy substance, it will no longer rest equally well in every position. It will now remain at rest only when the loaded part of the disc is Fig. s- either directly under or over the support. It is found on trial, however, that there is still a point between the loaded side and the centre, upon which the disc will rest in any position. In this case also it is clear that the force of gravity, acting upon the part of the disc to the right of the support, always exactly balances that to the left of the sup- port. Such a point can always be found, whatever may be the size or shape of a body, and of whatever material it may be made. This point is called the centre of gravity. The centre of gravity of a body, then, is a point such that the force of gravity acting upon the part of the body on one side of this point always balances the force of gravity act- ing upon the part on the opposite side, no matter how the body may be placed. i o. The Centre of Gravity not always in the Body itself. If a straight strip of metal or wood be fastened to the sides of a ring so as to pass through its centre, it will be found that the ring will rest in any position when the centre is supported; and that it will not remain at rest in every position on any other point. The centre of gravity, then, of a ring which is exactly alike throughout its whole extent is at the centre of the ring. If one part of the ring is heavier than the other, the centre of gravity will be found to be between the centre and the heavier part. 8 NATURAL PHILOSOPHY. When two balls of the same weight are connected by a straight rod (Figure 6) the centre of gravity will be found to be at the centre of the rod. If one ball be twice as heavy as the other, the centre of gravity will be in the rod at a point twice as near the heavier ball as the lighter ball. If the heavier ball be three Q '^ Q times the wei g ht of the Kghte 1 " ball > the centre of gravity will be thrice Q as near this ball as the other. If the balls are connected by a curved rod, the centre of gravity will no longer be in the rod, but in a straight line which joins the balls. Its distance from the balls will be as above. 11. Equilibrium. If the loaded disc in Figure 5 be placed with its loaded part down, it remains at rest. If it be turned a little either way and then let go again, it returns at once to its former position of rest. If now it be carefully poised with the loaded side up, it can be made to rest; but if we turn it the least either way, it does not go back to the position of rest which it has just left, but at once takes a new position of rest with the loaded side down. The disc a, which is of the same material throughout, remains at rest equally well in any position. When a body is at rest it is said to be in equilibrium. When it is at rest in such a position that on being slightly disturbed it again returns to this position, it is said to be in stable equilibrium. When it is at rest in such a position that on being slightly disturbed it seeks a new position of rest, it is said to be in unstable equilibrium. When a body remains at rest equally well in any position, it is said to be in indifferent equilibrium. 12. The Centre of Gravity always seeks the Lowest Point. We have just seen that when the loaded disc (Figure NATURAL PHILOSOPHY. 9 5) is in the position b, if we disturb it in the least it falls into the position c; and that, if it be moved from this position t, it will at once return to it. It will be seen that, in this position c, its centre of gravity is lower than in any other position. And so in every case it will be found that the centre of gravity of a body seeks the lowest position which it can take. 13. The Stability of Equilibrium. A sphere which is of the same material throughout, is in indifferent equilib- rium (n) on a level surface, because the centre of gravity can fall no lower than it is. If a portion of the upper part of the sphere be removed by making a hole there (Fig- ure 7), the equilibrium becomes sta- Fig. 7 . ble, because the centre of gravity is brought below the centre of the sphere, and will have to rise if the sphere is moved either way. If the upper part of the sphere be loaded by putting into the hole a cylinder which more than fills it, the equilibrium becomes unstable, be- cause the centre of gravity is now brought above the centre of the sphere, and any motion either way tends to lower it. When a body is so situated that its centre of gravity is raised by tipping it in any direction, it is in stable equilib- rium ; when any disturbance of the body tends to lower its centre of gravity, it is in unstable equilibrium ; when on being disturbed its centre of gravity neither rises nor falls, it is in indifferent equilibrium. In Figure 8, ge shows the path which the centre of gravity g must take when the body is tipped. Until g reaches the point e the body tends to go back, because in so doing the centre of gravity would fall ; but as soon as g passes e the body tends to go over, because in so doing the centre of gravity would fall, h e shows how much the centre of gravity must be raised to overturn the body ; and this distance is seen to be greater when the i* 10 NATURAL PHILOSOPHY. Fig. 8. ^ boity is resting on the side a b than when it is resting on the side b c. It will be found that much more force wil) be required to overturn it in the latter case than in the former. The more, then, the centre of gravity of a body has 10 be raised in order to overturn it, the more stable its equilibrium. It will also be seen from Figure 8 that the broader the base or' a body compared with its height, the more stable its equilibrium. If, however, the body is not upright, it may be in un- stable equilibrium even when the base is broad. In Fig- ure 9 ge is the path which the centre of gravity must Fig. 9. take when the body abed is overturned, and it will be seen that, as soon as is moved at all in the direction ge y it begins to fall and the body will go over. In the body NATURAL PHILOSOPHY. II lm n o the centre of gravity g is not supported, and the body will fall over of itself. It is evident, then, that a body may lean and yet be in equilibrium, provided the centre of gravity is directly over any point of the base. If this point Fig. 10. be well within the base, the equilibrium may be very stable, as in the case of the famous leaning tower at Pisa. On the other hand, a body may be in stable equilibrium even when the base is very narrow. Thus a cork may rest upon the point of a needle, and yet be in stable equilibrium. This may be done by sticking two forks into the cork, as shown in Figure 10. The forks bring the Fig. ii. centre of gravity below the point of support, so that the cork cannot be tipped without raising the centre of gravity. In the same way, the image in Figure IT is balanced on its toe by means of the two heavy balls be- neath. So, too, in the " prancing horse" (Figure 12) the centre of grav- ity is brought below the point of sup- port by the leaden ball at the end of the curved rod. 14. How to find the Centre of Gravity of a Solid. When a stone, as in Fig- ure 13, is hung by the cord A, the centre of gravity must be di- rectly under the point of support ; that is, somewhere in the line A B. If the same stone be hung by the cord C, its centre of gravity Fig. 12. 12 NATURAL PHILOSOPHY. Fig- 13- must still be below the point of support, somewhere in the line C D. Since the centre of gravity is in both the lines A B and C Z>, it must be at the point G, where they cross. To find the centre of gravity of a solid, then, suspend it from any point of its surface by means of a cord, and no- tice the direction which the cord takes. Then suspend it from another point, and again notice the direction of the cord. The point where lines drawn in these directions would cross each other will be the centre of gravity. SUMMARY. Matter exists in three states. (1-3.) Matter is acted upon by gravity. (4.) Gravity gives bodies weight. (5.) The weight of bodies may be found by means of the spring balance (6), the balance (7), or the steelyard (8). A point can always be found such that the force of gravity acting upon the part of a body to the right of it is always balanced by the force of gravity acting upon the part to the left of it, no matter in what position the body may be placed. This point is called the centre of gravity, and sometimes lies within a body and sometimes without it. (9, 10.) When a body is at rest it is said to be in equilibrium. Its equilibrium may be either stable, unstable, or indifferent (it.) NATURAL PHILOSOPHY. 13 The centre of gravity always seeks the lowest position which it can take. (12.) The stability of the equilibrium of a body depends upon the position of the centre of gravity, and upon how much it must be raised to overturn the body. (13.) The centre of gravity of a solid may be found by sus- pending the solid from two different points of its surface by means of a cord. (14.) PRESSURE OF LIQUIDS. 15. How to find the Weight of a Liquid. If a cup be placed in one pan of a balance and weighed, and then filled with water and weighed again, it will be found to weigh more in the second case. This shows that liquids, as well as solids, are acted upon by gravity, which causes them to exert a downward pressure. The weight of the water in the cup is the weight of the cup when full of water less the weight of the empty cup. If the cup is filled with quicksilver and weighed again, it will be found to weigh much more than when filled with water. This experiment shows that some liquids are heavier than others. 1 6. Liquids when acted upon by Gravity press, not only downward, but also upward and sideways. Fix a long tube into the top of a wooden cask, and put a stop-cock into the top, and another into the side of the cask. On filling the cask and the tube with water, and opening the stop-cocks, the water is driven out of both. This shows that the water in the cask, when acted upon by gravity, presses upwards and sideways as well as down- ward. The pressure which liquids exert sideways is called lat- eral pressure. 17. The Upward, Downward, and Lateral Pressures are equal for the same Depth of Liquid. In Figure 14 we NATURAL PHILOSOPHY. Fig. 14 have a glass vessel, into the top of which are inserted three glass tubes of exactly the same size, with their mouths at the same distance from the bottom. One of these tubes opens downward, one upward, and one sideways. On filling the vessel with water, by means of the funnel, the liquid rises to the same height in all three tubes. Now it is the upward pressure which causes it to rise in the tube opening downward, the lat- eral pressure which causes it to rise in the tube opening sideways, and the downward pressure which causes it to rise in the tube opening upward ; and since the tubes are all of the same size, and since the water rises to the same height in each, these pressures are all evidently equal. The upward, downward, and lateral pressures are then the same for the same depth of liquid. 1 8. The Upward, Downward, and Lateral Pressures of a Liquid increase with the Depth, but are not altered by tht Size or Form of the Vessel which holds the Liquid. The more water we pour into the vessel, in Figure 14, the higher the water rises in the tubes. The upward, down- ward, and lateral pressures increase with the depth of the liquid. If the tube into which the liquid was poured be re- moved from the vessel, and other tubes of different sizes and shapes, but of the same height, be put in its place and filled with water, the liquid rises to exactly the same height in the tubes ; showing that the upward, downward, and lateral pressures of a liquid are not altered by the size or shape of the vessel which holds it. For this reason, when vessels of different sizes and NATURAL PHILOSOPHY. 15 shapes are connected, as shown in Figure 15, if a liquid be poured into one of them it will rise to the same height in all. Fig. 15- 19. When a dosed Vessel is filled with a Liquid, and any additional Pressure is brought to bear on any Particle of this Liquid, every Particle is made to exert the same additional Pressure, upward, downward, and sideways. Suppose the four tubes in Figure 14 are all of exactly the same size, and that the vessel is full of water. Pour water into the left- hand tube until it rises to the line c d. The water rises in all the tubes to the same height. The water poured into the first tube brings an additional pressure to bear upon the particles of water at its mouth, and it is the additional pressure which the particles at the end of the other tubes are made to exert that causes the water to rise in them. Now the water rises to the same height in all the tubes, and since they are all of the same size there must be the same number of particles at the end of each ; therefore, the particles at the end of the three tubes are made to exert the same additional pressure upward, downward, and side- ways, as that brought to bear upon the particles at the end of the left-hand tube. At whatever depth these three tubes open, the water will be made to rise in them all to the line c d, showing that all the particles of the liquid are made to exert the same additional pressure upward, downward, and sideways. That the particles at different depths are all made to exert the same additional upward pressure is shown by the apparatus in Figure 16. The three tubes b c and d open 10 NATURAL PHILOSOPHY. Fig. 1 6. at different depths, and the vessel is first filled with water, which rises in c and d to the line ef. Pour water into the tube a till it rises to the line gh, and it will rise to the same line in all the tubes. This explains the action of the hydrostatic bellows, repre- sented in Figure 17. It con- sists of two boards connected by a band of leather, forming a closed vessel, and a tube is in- F j g . 17> serted in the top or at the side. Weights are placed on this board, and water is poured into the tube. As the water fills the tube, the board rises with the weights upon it. If the surface of the board is 100 times as large as the end of the tube, one pound of water in the tube will balance 100 pounds on the board. As the surface of the board is 100 times as large as the end of the tube, there are 100 times as many particles of water in contact with the board as there are at the end of the tube, and as each particle is made to exert the same pressure, one pound of water in the tube ought to balance 100 pounds on the board. The particles of a liquid under pressure act like bent springs pressing equally in all directions. In an open ves- sel, gravity acting upon the upper layer of particles makes them press upon those of the second layer, which then act like bent springs against all their neighbors, which in turn become as bent springs. In this way the pressure of the upper layer is transmitted equally throughout the whole mass. But gravity pulls down the second layer as well as the first, and their pressure also is transmitted through all the mass below, so that the third layer receives twice the NATURAL PHILOSOPHY. 17 pressure of the second. In the same way the fourth layer receives three times the pressure of the second ; and so on. When pressure is exerted upon any particle of a liquid in a closed vessel, it is made to act like a bent spring upon all its neighbors, which in turn act in the same way either upon other particles or upon the sides of the vessel. 20. The Hydrostatic Press. It follows, from what has just been shown, that by means of a liquid a small pres- sure upon a small surface may be made to exert a great pressure upon a large surface. In Figure 18 we have two cylinders, with a plunger, or piston, in each. Suppose that Fig. 18. the surface of the larger piston is thirty times that of the smaller; if the latter is pressed downward by a weight of one pound, an upward pressure of one pound will be brought to bear upon each portion of the surface of the large piston equal to that of the small piston. The whole upward pressure on the large piston will then be thirty times the downward pressure on the small one. If the surface of the larger piston had been sixty times that of the smaller, one pound on the latter would have balanced sixty on the former ; and so on. Advantage is taken of this fact in the construction of the hydrostatic press ; shown in Figures 19 and 20. The two cylinders A and B are connected by the pipe d. The piston #, in the small cylinder A, is worked by the handle O, and forces water into the large cylinder B, NATURAL PHILOSOPHY. Fig. 19. where it presses up the piston C. If the end of the pis- ton C is 1,000 times as large as that of the piston a, a pressure of 2 pounds on a would exert a pressure of 2,000 pounds, or one ton, upon C. If a man in working the handle O forces down the piston a with a pressure of 50 pounds, he would bring to bear upon C a pressure of 25 tons. This press is used for pressing cotton, hay, cloth, etc., into bales, for extracting oil from seeds, testing cannon, boilers, etc., and for raising ships out of the water. 21. Springs and Artesian Wells. All natural collec- tions of water illustrate the tendency of a liquid to find NATURAL PHILOSOPHY. Fig. 20. its level. Thus, the Great Lakes of North America may be regarded as a number of vessels connected together, and hence the waters tend to maintain the same level in all. The same is true of the source of a river and the sea, the bed of the river connecting the two like a pipe. Springs illustrate the same fact. The earth is composed of layers, or strata, of two kinds ; those through which water can pass, as sand and gravel, and those through which it cannot pass, as clay. The rain which falls on high ground sinks through the soil until it reaches a layer of this latter kind, and along this it runs until it finds some opening through which it flows as a spring. It is the same with Artesian Wells. These wells derive their name from the Province of Artois in France, the first part of Europe where they became common. It would seem, however, that wells of the same kind were dug in China and Egypt many centuries earlier. In Figure 21, suppose A B and CD to be two strata of clay, and K K to be a stratum of sand or gravel between them. The rain falling on the hills on either side will NATURAL PHILOSOPHY. filter down through this sand or gravel, and collect in the hollow between the two strata of clay which prevent its Fig. 21. escape. If now a hole be bored down to K K, the water, striving to regain its level, will rise to the surface at Jf, or spout out to a considerable height above it. The Artesian well at Grenelle, in France, has a depth of 548 metres, or about 1800 feet, and the water flows out at the rate of 656 gallons a minute, or nearly a million gallons a day. One in this country, at St. Louis, is 2,199 feet deep, and affords 75 gallons a minute. 22. A Body is buoyed up when placed in a Liquid. If a stone be fastened to one pan of a hydrostatic balance and weighed under water, it will seem to be lighter than when weighed in the ordinary manner in the air. We have already seen that at the same depth in a liquid the upward and downward pressures just balance, but that these pressures increase with the depth. The bottom of the stone in the above experiment being deeper in the wa- ter than the top, the upward pressure of the water against the bottom of the stone is greater than the downward pres- sure of the same liquid upon the top of the stone. The stone is accordingly lifted up a little when plunged under water, and being thus buoyed up, seems to be lighter than in the air. NATURAL PHILOSOPHY. 21 Fig. 22. 23. A Body is buoyed up in Water by a Force just equal to the Weight of the Water which it displaces. In Figure 22, A is a cup into which the cylinder B exactly fits. This cup then will hold just as much water as B displaces when under water. Hang this cup and cylinder to the hydro- static balance, and balance it with weights. Immerse the cylinder B in a vessel of water, and we find that it is more than balanced by the weights. Now, by means of a drop- ping tube fill the cup A with water from the vessel. When the cup is full, the cup and cylinder are seen to be again just balanced by the weights. This shows that a body when im- mersed in water is buoyed up by a force just equal to the weight of the water which it displaces. It is evident from this that, if a solid weighs exactly as much as the water it displaces when fully immersed, it will neither rise nor sink in the water. If it weighs more than the water it dis- places, it will sink ; if less, it will rise. When a body floats upon the water, it displaces exactly its own weight of wa- ter. It is well known that a lump of iron will sink, but the same lump of iron may be hammered out into a ves- sel which will displace its own weight of water without being wholly immersed. In this way, ships may be made of iron which will float upon water as well as ships made of wood. 22 NATURAL PHILOSOPHY. SPECIFIC GRAVITY. 24. Substances vary in Density. When the same bulks of different solids and liquids are weighed, their weights are found to be very different. A substance which weighs more, bulk for bulk, than another substance is said to be more dense, or to have a greater density. It is often desira- ble to know the relative weights of the same bulks of bodies which vary in density. In such cases, it is con- venient to compare the weight of each substance with the weight of the same bulk of some given substance. Water is taken as the substance with which the weights of other solids and liquids are compared. The weight of a given substance compared with the weight of the same bulk of water, is called its specific gravity. 25. Specific Gravity of Solids. To find the specific gravity of a solid or liquid, we must know the weight of the substance and that of the same bulk of water. The weight of the solid can be found in the ordinary way. The weight of a bulk of water equal to that of the solid can then be found by weighing the solid in water, and subtracting its weight in water from its weight in air. The difference of these weights is, as we have seen (23), just equal to the weight of the water it displaces, and this is, of course, a bulk of water just equal to its own bulk. 26. Specific Gravity of Liquids. The specific gravity of liquids is most conveniently found by means of an instru- ment, shown in Figure 23, called a hydrometer. It consists of a hollow glass cylinder, with a stem and scale-pan above, and a small bulb filled with mercury below, by which it is made to float upright in a liquid. The instrument is placed in water, and weights are added until it sinks to a point marked upon the stem. The weight of the hydrometer, together with the weights in the pan, is equal to the weight of the water displaced (23). If now the instrument be NATURAL PHILOSOPHY. 23 placed in another liquid whose density is not the same as that of water, as alcohol, and made to sink by weights to the mark on the stem, the weight of an equal bulk of that liquid can be found. The specific gravity of the liquid will, of course, be the weight of the liquid divided by the weight of the water. Fig. 23. Fig. 24. A more common form of hydrometer is shown in Figure 24. It consists of a glass tube and bulb loaded with mer- cury at the bottom. This, when put into a liquid in which it will float, always displaces just its own weight (23). It is first put into pure water, and the point to which it sinks is marked upon the stem. If it be now put into a liquid of less density, it will sink deeper; if into one of greater density, it will not sink so deep. By means of the scale on the stem, the specific gravity of the liquid into which it is put is indicated.* * See Appendix, I. 24 NATURAL PHILOSOPHY. SUMMARY. Liquids have weight as well as solids (15). When acted upon by gravity they press upward, downward, and side- ways (16). The upward, downward, and lateral pressures are always equal for the same depth of the liquid (17). These pressures increase with the depth of the liquid, but are not altered by the size or shape of the vessel which holds the liquid (18). When any pressure is brought to bear upon one particle of a liquid, every particle of the liquid is made to press with the same force upward, downward, and sideways (19). On this account, when a small force acts upon a few par- ticles of a liquid, an enormous force may be brought to bear on a large surface in contact with the same liquid. Advantage is taken of this fact in the construction of the hydrostatic press (20). Springs and Artesian wells illustrate the tendency of wa- ter to seek a level in connected vessels (21). A body is buoyed up in water by a force equal to the weight of the water which it displaces (22, 23). The specific gravity of a solid or liquid is the weight of the solid or liquid compared with the weight of the same bulk of water (24). To find the specific gravity of a solid or a liquid, we must know the weight of the substance and that of the same bulk of water. The weight of a bulk of water equal to that of the solid can be found by weighing the solid in air and in water The specific gravity of a liquid may be found by means of a hydrometer (26). NATURAL PHILOSOPHY. 25 PROBLEMS. WEIGHT OF LIQUIDS. 1. A glass flask when full of water weighs 180 grammes.* The flask itself weighs 84 grammes. How many grammes of water does the flask hold ? 2. The same flask when full of mercury weighs 1382 grammes. How many grammes of mercury does it hold ? 3. The same flask full of alcohol weighs 160 grammes. How many grammes of alcohol does it hold ? 4. The same flask full of sulphuric acid weighs 220 grammes. How many grammes of sulphuric acid does it hold? THE PRESSURE WHICH LIQUIDS EXERT BY REASON OF THEIR WEIGHT. In these problems it is assumed that in liquids the pressure increases at exactly the same rate as the depth. 5. When water is one centimetre deep in a vessel it ex- erts a pressure of one gramme on every square centimetre of surface at the bottom of the vessel. What would be the pressure exerted upon every square centimetre of surface at the bottom, if the water in the vessel were 3 centimetres deep ? 6. What would be the pressure upon 9 square deci- metres of surface at the bottom, if the liquid were 6 centimetres deep ? 7. What upon 13 square decimetres at the bottom, if the liquid were 17 centimetres deep? 8. A closed vessel is 3 decimetres deep, and has a tube projecting from the top to the height of one metre. The bottom of the vessel has a surface of 50 square decimetres, * See French Weights and Measures, p. lid. 26 NATURAL PHILOSOPHY. and the vessel is filled with water to the top of the tube. What is the whole pressure upon the bottom of the vessel ? 9. What would be the pressure upon a square centimetre of surface on the side of the above vessel, the centre of the surface being 3 centimetres from the bottom ? 10. What would be the pressure upon a square centi- metre of surface at the top of the vessel ? n. What would be the pressure upon the whole upper surface of the vessel, supposing it to contain 50 square decimetres ? 12. A cubical vessel, every side of which is a square metre, is filled with water. What would be the pressure upon its bottom ? 13. What would be the pressure upon each of its sides ? * 14. Suppose the top of the above vessel were closed and a tube one metre in length were inserted into it, on filling the tube to the top what would be the pres- sure exerted upon the top of the vessel ? 15. What would be the pressure upon the bottom of the vessel when the tube is full of water ? 1 6. What would be the pressure upon the sides of the vessel in the last case ? THE HYDROSTATIC PRESS. 17. The end of the small piston in a hydrostatic press has a surface of 10 square centimetres ; and the end of the large piston a surface of a square decimetre. A pressure of 10 kilogrammes upon the small piston would bring what pressure to bear upon the large piston? * To find the pressure upon any surface at the sides of a vessel, take the average depth of the surface, that is, the distance from the top of the water to the middle of that surface. NATURAL PHILOSOPHY. 27 1 8. If the small piston be the same as above, and the 2nd of the large piston contain a square metre of surface, 5 kilogrammes upon the small piston will cause what pres- sure to be brought to bear upon the end of the large piston ? 19. A pressure of 75 kilogrammes on the small piston would cause what pressure to be exerted upon the end of the large piston ? THE BUOYANCY OF LIQUIDS. $ip" A cubic centimetre of water weighs one gramme. 20. A body weighs 50 kilogrammes in air, and has a bulk of 40 cubic decimetres. How much does it weigh in water? 21. A stone weighs 80 kilogrammes in the air, and 55 kilogrammes in water. What is its bulk ? 22. A hollow vessel of copper weighs one kilogramme. What must be its bulk in order that it may just float in water ? 23. A hollow vessel of iron weighs 15 kilogrammes. What must be its bulk in order that it may sink one half in water ? 24. A boat displaces 12 cubic metres of water. What is its weight ? SPECIFIC GRAVITY. 25. A body weighs 150 hectogrammes in air, and weighs 2 kilogrammes in water. What is the weight of a bulk of water equal to that of the body ? 26. A flask full of water weighs 62 grammes : a piece of lead weighs 44 decagrammes in the air. It is put into the flask, and the flask is filled with water. It is found that the lead and water together weigh 462 grammes. What is the weight of a bulk of water equal to that of the lead ? 28 NATURAL PHILOSOPHY. 27. A piece of lead weighs 56 grammes in the air, and 51 grammes in water. What is the specific gravity of lead? 28. A flask holds 75 grammes of water : a lump of copper, which weighs 160 grammes in the air, is put into the flask, and it is found that the water and the copper together weigh 219 grammes. What is the specific gravity of copper? 29. The specific gravity of iron is 7.8. What weight of water will 45 kilogrammes of iron displace ? 30. The specific gravity of zinc is 7.2. What is the bulk of 90 kilogrammes of zinc ? 31. A piece of wood, which weighs 25 grammes in the air, is fastened to a piece of iron whose weight is 80 grammes ; and on immersing both in water and weighing them, it is found that they together weigh 45 grammes. What is the weight of the water displaced by the wood ? 32. A piece of wood, weighing 42 grammes, is fastened to a piece of zinc weighing 86 grammes, and both are weighed under water, and are found to weigh 34 grammes. What is the specific gravity of the wood ? 33. A flask weighing 20 grammes weighs 430 grammes when full of water, and 5555 grammes when full of mer- cury. What is the specific gravity of mercury ? 34. A hydrometer weighing 50 grammes requires a weight of 80 grammes to sink it to the neck in water, and a weight of 135 grammes to sink it to the same depth in sulphuric acid. What is the specific gravity of sulphuric acid? 35. A vessel holds 100 kilogrammes of water. How much mercury would it hold? 36. How much alcohol will it hold, if the specific gravity of alcohol is .79 ? NATURAL PHILOSOPHY. 29 THE PRESSURE OF GASES. 27. Gases have Weight. Weigh very carefully a thin copper globe when filled with air; then exhaust the air from it by means of the air-pump, and again weigh it. It will be found to weigh less in the last case than at first. This shows that air has weight. In like manner, it may be shown that all gases have weight 28. Gases ; like Liquids, press upward, downward, and sideways. Fasten over the mouth of a bell-jar, open at both ends (Figure 25), a piece of india-rubber, and place Fig. 25. the bell-jar on the plate of the air-pump, and exhaust the air from under the rubber. The rubber will be forced into the jar, showing the downward pressure of the air. If a bell-jar, with its mouth at the side, be closed, as before, with a piece of india-rubber, on exhausting the air from the jar the rubber is forced into it. This shows the lateral pressure of the air. If the neck of the jar is bent around still farther, so that it shall open downward, and the mouth is closed as before, on exhausting the air the rubber is forced into the jar. This shows the upward pressure of the air. 29. The Hand-Glass. If the first bell-jar in Figure 25 is small enough at the top to be covered with the palm of the hand, and the air be exhausted from it when thus covered, the hand will be held down with consider- able force by the pressure of the air upon it. NATURAL PHILOSOPHY. If a wet bladder be tied over the same bell-jar and dried, and the air be exhausted as before, the bladder will burst with a loud noise. These two experiments show the down- ward pressure of the air. 30. The Magdeburg Hemispheres. Figure 26 represents Fig. 27. Fig. 26. two brass hemispheres, some four inches in diameter, the edges of which are made to fit tightly together. The whole can be screwed to the air-pump by means of the stop- cock at the bottom. While the hemispheres contain air, they can be separated with ease, since the outward pressure is just balanced by the inward pressure ; but when the air within is pumped out, it is very hard to pull them apart. Since it is equally difficult to do this, in whatever position the hemispheres are held, the experiment shows that the air presses in all directions. This piece of apparatus is called the Magdeburg Hemi- spheres, from Otto von Guericke, of Magdeburg, by whom it was invented. NATURAL PHILOSOPHY. 31. The Weight Lifter. In Figure 28, A is a strong glass cylinder, open at both ends ; B a piston, working air- tight within it ; and C a brass plate, covering it closely, and having a hole in the centre to which a hose may be screwed for connecting it with the air- pump. When the air is ex- hausted from the cylinder, the piston rises, even if a heavy weight is hung from it as shown in the Figure. This experiment affords a very striking illustration of the upward pressure of the air. 32. The Expansive Force of Gases. If an india-rubber bag, partially filled with air, be closed air-tight and placed under the re- ceiver of the air-pump, the bag fills out, as shown in Figure 29, when the air is exhausted from the receiver. The same would be true if the bag were partially filled with any gas. All gases then tend to expand. 33. The Air-Pump. An instttb ment for removing the air from a vessel is called an air- pump. One form of such a pump is shown in Figure 30. It consists of a cylinder, in which a piston moves air-tight. In this piston is a valve opening upward. At the top of the cylinder is another valve also opening upward. The bottom of the cylinder is connected with the pump-plate by means of a tube. On this plate is placed the vessel from which the air is to be exhausted. This vessel is called che receiver. The piston is worked by means of the handle. 32 NATURAL PHILOSOPHY. As the piston is forced down the expansive force of the ail below pushes open the valve in the piston to get into the space left behind it. When the piston is drawn up again the expansive force of the air above closes this valve and opens the valve at the top of the cylinder, so that this air escapes. The expansive force of the air in the tube Fig. 30- and receiver causes it to fill the space behind the piston. When the piston is again pushed down, the downward pressure of the air outside closes the valve at the top of the cylinder, while the expansive force of the air below opens the valve in the piston, and some of the air passes through it. On drawing up the piston again this air is removed as before. By continuing this process the air is nearly all withdrawn from the receiver. It cannot be wholly withdrawn, because as it becomes more and more exhausted, the expansive force becomes less and less, until at last it is not sufficient to open the valve in the piston. NATURAL PHILOSOPHY. 33 34. A Body is buoyed up in the Air. If a hollow sphere be balanced in the air by a piece of lead, and then the whole apparatus be put under the receiver of an air- pump and the air exhausted, the lead will no longer bal- ance the sphere. This shows that a body is buoyed up in the air as well as in a liquid (22). Bodies seem to be lighter in the air than in a vacuum (that is, a space from which the air has been exhausted), for the same reason that a body seems lighter in water than in the air. The upward pressure of the air upon the bottom of the body is some- what greater than the downward pressure upon the top of the body. A body in the air, then, is buoyed up by a force just equal to the weight of the air which it displaces. If a body weighs more than the air it displaces, it sinks through the air ; if it weighs less than the air it displaces, it rises in the air. 35. Balloons. Balloons rise in the air because they are filled with some substance which makes them lighter than the air which they displace. If a glass bulb and tube filled with air be arranged, as in Figure 31, with the end of the tube under water, and the bulb be heated by means of a lamp, the air in it expands, and a part of it is driven out in bubbles through the water. This shows that air expands when heated. Paper balloons are sometimes made which are sent up by fastening a light just under an opening in the bottom of the balloon. The light heats the air inside, and causes it to expand, and a part to pass out. The remainder is then lighter than the air displaced by the balloon, and it con- sequently rises. Large balloons are made of strong silk, and filled with some very light gas, such as coal gas. This makes the balloon so much lighter than the air 2* C Fig. 31- 34 NATURAL PHILOSOPHY. Fig. 32. it displaces, that it will rise, carrying a car with two or three persons in it. Balloon ascensions are now quite common, and it is possible that the time will come when by their aid we may navigate the air as we now navigate the sea. As yet, how- ever, it has been found impossible to guide them. When once in the air they are at the mercy of the wind, and go in whichever way it happens to be blowing. 36. The Atmospheric Pressure will sustain a Column of Liquid in an inverted Vessel. If a glass jar be filled with water and inverted in a dish of water, care being taken to keep the mouth of the jar all the time under water, the liquid will not flow out of the jar when it is raised. If, however, the jar be par- tially filled with water, and inverted in a shallow dish of water, and placed un- der the receiver of an air- pump, and the air be ex- hausted, the water will flow out from the jar ; showing that it is the pressure of the atmosphere on the sur- face of the water in the dish which keeps the water in the inverted jar. If mercury or alcohol is used instead of water, the result is the same. 37. The Atmospheric Pressure will sustain a Column of Mercury about 30 Inches high. If a glass tube closed at one end and about 34 inches long be filled with NATURAL PHILOSOPHY. 35 mercury, and inverted in a cup of mercury, as shown in Figure 32, a part of the mercury will run out, leaving a column about 30 inches high in the tube. 38. The Atmospheric Pressure is -equal to about 15 Pounds to the Square Inch. Suppose the tube in the above ex- periment were one inch square, it follows, from the way in which liquids press, that the downward pressure at the bottom of the tube would be just equal to the downward pressure of the atmosphere on each square inch of the surface of the mercury in the vessel. If now we weigh the mercury in the tube, we shall find that there are about 15 pounds of it. This column of mer- cury then exerts a pressure of 15 pounds at the bottom of the tube. The air then presses with a weight of 15 pounds upon every square inch of surface. We do not perceive this great pressure, because the air presses equally in every direction. 39. The Atmospheric Pressure varies from Day to Day. If a glass tube be filled with perfectly pure mercury, so that it shall not become tarnished, and then inverted in a cup of mercury and left standing, and the height of the mercury column noted from day to day, it will be found to vary considerably, being sometimes as much as two inches higher than at other times. This variation in the height of the mercury column must be due to changes in the pressure of the air. 40. The higher the Place, the less the Atmospheric Pres- sure. If the height of the mercury in the tube be noticed at the base of a mountain, and it be then carried to the top of the mountain and the height of the mercury again noticed, it will be found considerably less in the latter case. This shows that the atmospheric pressure becomes less, the higher we go above the surface of the earth. The atmosphere is a great ocean of air which surrounds the earth, and at the bottom of which we live, as the fishes 36 NATURAL PHILOSOPHY. live at the bottom of the sea. The changes in the height of the mercury just described show that the pressure in creases with the depth. The daily variations in the pres- sure are probably due to large waves which run over the surface of this ocean. 41. The Barometer. An instrument for measuring the pressure of the atmosphere is called a barometer. One form of it is shown in Figure 33. It consists of a cup and tube filled with mercury, as in the experiment illustrated by Figure 32. These are fastened to a wooden frame. At the up- per part of the tube there is a scale with a sliding index, for measuring the height of the mercury. H is a thermometer. The mercury is often put into a leather bag instead of an open cup as here, since it is less likely to be spilled. As the leather is flexible the pressure of the air is brought to bear upon the mercury through the bag. 42. Uses of the Barometer. It has already been stated that the atmospheric pressure is less as the height above the earth is greater. When we have found at what rate it dimin- ishes, we can readily find the height of moun- tains by means of the barometer. We have to find the difference between the readings of the barometer at the level of the sea and at the top of the mountain. This shows how much the pressure has diminished, and from this we can find the height of the mountain. The barometer is also of considerable use in indicating the approach of storms, espe- cially of violent winds. It has been observed that such storms are very likely to occur im- mediately after a sudden diminution of atmos- NATURAL PHILOSOPHY. 37 pheric pressure, which is shown by a rapid fall of the mep cury in the barometer tube. On the other hand, a gradual rise of the mercury in the tube usually indicates the ap- proach of fair weather. The mere height of the mercury in the tube tells us little about the weather, but a careful study of the movements of the mercury enables us to judge pretty accurately what changes are likely to occur in the weather. 43. Pumps. As water is somewhat more than thirteen times lighter than mercury, the pressure of the atmosphere will sustain a column of this liquid about thirteen times thirty inches in height, or considerably more than thirty feet. If the tube is open at the top it is necessary to re- move the air from it before the water will rise into it. An instrument for raising water in this way is called a pump. The common lifting-pump is shown in Figure 34. It is really an air-pump, with piston and valves like those de- scribed above (33), and it works in the very same way. When the piston P is forced down, the air below it, by its expansive force, opens the valve O, through which it es- capes. When the piston is drawn up again, the valve O is kept shut by the pressure of the air above, and the air in A expands, pushes open the valve *S, and rushes into the vacuum above. The air being thus partly removed from A, the pressure of the air upon the water in the well outside is greater than that inside the pipe, and conse- quently forces the water up the pipe and through the open valve S. When the piston is pushed down again, the pres- sure of the water in the cylinder shuts the valve S, and opens the valve O. The water thus gets above the piston, which on going up again lifts it so that it flows out at the spout, as shown in the figure. Figure 35 represents the force-pump. In this pump the piston P is solid. When it is drawn up, the water below by its upward pressure opens the valve S and fills the 38 NATURAL PHILOSOPHY. Fig. 34- Fi & 35- cylinder. When the piston is pushed down, the valve S being shut by its own weight and the pressure of the water upon it, the water is forced up through the valve O into the pipe D. When the piston goes up again, the valve O is closed by its own weight and that of the water above, the valve 6" opens, and the cylinder is filled as before. In Figure 36 we have these two pumps combined. The air is pumped out through the valves S and O, and the water is forced up into the cylinder through the pipe A and the valve S, just as it was in the lifting. pump ; and the water is then forced through the valve O and the pipe D) as in the force-pump just described. NATURAL PHILOSOPHY. 39 In both these forms of force-pump the water is driven out of the pipe D only when the piston is going down. It may be made to flow out in a steady stream by adding an air- chamber above the valve O, as shown in Figure 37. As Fig. 36. Fig. 37. the water is forced into this chamber it compresses the air, which by its expansive force exerts a continuous pressure on the water, and drives it in a constant stream up the pipe. In the fire-engine, two force-pumps are usually connected with one air-chamber. The pumps are so arranged that the piston of one is going down while that of the other is going up, thus forcing water into the air chamber all the time. 44. The Siphon. Bend a tube into the form of the let- ter [/, making one arm somewhat longer than the other ; fill it with water, and close each end with the fingers ; then invert it and place the short end under the surface of wa- ter in a vessel. If now both ends are opened, the water will flow out of the vessel through the tube. A bent tube used in this way is called a siphon. To explain the action of a siphon, let us suppose it NATURAL PHILOSOPHY. Fig. 38. filled and the short arm placed in the water. The pressure then acting on C (Figure 38), and tending to raise the wa- ter in the tube, is the atmospheric pressure less the weight of the column of water CD. In like manner, the pressure on the end of the tube B is the atmospheric pressure less the pressure of the column of water A B. But as this latter column is longer than CD, the force acting at B is less than th% force acting at (7, and con> sequently the water will be driven through the tube by a force equal to the differ- ence of these two forces. The flow will therefore be the faster, as the difference of level between C and B is greater. 45. Tantalus's Cup. This is a glass cup, with a siphon tube passing through the bottom, as shown in Figure 39. If water be poured into the cup, it will rise both inside and outside the siphon until it has reached the top of the tube, when it will begin to flow out. If the water runs into the Fi cup less rapidly than the siphon carries it out, it will sink in the cup until the shorter arm no longer dips into the liquid and the flow from the siphon ceases. The cup will then fill again as before ; and so on. In many places there are springs which flow at intervals, like the siphon in this experi- ment, and whose action may be explained in the same NATURAL PHILOSOPHY. 4! way. A cavity under ground may be gradually filled with water by springs, and then emptied through an opening which forms a natural siphon. In some cases of this kind the flow stops and begins again several times in an hour. 46. The Air-Gun and the Condenser. We have seen that gases exert an expansive force which increases when they are heated (35). It increases also when they are compressed into smaller space. This is illustrated by the air-gun, which consists of a tube connected by a stop-cock with a small air-tight vessel of very great strength. If a large amount of air be forced into this vessel, and the stop-cock be then opened, the expansive force of the con- fined gas will drive a bullet from the tube as if it were fired from a musket. The firing of a musket is in fact another illustration of the very same kind. When the gunpowder is set on fire it forms an immense amount of gas, which, being condensed into a small space, has a very great expansive force, and therefore exerts a very great pressure upon the bullet. An instrument used for compressing air in this and other experiments is called a condenser. It consists of a strong cylinder with a piston and valves arranged precisely as in the force-pump in Figure 35. It works too in the same way as the force-pump ; the air rushing in through the valve 6* when the piston is raised, and being driven out through the valve O when the piston is pushed down. The vessel into which the air is to be forced is screwed to the pipe D. 47. Mariotte's Law. In Figure 40 we have a long glass tube closed at one end and bent up into the form of the letter U. Pour in a little mercury, and tip the tube a little, so that a part of the air may escape from the closed end, and the mercury may stand at the same level in both arms. The column of air in the closed arm is now evi- dently under a pressure equal to that of the atmosphere, 42 NATURAL PHILOSOPHY. which we have seen to be equal to that of a column of mercury 30 inches high (37). If now mercury be poured into the long arm until its level in that arm is 30 inches above that in the short arm, the air in this arm will be under a pressure of two atmospheres, or 30 pounds to the square inch. Un- der this pressure it will be seen that the column of air is just half as long as it was before. If more mercury be poured in, until its level in the long arm is 60 inches above that in the short arm, then the air in the short arm will be under a pressure of three atmospheres, or 45 pounds to the square inch; and it will be found to be only one third as long as at first When, therefore, the pressure upon a column of air is doubled, the bulk is reduced to one half; when it is trebled, the bulk is reduced to one third; and so on. The fact that the bulk of a gas be- comes less just in proportion as the pressure upon it becomes greater, or, in other words, that the volume of a gas is inversely as the pressure which it bears, is called Mariotte's law, from its discoverer. In the above experiment, it is evi- dent that when the bulk of the air has been reduced to one half, its expansive force, or its elasticity, has been doubled, since it balances double the pressure in the long arm that it did before. When its bulk is reduced to one third, it balances thrice the pressure; and so on. The elasticity of a gas then becomes greater just in pro- NATURAL PHILOSOPHY. 43 portion as its bulk becomes less, or as the pressure upon it becomes greater ; or, in other words, the elasticity of a gas is inversely as its volume, and directly as the pressure which it bears. 48. The Manometer. An instrument for measuring the expansive force, or pressure, of a gas is called a manometer. One form of the ma- nometer is shown in Figure 41. It consists of a glass tube closed at the upper end and filled with air. Its lower end is fastened into a small iron box containing mercury. The tube A serves to connect the box with the closed vessel holding the gas whose ex- pansive force is to be tried. The height to which the mercury is raised by the pressure of the gas is shown by a scale. 49. The Spirit Level. If a tube be filled with liquid except a mere bubble of air, and then closed, this bubble will always rise to the highest part of the tube, in whatever position it may be placed. Ad- vantage is taken of this fact in the con- struction of the spirit level. The most common form of this instru- ment (Figure 42) consists of a closed glass tube, AB, very slightly curved on the upper side. It is filled with spirit, with the exception of a bubble of air which tends Fig. 42. cj ;D to rise to the highest part of the tube. It is placed in a case CD, which is so arranged that when it is placed on a perfectly level surface the bubble of air is exactly in the middle of the tube, as represented in the figure. 44 NATURAL PHILOSOPHY. SUMMARY. Gases have weight. (27.) Gases, like liquids, press upward, downward, and side- ways. (28.) These pressures of gases are illustrated by the hand-glass, the Magdeburg hemispheres, and the weight-lifter. (29-31.) Gases are acted upon by an expansive force. (32.) The air can be exhausted from a vessel by means of the air-pump. (33.) Bodies are buoyed up in air by a force equal to the weight of the air which they displace. (34.) It is owing to this that balloons rise in the air. (35.) The atmospheric pressure balances a column of mercury about thirty inches high, and is equal to about fifteen pounds to the square inch. (37, 38.) This pressure varies from day to day, and becomes less as the height of the place increases. (39, 40.) The barometer is an instrument for measuring the at- mospheric pressure. (41.) It is used in finding the height of mountains, and, to a certain extent, it indicates changes of the weather. (42 ) The action of pumps is to be explained by the pressure of the atmosphere. (43.) The siphon also acts by reason of the atmospheric pressure. (44.) The expansive force, or elasticity, of gases is increased by heat and by pressure. (46.) The bulk or volume of a gas is in the inverse ratio of the pressure which it bears. The elasticity of a gas is in the inverse ratio of its votume^ or the direct ratio of the pressure it bears. These facts are known as Mariotte's law. (47.) The elasticity of gases is measured by means of the manometer. (48.) NATURAL PHILOSOPHY. 45 PROBLEMS. WEIGHT OF GASES. The specific gravity of a gas is its weight compared with that of an equal bulk of atmospheric air. 37. A glass globe of the capacity of one litre weighs 83 grammes after the air has been exhausted from it ; and 84.292 grammes when full of air. What is the weight of \ litre of air ? 38. The same globe, when full of ammonia gas, weighs 83.759 grammes. What is the weight of a litre of ammo- nia gas ? 39. The same flask, when full of carbonic acid, weighs 84.964 grammes. What is the weight of a litre of carbonic acid? 40. The same flask, full of hydrogen, weighs 83.089 grammes. What is the weight of a litre of hydrogen ? 41. The same flask, when full of oxyyen, weighs 84.428 grammes. What is the weight of a litre of oxygen ? 42. What is the specific gravity of ammonia gas ? What is the specific gravity of carbonic acid ? What is the specific gravity of hydrogen ? What is the specific gravity of oxygen ? 43. A vessel of the capacity of 985 litres would hold how many grammes of air ? Of carbonic acid ? 44. A vessel of the capacity of 416 litres would hold how many grammes of hydrogen ? Of oxygen ? PRESSURE CAUSED BY THE WEIGHT OF GASES. The atmospheric pressure is about one kilogramme upon every square centimetre of surface at the level of the sea. 45. The body of an ordinary-sized man has a surface of about 16,000 square centimetres. How many kilo- 46 NATURAL PHILOSOPHY. grammes of pressure does the atmosphere exert upon a man's body ? How many pounds avoirdupois ? 46. A room is 12 metres long, 9 metres wide, and 5 metres high. How many kilogrammes of pressure does the atmosphere exert upon the floor of the room ? How many pounds ? 47. How many kilogrammes of pressure does it exert upon each end of the room ? 48. How many on each side ? 49. How many kilogrammes of air does the room contain? 50. The atmospheric pressure will balance a column of mercury 76 centimetres high, and the specific gravity of mercury is 13.5. It will balance a column of water how many centimetres high ? How many feet high ? 51. If water is to be raised 1,200 centimetres high by means of the lifting pump, how much of this distance must the water be lifted ? 52. Water is to be carried over a hill 1,350 centimetres high. Can it be done by means of the siphon ? Why ? BUOYANCY OF GASES. 53. A block of wood has a bulk of 900 cubic metres- How much is it buoyed up in the air ? 54. A balloon when filled with gas weighs 500 kilo grammes. How many litres of bulk must it have in order that it may just float in the air ? 55. A balloon has a bulk of 1,000 cubic metres, ana weighs 25 kilogrammes. It is filled with coal gas, whose specific gravity is .6. By how many kilogrammes of pres- sure is it forced upward ? If a car, which, with all its fix- tures, has a bulk of 3 cubic metres and weighs 48 kilo- grammes, be attached to the balloon, with what pressure will the whole be forced upward ? NATURAL PHILOSOPHY. 47 II. MOTION. WE have now studied somewhat the pressures produced by gravity and other forces acting upon the three states of matter. We have seen that when a stone is held in the hand it presses upon it ; and it is well known that on re- moving the hand the stone falls to the ground. We are now to study the motions caused by gravity and other forces. FIRST LAW OF MOTION. It is a well-known fact that a stone or other body, when at rest, will not begin to move of itself, but only on the application of some force. It is equally well known that when any body, such as a ball, is in motion, it requires some force to stop it. 50. A moving Body when left to itself will always move in a straight Line and at the same Rate. If a heavy weight, such as a lead ball, be suspended from a point by means of a string or a wire, and it be set swinging, it will swing for a time and then come to rest. A ball thus suspended is called a pendulum. If this pendulum be placed under the receiver of an air pump, and the air partly exhausted, it will swing a longer time ; and the more the air is exhausted the longer the pendulum will swing. If the pendulum be nicely hung, so that there will be very little friction at the point on which it turns, it will, when once set going in an exhausted receiver, swing 24 or 30 hours. Since the length of the time that the pendulum will swing increases as the resistance it meets diminishes, we conclude that it would swing forever, provided there were no resistance to its mo- 48 NATURAL PHILOSOPHY. tion. Now, mathematicians have found that they can ex- plain this swinging of the pendulum by supposing that the ball of the pendulum, wheri once put in motion, would move on forever in a straight line and at the same speed, were it not acted upon by any other force. They have found, moreover, that this is the only way in which they can explain the motion of the pendulum. We conclude, then, that a moving body when left to it- self will always move in a straight line and at the same rate. This is usually called \htfirst law of motion. The inability of a body, whether at rest or in motion, to change its state, is often called inertia. 51. An unbalanced Force must act upon a Body in order to put it in Motion, or to change the Direction or the Rate of its Motion. A ball held in the hand remains at rest, be- cause the downward pull of gravity upon the ball is just balanced by the resistance offered by the hand. If the hand is removed so that the force of gravity is unbalanced, then the ball begins to move. If we push with the hands against the opposite sides of a book, the book will remain at rest as long as the push of one hand is just balanced by that of the other. Take away one hand, so that there shall be nothing to balance the push of the other, and the book begins to move. So, in every case, a body begins to move only when an unbalanced force acts upon it. And when a body is once in motion, it changes the di- rection and rate of its motion only when an unbalanced force is acting upon it. When a body is once in motion it is just as natural for it to continue to move in a straight line, with uniform speed, as it is for it to remain at rest when once it is at rest. It seems to us more natural for a body to be at rest, because, when a body is put in motion at the surface of the earth, it always meets with resistance which quickly brings it to rest again, unless the moving force continues to act upon it. NATURAL PHILOSOPHY. 49 52. The Effect of a Force acting for a Moment only. When the moving force acts upon a body only an instant, as when a ball is struck with a bat, or a bullet is fired from a gun, it has its greatest speed at first, and its motion is gradually wasted by the resistance it meets in passing through the air or over the earth. 53. The Effect of a Force acting continuously. When, however, a body is acted upon continuously by a force, as in the case of a railway train or a steamboat, the motion, slow at first, gradually increases till it reaches a certain point, when the speed remains unchanged so long as the moving force is unchanged. When the moving force is in- creased the speed increases, and when it is diminished the speed diminishes. 54. The Resistance a Moving Body meets increases as the Square of its Velocity. The steamboat in moving has to push aside a certain amount of water in a second, and this is the chief resistance it meets. Now, as the speed of the boat increases, more water must be pushed aside in a sec- ond, and each particle of water must be moved aside more quickly. Hence, the faster it moves, the greater the resist- ance. Suppose the speed of the boat to be doubled, twice as many particles of water must be pushed aside in a sec- ond, and each particle must be pushed aside in half the time. Hence, the resistance becomes fourfold when the velocity is doubled. The resistance, then, increases as the square of the velocity. This explains the fact that, in or- der to double the speed of a steamboat, the power of the steam must be quadrupled, and in -order to treble the speed the power must be increased ninefold. The same is true in the case of the train of cars, or of any moving body. When their velocity is doubled, they meet resistance at twice as many points in a second, and the resistance at each point must be overcome in half the time. 55. A moving Body may be in Equilibrium. We have seen 3 D 50 NATURAL PHILOSOPHY. (n) that a body at rest is in equilibrium. It is so be- cause the forces acting upon it are balanced. In the case of a train of cars, on first starting the force of the steam is not wholly balanced by the resistance ; hence it imparts motion to the train. But as the speed of the train in- creases, the resistance also increases, until it finally equals the force of the steam. All the force of the steam is now used in balancing the resistance, and the speed no longer changes. Since the two forces acting upon the moving body balance each other, it must be in equilibrium. Every body then moving in a straight line and with uniform speed is in equilibrium. SECOND LAW OF MOTION. 56. A Force has the same Effect in producing Motion, whether it acts upon a Body at Rest or in Motion, and whether it acts alone or with other Forces. In Figure 43, A B is a board ; Fig. 43- CD an arm moving upon it, turning on a hinge at C, and driven by a spring E ; at the end of the arm D is a hol- low, with its opening in the side of the arm large enough to contain a small ball, so that when the arm is driven by the spring E, the ball will be thrown horizontally ; at F is an- NATURAL PHILOSOPHY. 51 other chamber opening downwards, the lower opening being closed by the board G, which will be knocked away by a blow of the arm CD. If a ball be put in the chamber at D, and another in the chamber at F y the very same movement which throws the first horizontally forward will let the sec- ond drop at the same instant. On trying the experiment it will be found that both balls will reach the floor exactly together. So, too, if the machine and floor are both in- clined at just the same angle, the balls will both reach the floor together. In the case of the ball that is thrown horizontally, two forces have acted, one to throw it forward in a straight line, and the other to draw it to the earth in a straight line ; and it is seen that it is drawn just as far towards the earth in a given time as the ball that was let fall from a state of rest. From this and other experiments it has been found that, when two forces acting in different directions have been brought to bear upon a body so as to produce motion, the body at any given time will be just as far from the place it would have reached had only one of the forces acted upon it, as it would have been had it been at rest at this point, and acted upon by the other force alone for the same time. For example, suppose the spring would send the ball for- ward 30 feet in a second, and the force of gravity pulls it from a state of rest 16 feet towards the earth in the same time, the ball at the end of the second will be just 16 feet below the point it would have reached had only the force of the spring acted upon it. So, were a ball thrown directly upward with a velocity of 100 feet a second, at the end of the second it would be only 84 feet high, that is, 1 6 feet below the point it would have reached had not the force of gravity acted upon it. If it were thrown di- rectly downward from the top of a high tower with the same velocity, it would be at the end of a second 116 52 NATURAL PHILOSOPHY. feet below the top of the tower, that is, 16 feet below the point it would have reached had not gravity acted upon it. Now 1 6 feet is just the distance in each of the above cases that gravity would have pulled the ball in a second from a state of rest. Again, suppose that the current in a stream is strong enough to carry a boat down stream one mile in an hour, and a person attempts to row the boat directly across the stream at a rate which would take him across in an hour, at the end of the hour the boat would be at the opposite bank just a mile down stream. 57. A Body thrown horizontally or obliquely when acted upon by Gravity describes a curved Path. When both the forces acting upon the body are instantaneous, it moves in a straight line ; when one is instantaneous and the other continuous, as in the case of gravity acting on a ball thrown horizontally or obliquely, the path is curved. The curved path described by a body when acted upon by an instantaneous and a continuous force is well illus- trated by a jet of water issuing from the side of a vessel. The lateral pressure is the instantaneous force acting upon each particle of water as it issues from the opening ; and the force of gravity acting upon it after it leaves the open- ing is the continuous force. The curved path in this case is called a parabola. On account of this effect of gravity upon a body moving horizontally or obliquely, a cannon-ball describes a curved path. If then a cannon or a musket is fired at a distant object, it must be aimed above it. We have a good illustration of the second law of mo- tion in the case of falling bodies. NATURAL PHILOSOPHY. 53 FALLING BODIES. Fig. 44- 58. All Bodies would fall at the same Rate, were it not for the Resist- ance of the Air. As we see bodies light and heavy falling through the air, we come to think that the force of gravity causes heavy bodies to fall more rapidly than light ones ; but if we place a coin and a feather in a long glass tube and exhaust the air completely, on inverting the tube (Figure 44) the two bodies will fall through it in the same time. It must be therefore the resistance of the air which causes a lighter body to fall more slowly through the atmosphere than a heavy one does. When therefore the force of gravity is unimpeded in its action, it will ?ause every body, whatever may be vts size, shape, or density, to fall with exactly the same speed. 59. When a Body is moving di- rectly downward Gravity increases its Velocity at the Rate 0/32 Feet a Second. It is found by means of a pendulum that a body falls 16 feet the first second, and acquires a velocity of 32 feet during the time. As gravity has the same effect upon a moving body as upon one at rest, a falling body will gain in velocity 32 feet each second. When therefore a body is moving directly downward, gravity increases its ve- locity at the rate of 32 feet a second. 60. How to find the Distance a Body falls in a given Time. As we have seen, a body when falling from a 54 NATURAL PHILOSOPHY. state of rest has a velocity of 32 feet at the end of the first second, and falls 16 feet during that second. This distance is exactly the mean between o, its velocity at starting, and 32, its velocity at the end of the second. As it would gain a velocity of 32 feet during the next second, it would have a velocity of 64 feet at the end of that second. The velocity ' it has already acquired would cause it to fall 32 feet the second second, and the force of gravity acting upon it during that time would cause it to fall 16 feet more ; hence it would fall 48 feet during the second second. It will be noticed that 48 is just the mean of 32, its velocity at the begin- ning of the second, and 64, its velocity at the end of the second. During the first two seconds the body would fall 48 -f- 16 = 64 feet. This is just twice the mean of o and 64. Hence, to find the distance that any body would fall when acted upon by gravity alone during any number of seconds, find its mean velocity during the time, and multiply it by the number of seconds. To find the velocity of a falling body at the end of any second, multiply 32 feet by the number of seconds it has been falling. 6 1. When a Body is moving directly upward Gravity re- tards its Velocity at the Rate of 32 Feet a Second. We have already seen that gravity has the same effect on a body in motion as on one at rest. Since, then, it causes a body in falling from a state of rest to acquire a velocity of 32 feet a second, it must, in the case of a body moving directly up- ward, diminish its velocity at the rate of 32 feet a second. And it must also cause it to rise each .second 16 feet less than if it were not acting upon it. 62. How to find the Distance a Body, when thrown up- ward, will rise in a given Time. To find this distance, take the mean velocity of the body during the time, and multi- NATURAL PHILOSOPHY. '55 ply it by the number of seconds. To find the velocity at any particular second, multiply the number of seconds the body has been rising by 32, and subtract this from the velocity the body has at starting. 63. A Body always acquires the same Velocity in falling the same Distance. It has been found that a body in roll- ing down an inclined plane (allowance being made for fric- tion) acquires the same velocity that it would have acquired in falling a distance equal to the height of the inclined plane. So, too, in the case of a pendulum-ball, if it be drawn up to the point C (Figure 45), f . and then allowed to fall to B, it will, on reaching B, have the same velocity it would have had in falling from C to Z>. And it is found to be true in general, that bodies always acquire the same velocity in falling the same distance J) 1 from a state of rest, no matter what path they may take. PROBLEMS. SECOND LAW OF MOTION. Gravity causes a body to fall from a state of rest 4.9 metres in a second, and increases its velocity 9.8 metres in a second. 56. A body falls from a state of rest. How many metres of velocity has it at the end of the third second ? 57. A body is thrown downward with a velocity of 50 metres a second. What will be its velocity at the end of 7 seconds? 58. A body is thrown downward with a velocity of 23 metres a second. What will be its velocity at the end of 9 seconds ? 56 NATURAL PHILOSOPHY. 59. A body is thrown upward with a velocity of 42 metres a second. What will be its velocity at the end of 4 seconds ? 60. A body is thrown upward with a velocity of 75 metres a second. What will be its velocity at the end of 5 seconds ? 6 1. A body is thrown upwarrl with a velocity of 98 metres a second. How long will it continue to rise ? 62. How high will the above body rise ? 63. How far will it rise the first 3 seconds ? 64. How far will it rise the last 3 seconds ? 65. How far will it rise from the beginning of the 3d to the end of the 8th second ? 66. Two bodies are thrown upward, one with a velocity of 68.6 metres a second, and the other with a velocity of 137.2 metres a second. How many seconds will it be before e^ch begins to fall ? 67. To what height would each rise ? 68. One ball is thrown upward with a velocity of 78.4 metres a second, and another with twice this velocity. The last ball will rise how many times as high as the first ? 69. If the second ball had been thrown with thrice the velocity of the first, how many times as high would it have risen ? 70. If it had been thrown with four times the velocity, how many times as high would it have risen ? 71. A ball falls from a state of rest, and reaches the earth in 12 seconds. With what velocity does it strike the earth ? 72. From what height did the ball in the last example fall? 73. How far did it fall the first 5 seconds ? 74. How far did it fall the last 5 seconds ? 75. How far did it fall from the beginning of the 3d to the end of the 5th second? NATURAL PHILOSOPHY. 57 76. How far did it fall from the beginning of the 8th to the end of the nth second? 77. A ball is thrown downward with a velocity of 125 metres a second, and reaches the earth at the end of 7 seconds. What is its velocity on reaching the earth ? 78. From what height was the ball in the last example thrown ? 79. Through what distance did it pass from the begin- ning of the 3d to the end of the 6th second ? 80. A stone falls from a state of rest, and is 4 seconds in reaching the earth. With what velocity does it strike the earth ? Through what distance does it fall ? 8 1. If the stone had reached the earth in 8 seconds, what velocity would it have acquired, and through what distance would it have fallen ? 82. If the stone had reached the earth at the end of 12 seconds, with what velocity would it have reached the earth, and through what distance would it have fallen?* 83. A body in falling from a state of rest through 4.9 metres acquires a velocity of 9.8 metres a second. Through what distance must it fall in order to double this velocity? 84. Through what distance must it fall in order to treble this velocity ? 85. A stone falls from a height of 19.6 metres. With what velocity does it reach the earth ? NOTE. We see from problems 80 - 85 that the velocity of a body increases as the square root of the distance through which it falls from a state of rest. We see from problems 66-70 that the height to which a body will rise increases as the square of the velocity with ivhich it starts. * See Appendix, II. 3* 58 NATURAL PHILOSOPHY. THIRD LAW OF MOTION. 64. Momentum. If balls of lead of different size be placed in the cavity of the arm CD (Figure 43), and the arm be drawn back to exactly the same point each time, the balls will not all be thrown to the same distance. The smaller the ball the farther it will be thrown. If one ball is twice as heavy as another, it will be thrown only one half as far ; if three times as heavy, only one third as far ; and so on. The same is true when the balls are of different materi- als, provided their mass is different By the mass of a body we mean its quantity of matter. This is usually measured by its weight ; that is, if a body weighs twice as much as another, its mass is said to be double ; if thrice as much, its mass is said to be treble ; and so on. We see then that the same force acting upon bodies con- taining different quantities of matter does not impart to each the same velocity; and that the force acting upon each being the same, the velocity will be in the inverse ratio of the quantities of matter that they contain ; that is, if the quantity of matter in each be multiplied by its ve- locity, the products will all be equal. The product of the velocity of a body multiplied by its mass is called its momentum. The same force, then, will impart the same momentum Fig. 46. t a body, whether that body be large or small. 65. A moving Body cannot impart Motion to another Body without itself losing the same Quantity of Motion. Hang two balls of lead or clay side by side, as shown in Figure 46, and place behind them an arc graduated so that the line 2 b shall be four times as NATURAL PHILOSOPHY. 59 long as i a ; 3 pending upon their distances from the point of suspension but since they are united in one body, they are all com- pelled to vibrate in the same time. Consequently, the vibrations of the particles near the point of suspension are retarded by the slower vibrations of the particles below them ; and, on the other hand, the vibrations of the par- tides near the lower end of the pendulum are quickened by the more rapid vibrations of those above them. At some point between these there must be a particle whose 68 NATURAL PHILOSOPHY. vibration is neither retarded nor quickened, all the par- ticles above having just the same tendency to vibrate faster that those below have to vibrate slower. This point is called the centre of vibration, and it is obvious that the time of vibration of a compound pendulum is the same as that of a simple pendulum whose length is equal to the dis- tance of the centre of vibration from the point of sus- pension. This distance is the virtual length of the pen- dulum. When the form of the pendulum is given, the position of the centre of vibration can be found experimentally by making use of a remarkable property of the compound pendulum, namely, that if such a pendulum be inverted and suspended by its centre of vibration, its former point of suspension will become its new centre of vibration, and the time of vibration will be the same as before. This property is usually expressed by saying that the centres of vibration and suspension are interchangeable. To find the centre of vibration, then, we have only to reverse a pendulum, and by trial find the point at which it must be suspended in order to vibrate in the same time as it did before it was reversed. A pendulum constructed for this purpose is called a reversible pendulum. 82. The Use of the Pendulum for Measuring Time. The most important use of the pendulum is for measuring time. The common clock is merely a contrivance for re- cording the beats of the pendulum, and keeping up its motion. The essential parts of such a clock are shown in Figure 49. The toothed wheel R, called the scape-wheel, is turned by a weight or spring, and its motion is regulated by the escapement n m, which swings on the axis o; the vibrations of the pendulum being communicated to it by means of the forked arm a b. When the pendulum is at rest, one of the teeth of the scape-wheel rests upon the upper side of the hook m, and the clock does not go. If NATURAL PHILOSOPHY. 69 now the pendulum be set in motion, Fig. 49 . so that the hook m is moved from the wheel, the tooth which rested on it is set free, and the wheel begins to turn ; but it is soon stopped by the hook /z, which moves up to the wheel as m moves away from it, and catches on its under side the tooth next below. As the pendulum swings back, the hook n moves away, the wheel again begins to turn, but is stopped again on the oppo- site side by the hook m, which catches the tooth next to the one it held be- fore ; and thus each vibration of the pendulum allows the scape-wheel to move forward through a space equal to one half of one of its teeth. If then the wheel has thirty teeth, it will turn around once in sixty* beats of the pendulum. Upon the axis of this wheel the second-hand of the clock is placed. It is connected by cogs with another wheel, which takes sixty times as long to revolve, and which carries the minute hand ; and this latter wheel is connected with another, which turns in twelve times the period, and carries the hour-hand. Thus the second-hand registers the beats of the pendulum up to sixty, or one minute ; the minute-hand registers the revolutions of the second-hand up to sixty, or one hour ; and the hour-hand registers the revolutions of the minute- hand up to twelve, or half a day. Were it not for the pendulum and escapement, these wheels would be whirled round very fast by the action of the weight or spring, and the clock would soon run down. On the other hand, were there not some means 70 NATURAL PHILOSOPHY. of keeping up the motion of the pendulum, it would soon be brought to rest by the resistance of the air and the friction at the point of suspension. Its motion is kept up by means of the escapement, which is so con- structed as to give it a slight push at each vibration. The ends of the two hooks have inclined surfaces against which each tooth of the wheel, as it leaves them, presses with considerable force, so as to throw the escapement for- ward a little the moment the tooth is set free. The impulse thus given is communicated, through the axis 0, and the arm a b, to the pendulum. 83. The Use of the Pendulum for measuring the Force of Gravity. We have seen that the rate of the vibration of pendulums of the same length depends on the force of gravity. If we represent by g the velocity that a body fall- ing from a state of rest would acquire during a second, and by / the length of a pendulum beating seconds, then g will be equal to the length of the pendulum multiplied by the square of the number 3.1^16. To find g, we have only to measure the length of a pendulum beating seconds, and then to multiply this length by the square of the number 3.1416. Now it has been found that a pendulum beating seconds at London must be 39.13929 inches long. From this we get -=386 inches. One half of 386 inches is 193 inches, or 1 6 feet, i inch. This is the distance which a body will fall from a state of rest in a second. SUMMARY. A pendulum is a heavy body hung from a fixed point by means of a cord or rod. (75.) The laws of the vibration of the pendulum are best in- vestigated by means of a simple pendulum. (76.) These laws are four in number. NATURAL PHILOSOPHY. 71 i st. When the length of the pendulum remains the same, and the amplitude of the yibrations does not exceed 3, the pendulum always vibratts in the same time. (77.) 2d. For pendulums of the same length, the time of the vibrations is the same, whatever the pendulum may be made of. (78.) 3d. For pendulums of different lengths, at the same place, the time of the vibrations is proportional to the square root of the lengths. (79.) 4th. In different parts of the earth, the time of the vibrations for pendulums of the same length, is in the inverse ratio of the square root of the intensity of gravity. (80.) The pendulum in ordinary use is a compound pendulum. (81.) The pendulum is used for measuring time. (82.) It is also used for measuring the force of gravity. (83.) PROBLEMS. 95. If a pendulum beating seconds at Paris is .99394 of a metre long, what would be the length of one beating half-seconds ? Of one vibrating in two seconds ? 96. If a pendulum a-t Paris one metre long vibrates in 1.00304 seconds, what will be the time of vibration for a pendulum 9 metres long? What for one 25 metres long? What for one of a metre long ? What for one 2\ metres long? NATURAL PHILOSOPHY. 73 III. MACHINES AND SOURCES OF MECHANICAL POWER. THE LEVER. 84. When a workman wishes to raise a large stone, he places an iron bar under it, as in Figure 50, with a block under the bar near the stone, and then presses down upon the other Fig. 50. end of the bar ; or else he places the end of the bar under the stone, as in Figure 51, so that one end of it rests upon the ground, and then lifts upon the other end. The iron bar thus used constitutes one of the simple machines. It is called the lever. The stone to be raised is called the weight. The moving force applied at the other end of the bar is called the power; Fig. 51. and the point on which the bar rests is called the fulcrum. The parts between the fulcrum and the points where the power and weight act are the arms of the lever. In the first case, the fulcrum was between the weight and the power : in the second case, the weight was between the fulcrum and the power. In the fishing rod (Figure 52) one hand is the fulcrum, the other hand, P, is the Fi 52 power, and the fish is the weight. "1^^^-^^ f Here the power is applied between i the fulcrum and the weight. 85. Three kinds of Lever. We see from the above that there are three kinds of lever : (i.) That with the fulcrum between the weight and power. 74 NATURAL PHILOSOPHY. (2.) That with the weight between the fulcrum and power. (3.) That with the power between the fulcrum and the weight. These three kinds of lever are shown in Figure 53. Fig. 53- 86. The Law of the Lever. IK the lever of the first kind, if the fulcrum is just half way between the weight and power, then on moving the lever a little the weight and power will move through equal distances. In this case it is found that the weight and power must be equal in order to balance each other, or to be in equilibrium. If the power were twice as far from the fulcrum as the weight, then the weight would move through only half the distance that the power does, and in this case the power need be only half the weight in order to balance it. Thus we see that, in the case of the lever, the weight and power will balance each other when the power, multi- plied by the distance through which it moves, equals the weight multiplied by the distance through which it moves. That is, if the fulcrum of a lever were so placed that one end of the lever would move through a thousand inches while the other end moved through one inch, then a power of one pound on the former would balance a weight of one thousand pounds on the latter. NATURAL PHILOSOPHY. 75 87. The Law of Machines in General. The same is found to be true in the case of every machine, however complicated ; namely, that the power and weight will balance each other when, on setting the machine in mo- tion, the power multiplied by the distance through which it moves equals the weight multiplied by the distance through which it moves. There is no real gain of mechanical force in a lever or a machine of any kind. A machine is only an arrangement by which a small force acting through a great distance is converted into a great force acting through a small dis- tance, or else a great force acting through a small distance is converted into a small force acting through a great distance. When a small force, by acting through a great distance, is made to raise a great weight, or do a great deal of work, there is said to be a gain of power. in the machine. When on the contrary a great force, in moving through a small distance, lifts only a small weight, or does very little work, there is said to be a loss of power in the machine. But whenever there is a gain in power there is a corresponding loss in speed, and whenever there is a loss in power there is a corresponding gain in speed. For if in the machine a power of one pound is made to move a weight of ten pounds, then the weight moves only one tenth as fast as the power. But when a power of ten pounds is made to move a weight of one pound, then the weight moves ten times as fast as the power. 88. Gain and Loss of Power in the Lever. In a lever of the first kind, when the fulcrum is just halfway between the weight and power, there is neither gain nor loss in power. If the fulcrum is nearer the weight than the power, then there will be a gain in power and a loss in speed. If the fulcrum is nearer the power than the weight, there is loss in power and gain in speed. 76 NATURAL PHILOSOPHY. In a lever of the second kind, the power is always far- ther from the fulcrum than the weight, and consequently it always moves through greater distance. Hence in this kind of lever there is always a gain in power and a loss in speed. In a lever of the third kind, the weight is always farther from the fulcrum than the power, and consequently the weight always moves through the greater distance. There is therefore in this kind of lever always a loss in power and a gain in speed. 89. The Compound Lever, Sometimes two or more sim- ple levers are combined, as shown in Figure 54. Suppose that P be five times as far from the fulcrum f as A is, the point P will then move five times as fast as the point A, and a pull of one pound on P will exert a pull of five pounds on A. If B is five lg ' 54 ' times as far from the ful- crum F as W is, the five B __p pounds of pull on B will exert twenty-five pounds of pull at W. In this case, one pound of pull exerted at P will balance twenty- five pounds at W. But it would be found on trial that on pulling P down one inch, W would be raised only one twenty-fifth of an inch. Such a combination of levers is called a compound lever. 90. Bent Levers. Sometimes the arms of the lever are bent, as shown in Figure 55. In such a lever the lengths of the arms are straight lines drawn from the fulcrum at right angles to the lines -which show the direction in which the power and weight act. ( The common claw-hammer, as used for drawing nails, is an illustration of this kind of lever. NATURAL PHILOSOPHY. 77 THE WHEEL AND AXLE. 91. When a weight is raised by means of the lever, it can be raised but a short distance at a time. After rais- ing the weight a little way it must be propped up, and the lever must be readjusted. On this account the lever cannot be conveniently used when a weight is to be raised a considerable distance. 92. The Rack and Pinion. In Figure 56 we have a machine called the rack and pinion. It consists of the crank A, which can be made to turn a small toothed wheel called the pinion. On turning the pinion, its teeth one after another catch under the teeth of an upright bar B, and each tooth raises the bar a little. This upright bar is called the rack. On turning the crank, then, the rack rises without interruption ; and if the rack is placed under the weight, it will carry up the weight as it rises. As the weight can thus be raised the length of the rack without interruption, the rack and pinion is much more convenient than the simple lever, when the weight is to be raised a considerable distance. 93. The Rack and Pinion is a Modification of the Lever, in which the Pinion takes the Place of the short Arm. In the rack and pinion, the crank takes the place of the long arm of the lever ; the rod or axle upon which the pinion turns takes the place of the fulcrum ; and the pinion takes the place of the short arm. Each tooth of the pinion is in fact the short arm of a lever of which the crank is the long arm, and the pinion fs a^ contriv- ance by which the lever is furnished with several short arms instead of one. The advantage of multiplying the 7 8 NATURAL PHILOSOPHY. short arm in this way is this : when a short arm has raised the weight as far as it can, it is not necessary to prop up the weight and readjust the lever, for the next short arm then comes in play and raises the weight far- ther, and so on. 94. The Windlass. Another way to multiply the short arms of a lever would be to fill up the space between the teeth of the pinion so that it may become a barrel, and then fasten the weight to one end of a rope, the other end of which is fastened to this barrel. On turn- ing the crank the rope would be wound upon the barrel and the weight raised. The machine just described is called the windlass, and is shown in Figure 57. F i g> S7> In the windlass, the length of the short arm is the distance from the circumference, or out- side, of the barrel to its centre. This distance is called the ra- dius of the barrel, and in the barrel there are as many short arms as there are radii. The length of the long arm of the lever is the length of the crank. If the crank were ten times as long as the radius of the barrel, a power of one pound at the end of the crank would exert a force of ten pounds at the circumference of the barrel. On turning the crank round once, it is evident that the end of the crank would move through a path like that shown by the dotted line in Figure 56, and that this path would be ten times as long as the circumference of the barrel. On turning the crank once round, the rope would be wound round the barrel once, and the weight would be raised a distance equal to the circum- ference of the barrel. In this case, then, the power would move through ten times the distance the weight moves through in the same time, and, according to the NATURAL PHILOSOPHY. 79 law of machines (87), a power of one pound at the end of the crank ought to balance ten pounds of weight at the circumference of the barrel. 95. The Capstan. In the windlass, the longer the crank and the smaller the barrel, the greater the gain of power. If, however, the barrel is made too small, it is not strong enough to support the weight ; while if the crank is made too long, it cannot be conveniently turned with the hand. But the crank, or long arm of the lever, may be multiplied in the same way as the short arm was multiplied in the case of the pinion and the barrel. Thus in the windlass, just described, instead of one crank there may be a number of spokes, and a man by standing at one side may pull upon one spoke after another as they come within his reach, and thus turn the barrel, though he could not reach far enough to turn round a single spoke, if it were arranged like a crank. If the barrel were placed upright, a man or several men might walk round it, push- ing against the spokes. A windlass arranged in this way is called a capstan, and is much used on board ships. 96. The Wheel and Axle. If the F i g . 58. spokes are connected so as to form a wheel, as shown in Figure 58, the barrel is called the axle, and the ma- chine is called the wheel and axle. In the wheel and axle, the radius of the wheel is the long arm of a lever, and the radius of the axle is the short arm. Therefore, the larger the wheel and the smaller the axle, the greater the weight which a power of one pound applied to the circumference of the wheel will balance on the axle. Power may be applied to the wheel, either by means of pegs projecting from its rim, as in Figure 58, or by a rope or band passing around it, as in Figure 59. 8o NATURAL PHILOSOPHY. The law of machines (87) may be readily illustrated by means of the wheel and axle. Suppose that a rope passes over the wheel and another over the axle, and that the radius of the wheel is eight times as long as that of the axle. On hanging a weight of one pound to the rope from the wheel, it will be found that a weight of eight pounds must be hung to the rope from the axle in order to balance it ; and it will be found, on turning the wheel, that the weight hung from the wheel moves through eight inches, while that hung from the axle moves through one. 97. The Ratchet. The ratchet is an arrangement to keep the wheel from turning except in one direction. It consists of a catch c (Figure 59), which plays into the teeth v - of the wheel A B. It thus allows the *>& 59- wheel to turn to the left, but keeps the weight from pulling it back towards the right. 98. Wheel-work. In the wheel and axle, the larger the wheel and the smaller the axle, the greater the gain of power. But, as has already been said (95), if the barrel is made very small, it may not be strong enough ; and on the other hand, if the wheel is made very large, it will be too heavy and take up too much room. Instead of using such a large wheel, we may have several wheels and axles acting upon one another, like the levers in the compound lever (89). Such a combination, or train, of wheels and axles is often called wheel-work. The power is applied to the circum- ference of the first wheel, the axle of which acts upon the circumference of the second wheel, which in turn, by means of its axle, acts upon the circumference of the third wheel, and so on ; the weight being hung to the axle of the last wheel. NATURAL PHILOSOPHY. 8 1 99. Cog Wheels. There are various ways in which the axle of one wheel is made to act on the circumference of another. Sometimes the one turns the other by rubbing against it, or by friction. The most common way, however, is by means of teeth or cogs raised on the surfaces of the wheels and axles. The cogs on the wheel are usually called teeth, while those on the axle are called leaves, and the part of the axle from which they project is called the pinion, as in the rack and pinion already described (92). A train of wheels thus arranged is shown in Figure 60. Fig. 60. 100. The gain of power by Wheel-work. In the train of wheels in Figure 60, if the circumference of the wheel a is 36 inches, and that of the pinion b is 9 inches, or one fourth as great, a power of one pound at P will exert a force of four pounds on b. If the circumference of the wheel e be 30 inches, and that of the pinion C 10 inches, the four pounds acting on the former will exert a force of twelve pounds on the latter. If the circumference of the wheel/ be 40 inches, and that of the axle d 8 inches, the twelve pounds acting on f will exert a force of sixty pounds on d. One pound at P will then balance sixty pounds at W. 82 NATURAL PHILOSOPHY. Fig. 61. But in this case, as in that of the windlass (94), it will be seen that what is gained in power is lost in speed ; since the one pound at P must move through sixty inches in or- der to raise the sixty pounds at W one inch. Cog-wheels which have their teeth arranged as in Figure 60 are called spur-wheels. If the teeth project from the side of the wheel, as in Figure 61, it is called a crown-wheel. If their edges are sloped, as in Figure 62, the wheel is called a bevel -wheel. Bevel - wheels may be inclined to each other at any angle. In all cases the lines which mark the slope of the teeth of the two wheels will meet at the same point, as in Figure 62. 10 1. Belted Wheels. Another way in which the wheels and axles may be made to act upon one another is by means of a belt, or band, passing over them both. They Fig. 62. may thus be at any distance apart, and may turn either the same way or contrary ways, according as the belt does or does not cross between them. A cog-wheel and its pinion must, of course, always turn in contrary directions. NATURAL PHILOSOPHY. Fig. 63. THE PULLEY. 102. In Figure 63 H is a fixed ring. Through this a cord passes, to which the weight W is hung. By pulling down the cord at P, the weight is drawn up. It is often de- sirable thus to change the direction of the power. If we use a ring for this purpose, much of the power will be wasted by the friction, or rubbing, of the rope against the ring. We may get rid of a good deal of this friction by using, instead of the ring, a wheel with a groove around it for keeping the cord in place. Such a wheel is called a pulley. There would be no gain in power by the use of the pul- ley. It is evident that one pound on one side of the wheel would balance just one pound on the other side ; and that if the former were drawn down one inch, the latter would be drawn up just one inch. 103. Fixed and Movable Pulleys. In Figure 64, the frame of the pulley D C is fastened to the ceiling ; the frame of the pulley A B rises as the rope P is drawn down. A pulley like D C is called a fixed pulley ; one like A B, a movable pulley. The frame of the pulley is often called the block. 1 04. The Law of the Pulley. In the com- bination, or system, of pulleys in Figure 64, it is evident that the rope must have the same tension, that is, must have the same strain upon it, from one end to the other. This fact, namely, that a cord when stretched must have the same strain upon it throughout its length, is called the law of the pulley. 105. Systems of Pulleys with one Rope. In Figure 64. Fig. 64. W 8 4 NATURAL PHILOSOPHY. the tension or strain of the rope is equal to the power P, since it balances the power. If a weight of one pound is hung to the rope at P, there will be a strain of one pound on the part of the rope on that side of the pulley. There must then be a strain of one pound upon the part of the rope between A and Z>, and a strain of one pound between B and H. These two tensions, A D and B If, will evi- dently sustain a weight of two pounds at W. In this sys- tem of pulleys, then, a power of one pound balances a weight of two pounds. But in this case, as in every other of the kind, what is gained in power is lost in speed. If the power P is drawn down one foot, the weight W will rise only half a foot ; for of the one foot added to the length of CP, one half will be taken from A D and one half from B H. In the system of pulleys shown in Figure 65, we see that one pound at P will balance three pounds at W, since each Fig. 65. Fig. 66. W of the three parts of the rope on that side of the pulley C has a tension of one pound. But P must be drawn down three feet in order to raise W one foot. In Figure 66, we have a system of pulleys in which the NATURAL PHILOSOPHY. weight is four times the power ; and in this case the power evidently moves four times as far as the weight. 1 06. Systems of Pulleys with more than one Rope. Figure 67 represents a system of pulleys, in which two ropes are used. Here a weight of four pounds is balanced by a power of one pound. The parts of the rope A D and A B must each have a tension equal to the power. The rope A CB balances the two tensions, B P and B A, and must therefore have a tension of twice the power. The three Fig. 67. Fig. 68 tensions supporting the pulley A amount therefore to lour times the power. In the system shown in Figure 68, four ropes are used. The tensions of the several ropes will be readily under- stood from the numbers. It will be seen that in this case the power is doubled by each movable pulley which is added ; but, as in all the systems we have examined, what is gained in power is lost in speed. THE INCLINED PLANE. 107. When a heavy cask is to be raised into a cart or dray, a ladder is often used. One end of the ladder is 86 NATURAL PHILOSOPHY. placed upon the cart behind and the other end upon the ground, and the cask is rolled up the inclined surface thus formed. In this way one man is able to raise a load of several hundred weight with comparative ease. An inclined surface used in this way is called an in- clined plane. We have examples of the inclined plane on a large scale in roads. 1 08. The Law of the In- Fig> 69> dined Plane the same as that of other Machines. In Fig- ure 69 we have an inclined plane. W is the weight, which is balanced by the power P. B C is the height of the inclined plane, and A C is its length. It is evident that the power must descend a distance equal to the length of the inclined plane, in order to raise the weight a distance equal to its height. Now it is found on trial that, if the length of the inclined plane is six- teen feet, and its height four feet, a power of one pound will balance four pounds of weight. But one multiplied by sixteen equals four multiplied by four. That is, the power multiplied by the distance through which it acts equals the weight multiplied by the distance through which it is raised. It follows from the above, that the greater the length of the inclined plane, compared with its height, the less the force necessary to raise a weight, and the slower the weight rises. THE WEDGE. 109. Instead of lifting a weight by moving it along an inclined plane, we may do the same thing by pushing the inclined plane under the weight. When used in this way the inclined plane is called the wedge. A NATURAL PHILOSOPHY. nvedge which is used for splitting wood has Fi s- 7- usually the form of a double inclined plane, as in Figure 70. The law of the wedge is the same as that of the inclined plane, but since a wedge is usually driven by a blow in- stead of a force acting continuously, it is diffi- cult to illustrate this law by experiments. no. Uses of the Wedge. The wedge is especially useful when a large weight is to be raised though a very short distance. Thus a tall chim- ney, the foundation of which has settled on one side, has been made upright again by driving wedges under that side. So, too, ships are often raised in docks by driving wedges under their keels. Cutting and piercing instru- ments, such as razors, knives, chisels, awls, pins, needles, and the like, are different forms of wedges. THE SCREW. in. In Figure 71 we have a machine called the screw. It is a movable inclined plane, in which the inclined surface winds round a cylinder. The cylinder is the body of the screw, and the inclined surface is its thread. The screw usually turns in a block JV, called the nut. Within the nut there are threads exactly corresponding to those on the screw. The threads of the screw move in the spaces between those of the nut. The power is usually applied to the screw by means of a lever P. Sometimes the screw is fixed and the nut is movable, and sometimes the nut is fixed and the screw movable. Fig. 71. 88 NATURAL PHILOSOPHY. 112. Hunter's Screw. In Figure 71, if we turn the lever P round once, the weight W will be raised a distance equal to the space between two threads of the screw. Were the lever of such a length that its end would de- scribe a path 10 feet long, and were the distance between two threads of the screw \ of an inch, and were there no friction in the nut, a power of one pound applied to the end of the lever would exert a force of 480 pounds upon the weight. It will be seen from this that the mechanical advantage of the screw may be increased by increasing the length of the lever by which it is turned, or by bring- ing the threads closer together. But, if the threads are brought too near together, they become too weak ; while, on the other hand, the machine becomes unwieldy if the lever is made too long. These objections have been obviated in the differential screw, contrived by Hunter, and shown in Figure 72. N is the nut in which the screw A plays. We will suppose that the threads of this screw are T V of an inch apart. This screw A is a hollow nut, which re- ceives the smaller screw B, the threads of which we will suppose to be -^ of an inch apart. This small screw is free to move upward and downward, but is kept from turning round by means of the frame -work. If by means of the handle the larger screw be turned round ten times, and the smaller screw be al- lowed to turn round with it, the point W will rise an inch. If we then turn the smaller screw ten times backward, the point W will move down \\ of an inch. The effect of both these motions will be to raise the point W T ' T of an inch. But if the smaller screw has been turned upward ten times and then downward ten NATURAL PHILOSOPHY. 89 times, the effect is the same as if it had been kept from turning. Hence on turning the lever round ten times, the point W will be raised T * T of an inch, or the differ- ence of the distances between the threads in the two screws, while the point E has been raised an inch. Ac- cording to the law of machines, then, the pressure at W is eleven times as great as at E. 113. The Endless Screw. In Figure Fig. 73. 73, the thread of the screw works be- tween the teeth of the wheel. Hence on turning the screw the wheel must turn. Since as fast as the teeth at the left escape from the screw those on the right come up to it, the screw is acting upon the wheel continually. Hence this machine is called the endless screw. SUMMARY. A machine is a contrivance by which force is made to do work. (84.) In a machine there is no real gain of force, but a force may be changed in direction, and a small force acting through a great distance may be converted into a large force acting through a small distance, or a large force acting through a small distance may be converted into a small force acting through a great distance. (87.) The first simple machine is the lever. (84.) There are three kinds of levers, depending upon the rel- ative position of the weight, the fulcrum, and the power. (85-) In a lever of any kind the weight and power will balance each other when the weight multiplied by the dis- ance through which it moves is equal to the power multi- plied by the distance through which it moves. (86.) 90 NATURAL PHILOSOPHY. It is the law of every machine that the power and weight will balance each other when the power multiplied by the distance through which it moves is equal to the weight multiplied by the distance through which it moves in the same time. (87.) A compound lever is a machine in which two or more simple levers are combined. (89.) The rack and pinion is a lever whose long arm appears in the crank, and whose short arm is multiplied in the pinion. (9^-) In the windlass, the barrel and the rope take the place of the pinion and the rack. {93.) In the wheel and axle, the long arm of the lever is multi- plied as well as the short one. (96.) When the axle is upright the wheel and axle is called a capstan. (95.) Several wheels are often combined so as to act upon one another. (98.) The wheels may be made to act upon one another by means of cogs, or by means of belts. (99, 101.) The direction in which a force acts may be changed by means of a single fixed pulley. (102.) In a system of pulleys, the mechanical advantage de- pends upon the fact that a stretched rope will have the same tension throughout its whole length. (104.) A system of pulleys may be arranged with one rope, or with several ropes. (105, 106.) The fourth simple machine is the inclined plane. (107.) The fifth simple machine is the wedge. This is really a movable inclined plane which is pushed under the weight to be raised. (109.) The sixth simple machine is the screw. This is also a movable inclined plane arranged round a cylinder. Hunter's differential screw and the endless screw are im- portant modifications of this simple machine. (111-113.) NATURAL PHILOSOPHY. 91 PROBLEMS. 97. In a lever the short arm is 5 decimetres long, and the long arm 61 decimetres long. How far will the end of the long arm move while the end of the short arm moves through 3 centimetres ? 98. How far will the end of the short arm move while the end of the long arm is moving through 30 centimetres? 99. In a lever the short arm is 2 metres long, and the long one 50 decimetres long. A power of 2 kilogrammes is applied to the end of the long arm. What weight at the end of the short arm will it balance ? 100. While the weight in the last example is moving through 3 decimetres, how far will the power move? 1 01. A weight of 60 decagrammes is applied at the end of the long arm of the lever in the above example. What power must be applied at the end of the short arm to balance it ? 102. In a rack and pinion the radius of the pinion is 10 decimetres. What must be the length of the crank in order that a power of 8 grammes may balance 300 grammes of weight ? 103. In a wheel and axle the circumference of the wheel is 6 metres and that of the axle 30 centimetres. What weight will a power of 3 grammes balance? 104. In a train of wheels a power of i gramme balances a weight of 43 kilogrammes. What distance must the power move through while the weight moves through 50 decimetres? 105. In a system of pulleys a power of i gramme balances a weight of 245 kilogrammes. How far will the weight move while the power is moving through i metre? 9 2 NATURAL PHILOSOPHY. HAND POWER. 114. We have now seen how forces maybe transformed, so that a small force acting through a long distance shall be equivalent to a great force acting through a short dis- tance, or a great force acting through a short distance shall be equal to a small force acting through a great dis- tance. We next inquire what are the sources of mechan- ical power. 115. Hand Machines. One of the most familiar sources of mechanical power is the human hand. Machines by which this power is applied to doing work are called hand machines. An iron crow-bar is one of the simplest hand machines. It is, as we have seen (84), a lever of the first or second kind, according to the way in which it is used. The ordinary windlass and the capstan are examples of hand machines of the wheel and axle kind ; while the tackle which is so often used for hoisting weights is an example of a hand machine of the pulley kind. Fig. 74- 1 6. The Crab. The crab, shown in Figure 74, is NATURAL PHILOSOPHY. 93 Fig- 75- hand machine of the wheel and axle class. It consists of a pinion P turned by two cranks C and C, and acting upon the toothed wheel W. To the axis of this wheel is fixed the barrel Z>, to which the weight is hung by the rope r. The gain of power in this machine can be computed by the principles already explained. (94, 98.) The crab is much used for setting stone in the building of houses, and for other work of the same kind. 117. The Derrick. The derrick (Figure 75) consists of a mast M, which- is kept upright by means of ropes, or guys, G, G, fastened to posts driven into the earth. B is an arm, or boom, at- tached to the mast by a hinge, and kept in any re- quired position by means of the rope R '. The mast and boom serve as the supports of a system' of pulleys, worked by a crab at the foot of the mast. L is the load, or weight to be raised. The system of pulleys in the derrick represented here is precisely like that shown in Figure 65, and the mechanical advantage from its use will be the same as there explained ; and this, multiplied by the mechanical advantage obtained by means of the crab, will give the whole gain of power in the machine. 94 NATURAL PHILOSOPHY. Fig. 76. HORSE POWER. 1 1 8. The strength of horses is employed in drawing loads over our roads, which, as we have seen, are in many cases inclined planes. Horses are often used in raising weights by means of pulleys, as shown in Figure 76. 119. Hoxse Powers. Ma chines by which the strength of horses is applied to the do- ing of work are usually called horse powers. In some of these the horse walks round a circle, turning an upright shaft, which may give motion to a train oj wheels (98) for driving various kinds of machinery; or to a capstan (95), as shown in Fig- ure 77 cotton ; or to a screw, which may be used for pressing into bales, or any similar work. Fig. 77- In another class of horse powers, the horse is placed on NATURAL PHILOSOPHY. 95 the surface of a large horizontal wheel, or on a movable platform. In this case it is the road, and not the horse, that travels. One form of this kind of horse power is shown in Figure 78. It consists of a platform made of wooden Fig. 78. bars fastened to a chain, which passes round two wheels. The horse is put upon this endless platform, as it is called, and is harnessed to the frame of the machine, as repre- sented in the Figure. When the horse draws, he pushes the platform backward with his feet, and thus gives motion to the wheels round which it passes. To these wheels machinery may be connected in any of the ways already described. WIND POWER. 120. We have a familiar example of the wind as a source of mechanical power in the sailing of ships. These are rigged so as to present to the wind a large extent of canvas, called sails. The wind blowing against these urges the ship forward. Sometimes sails, or broad vanes of wood, are arranged Fig- 79- 9 6 NATURAL PHILOSOPHY. on the arms of a wheel which is mounted in a high tower. The wind blowing against these arms causes the wheel to rotate, and by means of wheel-work this is made to carry other machinery. Such an arrangement is called a wind- milt \ and is shown in Figure 79. Fig. 80. WATER POWER. 121. Water Wheels. One of the most important sources of mechanical power is that of falling water. The falling or running water is made to turn a wheel, called a water wheel, and this wheel by means of bands or gearing is made to work almost any kind of ma- chinery. Water wheels are of various forms. Some turn on an upright axis, and others on a hori- zontal axis. The latter are called vertical water wheels and the former horizontal water wheels. 122. Vertical Water Wheels. One of the most common forms of vertical water wheels is represented in Figure 80. It consists of a series of boxes, or buckets, arranged on the outside of a wheel or cylinder. Water is allowed to flow into these buckets on one side of the wheel, and by its weight causes the wheel to turn. The buckets are so constructed that they hold the water as long as possible while they are going down, but allow it all to run out be- fore they begin to rise on the other side. A wheel like this is called a breast-wheel. NATURAL PHILOSOPHY. 97 The overshot wheel is similar to the breast-wheel in all respects, except that the water is led over the top of the wheel and poured into the buckets on the other side. The undershot wheel has boards projecting from its cir- cumference, like the paddle-wheel of a steamboat. The water runs under the wheel, and turns it by the force of the current pressing against the boards. 123. Barker's Mill. In Figure 81 we have a hollow upright cylinder, Flg " 8lp with two horizontal arms at the bot- tom, and turning on an axis. The cylinder is open at the top, but closed below, except that it has two holes on opposite sides of the arms near the end, as shown in the Figure. If wa- ter be poured in at the top, the cylin- der begins to turn round, and will con- tinue to turn as long as the supply of water is kept up. If the holes in the arms are stopped up, the cylinder ceases to move. This apparatus is known as Barker's mill. Its action is easily understood when we recollect that liquids press equally in all directions (17). If the holes in the arms are plugged up, the water presses forward against the plug ; and it presses backward against the opposite part of the arm with an equal force. These two equal forces acting in opposite directions would just balance each other, so that there would be no motion. If now we remove the plug, there will be no pressure against that part of the arm to balance the backward pressure against the opposite side ; and the arm consequently turns backward. As the openings in the two arms are on opposite sides of the tube, the back- ward pressure on each arm tends to turn the cylinder round in the same direction. 5 G 98 NATURAL PHILOSOPHY. 8z - This machine is found to gain in power by bending round the arms, as shown in Figure 82 ; for the water is thus made to press more powerfully against the bend of the arm as it flows through the tube. It will be noticed that there are two forces which tend to turn the wheel in this case; (i) the reaction proper, caused by the removal of the pressure at the opening at the end ; and (2) the angular force of the current as it strikes against the bend of the arm. 124. The Turbine Wheel. The power of Barker's mill (Figure 82) would evidently be increased by increasing the number of the arms. Instead of these arms we might have curved partitions placed between two flat discs, form- ing a wheel, as shown in Figure 83. Such a wheel is called a reac- tionary turbine, since the reaction- ary force is still predominant. Suppose now that the discs and partitions were cut round where the dotted circle is seen in the fig- ure, and that the outer part were supported in some way beneath, so that it might turn round freely while the central parts of the wheel were kept stationary. If water were poured into the wheel from above, the outer part would, of course, turn round just as the whole wheel did before it was cut in two. For the action of the water against the partitions would evidently be the same as be- fore, and it was this action of the water which turned the wheel. And there would be this advantage in the use of the divided wheel, that the outer part, while turning, would not have to carry the weight of the whole column of water, as the wheel did before it was divided. NATURAL PHILOSOPHY. Fig. 84. Again, by turning the inner se'. of partitions as showa in Figure 84, the current is made to strike the outer par- tition in such a direction as to make its angular force the greatest possible. A wheel thus arranged is the ordinary turbine, and in it the angular force of the escaping current is the chief motive power. It is the most efficient water- wheel ever constructed. A section of one form of this wheel is shown in Figure 85. The wheel b b cor- responds to the outer part of the wheel in Figure 83. It is supported from below and turns on an axis, as represented. Within this wheel are stationary partitions curved, as shown in Figure 84. These partitions are placed at the bottom of a large cylinder, into which the water is brought by the pipe o. The water flows between the fixed partitions against the partitions of the wheel b b, causing it to turn round rapidly. The water is then discharged at the circumference of the wheel b b. There are many kinds of turbines, and their effective power is from 75 to 88 per cent of that in the acting body of water. In the best forms of overshot and breast wheels it is from 65 to 75 per cent, and in undershot wheels from 25 to 33 per cent. IOO NATURAL PHILOSOPHY. STEAM POWER. 125. Marcefs Globe. In Figure 86 we have a stout brass globe containing water, and serving as a boiler. Into the top is fastened a glass manometer tube (48) about three feet long, whose lower end dips under mercury placed in the bottom of the globe. Through another opening passes the tube of a thermometer, the bulb of which is in- side the globe. Open the stopcock seen on the right of the globe, boil the water for some time to expel the air, and then close the stopcock. As soon as the steam formed by boiling the water is thus prevented from escaping, the temperature of the globe begins to rise. At the same time, the expan- sive force of the steam will increase, raising the mercury in the manometer; and the hotter the globe gets, the higher the mercury rises. We see, then, that when steam is formed in a confined space, its expan- sive force, or elasticity, increases with the temperature. , 126. The Steam Engine. The elastic force of the steam thus formed can be made to work a piston by the arrange- ment shown in Figure 87. The steam coming from the boiler by the tube x passes into the box d. From this box extend two pipes, a and , for carrying the steam, one above and the other below, the piston. A sliding valve y is so arranged that it always NATURAL PHILOSOPHY. closes one of these pipes. In the right-hand Figure the lower pipe b is open, and the steam can pass in under the piston and force it up. At the same time the steam which has done its work on the other side of the piston passes out from the cylinder through the pipes a and O. Fig. 87. The sliding valve is connected by means of the rod i with the crank of the engine, so that it moves up and down as the piston moves down and up. As soon, then, as the" piston has reached the top of the cylinder, the sliding valve is brought into the position shown in the left-hand Figure. The steam now passes into the cylinder above the piston through the pipe a and forces the piston down, and the steam on the other side which has done its work goes out through b and O. The sliding valve is now again in the po- . -02- ***.*. NATURAL PHILOSOPHY. sition shown in the right-hand Figure, and the piston is driven up again as before ; and thus it keeps on moving up and down, or in and out. This kind of motion is called reciprocating motion. In using the engine for doing work, it is generally neces- sary to change this reciprocating motion into a rotary one ; that is, to make the piston, as it moves up and down, turn a wheel. This is usually done by means of a crank. Fig. ss. The crank is sometimes connected [^^-^^^ j= n with the piston-rod directly, the cylinder being placed either hori- zontally, as shown in Figure 88, or upright, as in the engine represented in Figure 90. In other cases, the piston-rod turns the crank by means of a walking-beam, the arrangement and action of which will be understood from Figure 89. The walking-beam is much used for large engines, especially on steamboats. In Figure 90 we have a picture of a small stationary steam-engine, which will serve to show how the parts of the machine already described are put together, and also to illustrate those parts which have not yet been mentioned. On the right is the cylinder P, which is supplied with steam from the boiler by the pipe x. The waste steam is carried away by the pipe L. Within the cylinder is the piston moving up and down as explained above. The 'piston-rod A moves the crank M, and thus turns the axle D, which may be connected with the machinery to be driven, by means of a belt X, as here, or by a train of wheels, or in various other ways. Q is a pump, like that shown in Fig. 36, which supplies the boiler with water, through the pipe ft. It is worked by the engine itself by means of the rod g and the cam, or eccentric, E. NATURAL PHILOSOPHY. 103 Fig 90. 104 NATURAL PHILOSOPHY. 127. The Governor. It often happens that the work to be done by an engine is liable to vary in an irregular way. Parts of the machinery which it drives may be stopped or started at any moment, or the work which the machinery has to do may be greater at one time than another. It is very desirable that there should be some means of regulat- ing the speed of the engine, so that it may not be too sud- denly quickened OT retarded by these variations in the resistance which it has to overcome. The governor is a simple contrivance by which the engine is made to regu- late its own speed. It consists of two arms, k r (Figure 90), carrying heavy iron balls, m, n, at one end, and attached by joints at the other end to the rod c. The whole is made to rotate by means of the bevel-wheels a and b (100), which are turned by the engine itself. If the speed of the engine is quickened, the governor rotates faster, and the arms and balls tend to separate more and more ; just as two balls hung side by side will do when the strings by which they are held are twirled by the hand. As the arms spread out they raise the ring r, which slides freely on the rod c ; and as r rises, it acts upon the levers s, t, and O, which partially close valve a in the pipe x. This valve is seen at v in Figure 87. The supply of steam from the boiler is thus diminished, and the speed of the engine is retarded. The governor now rotates less rap- idly, the arms drop a little, the ring r slides down, the valve in x is opened a little more, letting steam pass to the cylinder more freely, and the speed of the engine is quickened again. Thus any tendency to go faster or slower corrects itself very promptly through the agency of the governor, and the engine runs at almost exactly the same speed, however much the resistance may vary. 128. The Fly- Wheel. As has been stated, a crank is commonly used to change the reciprocating motion of the piston into a rotary one. But as the crank turns round, it NATURAL PHILOSOPHY. 105 will be seen that there are two points where the piston-rod is pushing exactly in the direction of the point round which the crank moves ; and that at these points it does not tend to turn the crank at all. There must therefore be some means of carrying the crank past these dead points, as they are called. This is the office of the fly-wheel V, a heavy iron wheel attached to the axle D. The great momentum of this heavy mass tends to carry the axle round with a uniform motion, notwithstanding the variations in the power acting upon it. 129. High Pressure and Low Pressure Engines. When the steam after doing its work in the cylinder is carried into a cold chamber, the engine is said to be of low press- ure; when it is forced out into the air, the engine is said to be of high pressure. In the former case, the steam is con- densed into water in the cold chamber, and a vacuum is thus formed behind the piston. In the latter case, the piston has to act against the pressure of the atmosphere, which, as we have learned (38), is equivalent to a weight of 15 pounds on each square inch of its surface. It is evident that a greater pressure of steam will be necessary to move the piston in the latter case. 130. The Boiler. In the boiler the steam is produced, and confined until it is used in moving the piston. It must therefore be capable of furnishing all the steam needed by the engine in any given time, and strong enough to resist the expansive force of the steam shut up within it. Boilers are usually made of plates of wrought iron or copper riveted together. Copper is the best material, but iron is almost always used on account of its cheapness. In order to get the full effect of the fire, the hot gas and smoke from it are usually made to pass through flues or tubes in the body of the boiler; and the water comes directly in contact with these flues or tubes. This is il- lustrated in the Cornish boiler, as it is called, shown in 5* 106 NATURAL PHILOSOPHY. Figure 91, and considered one of the best forms of boiler. F i g . 9I . It is a cylinder, frequently more than forty feet long, and from five to seven feet in diameter, with two cylindrical flues, B B, ex- tending its whole length. These flues serve as the furnace in which the fire is built. The hot gas and smoke after passing through the flues are made to circulate round the outside of the boiler before escaping into the chimney. Another form of boiler is represented in Figures 92 and 93. This boiler is cylindrical, but instead of the flues of the Cornish boiler, it has two long cylindrical tubes, B B, connected with it by upright pipes. These tubes are ex- posed to the direct flame of the fire. The hot gases and smoke after passing under the tubes to the other end of the boiler, return through the flue C to the front again, and are finally discharged into the chimney by the side flues D D. In Figure 92, 6" is the safety-valve. The weight acting on the lever keeps the valve closed until the pressure of the steam in the boiler becomes too great for safety, when it opens and allows a part of the steam to escape, and thus reduces the pressure, n is the tube through which water is supplied to the boiler ; m the tube by which the steam is sent to the cylinder. T is the man-hole, through which workmen can enter the boiler to clean or repair it. s is an alarm whistle, so arranged that it is opened by the float E when the* water sinks too low in the boiler. P is a con- trivance for showing the depth of water in the boiler by the rising and falling of the weight #, which is connected by the lever with the float F. A simpler and better arrange- ment for the same purpose consists of a strong glass tube placed outside the boiler, but communicating with the NATURAL PHILOSOPHY. 107 108 NATURAL PHILOSOPHY. water within. The water in this tube stands of course at the same height as that in the boiler (18). Figure 94 represents the usual form of the boiler of a locomotive engine. The furnace or fire-box, A, is within the boiler, and is surrounded by water except beneath and at the door D. A large number of stout tubes extend from Fig 94- che fire-box through the boiler to the smoke-box B. The hot gases and smoke pass through these before they escape into the chimney. E is the steam-dome, from the top of which a large tube conveys the steam into the chamber F, from which it passes by tubes on each side to the cylinders. The waste steam from the cylinders passes into the chim- ney through two pipes meeting at K, and thus increases the draught of the furnace. 131. The Locomotive Engine. This machine is shown in full in Figure 95. The boiler X Jf has just been described. D is the fire-box ; Y, the smoke-box ; a, the tubes con- necting the two ; O, the door for putting in fuel ; ;/, the glass water-gauge, already described, which shows the height of the water in the boiler ; H, the vent-cock, by which the water can be drawn off from the boiler ; R jR, the feeders which conduct water from the tender to two force-pumps (not seen in the Figure) by which it is forced into the boiler ; /, the safety-valves, kept down by spiral NATURAL PHILOSOPHY. 109 HO NATURAL PHILOSOPHY. springs in the cases e ; g, the steam-whistle ; G, a rod which controls the valve 7 by which steam is let into the steam-pipe A. The engineer is represented as holding in his hand the lever by which this valve is opened more or less, to regulate the speed of the engine. The steam-tube A passes through the boiler, as shown by the dotted lines, into the smoke-box, where it branches off to the two cylin- ders. In this engine there is no chamber like that marked F in Figure 94. One of the cylinders is seen at F, laid open to show the piston P. The sliding valve by which the steam is admitted to the cylinder is precisely like the one figured and described above (126) ; but, being behind F under the boiler, it does not appear here. E is the pipe by which the waste steam is discharged into the smoke- pipe Q. K is the connecting-rod, by means of which the piston turns the crank M on the axle of the driving wheels. In starting the engine the valves must be moved by hand. This is done by means of the lever B and the rod C. 1 1 are stop-cocks, through which any water condensed in the cylinders can be driven out ; v, the rod for opening these cocks. The other parts will be understood without any de- scription. It will be seen that the locomotive is a high pressure engine. SUMMARY. The human hand is a source of mechanical power. It maybe used to work any of the simple machines. (115.) The crab (116) and the derrick (117) are hand machines. The strength of the horse is a second source of mechan- ical power. (118.) The horse is employed to draw loads up inclined planes ; to elevate weights by means of pulleys ; to turn NATURAL PHILOSOPHY. Ill a crank or shaft ; and to turn a wheel by treading upon a movable inclined surface in the form of an endless plat- form. (119.) The wind is a third source of mechanical power. This source of power is employed to propel ships and to drive windmills. (120.) The downward and lateral pressure of water is a fourth source of mechanical power. (121.) The downward pressure of water is made to turn a ver- tical water wheel. (122.) The lateral pressure of water is made to turn a horizontal or reaction water wheel. (123.) The turbine wheel is a reaction wheel, and the most efficient water wheel known. (124.) The elastic force of steam is a fifth source of mechanical power. (125.) The machine by which this source of power is applied is called a s-team engine. (126.) The essential parts of the steam engine are the boiler, in which the steam is generated ; the cylinder, in which the expansive force of the steam is made to work a piston ; and the crank, by which the motion of the piston is made to turn a shaft. (130, 126.) Steam engines may be either of high or low pressure. (129.) PART SECOND. SOUND, LIGHT, HEAT, AND ELECTRICITY. I. SOUND. NATURE AND PROPAGATION OF SOUND. SOUND-WAVES. i. A Sounding Body is a Vibrating Body. If a glass bell-jar held by the knob be struck with the knuckle, it gives out a sound. If a bit of metal, ivory, or other hard substance be placed within the bell, as seen in Figure i, Fig. i. it is tossed up and down rapidly, showing that the bell is vibrating. By similar experiments, it is found that every body is vi- brating while giving out sound, and that it is only by caus- ing a body to vibrate that it can be made to give out sound. 2. Sound will not pass through a Vacuum. In Figure 2, the bell B is suspended by silk threads under the receiver of the air-pump. The bell is struck by means of clock- work, which can be set in motion by the sliding-rod r. If the bell be struck before exhausting the air, it can be dis- tinctly heard ; but as the air is exhausted, the sound be- SOUND. Fig. 2. comes fainter and fainter, until at last it can hardly be perceived even with the ear close to the receiver. Sound, then, cannot pass through a vacuum. The slight sound which is heard is transmitted by the little air left in the receiver, and by the cords which hold up the bell. 3. Sound passes through all Gases. If hydrogen or any other gas be now allowed to pass into the receiver, the sound of the bell is heard again. It will be noticed that the sound is different in different gases. 4. Sound passes through Liquids and Solids. If a bell be put under water and struck, it can be heard. If a person puts his ear close to the rail of an iron fence, and the rail be struck at a considerable distance, he hears the blow twice. The first sound comes through the rail ; the second, which soon follows, comes through the air. These experiments show that sound passes through liquids and solids. A slight scratch upon the iron rail, which could not be heard at all through the air, is heard distinctly when the ear is placed against the rail ; showing that the solid trans- mits the sound better than the air. By placing the ear near the ground, the tramp of horses or the tread of men can be heard at a great distance, the sound being conveyed by the solid earth. SOUND. t 5 5. Sound is propagated by means of Vibrations. We have seen (i) that sound is produced by vibrations. We next inquire how it is propagated. Let us first examine the condition of the molecules of the air in front of the sounding body. Let the middle line of dots in Figure 3 Fig. 3- a." b" c" A" e" o" p" * represent the position of the molecules when at rest. These molecules, as we have learned, are not in contact, and they are kept apart by an elastic force acting between them like a bent spring. Now, as the vibrating surface moves forward it pushes the molecules of the air before it ; but, since it takes time to transmit the motion from mole- cule to molecule, they do not all move on together. The lower line of dots in the figure represents their condition when the vibrating surface has ceased to move forward. The molecule d is just ready to come to rest, and the molecule e just ready to begin to move, while all the mole- cules between are moving forward. It will be seen that the molecules between a and e are crowded together, or compressed. Just as the molecule b' comes to rest, the molecule beyond e will begin to move ; when c comes to rest, the second molecule beyond e begins o move ; and so on. Thus the line of compressed molecules keeps of the same length, and continually moving xvX'ward. Suppose the surface to be at rest at a, and to move backward instead of forward. The elastic force acting 6 . SOUND. between the molecules in front of it will cause them to follow it one after another. If it is just as long in going backward as forward, the molecule e will be just ready to start when the molecule a stops. The upper line of dots represents the condition of the molecules when the vibrat- ing surface has ceased to move backward. The molecule a" is just ready to stop, and the molecule e" just ready to start, and the molecules between are moving backward. It will be seen that the molecules of this set are spread apart, or extended. When the molecule b" is ready to stop, the molecule beyond e" is ready to start ; and so on. Thus it will be seen that the line of extended particles keeps of the same length, and continually moving forward. As the vibrating surface moves backward the instant it has moved -forward, the set of extended particles follows on directly after the set of compressed particles ; and these two sets are sent out one after the other as long as the body is sounding ; that is, if from a'' to e' we have a set of ex- tended particles, from /' to o" we shall have a set of com- pressed particles, from o" to /" a set of extended particles, and so on. It will be noticed that the molecules in the first set are moving forward ; those in the second set, backward ; those in the third set, forward ; and so on. Of course each molecule is merely swinging backward and forward, or vibrating. We see, then, that when a body is sounding, the molecules of air about it are made to vi- brate, and that they vibrate in sets. Two successive sets of these vibrations constitute what is called a wave of sound ; that is, in the figure the portion of the upper line of dots from a" to o" is a wave. These sound-waves run out from a sounding body in every direction, just as the waves in water spread away in circles from the point where a stone has been thrown into it. So long as the sound- waves are passing through the air, their outline is spheri- cal. SOUND. 7 In like manner, sound is propagated through solids and liquids by means of vibrations. Sound, then, is produced by vibrations, and these vibra- tions are passed on from molecule to molecule through the intervening bodies to the ear. It will now be seen why sound cannot pass through a vacuum. 6. The Intensity of Sound depends upon the Amplitude of the Vibrations. If the bell-jar in Figure i be struck lightly, it will give out a faint sound, and the bit of metal will be but slightly agitated ; if it be struck a harder blow, it will give out a louder sound, and the metal will be more violently agitated. It is evident that in the latter case the bell-jar moves backward and forward through a greater space than in the former ; in other words, that the ampli- tude of its vibrations is greater. The intensity of sound, then, depends upon the amplitude of the vibrations of the sounding body. 7. The Intensity of Sound diminishes as the Square of the Distance of the Sounding Body increases. If we place a bell ten yards off, and four bells of the same size twenty yards off, we shall find that the sound of the one bell will be just equal to that of the four bells. At the distance of thirty yards, nine bells would be necessary to produce a sound equal to that of the one bell at ten yards. Sound, then, diminishes in intensity as the square of the distance from the sounding body increases. This is as we should expect. As the sound-waves spread away in all directions from the sounding body, a greater and greater number of particles of air must be set in motion, and the motion of each must be more feeble ; and, since the surfaces of spheres increase as the squares of their radii, the number of particles to be set in motion increases as the square of the distance from the sounding body. 8. Speaking-Tubes. If the sound-waves are prevented 8 SOUND. from spreading in all directions, the particles of air lose little of their motion, and the sound little of its intensity. Thus Biot found that through one of the water-pipes of Paris words spoken in a very low tone could be heard at the distance of about three quarters of a mile. The sides of the pipe kept the sound-waves from spreading. In the same way, conversation can be carried on between distant parts of a large building by means of small tubes, called speaking-tubes. 9. Sound travels through the Air at the Rate of 1,090 Feet a Second. The velocity of sound in air has been several times determined by experiment. In 1822, the French Board of Longitude chose two heights near Paris, and from the top of each fired a cannon at intervals of ten minutes during the night. The time between seeing the flash and hearing the report was carefully noted at both stations, and the average of the results showed that sound travels through the air at the rate of 1,090 feet a second. In such experiments, the time taken by the light to pass between the stations is too small to be per- ceived. 10. The Observed and the Computed Velocity of Sound. From the known elasticity and density of air, Newton com- puted that the velocity of sound should be 916 feet a second. That the observed velocity is greater is due to the change in the elasticity of the air in the two portions of the sound-wave, owing to the development of heat in the compressed part and its absorption in the extended part. That heat is developed by compression of the air may be shown by putting some tinder in a fire syringe (Figure 4) and quickly pushing down the piston : the tinder will take fire. Now heat increases the elasticity of the air, and the increased elasticity in the compressed part of the wave has the same effect as putting stiffer springs between the molecules in front, so that they will impart SOUND. 9 their forward motion to one another more promptly ; while the diminished elasticity in the extended portion has the same effect as placing weaker springs between the molecules behind, so that the molecules can also return more promptly. Thus it will be seen that the change of elasticity in the two portions of the wave, by the development and absorption of heat, increases the rapidity with which the mole- cules can impart their vibratory motion to one an- other ; and this rapidity is the velocity of sound. 11. The Velocity of the Sound-wave depends on the Elasticity as compared with the Density of the Medium. As long as the elasticity remains the same, the velocity of the sound-wave will be di- minished by increasing the density ; for, the greater the density, the greater the number of molecules to be put in motion, and the slower the motion will be transmitted. While the den- sity remains the same, the velocity increases with the elasticity, as we have seen above. This ex- plains the fact that the velocity of sound at a great height in the air is the same as near the earth. As we ascend, the temperature falls and the elastic force of the air becomes less, but the density of the air diminishes at the same rate. If the density and elasticity both in- crease at the same rate, the velocity will remain the same. The greater, then, the elasticity of the medium compared with its density, the greater the velocity of sound. It will be shown farther on how the velocity of sound in different gases can be ascertained. 12. The Velocity of Sound in Water is about 4,700 Feet a Second. This was determined at the Lake of Geneva, in 1826, by Colladon and Sturm. They found that, when a bell was struck under water on one side of the lake, the sound could be distinctly heard at a distance of nine miles i* 10 SOUND. on the other side by putting the ear to one end of a tube whose other end was in the water. It was thus found that the velocity of sound in water is about 4,700 feet a second. The method of finding how fast sound travels in different liquids will be explained in another place. 13. Sound travels through Solids faster than through Air. It is found by the experiment with the iron rail men- tioned above (4) that the velocity of sound in a solid body is greater than in the air. It will be shown hereafter how we can find the velocity of sound in solids. 14. On meeting a Medium of different Density the Sound- wave is partially reflected. The transmission of vibrations in a sound-wave from one particle to another may be illus- trated by means of two ivory balls hung side by side. If the balls are of the same size, and one be raised and dropped against the other, the first gives up all its motion to the second and itself comes to rest. If the first ball is smaller than the second and be let fall against it, the sec- ond moves forward and the first rebounds. If the first is larger than the second, it follows the second a little way and then falls back again. In the first case the balls illus- trate the condition of the molecules in a uniform medium : each molecule gives up all its motion to the next, and would come to rest were it not kept vibrating by the sound- ing body behind. In such a medium, then, the sound-wave moves steadily forward. In the second case the balls il- lustrate the condition of the molecules of a rarer medium contiguous to those of a denser medium. When the sound- wave meets this denser medium, the molecules of the rarer medium give up only a part of their motion to those of the denser, and themselves rebound, giving rise to a reflected wave. In the third case the balls illustrate the condition of the molecules of a denser medium contiguous to those of a rarer medium. Here it will be seen that the sound- wave is partially reflected on meeting a rarer medium. SOUND. II Whenever, then, the sound-wave meets a medium of differ- ent density, it is partially reflected. 15. When a Sound-wave is reflected \ the Angle of Reflec- tion is equal to the Angle of Incidence. In Figure 5 we have two parabolic mirrors, with a watch placed in the Fig. 5- rocus of the upper one. The sound-waves spread out from the watch, meet the surface of the upper mirror, and are reflected from that to the lower mirror, by which they are again reflected. If the mirrors are several yards apart, it will be found that the ticking of the watch can be heard distinctly on placing the ear at a, the focus of the lower 1 2 SOUND. mirror, though it cannot be heard at any other point near that mirror. This shows that the reflected sound-waves are all concentrated at the point a. By what path have they reached this point ? In Figure 6, F is the focus of the parabolic mirror N A Flg ' 6 ' M t and the line A X, =^ L passing through the focus and the centre of the mir- ror, is called its axis. The ; z lines M P and N P' are drawn so as to be perpen- dicular to the surface of ~~"" the mirror at the points M and N. If we draw the lines FMand. F N, showing the direction in which the sound-wave has travelled from F to these points, they will make the same angles with the perpendiculars as the lines ML and NO drawn parallel to the axis. This will be true whatever may be the situation of the points J/and N. If the sound-waves on meeting this mirror are all reflected in lines parallel to the axis, they will, on meeting the sec- ond mirror, be reflected to its focus. We have found, by the experiment with the watch, that they are reflected to the focus of the second mirror. They must, then, have been reflected from the first mirror in a direction parallel to its axis ; and the angle P ML, at which any portion of the wave left the mirror, must have equalled the angle F M P at which it struck the mirror. The former angle is called the angle of reflection, and the latter the angle of in- cidence. Whenever, then, a sound-wave is reflected, the angle of reflection is equal to the angle of incidence. 1 6. Echoes. When there is a sufficient interval between the direct and the reflected sound, we hear the latter as an echo. The reflected sound has the same velocity as the direct sound, so that the echo of a pistol-shot from the SOUND. 13 face of a cliff 1,090 feet distant is heard two seconds after the explosion. An echo in Woodstock Park repeats seventeen syllables by day, and twenty by night ; one on the banks of the Lago del Lupo, above the fall of Terni, repeats fifteen. The tick of a watch may be heard from one end of the abbey church of St. Albans to the other. In Gloucester Cathedral, a gallery of an octagonal form conveys a whis- per seventy-five feet across the nave. In the whispering gallery of St. Paul's, the faintest sound is conveyed from one side to the other of the dome, but is not heard at any intermediate point. . At Carisbrook Castle, in the Isle of Wight, is a well 210 feet deep and 12 wide. The interior is lined with smooth masonry. When a pin is dropped into the well, it is distinctly heard to strike the water. In some cases the sound is reflected several times, and a succession of echoes is heard, each feebler than the pre- ceding, since a part of the sound is lost at each reflection. In mountain regions such echoes are common, and some- times the effect is very remarkable. There is a deep val- ley called the Ochsenthal, near Rosenlaui, in Switzerland, where the echoes warble in a wonderful manner. Sounds are also reflected from the clouds. When the sky is clear, the report of a cannon on an open plain is short and sharp ; while a cloud is sufficient to produce an ^echo like the rolling of distant thunder. A feeble echo also occurs when sound passes from one mass of air to another of different density. Humboldt relates that, from a certain position on the plains of Antures, the sound of the great falls of the Orinoco resembles the beating of a surf upon a rocky shore, being much louder by night than by day. This is not due to the greater stillness of the night, for the hum of insects and the roar of beasts ren- der the night much noisier than the day. But between the place where Humboldt was and the falls lay a vast 14 SOUND. grassy plain, with many bare rocks rising from it. When exposed to the sun, these rocks became much hotter than the adjacent grass ; over each of them, therefore, rose a column of heated air, less dense than that which sur- rounded it. Thus by day the sound had to pass through an atmosphere which frequently changed its density ; the partial echoes where the rare and dense air met were in- cessant, and the sound was consequently enfeebled. At .night there were no such differences of temperature, and the sound-waves, travelling through an atmosphere of uni- form density, reached the ear without any loss from reflec- tion. 1 7. When a Sound-wave passes obliquely into a Medium of different Density it is refracted. Let a b (Figure 7) be Fig. 7. Fig. 8. a portion of a sound-wave moving in the direction of the arrow, and a c be the surface of a medium O of different density from J/, in which the wave has been moving. If the elasticity of O is such that the wave will move faster in it than in Jlf t the portion a of the wave which enters O first will move on faster than the portion b while the latter is moving in M. When a b is wholly within O, the second arrow shows the direction in which it will be moving ; and SOUND. 15 it will continue to move in this direction so long as it is wholly in this medium. When the direction of a wave is thus bent, it is said to be refracted. In this case it is bent away from a perpendicular P Q drawn to the surface of the medium O. If the elasticity of O is such that the sound-wave moves slower in it than in M, the portion a of the wave (Figure 8), when it has entered O, moves slower than b while the latter is in M. In this case it will be seen that the direc- tion of the wave will be bent towards the perpendicular It is evident that, if a b had not met the medium O obliquely, both ends of it would have entered O at the same time, and its direction would not have been changed. We see, then, that when a sound-wave passes obliquely into a medium of different density, it is refracted, and that, if it travels more rapidly in the new medium, it will be bent away from a perpendicular drawn to the surface of that medium ; while, if it travels less rapidly in the new me- dium, it will be bent towards a perpendicular drawn to the surface of that medium. Fig. 9. This refraction of a sound-wave has been shown by the experiment illustrated in Figure 9. B is a collodion bal- loon filled with carbonic acid gas ; w is a watch hung near i6 SOUND. Fig. 10. it ; and f is a glass funnel. By placing the ear at f and moving the funnel about, a point will be found where the ticking of the watch will be louder than elsewhere. This shows that the sound-waves have been converged to that point. Figure 10 shows how the sound-waves are refracted in passing through the carbonic acid, a b is a portion of the sound-wave. In passing into the carbonic acid, a me- dium in which it moves more slowly than in air, it is bent into the form of m o' n. On passing out from the carbonic acid, it is bent still farther in the same direction, and thus the two parts of the wave are made to converge. SUMMARY. Sound originates in a vibrating body, (i.) It is not propagated through a vacuum. (2.) It is propagated through all elastic substances, whether gases, liquids, or solids, by vibrations of their molecules. These molecules vibrate in systems, giving rise to waves. (3, 4.) Sound is propagated by vibrations. (5.) Its intensity increases with the amplitude of the vibra- tions, and diminishes as the square of the distance from the sounding body increases. (6, 7). The velocity of sound in air is 1,090 feet a second. (9.) Its observed velocity is greater than its velocity as com- puted by Newton, owing to the heat developed in the compressed portion of the wave. (10.) SOUND. 1 7 The velocity of sound in any medium depends upon its density as compared with its elasticity, (n.) The velocity of sound in water is about 4,700 feet a second. Its velocity in solids is greater than in the air. On meeting a medium of different density, the sound- waves are partially reflected and partially transmitted. The transmitted portion is refracted, unless the wave meets the surface of the medium perpendicularly. (14, 17.) Echoes are due to reflected sound-waves. (16.) Fig. ii. MUSICAL SOUNDS. 1 8. Difference between Noise and Musical Sounds. In Figure n we have an instrument called fat gyroscope, con- sisting mainly of a heavy brass ring d surrounding a disc which rests upon a steel axis. To this axis is fast- ened a small toothed wheel W. By winding a string round the axis and then drawing it suddenly out, the ring and the toothed wheel are made to spin rapidly. If a card c be held against the edge of the wheel as it rotates, a very shrill musical sound is produced. If the thumb be placed a moment against the ring, the speed of its rotation is checked somewhat, and the sound becomes less shrill. The more the speed is dimin- ished, the less shrill the 1 8 SOUND. sound becomes, until finally we hear the separate taps of the teeth against the card. We see, then, that when the taps are frequent enough, they blend so as to produce one continuous sound. Such a continuous sound is called a musical sound. In this experiment the card is made to vibrate by strik- ing the teeth of the wheel, and, as the teeth are at equal distances, the vibrations follow one another at equal inter- vals. A musical sound, then, is one in which the vibra- tions recur at regular intervals. If they do not recur at regular intervals, the sound is called a noise. 19. The Pitch of Musical Sounds. We have seen that, the faster the wheel turns, the shriller is the sound, or, in other words, the higher its pitch. Of course, the faster the wheel turns, the more rapid are the vibrations of the card. Hence the pitch of musical sounds depends on the rapidity of the vibrations. In musical sounds, as in all other sounds, the loudness depends upon the amplitude of the vibrations. 20. The Tuning-Fork. A convenient instrument for producing a musical sound is the tuning-fork, shown in Figure 12. It consists of a bar of steel bent into the form SOUND. Fig. 13- of the letter U y and attached to a standard. A B is a wooden case open at both ends, by which the intensity of the sound produced by the fork is increased. The fork may be set vibrating by striking it, or by drawing a violin bow across it. The elasticity of the steel causes the prongs to vibrate regularly, and thus to give out a musical sound. 21. The Siren. The siren is an instrument for pro- ducing musical sounds, and at the same time register- ing the number of vibra- tions. It consists (Figure 13) of a brass cylinder C, having a tube /opening into it at the bottom, and closed at the top by a brass plate a b. This plate is pierced with four series of holes arranged in circles. The innermost series contains 8, the next 10, the next 12, and the last 16 holes, d e is a brass disc pierced with four series of holes ar- ranged like those below. The holes in the plate a b are inclined a little in one direction, and those in de a little in the opposite di- rection. Through the cen- tre of the disc passes a steel axis, the lower end /' of which fits into the hole x in a b. The disc is made to rotate by blowing into 20 SOUND. Fig. 14. the tube /. The current of air striking against the slanting sides of the holes in a b is directed against the sides of the holes in d > 3. 1,056 1,267.2 " . ; 4. 1,320 1,584.0 . . 5. 1,584 1,900.8 Between several pairs of these tones we have a differ- ence of 53 vibrations. This difference implies a greater disturbance by beats than in the case of the fifth, or of the fourth, or of the major third. Hence the minor third is inferior as a consonance to all those intervals. Thus do we find that, as the numbers expressing the ratio of the vibrations become larger, the disturbing influ- ence of the beats enters more and more into the interval. The result, it is manifest, entirely harmonizes with the explanation that refers dissonance to beats. 42. The Musical Scale. In choosing a series of sounds for combination two by two, the simplicity alone of the ratios would lead us to fix on those expressed by the num- bers i, , |, f , -|, 2 ; these being the simplest ratios that we can have within an octave. But when the notes repre- 3 D 50 SOUND. sented by these ratios are sounded in succession, it is found that the intervals between i and J, and between j and 2 are wider than the others, and require the inser- tion of a note in each case. The notes chosen are such as form chords, not with the fundamental tone, but with the note f regarded as a fundamental tone. The ratios of these two notes with the fundamental are f and V 5 - I n - serting these, we have the eight notes of the natural or diatonic scale expressed by the following names and ratios : Names. C. D. E. F. G. A. B. C'. Intervals, ist. 2d. 3d. 4th. 5th. 6th. ;th. 8th. Rates of vibration. i, |, J, |, |, f, ^-, 2. Multiplying these ratios by 24 to avoid fractions, we ob- tain the following series of whole numbers, which express the relative rates of vibration of the notes of the diatonic scale. 24, 27, 30, 32, 36, 40, 45, 48. The meaning of the terms third, fourth, fifth, &c., which we have already so often applied to the musical intervals, is now apparent ; the term has reference to the position of the note in the scale. SUMMARY. When the combination of two notes is agreeable, they are said to form a chord; when their combination is disagree- able, a discord. The simpler the ratio of the vibrations of two notes, the more agreeable the chord which they form. (40.) Dissonance is due to beats. It is greatest when the beats occur at the rate of 33 a second, and wholly disappears when they occur at the rate of 132 a second. (41.) SOUND. . MUSICAL INSTRUMENTS. TRANSVERSE VIBRATION OF STRINGS AND STRINGED INSTRUMENTS. 43. In many musical instruments the sounds are pro- duced by the vibrations of strings or wires. These are called stringed instruments. We proceed now to examine the laws according to Fig. 30. which strings vibrate. 44. A String vibrating alone gives a very feeble Sound. In Figure 30 AB is a wooden bar placed across an iron bracket C. mn is an iron bar hung from AB by means of ropes ; and s / is a steel wire which is stretched by a weight. If we take hold of the middle of the string, pull it to one side and let it go again, its elasticity will cause it to vibrate, but the sound it gives out can scarcely be heard. If a similar string stretched by an equal weight be hung from a sounding-box AB (Fig- ure 31), and be set vibrating, the sound is heard distinctly. 45. Sounding-Boards. From these experiments we see that some kind of a sounding-board is necessary in all stringed instruments. It is not the chords of a piano, or harp, or violin, that throw the air into sonorous vibrations. It is the large sur- SOUND. Fig. 31- faces connected with the strings, and the air enclosed by these surfaces. The merit of such instru- ments depends mainly upon the quality and arrangement of their sounding-boards. The violin, for ex- ample, is made of wood of the most perfect elasticity. The strings pass from the tail- piece of the instru- ment over the bridge to the pegs by which they are tightened. The two feet of the bridge rest upon the most yielding part of the body of the violin ; that is, the portion be- tween the two^shaped openings. One foot is fixed over a short rod, the sound-post, which extends across to the back of the instrument. This foot is thereby made stiff, and it is mainly through the other foot, which is not thus sup- ported, that the vibrations of the strings are conveyed to the wood and thence to the air within and without. The sonorous quality of the wood is mellowed by the molecular changes which take place with the lapse of time. The very act of playing, too, appears to make the mole- cules of the wood conform more readily to the vibrations of the strings, and thus improves the instrument. 46. Laws of the Vibration of Strings. The laws of the vibration of strings are best investigated with the sonome- ter, which has already been described. The first law has SOUND. 53 already been found, and is stated thus : The rapidity of the vibrations is inversely as the length of the string. 47. The Rapidity with which a String vibrates varies as the Square Root of the Weight which stretches it. If the string B B> (Figure 32) be stretched with a weight of one pound and made to vibrate, a note of a certain pitch is ob- Fig. 32. tained. If the weight be made four pounds, the pitch will be raised an octave ; if sixteen pounds, it will be raised another octave; and so on. The rapidity of the vibra- tions, then, varies as the square root of the weight by which the string is stretched. 48. The Rapidity with which a String vibrates varies inversely as its Thickness. If strings of the same material but of different thickness be stretched over the bridges by equal weights, the thicker strings will be found to give the lower notes. If one string is just twice as thick as an- other, its note will be an octave lower. In general, then, other things being equal, the rapidity of the vibrations of a string varies inversely as its thickness. 49. The Rapidity with which a String vibrates is inversely as the Square Root of its Density. It is found that if a plat- 54 SOUND. mum and an iron wire of the same length and thickness be stretched by equal weights, they will not give notes of the same pitch. The greater the density of the string, the lower the pitch of the note which it gives. It is found on trial that the pitch of the sound rises as the square root of the density diminishes. The last two laws taken together may be stated thus : The rapidity with which strings vibrate is inversely propor- tional to the square root of their weight. In one class of stringed instruments, like the violin, violoncello, and guitar, notes of a great variety of pitch are obtained from a few strings by fingering the strings so as to change their length. In another class, like the harp and piano-forte, many strings are used varying in length and thickness, each of which gives but one note. SUMMARY. Musical sounds may be produced by the transverse vi- brations of strings. (43.) The sound of a vibrating string must, however, be en- forced by a sounding-board, in order to become audible. (44, 45-) The sonometer is an instrument for investigating the laws of vibrating strings. (46.) These laws are three in number : (i.) The rapidity with which a string vibrates varies inversely as its length. (46.) (2.) The rapidity with which a string vibrates varies as the square root of the weight which stretches it. (47.) (3.) The rapidity with which a string vibrates is inversely as the square root of its weight. (48, 49.) In some stringed instruments many notes are produced by few strings ; in others, there are as many strings as there are notes given. (49.) SOUND. 55 LONGITUDINAL VIBRATION OF STRINGS, RODS, AND COLUMNS OF AIR; AND WIND INSTRUMENTS. 50. The vibrations of strings which we have studied thus far take place at right angles to the length of the string. A string may also vibrate in the direction of its length. This may be shown by drawing a piece of resined leather along the wire of a sonometer. It will be noticed that the sound is much shriller than when the same wire is made to vibrate transversely. In this case it is the elastic force acting among the molecules of the wire which causes it to vibrate ; and, owing to the intensity of this elastic force, the vibrations are much more rapid than in the other case. 51. The shorter the Wire, the more rapid are its Longitu- dinal Vibrations. Let one end of a long iron wire be firmly fastened to a fixed wooden sounding-box, and the other end wound round a peg, which may be turned by a key so as to stretch the wire more or less. Pass a piece of resined leather to and fro along the wire, and a musical sound is heard. Put a bridge under the middle of the wire, and rub one of its halves. The sound heard is the octave of that heard at first, showing that the vibrations are twice as rapid. Place the bridge so as to cut off one fourth of the wire, and rub that fourth. The sound pro- duced is the octave of the last, showing that the vibrations are four times as rapid as at first. We see, then, that the shorter the wire the more rapid its longitudinal vibrations. 52. The Rapidity of the Longitudinal Vibrations is inde- pendent of the Tension of the String. Remove the bridge, so that the iron wire may vibrate throughout its entire length. Turn the key so as to change the tension of the wire, and again rub it. The pitch of the note does 56 SOUND. not change, showing that the rapidity of the longitu- dinal vibrations is independent of the tension of the wire. 53. How to find the Comparative Velocity of Sound in Wires of Different Materials. If a brass wire and an iron wire of the same length and thickness be made to vibrate longitu- dinally, their tones are not the same, that of the iron wire being considerably the higher of the two. In the case of these wires the sound is not produced by the wire itself, but by the sounding-box. As the wire vibrates longitudi- nally, its end alternately pushes and pulls upon the sound- ing-box, and thus throws the air within it into vibrations. This pushing and pulling is due to the passage of the sound-pulse to and fro along the whole wire. The time taken by the pulse in running the length of the wire and back is that of a complete vibration of the wire. In this time the wire gives one pull and one push to the box at its end, and one vibration to the air within it. The faster the pulse passes along the wire, the higher the note produced. If the brass wire be shortened until it gives a note of the same pitch as that given by the iron wire, it is evident that the sound-pulse traverses each of the wires in the same time. The length of the wires will be found to be in the ratio of n to 17, showing that sound travels only ^ as fast in brass as in iron. 54. The Longitudinal Vibrations of Rods free at one End. A smooth wooden or metallic rod with one of its ends fixed in a vise yields a musical note when rubbed with resined leather. When a rod fastened in this way yields its fundamental note (29), it simply lengthens and short- ens in quick succession. When rods of different lengths are compared, the pitch of the note is found to increase as the length diminishes. By taking advantage of this fact, a musical instrument has been constructed, such as is shown in Figure 33, which produces notes of different SOUND. 57 pitch by the longitudinal vibrations of wooden rods of different lengths. Fig. 33 . 55. Longitudinal Vibrations of Rods free at both Ends, Clasp a long glass tube at its centre with one hand, and rub a wet cloth over one of its halves with the other. A musical sound is produced. A solid glass rod of the same length will give the same note. In this case the centre of the tube or rod is a node, and the two halves lengthen and shorten in quick succession. This lengthening and shorten- ing of the halves of the rod is shown by the apparatus represented in Figure 34. a b is a brass rod held at its centre by the clamp s ; and an ivory ball hung by two strings from the points m and n rests against the end b of Fig. 34- the rod. On drawing a piece of resined leather gently over the rod near #, it is thrown into longitudinal vibra- tions. The centre s is at rest, but the motion of the ivory ball shows that the end b is in a state of tremor. Rub the rod more briskly, and its vibrations become more intense. a* SOUND. Fig. 35- and the ivory ball is thrown off violently whenever it comes in contact with the end of the rod. If a long glass tube be held at the centre, and one half of it be rubbed briskly with a wet cloth, the strain upon the glass caused by the longitudinal vibrations may be sufficient to shiver the other end, as shown in Figure 35. 56. How to find the Velocity of Sound in -different Solids. In all cases the longitudinal vibrations of rods are pro- duced by the passage of the sound- pulse to and fro along them. The pitch of the note given by rods of the same length depends upon the rapidity with which the pulse passes. The ve- locity of sound in different solids can be compared by means of rods free at both ends, as well as by means of wires. We -have only to take rods of the dif- ferent solids, of such lengths that they will give notes of the same pitch, and these lengths will be in the inverse ratio of the velocities required. 57- Resonance. When a tuning-fork is detached from the sounding-box and made to vibrate, it can hardly be heard. Let, now, the fork be held over a glass jar A B (Figure 36) some 1 8 inches deep, and the sound is still very faint Keep the fork in this position, and pour water with the least possible noise into the jar. As the column of air under the fork becomes shorter, the sound becomes louder ; and when the water has reached a certain level, it bursts forth with great power. Continue to pour water into the jar, and the sound becomes weaker and weaker, until it is as faint as at first. Pour the water carefully out, and we reach a point where the sound is reinforced again. SOUND. 59 In this way we find that there is one particular length of the column of\air which causes the fork above it to give Fig. 36. Fig. 37. 384 the loudest possible sound. This reinforcement of sound is called resonance. By trying tuning-forks of different pitch, we find in this way a column of air for each which gives the greatest resonance. These columns are of different lengths, becoming shorter as the forks vibrate faster. Figure 37 shows the rela- tive lengths of jars which give the greatest resonance for tuning-forks vibrating 256, 320, 384, and 512 times in a second. 512 6o SOUND. 58. The Length of the Column of Air which resounds to a vibrating Fork is equal to one fourth the Length of the Wave produced by the Fork. The greater volume of sound when the fork is vibrating over a resonant jar can be due only to the greater amount of motion communicated to the air. When is the fork enabled thus to increase the mo- tion ? We have seen that a fork vibrating 256 times a second produces a sound-wave 4 feet 4 inches long (23). In Fig- ure 38, suppose a prong of the fork to be vibrating between a b V Fig. 38. 20 inches ' the points a and b. In going from a to b, the prong gen- erates half a sound-wave ; and when it reaches b t the fore- most point of the wave will be at c, 2 feet 2 inches from the fork. it will be twice as long for every value. These lines are called the sines of the angles D CP&nd JV C S, and the law of refraction may be thus stated : When light passes from one medium into another, the ratio which the sine of the angle of incidence bears to the sine of the angle of refraction is always the same for the same media. LIGHT. 10 1 It is found, however, that this ratio varies with different media. Of course, when the incident ray is perpendicular to the surface of the new medium, no refraction takes place. 94. Index of Refraction. The ratio between the sines of the angles of incidence and refraction is called the index of refraction. This index varies with the media. For ex- ample, from air to water it is f ; from air to glass ; and so on. Of course, from water to air, it will be ; from glass to air f ; and so on. 95. Total Reflection. When a ray of light passes from a denser to a rarer medium, as from water into air, the angle of refraction is, as we have seen, greater than the angle of incidence. Hence when light passes through water from S to O (Figure 66) there is always a value of the angle of incidence S O B such that the an- ,,. gle of refraction A O R is a right angle. In this case the ray cannot pass from the water into the air. If the incident angle be made any larger, the light is thrown back in the direction of Q. In this case it is said to be totally reflected. This total reflection may be illus- trated by means of a prism whose section is an isosceles right angled triangle. It will be Fig. 67. seen that none of the light (Figure 67) can get through the prism, but it is all reflected in the direction HO. The angle at which light in pass- ing from water to air begins to be totally reflected is 48 35'; from glass to air, 41 48'.* * See Appendix, III. 102 LIGHT. 96. Mirage. In hot climates, especially on the sandy plains of Sahara in Africa, the ground has often the ap- pearance of a tranquil lake, on which are seen reflected houses and trees. This is caused by total reflection. The layers of air near the ground are more heated, and there- fore less dense than those higher up. A ray of light, then, coming from A (Figure 68) is bent round more and more Fig. 68. as it passes down through the successive layers until it reaches the point O, where the angle of incidence becomes such that it is totally reflected, and reaches the eye as if it came from A'. The same will be true of light coming from other parts of the tree, so that the tree will appear inverted, as if reflected in water. This phenomenon is called mirage, and often deludes the thirsty traveller on the desert with the appearance of water which vanishes as he draws near it. Another form of mirage, the reverse of this, is often seen on the water. In this case the layers of air near the water are colder and more dense than those above, so that the rays of light passing upward from an object are bent round more and more, until at last they are totally reflected down- LIGHT. 103 ward to the eye of the observer, who thus sees the object inverted in the air. 97. Some of the Effects of Refraction. Suppose a body to be at L (Figure 69) beneath the surface of water. The rays of light coming from it on reaching p . g the surface are refracted in the directions A C and B D, so that they appear to come from the point L'. Now as we see an ob- ject in the direction in which the light from it reaches the eye, the object L will appear to be at Z', or higher up than it really is. This explains why it is that a stick placed obliquely in the water appears bent, as in Figure 70. Each Fig 70 part of the stick in the water appears to be lifted up a little by refraction. In the same way light is refracted in passing through the air, and since the air is more and more dense as it is nearer the earth, a ray of light is bent more and more as it approaches the earth. Hence we see the sun and the stars before they rise and after they set. It will be evident from Figure 71 why it is that we always see a heav- FJ enly body higher up than it really is. Refraction varies with the condition of the atmosphere. Sometimes at sea it is so great that objects below the horizon, as ships and islands, are lifted up enough to become visible. Occasionally we have this extraordinary effect of refraction combined with mirage, so that a ship which is really below the horizon may be seen suspended in the air with its in- verted image beneath it. 104 LIGHT. Fig. 12. 98. Path of Rays through a Medium with Parallel Faces. When light passes through a medium with parallel faces, the rays leave this medium at the same angle at which they entered it. In Figure 72 let J/7V^be a plate of glass with parallel faces. / is the angle of incidence of the ray S A, and r the angle of refraction : ? is the angle of incidence of the same ray when it meets the air again, and / the angle of refraction. Since the ray in passing into the air is bent away from the perpendicular just as much as it was bent towards it in passing into the glass, the angle r 1 will evidently be equal to the angle i; that is, the ray leaves the glass at the same angle at which it entered it. Its direction, therefore, after leaving it is the same as before entering it. 99. Path of Rays through a Prism. In Figure 73 let A B C be the section of a Fig . 73 . prism. The ray of light O D on passing into the prism is bent towards a perpendicular drawn to the surface at D. On passing out into the air again it is bent away from a perpendicular drawn to the surface at K. We see, then, that a ray of light in passing through a prism is bent twice in the same direction, unless it meets one of the faces perpendicularly. LIGHT. 105 SUMMARY. When light falls on a transparent medium different from ihat in which it is moving, it is partially reflected and par- tially refracted. (90.) The angle of reflection equals the angle of incidence. (91.) The amount of light reflected depends upon the angle of incidence, the polish of the surface, and the nature of the medium. All bodies diffuse light, and it is by means of this diffused light that we see them. Light is also reflected from opaque surfaces. (92.) The ratio of the sine of the angle of incidence to that of the angle of refraction always remains the same for the same medium, but is different for different media. This ratio is called the index of refraction. (93, 94.) On meeting a rarer medium at a certain angle, light is totally reflected. (95.) Mirage and other atmospheric phenomena of the kind are caused by irregular refraction. (96.) On passing through a medium with parallel sides, a ray of light emerges parallel to its original direction. (98.) On passing through a prism, a ray is bent twice in the same direction. (99.) DISPERSION. TOO. The Solar Spectrum. Allow a beam of sunlight, S A (Figure 74) to pass through a small opening into a darkened room, and fall upon the prism P. If the prism be placed at the proper angle, the beam of light is not only bent from its course, but is spread out so as to form a long band of light on the opposite wall. This band is not white, 5* 106 LIGHT. like ordinary sunlight, but made up of the seven colors of the rainbow, violet, indigo, blue, green, yellow, orange, and red. This colored band is called the solar spectrum. Fig. 74- When prisms of different substances are used, the spectra obtained have the same colors and in the same order, but are of different lengths. This spreading out of a beam of light is called dispersion; and the power of any substance to produce this effect is called its dispersive power. We might think that the dis- persive power of a substance would be in proportion to its refractive power, but this is not the case. Thus the refrac- tive power of flint glass is almost the same as that of crown glass, but its dispersive power is nearly double. The liquid known as bisulphide of carbon has great disper- sive power ; hence it is often used for prisms. When a liquid is used in this way, it is enclosed in a hollow glass prism. In order to obtain a spectrum in which the colors are distinctly seen, the opening through which the light enters should be very narrow, and if the refracting angle of the prism is, as usual, 60, the screen on which the spectrum is received must be 5 or 6 yards distant. LIGHT. 107 10 1. Achromatic Prism. By combining a flint-glass prism CDF, (Figure 75), with a crown-glass prism C B F, the dispersive power of the latter p . may be neutralized, without whol- ly neutralizing its refractive pow- er. The reason of this will be evi- dent from the figure. The prism CDF, in order to have the same dispersive power as C B F, needs be only half as thick as the latter ; so that the edges B C and FD are still inclined as though they were sides of the larger prism A B F. Such a combination of prisms forms what is called an achromatic (colorless] prism. 102. The Prismatic Colors are Simple. If all the colors of the spectrum except one be cut off by a screen, and that one be allowed to fall on a second prism, as shown in Figure 76, it will be again refracted, but will not be sepa- Fig. 76. rated into different colors. Hence the colors of the spec- trum are said to be simple. 103. The Prismatic Colors are unequally Refrangible. The position of the colors in the spectrum shows that they are not equally refracted. The red is least, and the violet most refracted. That the colors are unequally refrangible may be shown by the following experiment. If the beam of light S, LIGHT. (Figure 77,) after passing through the horizontal prism A, be allowed to fall on the upright prism J3, it forms the Fig. 77. oblique spectrum v' r', proving that from red to violet the colors are more and more refrangible. 104. The Composition of White Light. These experi- ments with the prism seem to show that white light is not simple, but made up of the seven prismatic colors. This view is confirmed by the fact that white light can be pro- duced by the blending of these seven colors. If the spec- trum produced by one prism be allowed to fall upon a second prism exactly like the first, arranged as shown in Figure 78, the latter brings together again the rays which have been dispersed by the former, and white light is the result. The same may be shown by mixing these colors in the eye. This can be done by painting them in the proper proportions upon a circular disc (Figure 79) and making this disc rotate rapidly, as shown in Figure 80. The impression of each color remains in the eye during a LIGHT. I0 9 complete rotation of the disc, so that the seven are blended into one, and the disc appears white. Fig. 79. Fig. 80. Fig. 81. White light, or something which ordinary eyes cannot distinguish from it, may also be produced by the blending of a part of the prismatic colors. Thus red, yellow, and blue, or red, green, and blue, will form white. This fact has led some to suppose that the solar spectrum is made up of but three simple colors. Brewster chose red, yellow, and blue. He assumed that each one of these colors extended the whole length of the spectrum, as shown in Figure 81. The height of the curve shows the intensity of each color in different parts of the spectrum. On this theory the orange is produced by a mixture of the red and yellow ; the green by a mixture of the yellow and blue ; and so on. 110 LIGHT. But it has been shown by Maxwell and Helmholtz that " the direct mixture of the prismatic yellow and blue, in whatever proportion, can nohow be made to produce green." If, however, we take red, green, and blue as the three pri- mary colors, all the colors of the spectrum can be produced by mixing these in different proportions. The way in Fig 82 which these three col- ors must be distribut- ed through the spec- trum, in order to give the seven prismatic colors, is shown in Figure 82. 105. Complementary Colors. If we suppose the spectrum to be divided into any two parts, and the colors in each part mixed, they will form what are called complementary colors; that is, one will contain what the other needs to make white light. We often call colors complementary when their mixture would approach more or less nearly to white. SUMMARY. In passing through a prism a beam of white light is dis- persed, and forms a spectrum of seven colors. Different substances disperse light differently. Hence two prisms may be combined so as to form an achromatic prism. (100, 101.) Prismatic colors are simple and unequally refrangible. (102, 103.) The blending of the seven prismatic colors produces white light. It is possible to form the solar spectrum out of the three simple colors, red, green, and blue. (104.) Two colors whose mixture will produce white light are said to be complementary. (105.) LIGHT. Ill ABSORPTION. 106. If light be made to pass through a piece of colored glass, and then to fall upon a prism, the spectrum will be found to be wanting in certain colors. If red glass is used, the spectrum will contain little besides red light; if blue or green glass is used, the spectrum will be rich in blue or green, and deficient in other colors. A part of the light, then, is retained in the glass, and is said to be absorbed by it. In this way all colored transparent bodies are found to absorb a portion of the light which falls upon them. 107. The Color of Bodies. Opaque bodies, as well as transparent ones, absorb light. This explains why it is that, when white light is falling upon non-luminous bodies, they do not all appear of the same color. They are really sift- ing the light which they receive, absorbing a part and dif- fusing or transmitting the rest. Their color depends upon the light which they reflect, and this is of course the com- plement of that which they absorb. Thus a body which ab- sorbs all the prismatic colors except red appears red ; one which absorbs all except green appears green ; and so on. A painter does not add color to his canvas, but destroys a part of its color ; that is, he causes it to absorb a part of the white light which falls upon it, and to reflect only the remainder, instead of reflecting it all. His direct action is upon the tint complementary to that which he aims to produce. It sometimes happens that bodies transmit a color differ- ent from that which they reflect, and such bodies appear of a different color according as they are seen by trans- mitted or reflected light. This is the case with gold, which appears yellow by reflected light, and green by transmitted light, as may be seen by holding a piece of gold leaf be- tween the eye and the sunshine. 112 LIGHT. 1 08. The Analysis of Colors. The colors of objects may be analyzed by means of a prism. Take a very nar- row strip of the object, a mere line of colored light, and place it upon a perfectly black ground and in a very strong light. Examine this strip through a prism, whose edge is held parallel with it, and it appears dilated into a spectrum, which has only rays of those colors which combine to form its tint. A cheap and convenient instrument for this analysis may be made by fastening a metal plate, having in it a sharply cut and very narrow slit, to one end of a tube of metal or pasteboard, about an inch square and 12 or 14 inches long, and blackened within. A small prism of colorless flint glass is fixed within the other end parallel with the slit, so that when the tube is directed to a white cloud, the slit shall be seen dilated into a clear prismatic spectrurp The object to be examined must be placed so near the slit as to allow no other rays to enter than come from some part of its surface, and must be strongly illuminated either by direct sunshine or by means of a lens. When analyzed in this way all natural colors are found to be compound. 109. Spectrum Analysis. Let us now analyze more thoroughly the light given out by luminous bodies. We will begin with colored flames. If a piece of platinum wire be dipped in a solution of soda, and held in the colorless flame of an alcohol lamp, or a Bunsen's gas-burner, the flame becomes of an intense yellow. This color is due to the heated vapor of sodium in the flame. If we dip another platinum wire in a solution of lithium, and hold it in the colorless flame, a rich crim- son hue is imparted to the flame. The vapor of copper colors the flame green. Other metals give characteristic colors to the flame. no. The Spectroscope. These colored flames can be LIGHT. best analyzed by means of the spectroscope, shown in Figure 83. The light from the flame is admitted through a narrow slit into the tube B, where it is concentrated by lenses and Fig. 83. thrown upon the prism P. The spectrum formed is ex- amined with the telescope A. When the spectrum of the sodium flame is thus ex- amined, it is found to consist, not of a long strip of colored light, like the solar spectrum, but of a single bright yellow line, as shown at III. in Plate I. When other flames colored by metallic vapors are examined, it is found that their spectra in all cases consist of bright lines separated by dark spaces. In Plate I., II. shows the spectrum of potassium ; IV. the spectrum of ccesium ; and V. that of rubidium. The spectrum of each substance always consists of the same lines in the same relative positions. Hence the spec- H 114 LIGHT. troscope furnishes a ready means of detecting the presence of any substance ; for, even when several substances are mixed, each gives to the spectrum the characteristic lines which cannot be mistaken. This method of detecting a substance is remarkable for its delicacy. Thus, a portion of sodium less than the of a grain gives to the spectrum its yellow line. The compounds of lithium, which were formerly supposed to be contained in only four minerals, have been shown by the spectroscope to be substances of very common occur- rence, being found in minute quantities in almost all spring waters, as well as in tea, tobacco, milk, and blood. We can thus detect 6o ^ 000 of a grain of lithium. A still more striking proof of the value of spectrum analysis is the fact that several new metals have been dis- covered by this means. Among these are ctesium and rubidium, the spectra of which are shown in the plate. in. Gases absorb the Same Kind of Light as they emit when heated to Incandescence. If a piece of lime be held in a flame of burning oxygen and hydrogen,* it becomes white hot, and gives out an intense light. If this light is ex- amined with the spectroscope, its spectrum is seen to be an unbroken strip of colored light, or a continuous spec- trum, as it is called, to distinguish it from the spectrum of a gas, which is made up of bright lines separated by dark spaces. If this lime light is allowed to pass through the yellow sodium flame, and is then examined with the spec- troscope, a dark line is seen to occupy the place of the yellow line of the sodium spectrum. This must be due to the fact that the sodium vapor has absorbed just the kind of light which it gives out, and thus caused that portion of the spectrum to be comparatively dark. In this case the sodium spectrum is said to be reversed. In like manner * See the " Chemistry " of the " Cambridge Physics," 132, 185 LIGHT. 115 the spectra of many other substances have been reversed, each substance in a state of vapor having the power to absorb the same rays which it gives out when heated to in- candescence. 112. Fraunhofer's Lines. When the light of the sun is examined with a spectroscope, it is found that the spectrum is crossed by a great number of dark lines, known as Fraunhofer 1 s tines, from their discoverer. A few of the stronger ones are shown at I. in Plate I. The only satis- factory explanation of these lines is that the white light given out by the solid or liquid mass of the sun is partial- ly absorbed by vapors in his atmosphere. We must then have in the solar spectrum the reversed spectra of the sub- stances which exist in that atmosphere. Strange as it may seem, we have then in the spectroscope a means of analyz- ing the atmosphere of the sun. We have only to find whether the dark lines in the solar spectrum correspond with the bright lines in the spectra of substances known to us. Many such coincidences have been detected, and we are now quite certain that iron, sodium, magnesium, cal- cium, chromium, nickel, barium, copper, zinc, and hydrogen exist as gases in the atmosphere of the sun. Nor is this all. The spectra of the stars all show dark lines. These are for the most part different from the solar lines, and from those of one another. Hence we conclude that the composition of the solar and stellar atmospheres is not the same. Many of the substances known on this earth have been detected in the atmosphere of the stars by Huggins and Miller, to whom we owe this important discovery. The star known as Aldebaran has in its at- mosphere hydrogen, sodium, magnesium, calcium, iron, tel- lurium, antimony, bismuth, and mercury ; while in the at- mosphere of Sirius only sodium, magnesium, and hydro- gen have with certainty been detected. Il6 LIGHT. SUMMARY. Different bodies absorb light of different colors. It is the sifting of the rays of light by absorption which gives bodies their color. (106. 107.) The color of bodies may be analyzed by means of a prism. (108.) Different substances emit light of different colors. (109.) Incandescent gases give dark spectra crossed by bright lines. The presence of any substance in the flame can be de- tected by means of the spectroscope, (no.) By means of the lime or magnesium light, the spectra of the elements may be reversed, since a substance absorbs readily those rays which it can emit, (m.) Solar and stellar spectra are crossed by dark lines, known as Fraunhofer's lines. These are due to absorption. The composition of the atmosphere of the sun and stars may be ascertained by analyzing their light. (112.) INTERFERENCE AND THE UNDULATORY THEORY OF LIGHT. 113.' Colors of Soap-Bubbles* If a soap-bubble be blown in a clear circular saucer, so as to be somewhat more than hemispherical, and then be placed under a glass cover to keep it from gusts of air, the colors which in the blowing had wandered irregularly over its surface will gather into 'regular concentric rings at its top. If the bubble be a thick one, only faint colors will appear at first ; but they will gradually grow more vivid. Each color, however, does not become brighter, but spreads away, and a new and richer one takes its place. In this way the * See Appendix, TV. LIGHT. 1 1 7 rings go on increasing in number and brilliancy, until at length a very clear white spot appears at the top, and is quickly followed by a perfectly black one. Soon after this the bubble bursts. During all this time the bubble has been gradually becoming thinner" by the slow running down of the liquid from the top. The ring-like arrangement of the colors around the thinnest part of the bubble as a centre seems to show that the tint depends upon the thick- ness of the liquid film at the point where the color ap- pears ; a certain tint being developed at a certain thickness and at no other. The order of the colored rings and of the tints in them is always the same, after the black central spot has once formed. None of these tints are pure pris- matic colors. To see them to the best advantage the bub- ble must be illumined by diffused light, not by direct sun- light. If the bubble is illumined by letting the colors of the spectrum fall upon it one by one, when the red light falls upon it the rings will appear all red, separated by black spaces ; when the yellow light falls upon it, they will be yellow with black spaces ; and so on for all the colors. In all cases the rings are more numerous than when the bub- ble is illumined by white light, but the diameter and breadth of the rings vary with the color used, being greatest for the red and least for the violet. This explains the composite colors of the rings when white light is used ; for in this case we have the rings of the seven colors overlapping one another in various ways so as to produce a variety of tints. 114. These Colors do not depend upon the Liquid of which the Bubble is made. What now is the cause of these colored rings? They do not depend on the material of which the bubble is made, for a film of any substance whatever will produce them, if it be thin enough. They are seen in the oily scum upon stagnant water ; in the Il8 LIGHT. gayly painted wings of insects ; and even on polished steel. Bubbles may be blown with a variety of liquids and even of glass, and they all display the same hues in the same order. In fact it requires no medium at all to produce them, but only an interval between two reflecting surfaces. They are seen in a crack which does not extend complete- ly through a thick piece of glass, and in mica when two of its layers are partially separated. It may be said that there is air between the surfaces ; but under the exhausted receiver of an air-pump the rings remain unchanged. 115. These Colors are due to Interference. It is, then, to the interval between the reflecting surfaces that we are to look for the origin of these colors. A part of the light will of course be reflected at each surface, and the rays reflected from both will take very nearly the same direction. When simple or homogeneous light, as it is called, is allowed to fall on the bubble, the colored rings, as we have seen, are separated by dark spaces. At certain distances between the surfaces, then, the rays of light reflected from them destroy each other, and produce darkness ; while at other distances they combine and produce more intense light, Since the rings of the more refrangible colors are narrower, it follows that the distances at which the rays of these col- ors destroy each other are less than for the less refrangible rays. The rays which destroy each other are said to in- terfere, and the colored rings are evidently due to in- terference. 1 1 6. The Undulatory Theory of Light. We have now seen that rays of light are reflected, are refracted, and in- terfere in the ame way as those of sound. It seems prob- able, then, that both light and sound are propagated in the same way. We have seen that sound is propagated by means of waves, and it is therefore probable that light is propagated by waves. We have seen, too, that sounds in- terfere with each other so as to produce silence, when their LIGHT. 119 waves meet in opposite phases (36) ; and from the way in which sounds interfere we should be driven to conclude that sound is propagated by waves, even if we did not know the fact already. Do the rays of light interfere in such a way as to show that light is propagated by waves ? 117. When Light is reflected from the Surface of a Rarer Medium, the Phase of the Wave is Changed. We have seen in the soap-bubble that as the top becomes very thin it ap- pears black, and the blackness grows more intense until the thickness becomes nothing, and the bubble bursts. Just before it bursts, the two surfaces of the film are virtu- ally together, and the rays reflected from them must there- fore start back together ; and it would seem that they should produce light instead of darkness, that is, that their phases should coincide rather than interfere, if light, like sound, is really propagated by waves. This interference, then, seems at first inconsistent with the wave theory of light. The following illustration of Herschel's, however, will show how it is. reconciled with that theory. Imagine a number of ivory balls all of a size placed in a row, in contact with one another, but con- nected only by a rubber cord which runs through them all and is fastened at the centre of each. Let an ivory ball of exactly the same size be driven against the end of the row. According to the law of the collision of elastic bodies, this ball will give up all its motion to the one it strikes, and this to the next, and so on to the end of the row. None of the balls move except the last, but they are all made to press against one another, ar\4 a wave of compression may be said to run along the line. The last ball has nothing to which to give its motio^ and therefore starts off; but it is quickly checked and drawn back by the elasticity of the rubber cord. But at the same time it pulls the next ball forward, and this the next, and so on to the end of the line. In this way a wave of extension runs back along the row. 120 LIGHT. Here then the direct wave changes its phase on being reflected. This is, however, an extreme case, and unlike anything which we find in the transmission of light ; for when it passes from one medium into another there are al- ways particles beyond to which the moving particles can impart their motion. Let us now suppose that there is a second row of smaller elastic balls, near the end of the first, and arranged exactly in the same way ; and that at the end of the first there is a detached ball of the same size as those in the second row. The line of larger balls will represent the condition of the particles of a denser medium in contact with those of a rarer one. Let now an impulse be sent along the row of larger balls, as at first. The last ball of the line drives the detached ball off against the first ball of the second row, and thus sends forward a wave of compression. But the smaller ball will not carry off all the motion of the larger one, which will also ad- vance till it is checked by the rubber cord. While this ball is drawn back it draws forward the ball behind it, and this the next, and so on. In this case, part of the wave is reflected, and in an opposite phase from the direct wave. If the balls in the first row are smaller than the detached ball and those in the second row, they will represent the condition of the particles of a rarer medium in contact with those of a denser one. If an impulse be sent along the first line, as before, the detached ball will not only move forward, but also cause the ball behind it to rebound. Here the reflected wave has the same phase as the direct one. When, therefore, a wave is reflected from a rarer me- dium, it changes its phase ; but not when reflected from a denser medium. We see, then, that the fact that the top of the bubble is black is not an objection to the theory that light is propa- LIGHT. I 2 I gated by waves ; for at the outer surface of the bubble the rays of light are reflected from a denser medium, while at the inner surface they are reflected from a rarer medium, and they should therefore start back in opposite phases when the surfaces are together. 1 1 8. When Homogeneous Light is used, the Distance be- tween the Reflecting Surfaces at the second, third, and fourth Dark Rings if twice, thrice, and four times that at the first, and so on. If the dark rings are due to the meeting of waves of opposite phases, the distance between the reflect- ing surfaces at the second ring should, when homogeneous light is used, be twice as great as at the first ; at the third, thrice as great as at the first ; and so on. For at the first ring the light reflected from the inner surface must travel over a distance of a wave-length more than that reflected from the outer surface, in order that the waves may meet in the opposite phase ; and at the second ring it must travel over the length of two waves more ; at the third ring, over the length of three waves more ; and so on. Is this the case ? The thickness of the soap-bubble at the different points cannot be directly measured ; but we have seen that the rings can be obtained by other means. The following arrangement enables us readily to measure the distance between the reflecting surfaces. Upon a perfectly flat and smooth plate of glass is placed another piece equally smooth, but with its under surface slightly curved, as shown in Figure 84. This curved sur- face should be a portion of the r r j- Fig. 84. surface of a sphere whose radius' n nr Cn fppf Whfn ^ ^*- 1*-'V^L. li^ll this curved glass is pressed firm- ly down upon the plate, the centre appears black, and is surrounded by colored rings (Figure 85), as in the soap- bubble. Suppose that homogeneous light of some color, 6 122 LIGHT. Fig. 85. as red, be allowed to fall perpendicularly upon the upper glass. Dark rings will be formed at i, 2, 3, and 4 (Figure 86), and the diameters i i, 2 2, etc. of these rings can be easily meas- ured. They are always found to be in the proportion of i, 1.414. 1.732, 2.000, and so on. Now these numbers are the square roots of the numbers i, -2, 3, 4, and so on ; and we know from the form of the sphere that the distances i , 2 c, 3 d, 4 ^, etc. are to one another as the -squares of the chords i i, 2 2, 3 3, 4 4, etc. Hence the distance between the reflecting surfaces at the second dark ring is twice that at the first, and so on. 119. Light is prop- agated by means of the Ether. We have now seen that light interferes in such a way as to show that it is prop- agated by waves. If, however, a lighted lamp be placed behind the receiver of an air-pump, and the air be exhaust- ed, the flame still shines through the receiver, showing that light is not propagated by means of the air, as is the case with sound. We know also that the heavenly bodies are far beyond the limits of the earth's atmosphere, which ex- tends to a height of only about 50 miles. We must therefore conclude that all space is filled with an elastic medium through which the light-waves are prop- agated as the sound-waves are sent through the air. LIGHT. I2 3 This medium is called the ether, and it fills not only the spaces between the heavenly bodies, but also those be- tween the molecules of all substances. It cannot be ex- hausted from a receiver, since it readily passes through the glass. 120. The Length of the Light- Wave, We have seen that the light reflected from /"(Figure 86) must travel a wave- length farther than that reflected from i, in order that the waves reflected from these points may meet in oppo- site phases, and so give a dark ring. Now the wave re- flected from f must evidently travel over the space if twice : hence i/"must be J the length of a luminous wave, and we have seen that this is J of 4 /. Now we can easily find the length of 4 /. 4 m is half the diameter of the fourth bright ring, and can be found by measurement. We know the length of the radius 4 C, and 4 m C is a right-an- gled triangle. In this triangle we know the length of the hypothenuse 4 C, and of the side 4 m. Hence we can find the length of C m. The radius C a Cm = am^=^i. In this way the lengths of the waves of light of the differ- ent colors have been found. The following table shows the lengths of these waves, and also the number that enter the eye in a second : Colors Length of waves in parts of an inch. Number of waves in an inch. Number of waves in a second. Extreme Red .0000266 37,640 458,OOO,OOO,OOO,OOO Red Orange .0000256 .0000240 39,l8o 4I,6lO 477,000,000,000.000 506,000,000,000,000 Yellow .OOOO227 44,000 535,OOO,OOO,OOO,OOO Green .0000211 47,460 577, ooo, ooo, ooo, ooo Blue .0000196 51,110 622,000,000,000,000 Indigo .OOOOI85 54o7o 658,000,000,000,000 Violet .0000174 57.49 699,000,000,000,000 Extreme Violet .0000167 59>75 727,000,000,000,000 According to Eisenlohr the length of the waves in the ex- 1 24 LIGHT. treme red ray is just double the length of the waves in the invisible rays beyond the violet. The whole range of rays, then, extends only over what is equivalent to a single octave in music. 121. The Origin of Light. We have now seen that light, as well as sound, is propagated by waves in an elas- tic medium, and that sound originates in vibrations of the particles of the sounding body. It is very probable, then, that light also has its origin in the vibrations of the par- ticles of a luminous body. In ordinary combustion, which is the most familiar source of light, the atoms of the oxygen in the air are rushing into combination with the atoms of the burning body ; and the collision of these atoms will be very likely to set them vibrating. These vibrations will be communicated to the atoms of the surrounding ether, and by these transmitted to the eye. The color of the light depends on the rapidity of the vibrations. The particles of certain substances seem to be capable of vibrating in all periods, and thus of producing white light ; while those of other substances seem to be capable of vibrating only in particular periods, and therefore they produce light of different colors. It is seldom, however, that the vibrations of the molecules are limited to one period, and therefore that a luminous body gives out homo- genous light. We can now understand how it is that we can detect certain substances by the light they give. Their particles can vibrate only in certain ways, and they of course cause the particles of ether nearest them to vibrate in the same way. The vibrations are sent on unchanged from particle to particle of the ether, and are ready at any point to reveal the nature of the substance in which they origi- nated. The vibrations are so minute that it would seem impossible to find out their character, but the spectroscope enables us to do this with ease and accuracy. When a number of strings of different lengths and ten- LIGHT. 125 sion are stretched in the air, as in the ^olian harp, they absorb all the vibrations accordant to their own which fall upon them, while they allow all the discordant ones to pass on. In much the same way we must imagine the molecules of a body suspended in the ether, from which they absorb all accordant vibrations while they transmit all discordant ones. Transparency is then synonymous with discordance, and opacity with accordance. This explains the fact that dif- ferent substances absorb light of different colors, and also the fact that incandescent gases give out light of the same color as that which they absorb. 122. Diffraction Fringes. Take a glass lens whose focal length is about an inch, and let a beam of sunlight fall upon it in a darkened room. The light will be con- centrated into a very small image of the sun about an inch from the lens, and will then diverge from it in a luminous cone, and may be received upon a screen. Place any small opaque body within this cone of light, so that it may cast a shadow upon the screen. This shadow, instead of being sharply denned, as we should expect (85), is somewhat larger than it should be, and is surrounded by three colored fringes, the outer one being extremely faint. If homoge- neous light is used, instead of the fringes we get bright rings separated by dark spaces, the breadth of the rings varying with the color of the light. When white light is used, these different sets of colored rings blend so as to produce the fringes. If the opaque body is long and very narrow, as a hair or a very thin strip of card, besides the colored fringes al- ready described, others are seen within the shadow, paral- lel to its length, and similarly arranged on the two sides of a central white line. When light is transmitted through a very narrow slit, the fringes become even more curious and complicated. 126 LIGHT. Fig. 87. To see these diffraction fringes to the best advantage, a magnifying glass should be used, putting the eye in place of the screen.* 123. Diffraction Fringes are produced by Interference. Diffraction fringes are fully explained by the interference of light, according to the undulatory theory. Suppose a b (Figure 87) to be a portion of a wave of light. Every particle of ether along this curve is a centre of a set of waves, which tend to run not only forward but sideways as well. But as each particle Fig 88 sends equal waves in opposite directions at the same instant, the lateral waves destroy one another ; while the advancing portions unite to form one con- tinuous wave. When, dowever, the wave rtieets an opaque body /Figure 88), the par- dele of ether nearest the edge of the opaque body, since there are vibrating particles on only one side of it, can start a new set of waves. These waves meet the original waves in opposite phases at the points marked by the little circles ; in the same phases at the points marked by the crosses. They of course interfere in the former * See Appendix, V. LIGHT case and coincide in the latter, and thus give rise to the colored fringes. If the opaque body is narrow, as shown in Figure 89, the waves which start up at each edge of it interfere and coincide behind it, so as to produce the interior fringes and the central bright line. That these interior fringes are due to the interference of the waves which thus bend round the edges of the opaque body is clearly shown by their disappearance when the light is cut off from one edge by a screen. SUMMARY. Soap-bubbles and other thin films, when exposed to light, exhibit colored rings. (113.) These rings are always seen when light is reflected from two surfaces separated by a very small interval. (114.) They are caused by interference. (115.) Light, like sound, is propagated by means of waves. (116.) When light is reflected from the surface of a rarer me- dium, the phase of its wave is changed. (117.) Light is propagated by means of the ether, (i 19.) LIGHT. The length of the luminous waves can be found by means of interference rings. (120.) Light has its origin in the vibrations of the molecules of a luminous body. The molecules of a body are usually capable of vibrating in several periods. Hence a luminous body seldom gives out homogeneous light. A body absorbs such vibrations as are accordant with those of its own molecules, and reflects or transmits such as are discordant. (121.) When small bodies are seen in divergent light, they appear surrounded by colored ' fringes, called diffraction fringes. (122.) These fringes are caused by interference. (123.) DOUBLE REFRACTION AND POLARIZATION. 124. Uniaxial and Biaxial Crystals. We have now seen that a beam of ordinary light is an assemblage of minute vibrations of different periods, and we have studied somewhat the effect of a transparent uncrystalline body on such a beam. We will next study the effect of transparent crystals on the same. We will select for this purpose a crystal of Iceland spar (crystallized carbonate of lime). Such a crystal is shown in Figure 90. A crystal of this Fig shape is called a rhomb. It has six faces, which are equal par- allelograms. These parallelo- grams are so arranged that three of them have one of their ob- tuse angles at a ; and the other three, one of their obtuse an- gles at b. The parts of the crystal are therefore arranged symmetrically about the line a b, which is called the axis of the crystal. LIGHT. 129 If now a ray of light be allowed to fall on one face of this crystal in a darkened room, it will be divided into two rays. One of these rays is found to conform to the law of ordinary refraction, and is therefore called the ordinary ray. The other ray does not lie in the same plane as the incident and the ordinary rays, and does not conform to the law of sines (93). It is therefore called the extraordi- nary ray. By cutting parallel plates from a rhomb of Ice- land spar in various directions, it is found that, when the plates are cut perpendicularly to the axis of the crystal, they will allow a ray of ordinary light to pass through them perpendicularly without dividing it into two parts ; but this is true of plates cut in no other direction. In other words, a ray of light which passes through a rhomb of Iceland spar parallel to its axis is not doubly refracted ; while every ray which passes through it in a different direction is thus refracted. For this reason the axis of the crystal is also called its optical axis. The ordinary and extraordi- nary rays separate most widely when they pass through the crystal perpendicularly to its optical axis. In many crystals, as saltpetre and mica, there are two directions in which light may pass through them without being doubly refracted. Such crystals have two optical axes and are called biaxial crystals, to distinguish them from uniaxial crystals, which have only one such axis. When a ray of light passes through a biaxial crystal in such a direction as to be doubly refracted, both rays are usually extraordinary rays. 125. The Double-refracting Prism. Since the opposite faces of a rhomb of Iceland spar are parallel, the ordinary and extraordinary rays emerge from the crystal parallel to the incident ray and to each other, but quite near together. If, however, the crystal be cut into the form of a prism in such a way that its refracting edge may be parallel to the optical axis, the ordinary and extraordinary rays, after leav- 130 LIGHT. ing the prism, will diverge, so that we may easily insulate either and examine it separately. Such a prism will of course disperse both rays so as to produce spectra, but it may be rendered sufficiently achromatic by combining with it a second prism of glass, whose dispersive power is different from that of the crystal. This prism is usually mounted as shown in Fig- ure 91. 126. The Ordinary and Extraordinary Rays are both Polarized. If a beam of ordinary light be allowed to fall on a double-refracting prism, and the extraordinary ray be cut off by a screen, and the ordinary ray be allowed to fall on a second similar prism whose refracting edge is held parallel to that of the first, it will be refracted singly and ordinarily. If the refracting edge of the second prism be held perpendicular to that of the first, the ray will be re- fracted singly but extraordinarily. In every intermediate position, it will be doubly refracted, more of the light pass- ing into the ordinary or the extraordinary ray according to the inclination of the edges of the two prisms. At an incli- nation of 45, the light is equally divided between the two ; in passing from 45 to 90, more and more of the light passes into the extraordinary ray; from 45 to o, more and more into the ordinary ray. If the ordinary ray be cut off, and the extraordinary ray be allowed to fall on the second prism, it will be refracted singly and extraordinarily when the edges of the prisms are parallel ; singly and ordinarily when the edges are perpendicular ; doubly in every other position. If the ordinary ray be allowed to fall upon a flat plate of tourmaline whose faces are cut parallel to the optical axis, it will be found, when the plate is held in a certain position, that the ray is wholly absorbed ; but when the plate is turned round from this position, a part of the LIGHT. 131 ray begins to be transmitted ; and when it has been turned through 90, the whole ray is transmitted. If the extraordinary ray be allowed to fall on the tour- maline, it will be wholly transmitted where the ordinary ray was wholly absorbed, and absorbed where that was transmitted. If the ordinary ray be allowed to fall on a smooth plate of glass at an angle of incidence of 56^, it is found that, when the plate is held in a certain position with reference to the ray, it will be wholly reflected. On turning the glass round, keeping the angle of incidence unchanged, the ray begins to be partly transmitted, and when the glass has been turned through 90 it is wholly transmitted. If the extraordinary ray be used, it will be transmitted where the ordinary ray is reflected, and reflected where that is transmitted. The above experiments show that both the ordinary and extraordinary rays are different on different sides. When the prism of Iceland spar was turned round through 90, the ray which had been at first refracted ordinarily was refracted extraordinarily. When the tourmaline was turned round through 90, the ray which had been absorbed was transmitted. . When the glass plate was turned round through 90, the ray which had been reflected was trans- mitted. Both rays, then, have acquired sides, so to speak ; and the corresponding sides of the two rays are at right angles to each other. In other words, the extraordinary ray is like the ordinary ray turned round through 90. Light which has thus acquired sides is said to be polar- ized. The ordinary ray is said to be polarized in a plane parallel to the optical axis of the crystal ; and the extraor- dinary ray in a plane at right angles to that axis. 127. The Explanation of Polarization and Double Refrac- tion. We have now seen that both light and sound are I 3 2 LIGHT. propagated by vibrations, and that a ray of light when po- larized has acquired sides. In a sound-wave, the particles are vibrating to and fro in the direction in which the wave is advancing, and it is therefore difficult to imagine how a ray of sound can have sides. We are therefore driven to conclude that the ethereal particles vibrate in a direction transverse, or at right angles, to the direction in which the wave is moving. How such vibrations would make the wave different on different sides will be readily seen from the following illustration. If a b (Figure 92) be a rope fastened at a and held by the hand at b. and the hand Fig. 92. be moved up and down, waves will run along the cord in the direction of its length. The particles of the cord will vibrate up and down, or transversely to this direction of the waves. The cord thus vibrating rep- resents a ray of light in which the vibrations are trans- verse, and it will be seen at a glance that such a ray will be different at the right and the left from what it is above and below, or, in other words, that, like polarized light, it has sides. If the hand be moved to and fro horizontally, the sides will be above and below rather than at the right and the left, as at first. If the cord in the first case be taken to represent an ordinary ray, it will in the second case repre- sent an extraordinary ray. If the hand be moved rapidly to and fro, first up and down, then obliquely, then right and left, and so on around, the particles of the cord will be made to vibrate in these different directions in rapid succession. If the particles of the ether are vibrating in the same way, it is evident that the ray can have no sides, since it would be alike above and below, to the right and to the left. It is LIGHT. 133 possible, then, even with transverse vibrations, to have a ray of light without sides, as is the case with ordinary light. We conclude, then, that light is propagated by trans- verse vibrations ; and that in a ray of ordinary light these vibrations take place in every plane. On passing through certain crystals, as Iceland spar, these vibrations are sifted and arranged in two sets ; the vibrations in one set being in one plane, and those in the other set being in a plane at right angles to this. One of these sets is retarded more than the other in passing through the crystal, and is therefore bent more from its course ; and this is generally the ordinary ray. The extraordinary ray also passes through the crystal more readily in some directions than in others, and hence it is usually refracted, even when the incident ray falls perpendicularly upon the crystal ; and it seldom lies in the same plane with the incident and ordinarily refracted rays. 128. Action of Tourmaline on Ordinary Light. If a ray of ordinary light be allowed to fall upon a flat plate of tourmaline, like that described above, and the transmitted light be allowed to fall on a second similar plate, it will be wholly transmitted when the plates are parallel, and wholly absorbed when they are at right angles ; while in inter- mediate positions it will be partly transmitted and partly absorbed. If the light which has been transmitted through the first plate be received upon a plate of glass at an angle of incidence of 56^, it will be wholly reflected, in a certain position of the glass, and wholly transmitted when the glass has been turned round through 90. The ray is reflected and transmitted in the same manner as the ex- traordinary ray obtained by refraction in a crystal of Ice- land spar. The tourmaline, then, not only impedes one set of vibra- 134 LIGHT. tions more than the other, but wholly absorbs those which are parallel to its optical axis, while it allows those at right angles to this axis to pass readily. 129. Light Polarized by Reflection and Refraction. If a ray of ordinary light A C ( Figure 93) fall upon a plate of glass PQ at an angle of incidence of 56^, a small part CB will be reflected, and the remainder C D transmitted. On exami- nation- the reflected por- tion will be found to be wholly polarized in the plane of reflection ; and the refracted portion will be par- tially polarized in a plane at right angles to this ; the refracted beam containing just as much polarized light as the reflected one. At any other angle of incidence the reflected portion is only partially polarized. When the reflected ray is wholly polarized, as above, its direction is always perpendicular to the refracted ray. Light is wholly polarized by reflection from other sub- stances, as water, diamond, and the like ; but the angle at which complete polarization takes place, or the polarizing angle, as it is called, is different in different substances. For water, the polarizing angle is 53 n'; for diamond, 68 6' ; but in every case the reflected ray is perpendicular to the refracted one. When light falls upon glass at the polarizing angle, the reflected portion is, as we have seen, wholly polarized; but the reflected portion is only about ^ that of the trans- mitted, and consequently has but feeble intensity. If, how- ever, several plates of glass are laid one upon another, as in Figure 94, more and more of the light will be polarized on reflection from each surface. In this way, if plates enough are used, the ray will be divided into two nearly LIGHT. 135 equal portions, each wholly polarized in planes at right angles to each other. A frame containing five or six squares of good win- Fig dow glass, laid one up- on another and backed with a piece of black velvet, is one of the cheapest and best in- struments for getting polarized light 130. Polarizer and Analyzer. Any instrument used to polarize light is called a polarizer ; and any instrument used to examine polarized light is called an analyzer. Thus a tourmaline plate, when used to polarize light, is a polarizer ; but when used to examine polarized light, it is an analyzer. 131. Nicofs Prism. NicoFs prism is one of the most valuable means of polarizing light, for it is perfectly color- less, polarizes light completely, and, like tourmaline, allows only one beam to pass. It is made from a rhomb of Ice- Fig. 95. land spar, about an inch in height, and a third of an inch in breadth. The rhomb is first bisected in the plane which passes through the obtuse angles, as shown in Figure 95. The two halves are then joined together again with Canada balsam. The principle of Nicol's prism is this : the refractive index of Canada balsam (1.549) is less than the ordi- nary index of Iceland spar (1.654), but greater than its extraordinary index (1.483). Hence, when a luminous ray S C (Figure 96) enters the prism, the ordinary ray undergoes total reflection at the surface of the Canada balsam a , and takes the direction C d O, and thus is i 3 6 LIGHT. Fig. 96. carried out of the prism ; while the extraordinary ray Ce emerges alone. This prism can, like tourmaline, be used either as a polarizer or an analyzer. It is better than tourmaline, since the latter is always colored. 132. Interference of Polar- ized Light. Two rays are said to be similarly polar- ized when they are polarized in the same plane, and op- positely polarized when polarized in planes at right angles to each other. If now in polarized light the particles all vibrate in the plane of polarization, it will at once be seen that only similarly polarized rays can interfere so as to destroy each other ; for it will be remembered that, where waves interfere, the particles are compelled to remain at rest by being urged by equal forces to move in opposite directions. This of course cannot take place when par- ticles are moving to and fro in planes at right angles to each other, but only when they are moving to and fro in the same plane. Cut two parallel slits very near each other in an opaque screen, place it before a brilliant point of light, examine it with a magnifying glass, and interference fringes will be seen. Cover now both slits with exactly similar plates of tourmaline. When the plates are parallel, the rays which they transmit are similarly polarized ; when they are at right angles to each other, the transmitted rays are oppo- sitely polarized. In the first case the fringes are distinctly seen, but they wholly disappear in the second. We thus see that experiment and theory agree with respect to the interference of polarized light. 133. Circular and Elliptical Polarization. Although vibrations cannot destroy each other unless they are per- formed in the same plane, it does not follow that they LIGHT. 137 cannot disturb each other at all. When a boat is rowed against a stream with a force just equal to that of the current, it remains at rest. When, however, it is rowed across the stream, it does not remain at rest, although it does not take the same course it would were there no cur- rent. In this case the boat would move in a straight line, and in a direction diagonal to that of the current and that in which the boat is rowed. Again, when a ball is thrown horizontally, it does not move in a straight line, as it would were no other force acting upon it, but is compelled by gravity to move in a curved path. So, too, when two rays of light whose vibrations are performed in different planes meet, the resulting vibrations are sometimes in a direction diagonal to those of the components ; and some- times, instead of moving to and fro in straight lines, the particles are made to describe curved paths. When they are made to move in circles, the light is said to be cir- cularly polarized, and when they move in ellipses, it is said to be elliptically polarized. When a ray of polarized light is reflected from a pol- ished surface in a different plane from that in which it is polarized, it becomes elliptically polarized ; when it is reflected from a metallic surface, this ellipticity becomes very considerable. When such a ray is totally reflected, it may become circularly polarized. 134. Rotatory Polarization. When a ray of polarized light is transmitted along the optical axis of quartz and a few other crystals, and through certain liquids, its plane of polarization is twisted round more or less, according to the thickness of the medium traversed. This is called rotatory polarization. Some substances turn the ray round to the right, and some to the left, but the same substance always turns it in the same direction. The amount of twisting of the ray is different for each of the prismatic colors. 138 LIGHT. Light polarized in this way appears to the unaided eye like ordinary light. When, however, it is analyzed by Nicol's prism or a tourmaline plate, the light appears colored, the tint varying with the thickness of the medium traversed by the ray. For the same thickness of the me- dium, the tints change as the analyzer is turned round the ray. When the plane of polarization has been rotated to the right, we get a certain succession of tints on turning the analyzer to the right. When the plane has been rotated to the left, we get the same succession of tints on turning the analyzer to the left. These tints therefore enable us to detect this kind of polarized light, and to determine whether the plane has been rotated to the right or to the left. A solution of sugar rotates the plane of polarization to the left, and the amount of sugar in a solution can be ascertained by passing a ray of polarized light through it, and noticing the tints which it gives upon analysis. An instrument used for this purpose is called a saccharometef (sugar-measurer. ) The production of the tints when this kind of polarized light is analyzed is easily explained. Suppose a tourmaline plate is used as the' analyzer. It will be remembered that the amount of polarized light absorbed by such a plate varies with the plane of polarization. Now, as the plane of each prismatic color is rotated a different amount, it follows that the colors will be absorbed in different proportions by the tourmaline, and the transmitted ray of light cannot therefore be white, but must be of the color complementary to that absorbed. As the plate is turned round, the tints will change, since the pro- portion in which the different colors are absorbed will change. When a Nicol's prism is used as an analyzer, the differ- ent tints are due to the fact that only one of the rays is LIGHT. 139 transmitted, and that the amount of light which passes into the ordinary and extraordinary ray differs with the angle of polarization and the position of the prism with reference to the ray. 135. Colors exhibited by Crystalline Plates on Exposure to Polarized Light. If a crystalline plate cut from a uni- axial crystal perpendicular to the optical axis be held be- tween the eye and a source of polarized light, nothing is seen which would lead to the suspicion that the plate is anything more than an ordinary piece of glass. If, how- ever, the light which has passed through the plate be ana- lyzed before it enters the eye, a series of brilliantly colored rings will appear. These rings change their color and their brilliancy as the analyzer is turned round. When the analyzer is in one position, the rings are crossed by two white bars at right angles to each other (Figure 97) ; and when the analyzer has been turned through 90, these white bars are replaced by black ones (Figure 98), Fig. 97. Fig. 98. while the colors of the rings are changed to their com- plementary ones. When the plates are properly cut from biaxial crystals, two sets of rings and bars are seen, as shown in Figures 99, 100, and 101. These rings are due to the interference of polarized rays. Their mode of formation, and the reason that 140 LIGHT. they appear only when the analyzer is used, will be evi- dent on referring to Figures 102 and 103. Every ray of Fig. og. Fig. 100. Fig. lox. polarized light diverging from P is separated, on passing through the crystalline plate C, into an ordinary and an Fig. 102. Fig. 103. extraordinary ray. The only rays which would come to- gether so that they could interfere, as seen in Fig- ure 102, are the ordinary ray of one set and the ex traordinary ray of the next, as o e 1 and o' e". These rays are unequally retard- ed in passing through the plate, and would therefore be in a LIGHT. 141 condition to interfere were they not oppositely polarized. When, however, these rays fall on the analyzer A, each is again divided into an ordinary and an extraordinary ray. Of these rays two are suppressed, while two, polarized in the same plane, are allowed to pass on, and in doing so interfere and produce the colored rings. 136. Other Phenomena of Polarization. Transparent substances, like glass, when their particles are subjected to unequal strain, have the same effect upon polarized light as crystalline plates. If a ray of polarized light be allowed to pass through a plate of well-annealed glass, and then be examined with the analyzer, no colored rings appear. Rings, however, appear as soon as any strain is brought to bear upon the glass either by pressure or by the unequal heating of its parts. When unannealed glass is used, the rings are very brilliant, and have different forms accord- Fig. 104. Fig. 105. Fig. 106. Fig. 107. Fig. 108. Fig. 109. ing to the way in which the glass is cut, as shown in Figures 104-109. 142 LIGHT. Again, place a piece of borax glass within a helix of copper wire, and allow a ray of polarized light to pass through it. The ray is unchanged; but as soon as the electric current is sent through the helix, the plane of polarization is twisted round ; showing that the electric current changes the condition of the glass, as it would change that of iron under the same circumstances. The effect of the electric current upon the glass is however shown in nothing else than its action upon polarized light. In polarized light we have a most delicate means of ex- amining the molecular condition of a transparent body, since it reveals the slightest change in this condition, and also tells us whether or not the substance is crystalline in structure. 137. The Tourmaline Pincette. The colors exhibited by polarized light are exceedingly beautiful. The simplest and most convenient apparatus for showing these colors is given in Figure in, and is called the tourmaline pincette. It consists of two tourmaline plates cut parallel to the axis, mounted as shown in the figure. The plates are so ar- ranged that they can be turned round and inclined to each Fig. no. Fig. in. M other at any angle. The plate to be examined is fastened to the centre of a cork disc M (Figure no), and then placed between the tourmalines. The pincette is then held before the eye in diffused daylight. The tourmaline farthest from the eye acts as a polarizer, and the other as an analyzer. LIGHT. 143 SUMMARY. When a ray of light passes through a crystal of Iceland spar it is usually doubly refracted, one of the refracted rays being called the ordinary, and the other the extraordinary ray. When a doubly refracting crystal converts both portions into extraordinary rays, it is called a biaxial crystal. (124.) The ordinary and extraordinary rays can be separated by a doubly refracting prism. (125.) Both the doubly refracted rays have acquired sides, and are said to be polarized. They are polarized in planes at right angles to each other. (126.) Polarization shows that light is propagated by transverse vibrations ; and that in ordinary light these vibrations are executed in every plane, while in polarized light they are executed in only one plane. (127.) Tourmaline absorbs one of the polarized rays. (128.) Light may be polarized by reflection, and by single re- fraction. (129.) The polariscope consists of a polarizer and an analyzer. (130.) Nicol's prism is constructed so as to shut out one of the polarized rays. (131.) Polarized rays can interfere so as to destroy each other only when they are polarized in the same plane ; but they may interfere so as to produce circular, elliptical, and rotatory polarization when they are polarized in different planes. (132-134.) When crystalline plates are examined in polarized light by means of an analyzer, they exhibit interference rays. Polarized light affords an excellent means of examining the molecular condition of bodies. (136.) 144 LIGHT. THE RAINBOW. 138. The Appearance of the Rainbow. The rainbow, in its most perfect form, consists of two colored arches pro- jected upon falling rain upon which the sun is shining from the opposite quarter of the heavens. The lower or inner arch is called the primary bow ; the upper or outer, the secondary bow. Each contains all the colors of the spectrum, but the order of the colors in one is the reverse of that in the other. Red is outermost in the primary bow, and innermost in the secondary. The primary bow is the narrower and brighter of the two, and when it is of unusual brightness narrow red arches are seen just within it, called supernumerary bows. These are sometimes three or four in number, but they can be traced only a short distance. The common centre of the bows is in a line drawn from the sun through the eye of the observer. 139. The Cause of the Rainbow. The rainbow is pro- duced by the refraction and reflection of the sunlight with- in the rain-drops. Its colors are due partially to the dispersion, and partially to the interference of the light thus refracted and reflected. Let the circle in Figure 112 LIGHT. 145 be a drop of rain. A ray of sunlight S A which passes through the centre of the drop will not be refracted, since it meets the surface of the drop perpendicularly ; and the portion of it reflected at n will be thrown directly back. As we pass from A to a the rays become refracted more and more, since they meet the surface of the drop more and more obliquely, and, on being reflected from the inner surface of the drop, emerge in directions differing more and more from A S. The ray s a takes the direction abed; the ray s B, the direction Bgep. As we pass beyond B the rays are refracted so much that they begin to fall below g, and continue to fall farther and farther below it until we come to C, where the rays begin to pass by the drop. Hence all the light which falls upon the drop between A and C is refracted upon the inner surface between g and n. The light which falls upon the drop for a considerable distance each side of B is refracted very nearly to g, and, on being reflected, emerges from the drop very nearly in the direction ep; while the rays falling upon the drop farther from B are, on emerging from the drop, scattered over the space between e and A. Hence the light which emerges from the drop after refraction and re- flection is much more intense in the direction e p than elsewhere ; and it is only here that it is intense enough to affect the eye at any distance. But the light which falls upon the drop a little below B has to traverse a slightly different distance in passing through the drop than that which falls upon it a little above B. Hence these portions of light are unequally re- tarded in passing through the drop, and therefore emerge from it with their waves in somewhat different phases, so that they are in a condition to interfere. Since the differ- ent-colored rays are differently refracted in passing through the drop, the direction ep in which the light emerges with the greatest intensity is not the same for the different 7 J 146 LIGHT. colors. For red light the direction ep differs from that of A S, or of the sun's rays, by an angle of about 42 ; while for violet light these directions differ by an angle of about 40. For the other colors the difference of direction is intermediate between these two. As the emerging rays of each of the colors are in a con- dition to interfere, they will of course give rise to colored bands separated by dark spaces. Let us consider the first bright band of each color. Suppose a person is looking at rain-drops illumined by the sun when near the horizon. Wherever he can direct his eye so that a line drawn from it to a rain-drop shall make an angle of 42 with a line drawn from the same drop to the sun, as at r in Figure 1 13, Fig. 113. he will see a band of red light ; and since the drops are spread out over all the space before him, and since the sun's rays are all parallel, this band will evidently be LIGHT. 147 continuous, and will have the form of an arc of a circle. The centre of this arc will lie in a line drawn from the sun through the eye of the observer, and its radius will be 42. Whenever he can see a drop, as at v, such that a line drawn from his eye to it shall make an angle of 40 with a line drawn from the drop to the sun, he will see a band of violet light. This band also will have the form of an arc of a circle whose radius is 40, and whose cen- tre is the same as that of the red arc. Between these two bands will be seen the bands of the other prismatic colors. The first band of each of the other prismatic colors is situated between the first and second bright bands of the red light ; while the second band of each of these colors falls outside of the first violet band. This is the reason of the purity of the colors of the rainbow. The second band of each of the colors is much feebler than the first, seldom bright enough to be visible. When bright enough to be visible, they form the supernumerary bows/^. The outer bow is caused by the rays which meet the eye after being twice reflected within the rain-drop, as seen at / and if. It is owing to this double reflection that the colors are feebler than, and in the reverse order of those in the primary bow, where the light is reflected but once. SUMMARY. The rainbow is seen opposite the sun. It contains all the colors of the spectrum, the red being outermost in the primary bow and innermost in the sec- ondary. (138.) The rainbow is produced by the refraction and reflection of light within the rain-drop. The colors of the bow are due partly to dispersion, and partly to interference. (139.) i 4 8 LIGHT. OPTICAL INSTRUMENTS. LENSES. 140. Forms of Lenses. Lenses are pieces of glass, or other transparent substance, bounded on one or both sides by a curved surface. The forms of lenses used in optical instruments are shown in Figure 114. A is bounded by Fig. 114. ABC D E F two spherical surfaces, and is called a double-convex lens. B has a spherical surface on one side, and a plane surface on the other, and is called a plano-convex lens. C has a convex surface on one side, and a slightly concave surface on the other, and is called a meniscus, from a Greek word meaning a crescent. D has two concave surfaces, and is called a double-concave lens. E has a concave and a plane surface, and is called a plano-concave lens. F has a con- cave surface on one side and a slightly convex surface on the other, and is called a concavo-convex lens. Allow a beam of sunlight to fall upon a double-convex lens in a darkened room. On leaving the lens, the rays will converge to a point, called the focus (the Latin word for fireplace], since the heat as well as the light is concen- trated there. This action of the lens upon the light will be understood from Figure 115. It will be seen that the section of the lens is like that of two prisms placed back to back ; and it will be remembered that a ray of light, in passing through a prism, is bent twice in the same direc- LIGHT. 149 tion. The rays falling upon the upper part of the lens will be bent downward, and those falling on the lower 115. part will be bent upward, and they will all meet at F. If a beam of sunlight be allowed to fall on a plano-con- vex lens or a meniscus, the rays will also be converged to a focus. If, however, we use any one of the concave lenses, it will be found that the rays of light, instead of converging, are made Flg- II6 ' to diverge, on leaving the lens. The reason of this divergence will be evident from Figure 1 1 6. Since the convex lenses all cause parallel rays to converge, they are called convcrging\&bS& ; while the concave lenses are called diverging lenses, since they cause parallel rays to diverge. 141. Images formed by Lenses. Place a lighted candle before a double-convex lens in a darkened room, and a screen behind it. It will be found that, at a certain dis- tance from the lens, a distinct inverted image of the candle will be formed upon the screen. Move the candle nearer the lens, and the image will become blurred, but will be- come distinct again on moving the screen farther from the lens. If the candle be moved away from the lens, the image becomes blurred ; but it becomes distinct again when the 150 LIGHT. screen is brought nearer the lens. The nearer the candle is to the lens, the larger the image formed. If now the lens be taken away, and one of greater con- vexity be used, it will be found that the candle must be brought nearer the lens in order that its image may be formed upon the screen, and the image becomes larger. The more convex the lens used, the nearer the candle must be brought to it, and the larger the image. If, on the other hand, a less convex lens be used, the candle must be put fjarther off, and the image becomes smaller. Instead of using a more convex lens, we may add a second convex lens, with the same effect. Let us suppose that the lens is made of some elastic substance, so that we may change its convexity by pulling out or pushing in its sides ; and that the lens is first made very flat, so that an image is formed upon the screen when the candle is at a great distance. If we move the candle nearer, the lens must be made more and more convex, in order to keep the image on the screen distinct, and the image at the same time will grow larger and larger. When the candle and the screen are both at the same distance from the lens, the image will be of the same size as the candle ; when the candle is farther from the lens than the screen is, the image will be smaller than the candle ; and when the candle is nearer the lens than the screen is, the image will be larger than the candle. Why the image is thus formed on the screen will be evi- dent from Figure 117. All the light which radiates from the point A of the candle is refracted, in passing through the lens, and concentrated at a; and all radiating from B is concentrated at b, and all radiating from points between A B will be concentrated at corresponding points between a and b. Hence the space between a and b must have the same light and shade as the flame itself, and must there fore appear exactly like it. LIGHT. 151 It will be seen that the image lies between the lines, A a B l>, drawn from the extremities of the object through Fig. 117. the centre of the lens. It follows from this that the image and the object must be of the same size when they are at the same distance from the lens, and that the one which is nearer the lens must be the smaller. The reason why the image recedes from the lens as the object approaches is also evident. As the object ap- proaches, the rays which fall upon the lens become more and more divergent, and of course will not meet so soon on the other side of the lens. The place where the image is formed is called the focus of the lens (140). The focus of a lens, then, changes with the divergence of the rays which fall upon it. The point where parallel rays are made to meet is called the principal focus. If an object were placed in the principal focus, the rays diverging from it would become parallel, on emerging from the lens. If the object were placed nearer the lens than the principal focus is, the rays would be still diver- gent on leaving the lens, though less so than on enter- ing it. 152 LIGHT. SUMMARY. There are two classes of lenses. One class causes parallel rays to converge, and the other causes them to diverge. (140.) When objects are placed in front of a converging lens, images of them are formed at its focus behind it. The magnitude of the image increases with its distance from the lens, and also with the convexity of the lens. The image is of the same size as the object when it is the same distance from the lens, smaller when it is nearer the lens, and larger when it is farther from it. (141.) THE EYE. 142. The Camera Obscura. If a converging lens be placed before an opening in the shutter of a darkened room, a small and beautiful picture of the landscape will be seen upon a screen placed a short distance behind the lens. In this picture every motion of the branches and leaves of the trees and all other objects will be exactly delineated. An arrangement of this kind by which im- ages of external objects are formed upon a screen in a darkened room is called a camera obscura. Figure 118 represents the camera used by photographers. C is a dark chamber ; E is the screen of ground glass upon which the image is received ; A is a tube containing the combination of lenses used to form the image. This camera can be adjusted to objects at different distances by changing the position of the screen, or of the lenses (which may be moved by the screw Z>), or both. In the ordinary camera the image is smaller than the object, since it is nearer the lens. Any transparent substance with convex surfaces, placed 153 in a medium less refractive than itself, causes the rays of light traversing this medium to converge to a focus. If a watch-glass be fitted into the side of a box, and the box be filled with water, a candle may be placed at such a dis- tance in front of the watch-glass that an image of its flame shall be formed on the opposite wall of the box. If now a convex lens of glass be introduced into the water in the path of the rays, it will cause them to come to a focus sooner, because glass refracts light more strongly than water does. An arrangement like the above might be called a water camera. 143. The Eye a Water Camera. The eyeball is com- posed, in the first place, of a tough, firm, spherical case, Scl (Figure 119). The greater part of this case is white and opaque, and is called the sclerotic coat, or the white of the eye. In front this case becomes transparent, and is called the cornea, Cn. The cornea is more convex than the sclerotic. This case of the eye is kept in shape by being filled with fluids called the humors. One of these, the aqueous humor, Aq, fills the corneal chamber ; and the other, the vitreous humor, ?, the sclerotic chamber. The two humors are kept separate by the double-convex crystal- 7* 154 LIGHT. line lens, Cry, which is denser, and capable of refracting light more strongly, than either humor. The crystalline lens is highly elastic, more convex behind than in front, M.I. and is kept in place by a delicate but very strong and elastic ligament which extends from the edge of the lens to what are called the ciliary processes of the choroid coat. This choroid coat, Ch, is of a dark color and highly vascu- lar (that is, full of vessels), and it lines the whole inner chamber of the eye. When it reaches the front part of the chamber, its inner surface becomes raised into longitudinal ridges with rounded ends. These ridges are the ciliary processes, C.p. The iris, Ir, is a curtain with a round hole in the middle called the pupil. The iris has two sets of muscular fibres ; one circular and the other radiating. By the action of these the pupil is enlarged or contracted. It is the iris which gives the color to the eye ; and hence its name. The optic nerve, Op, enters the back of the eye a little LIGHT. 15 way from the centre towards the nose. It then spread v out over the choroid coat, forming the retina, Rt. The eyeball is thus seen to be a water camera. The cornea answers to the watch-glass ; the sclerotic, to the box ; the humors, to the water ; and the crystalline lens, to the glass lens. In an ordinary camera it is found desirable to have what is called a diaphragm, to moderate the light, and to cut off all the rays except those which fall on the central part of the lens. In the eye the iris acts as a diaphragm, and has the advantage of being self-regulating. It dilates the pupil and admits more light when the illumination is too weak ; it contracts the pupil and cuts off a part of the light when there is too much of it. 144. The Adjustment of the Eye. That the eye must adjust itself in order to see distinctly at different distances is shown by the following simple experiment. Stick two stout needles into a piece of wood, so that one of them, a, shall be about six inches from the eye, and the other, b, .about twelve, very nearly in the same direction. If now you look at the needle b, you will see it distinctly and with- out the least sense of effort ; but the image of a will be blurred. Try now to make this blurred image of a distinct, and you find that you can do it, but not without effort. In proportion as a becomes distinct, b becomes blurred, and no effort will enable you to see both distinctly at the same time. Very many explanations have been given of this remark- able power of adjustment possessed by the eye. It is only within a few years that it has come to be clearly under- stood. When a lighted taper is held near and a little to one side of a person's eye, any one on looking into the eye from the proper position will see three images of the flame ; one reflected from the cornea, one from the front surface of the crystalline lens, and one from its rear sur- '56 LIGHT. face. Suppose now the person's eye be steadily fixed on a distant object, and then adjusted to a nearer one in the same direction. The position of the eyeball of course re- mains the same. It is also found that the images reflected from the cornea and from the rear surface of the lens re- main unchanged; while the image reflected from the front surface of the lens changes its position and size in such a way as to show that this surface has been brought forward and at the same time made more convex. The eye then adjusts itself to dif- ferent distances by altering the convex- ity of the crystalline lens. This change in the form of the lens is shown in Figure 120. The half A shows the form of the lens when the eye is ad- Fig. 120. justed for distant objects ; and the half B, when it is adjusted for near objects. 145. The Structure of the Retina. Figure 121 represents a portion of the retina highly magnified, since the whole thickness of this membrane does not exceed the ff \y of an inch. The inner side a, which is in contact with the vitreous humor, is lined with what is called the limiting membrane. Externally and next to the choroid coat it consists of a great number of minute rod-like and conical bodies, , as if they came from O" ; and another part, twice reflected, at A and B, as if they came from O"'. By placing the mirrors at dif- ferent angles, a variety of images may be obtained. Their number and their arrangement (which will always be symmetrical) will depend upon the angle at which the mirrors are placed. The kaleidoscope, invented by Sii* David Brewster, depends upon this effect of inclined mirrors. It consists of a tube in which there are three mirrors inclined at an angle of 60. One end of the tube is closed with a piece of ground glass, and the other end with a cap in which there is a small opening. Small irregular pieces of colored glass are placed between the ground glass and another glass disc. On looking into the tube, these objects and their images seem arranged in beautiful and symmetrical forms, which continually change as the tube is turned round. 1 68. Concave Mirrors. A concave mirror is a portion of a spherical surface viewed from within. The action of such a mirror upon parallel rays is shown LIGHT. 179 in Figure 140. Cis the centre of the sphere of which the mirror is a part. The radii C A, C B, and C D are of Fig. 140. course perpendicular to the surface of the mirror at the points A, B, and D. The parallel rays H, G, and Z, on meeting the mirror, are reflected so as to make the angle of reflection equal to that of incidence ; that is, making C B H equal to C B F, C D G to C D F, etc. Hence the reflected rays are made to converge. If the mirror is not more than 8 or 10 in breadth, the rays will all meet at F, half-way between C and A. This point is called the principal focus of the mirror. Fig. 141. Figure 141 shows the action of a concave mirror upon diverging rays. The rays diverging from the point L meet the mirror at a smaller angle of incidence than if they were parallel, and their angles of reflection will also be less. They will therefore meet at a point, /, farther from the mirror than the principal focus is. If the luminous point were at /, the rays would be brought to a focus at L. The points L and / are called conjugate foci. As L approaches C, I also approaches it, until at C the i8o LIGHT. two coincide. As L recedes from C, / approaches F; until L is removed so far that the rays become sensibly parallel, when / coincides with F. If L is at F, the reflected rays will be parallel ; if L is inside F, they will be divergent, but less divergent than on meeting the mirror. If a candle AB (Figure 142) be placed before a con- Fig. 142. cave mirror, the rays diverging from A are brought to a focus at a ; those from B, at b ; and those from points be- tween A and B, at corresponding points between a and b. So long as A B is to the left of C, the image will be small- er than the object; when AB is to the right of C, the image will be larger than the object ; and in both cases it will be inverted. If, however, the candle is inside the principal focus, it will be seen reflected in the mirror, up- right and enlarged, since the rays are rendered less diver- gent on leaving the mirror. 169. Convex Mirrors. A convex mirror is a portion of the surface of a sphere viewed from without Fig- 143- Such a mirror renders parallel rays divergent, and diver- gent rays more divergent (Figure 143). Hence an ob- ject reflected in it appears smaller than it really is. LIGHT. 1 70. The Reflecting Telescope. A concave mirror may be used instead of the object-lens of a telescope, as is showr, in Figure 144. The rays from an object falling upon the Fig. 144. Fig. i45 concave mirror M are reflected so as to form an image at the focus, and this image is viewed with the eyepiece o. As the image here is formed by reflected light the instru- ment is called a reflecting telescope. The ordinary tele- scope is called a refracting telescope, since the image is formed by refracted light. The largest reflecting telescope ever made is the cele- brated one of Lord Rosse, which has a diameter of 6 feet and a focal length of 53 feet. 171. Parabolic Mirrors. The mirror shown in Figure 145 has what is called a parabolic surface, and is therefore called a para- bolic mirror. The point F is called the focus, and the line A X the axis, of the mirror. If parallel rays be allowed to fall upon such a mirror, they are reflected exactly to the focus F, whatever may be the breadth of the mirror. On the other hand, if a light be placed at the focus, its rays will be reflected from the mirror in parallel lines. This is be- 1 82 LIGHT. cause the curvature of a parabolic surface is such that if a perpendicular be drawn to any point, as M, the angle which it makes with the line M L, drawn parallel to the axis, is equal to the angle it makes with the line M F drawn to the focus. Parabolic mirrors are used for the lanterns placed in front of locomotive engines and in many light-houses. SUMMARY. Any smooth reflecting surface is called a mirror. When the surface is flat, it is called a plane mirror ; when it is curved, a concave or convex mirror. (166, 168.) An object is seen reflected in a plane mirror without enlargement, but it appears as far behind the mirror as it really is before it. (166.) In a convex mirror an object appears smaller, and in a concave mirror larger, than it really is. (168, 169.) An inverted image of an object is formed in the focus of a concave mirror. (168.) A concave mirror may be used in place of the object- glass in a telescope. (170.) A parabolic mirror renders the rays which diverge from its focus parallel. (171.) PHOTOGRAPHY. 172. The Chemical Action of Light. If a surface coated with chloride or iodide of silver be exposed to light, it gradually blackens. The stronger the light, the more rapidly the change of color takes place. There are many other chemical substances which are more or less affected by the action of light. In some cases the light does not actually decompose the substance, but gives it a disposition to break up. This chemical action of light is the basis of the art of photography. LIGHT. 183 173. The Daguerreotype. If the image in the camera obscura (142) be allowed to fall for a short time upon a copper plate coated with iodide of silver, and the plate be removed and examined, no change appears to have taken place. If, however, the plate be now exposed to the vapor of mercury, an image appears exactly like that formed in the camera. The mercury condenses upon those parts of the plate which have been most strongly illu- mined, and thus develops the picture which before was latent. If this plate were now exposed to the light, the remaining iodide of silver would blacken so as to obliter- ate the picture. But if the iodide be dissolved and washed off by a solution of hyposulphite of sodium, the picture is fixed. This process of obtaining pictures by means of light was discovered in 1839 by a Frenchman named Daguerre, and from him the pictures are called daguerre- otypes. The theory of the daguerreotype process is thus stated by Miller *:- " Under the influence of light, the superficial layer of iodide of silver is modified so as to render it susceptible of decomposition. When the plate is acted upon by the mercurial vapor, the iodine is driven to the deeper layer of silver, and a film of silver is liberated upon the surface of those parts which have been exposed to the action of light, the thickness of this film varying with the intensity and duration of the light. The reduced silver combines with the mercury, and a film of silver amalgam is formed, which varies in thickness with the thickness of the silver film, in consequence of which the reflected tints differ according to the varying thickness of this film : those parts of the iodized plate which have not been exposed to the light of course do not combine with the mercury. After the plate has been treated with hyposulphite of sodium, the * Elements of Chemistry (3d Edition), Part II., page 895. 184 LIGHT. excess of iodide of silver is removed, and the blacks con- sist of metallic silver. Experiment proves that those parts of the plate immediately beneath the highest lights are more deeply corroded than the others by the action of the iodine which has been driven inward during the process of mercurialization. " In complete accordance with the foregoing explanation is a curious fact first pointed out by Mr. Shaw, that if a plate, after it has received the impression in the camera, but before it has been mercurialized, be exposed to the vapor of iodine or of bromine for a few seconds, the image is completely effaced, and is no longer producible by mercury." 174. The Collodion Process. This process, which is the one now almost universally employed, was invented by Mr. Archer, in 1851. A solution of gun-cotton in ether is impregnated with a small quantity of iodide of potas- sium or cadmium, forming what is -called iodized collodion. A film of this is spread on a plate of glass, which is then immersed in a solution of nitrate of silver. The collodion film thus becomes coated with yellow iodide of silver, which is very sensitive to light. The plate thus prepared requires an exposure of only a few seconds in the camera to produce the latent image, which is afterwards developed by pouring over the surface a weak solution of pyrogallic acid mixed with acetic acid. A solution of ferrous sul- phate is also often used for the same purpose. The image is r\Qvjjixed, as described above, by pouring over the plate a solution of hyposulphite of sodium or of cyanide of po- tassium. The negative picture thus obtained can then be employed for printing a positive, as explained in the next section. 175. Photographic Printing. In 1839 Mr. Fox Talbot of England discovered the process now known as photo- graphic printing. " It consisted in soaking ordinary writ- LIGHT. 185 ing-paper in a weak solution of common salt, and, when dry, washing it over upon one side with a solution of nitrate of silver, consisting of one part of a saturated solu- tion of nitrate with 6 or 8 parts of water. This operation was performed by candle-light, and the paper was dried at the fire ; in this manner a film of chloride of silver, mixed with an excess of nitrate of silver, was formed upon the surface of the paper. Suppose that it were desired to obtain a copy of an engraving, or of the leaf of a tree : one of the sheets so prepared was laid under the engraving or the leaf which was to be copied ; the two were pressed firmly together between two plates of glass, and exposed to the direct rays of the sun, or even to diffused daylight, for a period of half an hour or an hour. The impression thus obtained was a negative one, that is to say, the shadows were represented by lights, and the lights by shadows ; those portions of the surface which had been exposed to the strongest light becoming dark, and the parts correspond- ing to the deep shadows in the engraving remaining white. The pictures were then fixed by immersing them in a strong solution of common salt. Considerable improve- ments have been introduced into this process since it was first published, but, in principle, this operation, which has been termed photographic printing, remains unchanged." (Miller.) Of course, when negative pictures are copied by this pro- cess, positive ones (or those having the proper distribution of light and shade) are obtained. 176. Chemical Action of the Solar Spectrum. If a pure solar spectrum be allowed to fall upon a sheet of sensitive paper, it will be soon seen that the chemical action is not uniformly distributed over the luminous image. The maxi- mum of light falls in the yellow rays about Fraunhofer's line Z>, while that of chemical action occurs in the blue portion of the spectrum near the line G, about one third i86 LIGHT. of the way between that line and H. The blackening effect extends nearly to F in the green, while it is pro- longed beyond the violet end of the spectrum a distance nearly equal to two thirds of the length of the luminous spectrum, the chemical effect gradually shading off until it is imperceptible. The maximum point, however, varies with the preparation used. With the Talbotype iodized paper, the greatest blackening is found on the extreme limit of the violet ray. When bromide of silver is the sen- sitive material, the chemical action is prolonged towards the red rays. When chloride of gold is used, the maxi- mum is found between the green and the blue rays, and the chemical action does not extend beyond the violet more than half as far as when the salts of silver are used. In Figure 146, i represents the space occupied by the F E luminous spectrum on white paper ; 2, the chemical spec- trum on bromide of silver ; 3, the Talbotype spectrum. Inactive spaces occur in the chemical spectrum, which, as Becquerel and Draper have shown, correspond exactly with the dark lines found in the visible spectrum ; but they extend also into the prolongation beyond the violet, and occur there in great numbers. These fixed lines may be obtained upon Talbotype paper, or, better still, upon a surface of collodion. LIGHT. 187 SUMMARY. Light either causes certain chemical compounds to decompose or gives them a disposition to do so. (172.) Hence light can be made to fasten upon properly pre- pared surfaces the images which fall upon them in the camera. (173.) The daguerreotype process was discovered by Daguerre, in 1839 ; photographic printing, by Talbot, in the same year; the collodion process, by Archer, in 1851. (173-175.) The most refrangible rays of the spectrum have the most powerful chemical action. The chemical spectrum extends beyond the luminous spectrum at the violet end, and has blank spaces. These spaces correspond to Fraunhofer's lines, which are also chemically inactive. (176.) CONCLUSION. A luminous body sends out light in every direction, which diminishes in intensity as the square of the distance increases. These rays of light traverse space in straight lines, and with a velocity of about 190,000 miles a second. When rays of light meet a different medium from that through which they have been passing, they are partially reflected and partially transmitted. The reflected portion is either diffused or else reflected regularly. In the latter case the angle of reflection always equals the angle of in- cidence. The transmitted portion is refracted towards or from a perpendicular to the surface, according as the new medium is more or less dense than the old one. In passing through a prism a ray of light is twice re- fracted in the same direction, and also dispersed into a colored band, called the spectrum ', which differs in length l88 LIGHT. with the material of the prism. This dispersion shows that a ray of white light is really a bundle of rays of different colors and of different refrangibility. The rays of white light are continually sifted as they fall upon bodies, each body absorbing some particular color or colors, and trans- mitting or dispersing the others. It is this which gives bodies their color. Incandescent solids give out rays of all the prismatic colors, but incandescent gases give out rays of only partic- ular colors. By means of the spectroscope we can ana- lyze the light emitted by an incandescent gas, and find out the elements of which it is composed. A gas absorbs the same rays that it emits when incandescent. When examined with the spectroscope, solar and stellar light give spectra crossed by dark lines. Such spectra show that the light comes from a solid or liquid nucleus, surrounded by a gaseous envelope, and enable us to find what elements exist in these envelopes. Rays of light interfere in such a way as to show that light is propagated by means of waves. These waves are exceedingly minute, and are longest in red, and shortest in violet light. Difference in color is then analogous to dif- ference in pitch, the difference in both cases being caused by a difference in the rapidity of vibration. Tint in color is analogous to quality in sound, both being the result of the mixture of vibrations of different periods. While sound-waves are propagated chiefly in the air, light-waves are propagated in the ether. Light, like sound, originates in the vibrations of particles of gross matter ; but the vi- brations which originate light are much more minute and more rapid than those which give rise to sound. The molecules of a luminous body are usually capable of exe- cuting vibrations of several periods, and hence the light which they give out is seldom homogeneous. As in sound, so in light, a body is capable of intercepting or absorbing LIGHT. 1 89 the vibrations whose periods are synchronous with those of its own molecules.* Double refraction and polarization show that while in sound the vibrations are longitudinal, they are transverse in light, and that in ordinary white light these vibrations are executed in every plane. On passing through a crystalline body these vibrations are sorted and arranged in two sets. When the vibrations are all executed in the same plane the ray is said to be polarized. Two rays of polarized light cannot interfere so as to destroy each other unless they are polarized in the same plane ; but they may interfere so as to make the molecules of the resultant ray move in circles or ellipses, or so as to twist the plane of polarization. The rainbow is caused by the reflection and refraction of light in the rain-drop. The colors are due partially to dispersion and partially to interference. An image of an object can be formed in the focus of a converging lens or of a concave mirror. The rays of light on entering the eye are brought to a focus upon the retina by means of the cornea and crystalline lens. The vibra- tions of the ether are taken up by the rods and cones, and communicated to the nerve-fibres, and thence to the brain. The distinctness of vision increases with the dis- tinctness, the size, and the brightness of the image upon the retina ; provided the illumination is not too strong, in which case the eye is blinded. Perfect eyes can adjust themselves to any distance from a few inches to infinity. Other eyes, owing to a defective form of the ball, can ad- just themselves only to a limited range of distances, some being able to see with distinctness only near objects, and others only remote ones. These defects can be partially remedied by the use of glasses. As the eye grows old it loses its power of adjustment. The size of the image upon the retina increases as the object is brought nearer to the eye. The microscope is an 190 LIGHT. instrument which enables the eye to see an object at a very short distance ; and the telescope, an instrument which enables it to see a very distant object. The more refrangible rays of the spectrum have a chem- ical action, which is now employed in taking photo- graphic pictures. III. HEAT NATURE AND PROPAGATION OF HEAT. RADIATION. 177. Heat is Radiated in all Directions. When we come near a stove we feel its heat, no matter on what side of it we may be ; that is, the stove radiates its heat in all di- rections. Again, if a small metallic sphere be heated, and delicate thermometers be placed on different sides of it at equal distances from its centre, they will all indicate the same temperature ; showing that the sphere radiates heat equally well in every direction. Radiant heat, like light, diminishes in intensity as the square of the distance increases, and for the same reason. 178. Heat traverses Space in Straight Lines and with the Velocity of Light. Heat and light come to the earth .to- gether in the sun's rays, and we have seen that these move in straight lines and with a velocity of about 190,000 miles a second. 179. Luminous and Obscure Heat. Heat which is radi- ated from a non-lurninous source, as from a ball heated below redness, is called obscure heat ; while that radiated from a luminous source, as from the sun or from a ball heated to redness, is called luminous heat. 1 80. Diathermanous Bodies. Some substances, as air, allow radiant heat to pass readily through them, and are 9 M 194 HEAT. called diathermanous. The term is derived from the Greek words dia, through, and thermos, heat. If a plate of glass be held up before an iron ball heated to dull redness, a delicate thermometer held behind the plate will be scarcely, if at all, affected. If, however, a plate of rock salt be put in place of the glass, the ther- mometer rapidly rises. Glass, then, though one of the most transparent bodies, is by no means one of the most diathermanous. Rock salt is the most diathermanous of all known solids, and is to radiant heat what glass is to light. 1 8 1. Heat is Reflected in the Same Way as Light. That luminous heat is reflected in the same way as light is shown by the fact that, when the sun's rays are reflected to a focus by a concave mirror, that focus is the hottest, as well as the brightest, part of the beam. At A (Figure 147) in the focus of the concave mirror B C is placed a copper ball heated below redness, and the Fig. 147- bulb of a delicate thermometer is placed at D in the focus of the concave mirror E F. The mercury rises at once. If the thermometer be moved away from D in any direction, the mercury falls. It is evident, then, that the heat-rays are concentrated at the focus of the mirror E F. Now we HEAT. 195 know that light-rays diverging from A would, on falling upon the mirror B C, be reflected in parallel lines to the mirror F, and from this mirror to its focus D ; and it is clear that the heat-rays have been reflected in the very same way. Radiant heat, then, both luminous and obscure, is re- flected in the same way as light. 182. Radiant Heat is Refracted in the Same Way as Light. That luminous heat is refracted like light is shown by the fact that the heat of the sun's rays is re- fracted by a converging lens to the same focus as the light. The refraction of ordinary obscure heat cannot be shown by a glass lens, since it is not sufficiently diathermanous (180). If, however, a lens of rock salt be held before a source of obscure heat, as shown in Figure 148, and the face of a thermopile * be placed at the focus of this lens, Fig. 148. the galvanometer needle at once turns aside, showing a rise of temperature. If the face of the pile be placed anywhere else than at the focus, no rise of temperature is indicated. Fig. 149. Again, if the rays of obscure heat be allowed to fall upon a prism of rock salt, they will be turned aside, as shown in * For the thermo-electric battery, or thermopile, see 248, p. 248, and 286, p. 284. 196 HEAT. Figure 149, in exactly the same way as rays of light would be in passing through the same prism. These experiments show that radiant heat, whether lu- minous or obscure, is refracted just like light. 183. Heat is Dispersed in the Same Way as Light. In Figure 150 we have a thermopile of peculiar construction. In the middle of the brass plate A B is a narrow vertical slit, so arranged that its width can be varied at pleasure. Behind this slit is the face of the thermopile, whose ele- ments are arranged not in a cube, as usual, but in a single row. By means of the ivory handle seen at the bottom, the brass plate which serves as a screen can be moved to and fro with great regularity and precision. If now this thermopile be connected with a delicate galvanometer, and the solar spectrum from an ordinary glass lens be al- lowed to fall upon the screen, the needle at once indicates a rise of temperature. If we move the face of the pile backward and forward, we find that the heat is dis- persed throughout the whole length of the spectrum, but that it grows more and more intense as we approach the red or least refrangible end ; and when we move the slit into the dark space beyond the red, we are surprised to find that the heat is more intense there than anywhere else. The heat, however, extends but a little way beyond the red end. This experiment shows, (i) that radiant heat is dis- persed like light in passing through a prism ; (2) that HEAT. 197 obscure as well as luminous heat is radiated from a lu- minous source ; and (3) that obscure heat is less refrangi- ble than luminous heat. 184. Heat and Light are one and the same. We have now seen that radiant heat and light are reflected, re- fracted, and dispersed in precisely the same way. It has also been found by difficult and delicate experiments that radiant heat can also be polarized in the same way as light. These facts seem to lead to the conclusion that light and heat are the same thing, and the following fact proves this beyond a doubt. We have learned that the solar spectrum is crossed by dark lines, known as Fraunhofer 's lines (112). Now atf examination of the spectrum with a very delicate ther mopile has shown that these dark lines are also devoid of heat, and, furthermore, that similar dark or cold lines exist in the obscure part of the spectrum beyond the red end, where the heat is most intense. Again, these dark lines have been shown to be chemically inactive, and similar inactive lines are found beyond the violet end in the obscure chemical part of the spectrum. The existence of these blank lines throughout the whole length of the spectrum, in the obscure as well as in the luminous part, and the absence of both heat and chemical activity in the dark lines found in the luminous part, prove con- clusively that the thermal, the luminous, and the chemical rays are one and the same thing. Passing from the obscure end of the spectrum beyond the red to the obscure end beyond the violet, we meet with vibrations of greater and greater rapidity, but differing in nothing else. A portion of these vibrations at the lower or thermal end of the spectrum are able to affect only those nerves which give us the sensation of heat ; another portion, including the luminous part of the spectrum, are able to affect these nerves and at the same time the 198 HEAT. nerves of the eye, and also to develop chemical action ; a third portion, or those beyond the violet end, are able only to cause chemical action. Luminous heat and light, then, are exactly the same thing ; and obscure heat differs from luminous heat only as one color of the spectrum differs from another. If there is need of further proof that obscure heat differs from light only in the rapidity of the vibration, it is fur- nished by an experiment of Dr. Draper's. He gradually raised the temperature of a platinum wire till it was of a white heat, and examined its spectrum throughout the pro- cess. At first the spectrum contained only the obscure thermal rays ; then the least refrangible red rays appeared, followed in succession by the orange, yellow, green, blue, indigo, and violet ; and after these came the obscure chemical rays. 185. The Proportion of Obscure and Luminous Radiation in the Electric Light and in Sunlight. Professor Tyndail discovered that a solution of iodine in bisulphide of carbon, which is so opaque that a layer of .07 of an inch in thick- ness is sufficient to cut off all the light from the most brilliant gas-flame, is almost perfectly diathermanous to obscure heat, even in very much thicker layers. A solu- tion of this kind, contained in a narrow cell whose sides are polished plates of rock salt, separates sharply the obscure from the luminous heat, whatever may be their source. With this delicate apparatus he examined the obscure heat in the rays of the sun and in the electric light, and found that it was far greater than the luminous heat. By giving the cell the form of a prism, he obtained a spectrum of this obscure heat. Figure 151 shows the proportion of the obscure thermal to the luminous part of the spectrum of the electric light. The height of the curve shows the intensity of the radiation at each point. It is seen that the luminous rays of the electric light are HEAT. 199 insignificant in comparison with the obscure ones. This same thing is true of the radiations from the sun, though the disproportion between the luminous and the obscure Fig- 151- B jj parts is not quite so great, owing probably to the fact that many of the obscure rays are absorbed in passing through the atmosphere. 1 8 6. The Obscure Radiation increases in Intensity with the Temperature. Tyndall heated a spiral of platinum wire from dull redness to full white heat, and by means of the iodine solution examined its obscure radiations. He found that as its temperature rose it not only gave off more and more refrangible rays, as Draper had shown (184), but also that its obscure radiations were powerfully augmented. It had previously been supposed that the effect of raising the temperature of a body was only to add to its radiations those of sherter periods. Tyndall's experiment, however, has shown that the effect of raising the temperature is both to add quicker vibrations and to augment the intensity of those which already exist. The hotter a body, then, the more powerful its obscure radiations. 187. Invisible Foci. By means of the opaque iodine solution, Tyndall was able to show effects of obscure heat far more striking than had ever been shown before, for he could use the obscure radiations from the most intense 200 HEAT. sources of heat. He placed a concave mirror behind the carbon points in the electric lamp, and converged its pow^ erful beam to a focus a short distance in front. In this focus there was, of course, formed a very bright luminous image of the carbon points. He then cut off all the lumi- nous rays with an iodine cell. The image disappeared from sight, but an invisible " thermograph " remained. It is only the peculiar structure of our eyes which prevents our seeing such a picture. Place a piece of white paper at the focus of the mirror, and the image chars itself out. If black paper is used, two holes are burned in it,, corre- sponding to the images of the two carbon points. If a thin piece of carbon in a vacuum be placed at the focus, the radiant heat is converted into light, and the latent image becomes visible. A thin sheet of platinized plati- num will bring out the image even in the air. The intense heat at this invisible focus may be shown by many other experiments, as the melting of lead, the burning of zinc and magnesium, and the like. Similar experiments may be tried by bringing the lumi- nous rays to a focus by a rock-salt lens, and interposing an iodine cell, or, what is better, a hollow lens of rock salt filled with the iodine. Sunlight produces similar effects, and in using it a glass lens may be substituted for a rock- salt one, though with less brilliant results. 188. Calorescence and. Fluorescence. In the above ex- periment of Tyndall's, the platinum foil cannot have be- come hotter than the focus itself, yet it became luminous while the focus was obscure. Again, when a cylinder of lime is put in the oxy-hydrogen flame, its temperature can- not be higher than that of the flame, yet it becomes intensely luminous. Platinum, then, and other solids have the power of raising the refrangibility of the obscure rays so as to render them luminous. This change of re- frangibility is called calorescence. HEAT. 201 On looking through a prism at the incandescent image of the carbon points on the platinum foil, Tyndall found that the light from it gave a complete spectrum, showing that the obscure rays had been converted by the platinum into red, orange, yellow, green, blue, and even violet. When the ordinary spectrum is allowed to fall on a screen washed over with a solution of the sulphate of quinine, the ultra-violet rays become luminous, showing that their refrangibility has been lowered. This phe- nomenon, which is just the opposite of calorescence, is called fluorescence. Phosphorescence, that is, the property which certain bodies have of shining in the dark after they have been exposed to the light, is probably nothing but a persistent form of fluorescence. SUMMARY. Heat is radiated from its source in all directions. (177.) It traverses space in straight lines with the velocity of light. (178.) Radiated heat may be luminous or obscure. (179.) Bodies which allow heat to pass readily through them are called diathermanous. (180.) Radiant heat is reflected, refracted, . and dispersed in the same way as light. Obscure heat is less refrangible than luminous heat. (181-183.) Heat and light are the same thing. The different kinds of heat differ only in the rapidity of the vibrations in which they originate and are propagated. (i8 4 .) The obscure radiations of the electric lamp and the sun are much more abundant than the luminous radiations. (185-) 9* 202 HEAT. The obscure radiations increase in intensity as the tem- perature of the body rises. (186.) Invisible foci may be formed by obscure radiations. (i8 7 .) The refrangibility of the obscure thermal radiations may be raised so that they will become luminous ; while that of the obscure chemical radiations may be lowered. The former change of refrangibility is called calorescence ; the latter, fluorescence. (188.) ABSORPTION. 189. Different Solids and Liquids absorb the Same Kind of Heat with Different Degrees of Readiness. In Figure 152 M is a perforated screen, B is a copper ball heated to dull redness, and T is a thermopile. A plate of glass is put upon the shelf at S behind the screen. Few rays Fig. 15*. of heat reach the pile. If a plate of rock salt of the same thickness be substituted for the glass, abundance of heat reaches the pile. The diathermancy of liquids can be found in the same way, by enclosing them in a glass, or, better, a rock-salt cell, which is placed upon the shelf. It is found in this way that different solids and liquids absorb the same kind of heat very differently. HEAT. 190. The Same Solid or Liquid absorbs Heat of Different Kinds in Different Proportions. By using different sources of heat, such as a Locatelli lamp, copper of different tem- peratures, and incandescent platinum, it is found that the same solid or liquid absorbs heat from these sources in very different proportions. In this way Melloni constructed the following Table, in which the heat from each source transmitted by each substance is compared with that from the same source transmitted by the air, the latter being called 100 : Names of substances reduced to a common thickness of .1 of an inch (2.6 millim.). Transmissions : percentage of the total radiation. Locatelli Lamp. Incan- descent Platinum. Copper at 400 C. Copper at 1 00 C. I Rock salt 92.3 74.0 72.0 54-0 39-o 39-o 38.0 37-o 34-o 330 32.0 24.0 23.0 2I.O 21.0 1 8.0 1 8.0 1 8.0 14.0 II.O II.O II.O 9.0 8.0 6.0 92-3 7 7 .0 69.0 28.0 24.0 28.0 28.0 28.0 24.0 23.0 1 8.0 19.0 9.0 5-o 12.0 16.0 3-o 5-0 2.0 3-o 5-0 2.0 1.0 o-5 92.3 oo.o 42.0 6.0 6.0 6.0 6.0 15.0 4.0 4.0 3-o 6.0 2.0 0.0 8.0 3-o 0.0 0.0 o.o o.o 0.0 0.0 0.0 o.o 92.3 54-o 33-o O.O o.o 0.0 3-3 3-o o.o o.o o.o 0.0 0.0 0.0 o.o 0.0 0.0 0.0 o.o 0.0 0.0 0.0 o.o o.o 0.0 2 Sicilian sulphur 3 Fluor spar A Bervl 5 Iceland spar 6 Glass 7 Rock crystal (clear) 8 Smoky quartz , 9 Chromate of potash 10 \Vhite topaz II Carbonate of lead 12 Sulphate of baryta. . . . 13 Felspar . . 14 Amethyst (violet) 15 Artificial amber 1 6 Borate of soda 17 Tourmaline (deep green) . . . 1 8 Common gum. 19 Selenite 20 Citric acid 21 Tartrate of potash 22 Natural amber 27 Alum 24 Sugar candy 25 Ice The following Table gives the per cent of total radiation transmitted by different liquids : 404 HEAT. Name, of Liquid, Bisulphide of carbon .......................... 63 Bichloride of sulphur ......................... 63 Protochloride of phosphorus ................... 62 Essence of turpentine ........................ 31 Olive oil .................................... 30 Naphtha .................................... 28 Essence of lavender .......................... 26 Sulphuric ether .............................. 21 Sulphuric acid ............................... 17 Hydrate of ammonia .......................... 15 Nitric acid .................................. 15 Absolute alcohol ............................. 15 Hydrate of potash ............................ 13 Acetic acid .................................. ia Pyroligneous acid ............................ 12 Concentrated solution of sugar ................ 12 Solution of rock salt: . ........................ 12 White of egg ................................ 1 1 Distilled water ............................... 1 1 191. Quality of Heat. If the rays which have passed through a plate of any substance be allowed to fall upon a second plate of the same, they are transmitted in much larger proportion than at first. The rays which fall upon the first plate are sifted, and those which cannot pass through that substance are absorbed. When, therefore, the rays fall upon the second plate, they are nearly all transmitted. From the fact that the heat radiated from different sources is absorbed differently by the same substance, it is said to be of different quality. In no case is the heat homogeneous, and in the heat radiated from different sources vibrations of different periods are differently mixed. It is these different mixtures of vibrations of different periods that give to the heat from each source its peculiar quality ; as the mixture of rays of different periods gives to the light from different bodies its peculiar tint. HEAT. 205 192. Different Gases absorb the Same Quality of Heat in Different Proportions. In Figure 153, A is a copper box, against one face of which a steady gas-flame is made to play. G is a chimney, and B is an air-chamber, beyond which is a long glass tube, both ends of which are closed with rock-salt plates. The pipe D connects this chamber with an air-pump. The chamber is surrounded with a collar through which water is kept flowing, in order that Fig. 153- the walls may not become heated. The heat radiated from the copper box passes first through this chamber and then through the tube beyond. The tube is first filled with carefully dried air, and the deflection of the galva- nometer needle is noted. The tube is next filled with carefully dried olefiant gas ; and it is found that only about .001 as much heat is radiated through the tube as at first. This shows that different gases absorb the same quality of heat very differently. 206 HEAT. The following table is taken from Tyndall : Absorption under Name of Gas. a pressure of one atmosphere. Air i Oxygen I Nitrogen I Hydrogen I Chlorine 39 Hydrochloric acid 62 Carbonic oxide 90 Carbonic acid 90 Nitrous oxide 355 Sulphide of hydrogen 390 Marsh gas 403 Sulphurous acid 710 defiant gas 970 Ammonia 1 195 If, instead of comparing the gases at the common pres- sure of one atmosphere, or 30 inches, we compare them at the common pressure of one inch, we shall find their absorptive power differing in even a more striking man- ner, as is shown in the following table from Tyndall : Absorption Name of Gas. under i inch pressure. Air i Oxygen I Nitrogen i Hydrogen i Chlorine 60 Bromine 160 Carbonic oxide 750 Hydrobromic acL' 1005 Nitric oxide i ~jQ Nitrous oxide 1 860 Sulphide of hydrogen 2100 Ammonia 7260 Olefiant gas 7950 Sulphurous acid 8800 "What extraordinary differences," Tyndall adds, "in HEAT. 207 Fig- 154- the constitution and character of the ultimate particles of various gases do the above results reveal ! For every individual ray struck down by the air, oxygen, hydrogen, or nitrogen, the ammonia strikes down a brigade of 7,260 rays ; the olefiant gas, a brigade of 7,950 ; while the sul- phurous acid destroys 8,800." 193. The Same Gas absorbs Different Qualities of Heat in Different Proportions. In Figure 154 we have what is called a platinum lamp, s is a spiral of platinum wire within a glass globe ; d is an open- ing in the side of the globe through which the heat from the spiral is radiated ; a is a concave mirror for collecting and condensing the heat. The platinum spiral is connected with a galvanic battery, and by regulating the strength of the current we can heat the wire to any desired tem- perature. By using this lamp as a source of heat, Tyndall showed that the same gas or vapor absorbs different qualities of heat very differently. Some of the results of his experiments are given in the following Table: Name of Vapor. Source of heat : platinum spiral. Barely visible. Bright- red. White- hot. Near fusion. Bisulphide of carbon 6. 5 9.1 12.5 21. 3 26.4 35-8 43-4 46.2 49.6 II 9.6 17.7 20.6 27-5 3M 31-9 34-6 2.9 5 .6 7-8 12.8 16.5 22.7 25-9 25.1 27.2 2-5 3-9 23-7 21.3 Chloroform Iodide of methyl. .... " " ethvl Benzole Amylene Sulphuric ether Formic " Acetic " ... 208 HEAT. The gradual increase of penetrative power as the tem- perature rises is here very manifest. By raising the tem- perature of the spiral from a barely visible to an intensely white heat, we reduce the absorption in the case of bisul- phide of carbon and chloroform to less than one half. 194. Vapors absorb the Sam? Quality of Heat in the Same Order as their Liquids. Tyndall has arranged the follow- ing liquids and their vapors in the order in which he found them to absorb the same quality of heat, the quantity of vapor used in each case being proportional to that of the liquid : Liquids. Vapors. Bisulphide of carbon, Bisulphide of carbon, Chloroform, Chloroform, Iodide of methyl, Iodide of methyl, " " ethyl, " " ethyl, Amylene, Amylene, Sulphuric ether, Sulphuric ether, Acetic, " Acetic " Formic, " Formic " Alcohol, Alcohol, Water, Water.* We see from this table that the order of absorption in vapors and their liquids is the same. When the molecules are freed from the bonds which hold them in the liquid state, they do not change their absorptive power. 195. Good Absorbers are Good Radiators. Coat all the sides of a tin box except one with a varnish or lamp-black, fill it with boiling water, and expose each side in turn to the face of a thermopile. It will be found that the heat is radiated slowly from the metallic surface as compared with the coated surfaces. * Aqueous vapor, when unmixed with air, condenses so readily that it cannot be directly examined in the experimental tube. 2OQ In Figure 155 we have Fig. 155. a plate of tin m n uncoat- ed, and another op coat- ed with lamp-black. The plates are connected by a wire at the top, and to the back of each is sold- ered a little bar of bis- muth. These bars are connected with a delicate galvanometer. If we heat the junction of one of these bars with the plate by putting the finger upon it, the galvanometer shows that the current is flowing in one direction ; if we allow this to cool and heat the other in the same way, the galvanometer shows a current flowing in the opposite direction ; if we heat them both equally at the same time, no current is indicated. A heated copper ball is now placed just half- way between the two plates, so as to radiate heat equally to each. The needle at once shows a current flowing from the plate op, which must therefore have become more heated than m n. The coated plate, which was the best radiator, is, therefore, the best absorber. In Figure 156 fis a thermopile connected with a gal- vanometer ; C, a heated copper ball placed above a tube A. The direct radiation of the ball is cut off from the pile by means of the screen S. L is a cube filled with hot water and placed at such a distance from the pile as to warm the face towards it just as much as the opposite face is warmed by the current of air streaming up over the hot ball. Different gases are now forced through the tube against the ball, by which they are heated. On rising above the screen, they radiate their heat to the pile. If they radiate just as much heat as the air, the needle will N 210 not move ; if they radiate more heat than the air, it will move in such a way as to show that the left face of the pile is heated more than the other ; if less than the air, it will move in the opposite direction. By noticing how much the needle turns in each case, we can compare the radiating power of the different gases used. In this way it is found that those gases which are the best ab- sorbers are also the best radiators. 196. The Molecules of a Substance radiate Heat by Com- municating their Motion to the Ether, and absorb Heat by Taking up Motion from the Ether. In the study of light we have learned that the molecules of substances are im- mersed in the all-pervading ether, and that the molecules of each substance are capable of vibrating in certain defi- nite periods. When the ethereal vibrations dash against the molecules of a body, these molecules will take up the vibrations which are synchronous with their own, and allow the others to pass on. The former vibrations are said to be absorbed, the latter transmitted. Diathermancy, then, is synonymous with discord; and adiathermancy (the opposite of diathermancy) with concord. Hence arises the power of bodies to sift the vibrations which fall upon them. The molecules select and absorb the vibrations HEAT. 211 which are synchronous with their own, and allow the others to pass. When, on the other hand, bodies radiate heat, they im- part some of their motion to the ether which surrounds them. Bodies can radiate only those vibrations which their own molecules can perform. Hence different bodies radiate different qualities of heat. That bodies radiate the same kind of heat as that which they absorb is shown by the fact that they are nearly opaque to their own radia- tions. Even rock salt, which is so diathermanous, is near- ly opaque to the vibrations given out by heated salt. 197. The Absorptive Power of a Body depends upon its Molecular Constitution. An examination of the pre- ceding tables will show that elementary bodies, such as the metals, oxygen, and nitrogen, are poor absorbers, while compound bodies, such as olefiant gas, sulphurous acid, and ammonia, are good ones. This is as we should ex- pect, since the more complex a molecule becomes by the combination of different atoms, the more likely it will be to intercept the vibrations of the ether in which it is im- mersed. The great absorptive power of lamp-black, one of the forms of carbon, would seem to be at variance with this view. Lamp-black, however, is not pure charcoal, but contains various compounds of carbon and hydrogen ; while charcoal itself is an allotropic state of carbon. And the most probable explanation of allotropic states is that the atoms are differently grouped into molecules. While oxygen is almost perfectly transparent to heat, ozone, an allotropic state of oxygen, is quite a good absorber. This is probably due to the fact that in the charcoal and ozone the atoms are grouped in such a way as to form complex molecules. The power of bodies to absorb vibrations from the ether is likely to throw much light on their molecular constitution. 212 HEAT. 198. The Molecules of all Bodies are in Motion. It would seem, then, that all the molecules of gross matter are in constant vibration ; and that, when acted upon by heat or other force, these molecules are made to perform their fundamental vibrations with greater energy, and to add to these higher and higher harmonics. Our organs of sense are instruments for intercepting these vibrations and transmitting them to the brain, where they tell us all that we know of the external world. The eye seems to have been especially formed to give us a glimpse of the beauty of these vibrations. SUMMARY. Different qualities of heat result from different mixtures of vibrations of different periods. (191.) The same solid, liquid, or gas absorbs different qualities of heat in different proportions ; while different solids, liquids, or gases absorb the same quality of heat in differ- ent proportions. (189-193.) Vapors absorb the same qualities of heat in the same order as their liquids. Water is the best absorber among liquids, and watery vapor among gases. (194.) Good absorbers are good radiators. (195.) The molecules of a substance radiate heat by communi- cating their vibrations to the ether, and absorb heat by taking up vibrations from the ether. (196.) The absorptive power of a body depends on its molec- ular constitution. (197.) The molecules of all bodies seem to be in vibration ; and when they are heated their original vibrations are ren- dered more intense, and more rapid vibrations are added HEAT. 2I 3 EFFECTS OF HEAT ON BODIES. CONDUCTION. 199. The Molecules of a Body communicate their Vibrations to one another. We have now seen that on absorbing heat the molecules of a body are made to vibrate with greater energy and in quicker periods. When one end of a poker is placed in the fire, it soon becomes red hot, and the heat slowly travels from this end to the other. This heat cannot have been radiated, since radiant heat travels at the rate of 190,000 miles a second. The molecules of a solid are then able to communicate their vibrations to one another as well as to the ether. This transmission of heat from molecule to molecule of gross matter is called conduction. 200. Different Solids conduct Heat differently. If several thermometer bulbs be inserted in a metallic rod, as shown Fig. 157- in Figure 157, and one end of the bar be heated, the mercury will begin to rise in the thermometer nearest the heated end, and then in the others successively ; but no 214 HEAT. amount of heating will make the mercury rise as high in the last thermometer as in the first. If now rods of other metals of the same length and thickness are tried in the same way, it will be found that the difference of tempera- ture at the ends of the rods is not always the same. The less the difference of temperature, the better the body conducts heat. The following Table of conductivity is from Tyndall : Name of Substance. Conductivity. For Electricity. For Heat. Silver IOO 73 59 22 23 13 II IO 6 2 IOO 74 53 24 15 12 6 2 Copper Gold Brass Tin Iron Lead Platinum German silver. Bismuth It will be seen that the metals differ widely in con- ductive power, and that those which are good conductors of heat are also good conductors of electricity. 20 1. Liquids and Gases are Poor Conductors of Heat. In Figure 158 a differential thermometer (that is, a ther- mometer for finding the difference of temperature at two points) is placed in a glass vessel filled with water. Heat is applied to the surface of the water by means of a dish of heated oil. If the water conducted the heat, the upper bulb of the thermometer would be- come heated sooner than the lower one, and the thermometer would at once indicate a difference of tem- perature between the two bulbs. But the thermometer is scarcely affected. HEAT. 215 This experiment shows that water is a poor conductor of heat. The same is true of other liquids, and even more so of gases. SUMMARY. " The molecules of a heated solid communicate their vibrations to one another as well as to the ether. Heat thus communicated is said to be conducted. (199.) Some solids conduct heat better than others. (200.) Liquids and gases are poor conductors. (201.) TEMPERATURE. 202. Heat raises the Temperature of a Body. The most obvious effect of the heat absorbed by a body is a rise of temperature. This rise of temperature is indicated by the sense of touch, but more accurately by a thermometer. 203. A Body in cooling i gives out just as much Heat as it takes to heat it i. Boil a quarter of a pound of water in a beaker, and plunge the bulb of a thermometer into it, and it will indicate a temperature of 212. Remove the beaker from the source of heat, and add a quarter of a pound of water of a temperature of 70. Stir the mixture a short time with the bulb of a delicate thermometer, and the temperature will be found to be 141. The first quarter of a pound of water has then lost 71 and the second has gained 71 ; in other words, the first in cooling i has given out just heat enough to warm the second i. The same is true of all other bodies. 204. It requires Different Ainounts of Heat to raise the Temperature of the Same Weight of Different Bodies i. If a piece of tin be heated to 212 by plunging it into boiling water, and it then be plunged into its own weight of water at 70, the resulting temperature will be considerably below 141 ; showing that tin in cooling i does not give 2l6 HEAT. out heat enough to raise the water i. But the tin in cooling i gives out just as much heat as it takes to raise its temperature i. Hence it takes more heat to raise the temperature of a pound of water i than to raise that of a pound of tin i. If copper be used instead of tin, the resulting temperature will be higher, but still below 141. It requires, then, less heat to raise the temperature of a pound of copper i than to raise that of a pound of water i, but more than it takes to raise that of a pound of tin i. In this way it is found that it takes very different amounts of heat to raise the temperature of the same weight of different substances i. 205. Unit of Heat. The thermometer indicates the rise of temperature in a body, but tells us nothing of the amount of heat required to raise the temperature. It is therefore desirable to have some unit by which the heat received by a body may be expressed. The unit usually taken is the amount of heat required to raise the tempera- ture of a pound of water i. A unit of heat, then, is the amount of heat required to raise the temperature of one potind of water i. 206. Specific Heat. The amount of heat required to raise the temperature of a pound of any substance i, ex- pressed in units, is called the specific heat of that substance. Thus it requires ^ of a unit of heat to raise the tempera- ture of one pound of mercury i ; and the specific heat of mercury is therefore ^ or .033. When we know the specific heat of a body and also its weight, we can readily find how many units of heat it will take to raise its temperature any number of degrees. For instance, 10 pounds of iron have been raised 100 in temperature, and the specific heat of iron is .1138. To raise 10 pounds of iron i in temperature would, then, require 1.138 units of heat. To raise it 100, would require 113.8 units of heat. HEAT. 217 207. The Method of finding Specific Heat by Mixture. One of the readiest ways of finding the specific heat of a body is by the method of mixture^ as it is called. The substance is first weighed, then heated to a certain tem- perature, and plunged into a vessel of water, and the resulting temperature is noted. The weight of water and its temperature at the beginning of the experiment are supposed to be known. We then can find the number of units of heat which the water has received, and which of course have been lost by the heated substance. We also know the number of degrees the substance has cooled, and can therefore find how many units of heat one pound of it would give out in cooling i. Now this is the amount of heat which it would take to raise the temperature of one pound of it i, or its specific heat. This method is simple, and would be satisfactory, were not the water losing heat by radiation during the experi- ment. We can, by trial, find very nearly the rate at which the water is radiating its heat, and thus calculate the loss. 208. The Method of finding Specific Heat by Melting. Another method of finding specific heat is by melting ice. The substance is first weighed, then heated to a certain temperature, as 100, and placed in the vessel M (Figure 159). This vessel is placed within the vessel A, the space between the two being filled with ice. The vessel A is placed in another, B, from which it is also separated by ice. Since the vessel A is surrounded by ice, the heat which melts the ice within it must come wholly from the vessel M. As the ice in A melts, the water runs off through the pipe D. It is necessary to know how much ice will be melted by one pound of water cooling i, or by one unit of heat. We need, then, only know how much ice is melted by any substance within the box M t in order to find how many units of heat it has given up. Dividing this by the weight of the substance 10 218 HEAT. and by the number of degrees it has cooled, we get its specific heat. Fig. 159- Thus, suppose ten pounds of iron heated to 132 be placed in Jlf t and allowed to cool 100, and that it is found to give out 109 units of heat. 109 -j- 10 10.9, which is the number of units of heat which would be given out by one pound cooling 100 ; and 10.9 -f- ioo = . 109, which is the number of units one pound would give out in cool- ing i, or the specific heat of iron. The specific heat of solids can be found by either of the above methods. The specific heat of a few substances is given in the following table : Substance. Mean Specific Heat. Between 32 and 212. Between 32 and 572. Iron 0.1098 0.0330 0.0927 0.0507 0-0557 0.0949 0.0355 0.1770 0.1218 0.0350 O.IOI5 0.0549 0.0611 0.1013 0-0355 0.1990 Mercury Zinc Antimony Silver Copper. . Platinum Glass HEAT. 2I 9 It will be seen from this table that the specific heat of a solid increases with the temperature. It will be noticed that the specific heat of solids is low compared with that of water, which is of course i.oo. 209. Specific Heat of Liquids. Regnault has found the specific heat of a number of liquids by the following method. The liquid to be tried is put in the vessel O (Figure 160), which is placed in a large vessel, R, fiDed Fig. 1 60. with hot water, and is thus kept at a definite temperature. C is a calorimeter, or heat-measurer. It consists of three vessels placed one within another. The inner one is surrounded with water, and the middle one with air. As air is a very poor conductor, all the heat given out by the inner vessel is kept in the water. The radiant heat of R is shut off from C by the screen P. When the cock r is opened, the liquid in the vessel O runs into the inner vessel of C, and there gives up its heat to the water in the middle vessel. The weight of the water in this vessel is 220 HEAT. supposed to be known, and its temperature at the be- ginning and end of the experiment is noted. We can then find how many units of heat the liquid in the inner vessel has given up to the water, and also how many degrees it has cooled. By finding the weight of the liquid in that vessel, we can find how many units of heat one pound of it would give out in cooling i, or its specific heat. It is found in this way that the specific heat of a sub- stance when in the liquid state is greater than when in the solid state ; and that the specific heat of a liquid increases with the temperature, and more rapidly than that of solids. 210. Specific Heat of Gases. Regnault used the follow- ing method for finding the specific heat of gases. The gas is first forced into a large receiver, R> (Figure 161), where Fig. 161. it is kept at a constant temperature by the water surround- ing it. On opening the stopcock / the gas may, by an arrangement at r y be made to flow out through the pipe in a uniform stream. It is then passed through the coiled pipe in the chamber S, where it is heated to a high tem- HEAT. 221 perature, which is measured by the thermometer T'. It is then sent through the calorimeter C, where it gives up its heat to the water. By means of a manometer the pressure of the gas in R is found at the beginning and at the end of the experiment. The difference of pressure enables us to find the weight of gas which has passed through the calorimeter, for the density of a gas is inversely propor- tional to its pressure. If, for instance, the pressure of the gas at the end of the experiment is one half what it was at the beginning, its density will be only one half; and there- fore one half of the gas must have passed out. When we know the weight of the gas which has passed through C, and the heat it has given up to the water, we can easily find its specific heat. The following Table gives the specific heat of certain gases and vapors : Gas or Vapor. Equal Vols. Equal Weights. Air. O.237S Oxygen O.24.O? 0.2171; Nitrogen 0.2368 O.24T.8 Hydrogen O 23S9 j 4.OQO Chlorine O.2Q6A O.I2IO Bromine. . . o. 3040 O.OS 1 ? 1 ? Nitrous oxide O.744.7 O.2262 Nitric oxide ^snni o 2406 O 23.17 Carbonic oxide 0.2370 o 24^0 Carbonic acid. ... O.33O7 0.2169 Bisulphide of carbon . O.4I22 0.1^69 Ammonia . . O 2996 J r> o ^084 Marsh gas O 3277 O ^929 Olefiant gas o 4160 o 4040 Water O.2Q8Q o 4805 Alcohol O.7I7I O 4"? 34 211. Influence of the State of a Substance on its Specific Heat. The same body has a higher specific heat in the liquid than in the solid state ; while in the gaseous con- dition, again, its specific heat is less than when it is liquid. Thus, for instance, the specific heat of water is twice as 222 HEAT. great as that of ice, and more than twice as great as that of steam. The following Table exhibits the dependence of the specific heat on the physical state of the substance : j Specific Heat. Solid. Liquid. Gaseous. Water o ^040 I OOOO o 480*5 Bromine 008'?'? o 1060 O.O^S Tin o ex 62 o 0637 Iodine O O, is filled with pounded ice, and the other, T, with oil. The latter case is enclosed in a furnace, so that its temperature can be raised to any desired point. The density of the mercury in the tube B will diminish in the exact ratio of its expansion, and the temperature of the mercury in the tube A is always at the freezing-point. It will therefore rise in the other tube in proportion as it 236 HEAT. expands ; that is, if the mercury in B should be expanded so as to double its volume, it would stand twice as high in that tube as in A, since its density would be only half as great. By noticing, then, the difference in the height of the mercury in the two tubes for any rise of temperature, Fig. 167. we can ascertain the expansion of the mercury ; and this expansion, divided by the number of degrees the tempera- ture has risen, will give the coefficient of expansion. 233. How to find the Coefficient of Expansion for any Liquid. Let a glass bulb having a projecting tube, be filled with any liquid and be heated. The liquid will at first fall in the tube, and then begin to rise and continue to rise steadily as the temperature increases. The falling of the liquid at first is owing to the fact that the glass, being first heated, expands before the liquid does. After this the liquid expands more rapidly than the glass, and therefore rises in the tube. The expansion of a liquid as measured in such a bulb HEAT. 237 is only its apparent expansion. Its real expansion is this apparent expansion plus the expansion of the bulb. The expansion of the bulb can be found by means of mercury. In Figure 168 we have a bulb with a projecting tube drawn out to a fine point. This bulb is first weighed, Fig. 168. and then filled with mercury and weighed again. The difference of these weights is the weight of the mercury at the ordinary temperature. The bulb is now heated, and a part of the mercury runs out. The bulk of the mercury which runs out is equal to the excess of the expansion of the mercury over that of the bulb. Now we know the real expansion of mercury, and the excess of this over its apparent expansion, as just found, is the expansion of the bulb. This expansion, plus the apparent expansion of any liquid put into the bulb, gives, as we have seen, the real expansion of the liquid for any rise of temperature ; and this divided by the number of degrees the temperature has risen gives the coefficient of expansion. 234. How to find the Coefficient of Expansion for any Solid. The volume and weight of the solid whose ex- pansion is to be found are first ascertained. It is then put into a glass tube, of known weight, which is filled with mercury and drawn out to a fine point. The weight of the whole, minus the weight of the tube and the solid, is the weight of the mercury. The whole is now heated to a certain temperature, and the mercury which runs out is weighed. Now, since we know the rate of expansion of the glass and of the mercury, we know how much mercury 2 3 8 HEAT. should have run out had the solid not expanded at all ; and the excess of the mercury which actually runs out over, this amount is equal to the expansion of the solid. This divided by the number of degrees the temperature has risen gives the coefficient of expansion. 235. How to find the Coefficient of Expansion for Air and other Gases. In Figure 169 b is a large glass bulb filled with air and connected by a glass tube with the upright tube T. The latter opens into a vessel of mercury, as does also Fig. 169. the tube T'. By means of the screw S the mercury can be kept at the same height in the two tubes. The bulb is first surrounded with melting ice, and the mercury in the two tubes is brought to the same level. The bulb is next immersed in steam, and the mercury in the tubes again brought to the same level. The difference of the heights HEAT. 239 of the mercury in the two cases is equal to the expansion of the air for a rise of temperature between 32 and 212 F., and from this we can easily find its coefficient of ex- pansion. Since the air on expanding partially fills the tube T, it is necessary that the tubes T and T' should be surrounded with boiling water, in ordf^r that all the air may be kept at the same temperature. It is found in this way that air expands ,367 of its vol- ume for a rise of temperature from 32 to 212. The following Table shows the expansion of .eve**ai gases for this rise of temperature : Hydrogen 0.3661 Atmospheric air 0.3670 Carbonic oxide 0.3669 Carbonic acid 0.3710 Nitrous oxide -37 I 9 Sulphurous acid 0.3903 Cyanogen 0.3877 It will be observed that hydrogen, carbonic oxide, and atmospheric air, gases which cannot be condensed and whose temperature must therefore be far above the boiling- points of their liquids, expand almost exactly alike, while the other gases, which can easily be condensed and must therefore be near their boiling-points, expand more rapidly and somewhat more unequally. This is probably because the molecules in the latter are still so near together that they exert considerable influence on one another. At a greater distance from the boiling-point the molecules may get so far apart that they exert no sensible influence upon one another. Such gases are called perfect gases. 236. When a Gas is not allowed to expand, its Elasticity is increased by Heat. As the bulb in Figure 169 becomes heated, the expansion of the gas drives the mercury from the tube T. The mercury can, however, be kept at the same height by increasing the pressure upon the mercury 240 HEAT. in the box by means of the screw S. This increase of pressure will also cause the mercury to rise in the tube T'. The difference of height in the columns of mercury in the tubes shows how much the elastic force of the gas is increased. In this way it is found that the elasticity of air when not allowed to expand is increased about .367 for a rise of temperature from 32 to 212. SUMMARY. The heat absorbed by a body is used partially in push- ing the molecules apart, or expanding it. (226.) Different solids and liquids expand unequally, and dif- ferent gases equally, for the same rise of temperature. (227, 231.) The coefficient of expansion for a body is the amount it expands for a rise of temperature of i C. (232 - 235.) When a gas is not allowed to expand, its elasticity is increased by heat. (236.) CONVECTION. 237. We have now .seen that the molecules of a body are separated when it becomes heated ; and, since the mole- cules of liquids and gases are free to move, this expansion ought, when they are heated unequally in different parts, to create currents ; for the unexpanded and heavier por- tions will tend to displace the lighter ones and to compel them to rise. As these heavier portions become heated, they will in turn tend to rise and give place to colder por- tions ; and so on. These currents, of course, tend to distribute the heat, and this mode of distribution is called convection. 238. Convection of Liquids. In Figure 170 we have a glass beaker filled with water heated by a lamp below. A HEAT. 241 little sawdust is added to the water, and its motions show that a current is passing up the centre of the vessel and down at the sides, as indicated by the arrows in the figure. Each molecule is thus seen to come to the bottom to get heated, and then to return Fig 1?a to the surface. It is in this way that water, which is so bad a conductor, is so readily heated when the heat is applied below. 239. Oceanic Currents. Oce- anic currents are produced by convection. The temperature of the sea in the tropics is about 50 higher than at the poles, and the specific gravity of the water is therefore much less. To restore the equilibri- um, the warmer and lighter wa- ter of the tropical regions flows towards the poles, and the colder and denser water of the polar regions flows towards the equator. If the whole earth were covered with water of the same saltness, we should everywhere have a surface- current from the equator towards the poles, and an under- current from the poles towards the equator. But owing to the obstructions offered by the land and by the inequalities in the bed of the ocean, and to the different degrees of saltness, and therefore of density, in different parts of the sea, these two great currents are broken up into innumer- able currents and counter-currents, which diversify the face of the ocean and mark out the highways of commerce. The most remarkable of these currents is the GulJ Stream, which issues from the Gulf of Mexico, flows north- ward off the coast of the United States, and, crossing the Atlantic in a northeasterly direction, washes the western coast of Europe. ii p 242 HEAT. 240. Convection of Gases. If a lighted candle be put in a beam of solar or electric light which is thrown upon a screen by means of a lens, the currents of air which are streaming up around the flame can be readily seen. Again, if a lighted candle be held in the crack of a door which opens from a warm into a cold room, the flame will be blown outward at the top of the door and inward at the bottom, while half-way up it will burn steadily. A current of cold air is thus seen to be passing into the room at the bottom, driving out a current of warm air at the top. It is mainly by convection that the air in a room is heated. The air next the stove is heated and expanded, and then forced upward by the current of colder air. When a building is heated by a furnace, this is placed in the cellar and encased in brick-work or in sheet-iron. The space between the fire-pot and the casing is connected by means of the air-box with the outer atmosphere, and by means of flues or pipes with the rooms to be heated. The air about the fire-pot first becomes heated, and is driven up through the pipes by the cold air from without. SUMMARY. When a gas or a liquid is heated beneath its surface, currents are produced which distribute heat by convection. It is in this way that the Gulf Stream and other oceanic currents are produced. (237 - 240.) THE RELATION OF WATER TO HEAT. 241. The High Specific and Latent Heat of Water. Water, because of its specific and latent heat, which are higher than those of any other liquid, exerts a marked influence upon climate. It makes the transition from win- ter to summer and from summer to winter more gradual. HEAT. 243 In the spring, when the snow begins to melt, a large amount of heat is absorbed from the air and rendered latent. After the snow and ice are all melted, such is the specific heat of water that it requires a great deal of heat to raise its temperature. In the fall, on the other hand, as the water cools down and freezes, it gives out all the heat which it had absorbed and rendered latent in the spring. 242. The Irregular Expansion and Contraction of Water. Bodies, as we have seen, usually contract when cooled. Liquids continue to contract, not only until they are frozen, but even after freezing. Fill a test-tube with water at a temperature of 70 and close it with a rubber cork through which passes a fine glass tube. Press the cork in so that the water shall rise in the tube. Plunge the tube into a freezing mixture, and the water gradually falls until its temperature is about 39. It then slowly rises until its temperature is 32. It now begins to freeze, and suddenly expands. If, therefore, water at the temperature of 39 be either warmed or cooled, it expands. This temperature is hence called the point of maximum density of water. This expansion of water in freezing is often illustrated by the bursting of pipes and vessels in which water is allowed to freeze. Water is the only liquid which has such a point of maximum density, and there are but very few substances which expand when they become solid. Iron is such a substance, and it is owing to this property that it is so well adapted for castings. As it solidifies, it expands so as completely to fill the mould. Bismuth expands in the same way, and also the alloy of antimony, lead, and tin, which is used for type-metal. This irregular expansion of water is of the greatest im- portance. Before freezing it begins to grow lighter, so that the freezing begins at the surface ; and the ice, being lighter still and also a poor conductor of heat, floats upon the water and keeps it from freezing very deep. If water 244 HEAT. continued to contract as it cooled, it would begin to freeze at the bottom, and during the winter our lakes and rivers would become solid masses of ice. This would be fatal to all animal life in the water ; and, as water is a very poor conductor of heat, it would melt only to the depth of a few feet during the summer. 243. Latent Heat of Steam and Vapor. Not only is the latent heat of water greater than that of any other liquid, but that of steam and watery vapor is greater than that of any other gas or vapor, hydrogen alone excepted. 244. Heating by Steam. It is now quite common to warm buildings by steam. Pipes run from the boiler through the rooms to be heated, and then back to the boiler again. The steam passes from the boiler into these pipes, where it is condensed and runs back as water to the boiler. Now every pound of water converted into steam in the boiler takes up over 900 units of heat, and every pound of steam which condenses in the pipes gives out the same amount of heat into the rooms. The water is thus made to act as carrier of heat between the furnace and the room where it is wanted. As fast as it gives up the heat which it has absorbed from the furnace, it runs back to the boiler for more. SUMMARY. The high specific and latent heat of water tends to make the transition from winter to summer and from summer to winter more gradual. (241.) The irregular expansion and contraction of water when heated and cooled prevents the lakes and rivers from freez- ing solid in the winter. (242.) Steam has a high specific and latent heat, which becomes sensible on condensation. It is, therefore, used for heating buildings. (243, 244.) HEAT. 245 THERMAL INSTRUMENTS. 245. The Mercurial Thermometer. The ordinary ther- mometer is one of the most important thermal instruments, and is used, as its name implies, to measure temperature. It consists of a fine glass tube with a bulb blown upon one end of it. At the ordinary temperature the bulb and a part of the tube are filled with mercury. In order to fill the tube with mercury, a cup of glass or india-rubber is connected with the top of the tube. This cup is filled with mercury, and the bulb heated so as to drive out a part of the air. The bulb is then allowed to cool, and a part of the mercury falls into the tube to take the place of the air driven out. This mercury is now boiled a short time, and in this way the remainder of the air is expelled. The bulb being allowed to cool again, more mercury passes in and fills both bulb and tube. The mercury is now heated up to the highest temperature which the thermometer is intended to measure, and the end of the tube is sealed air-tight by melting the glass. As the bulb cools again, the mercury falls in the tube, leaving a vacuum above it. The next thing to be done is to graduate the thermome- ter. On the thermometer scale there are two fixed points, that at which ice melts, and that at which water boils. These are called i\\e freezing-point and the boiling-point. The freezing-point is found by plunging the bulb into melting ice, and noting the position of the mercury in the tube. Melting ice is used rather than freezing water, be- cause it is found that if water be kept perfectly still it can be cooled several degrees below the freezing-point before 2 4 6 HEAT. it congeals ; while ice, at the ordinary pressure, always melts at the same temperature. We have also seen that the boiling-point of water is affected by various circumstances. Hence the boiling- point of the scale cannot be found by plunging the bulb into boiling water. But whatever may be the temperature at which water boils, its steam always has the same tem- perature at the ordinary pressure. The boiling-point is then found by enclosing the bulb and tube in a steam- bath, as shown in Figures 171 and 172. On the Fahrenheit scale, which is the one in common use in this country and England, the freezing-point is Fig. 171. Fig. 172. marked 32, and the boiling-point 212. The space between the two is consequently divided into 180 equal parts. The rise of temperature corresponding to the rise of the mer- cury through one of these parts is called one degree. The HEAT. 247 equal divisions are continued above the boiling-point and below the freezing-point. The scale, however, is not ex- tended below 38 nor above 576, since mercury freezes at one of these points and boils at the other. On the Centigrade scale, which is the one commonly used in France, the freezing-point is marked o, and the boiling point 100. 5 of this scale correspond, then, to 9 of the Fahrenheit scale. Since the Centigrade scale is a decimal one, it has been adopted by most scientific men throughout the world. A third scale, known as Reaumur's, is in general use in Germany. On this scale the freezing-point is marked o, and the boiling-point 80. 246. The Alcohol Thermometer. When temperatures below 38 are to be measured, alcohol is used instead of mercury. An alcohol thermometer is not, however, so accurate as a mercurial one. 247. The Air Thermometer. Mercury, as we have seen, cannot be used to measure very high temperatures. There are various ways of measuring such temperatures, but the best is by means of the air thermometer. The expansive force of air is very regular for all known temperatures, but it expands so rapidly that to measure the ordinary range of temperatures would require too long a tube. The expansion of the air in the tube can be indicated by the movement of a column of liquid upon which it acts. 248. The Differential Thermometer. Leslie constructed an instrument which shows the difference in temperature between two neighboring substances or places, and which is hence called the differential thermometer. In this instru- ment two bulbs, A and B, filled with air, are connected by means of a bent tube, as in Figure 173. A little colored liquid fills the lower part of this tube, and rises to the levels C and D when both bulbs are of the same tempera- ture. But should A become warmer than B, since air 248 HEAT. Fig. 173- expands very much for an increase of temperature, the. column of liquid will be pushed down at C and made to rise at D ; and this motion will be reversed when B becomes warmer than^. Such an instrument will therefore indicate any difference of temperature with great delicacy. The liquid in the tube ought to be one which is not volatile. Sulphuric acid is frequently used. The most delicate of all differential thermometers is the thermo-electric pile, which, with its .. accompanying galvanometer, will be described here- after (see Electricity, pages 265 and 283). 249. Breguefs Metallic Thermometer. This instrument consists of a spiral (Figure 174) composed of silver, gold, and platinum, rolled to- Fi gether so as to form a very fine ribbon. In this state it is sensitive to an exceedingly slight change of temperature, becoming coiled or un- coiled, owing to the dif- ferent expansion of the metals of which the compound ribbon is made. A needle at- tached to one extremi- ty of the coil points to a scale which is gradu- ated by the aid of an ordinary thermometer, a is a rod put in the axis of the spiral to keep it in place. HEAT. 249 250. Effect of Temperature upon Measures of Time. The rate of a clock depends upon the time in which its pendulum vibrates, and that of a watch upon the time of oscillation of its balance-wheel. Now the time of vibra- tion of a pendulum depends upon its length ; and since the change of temperature alters the length of a pendu- lum, it likewise alters its time of vibration. The higher the temperature, the longer does the pendulum become, and the more slowly does it vibrate. In like manner a change of temperature, by altering the dimensions of the balance-wheel of a watch and the force of the spring, will alter its time of oscillation in such a manner that it will vibrate more slowly in hot weather than in cold. These sources of error may be obviated by means of certain compensations. 251. Graham's Mercurial Pendulum. The first attempt to compensate for change of length in a pendulum was made by Graham, an English clockmaker. The rod of his pendulum, Figure 175, was made of glass, p . to the lower end of which was attached a cylin- drical vessel containing mercury. As the glass rod expands by heat, the bottom of the vessel which contains the mercury will of course be rendered more distant from the point of suspen- sion, but since the column of mercury resting on this base expands upwards, its centre of gravity is raised, or brought nearer the point of suspen- sion. The lowering of the centre of gravity, due to the expansion of the glass, may thus be coun- teracted by the rise of the same, due to the ex- pansion of the mercury. The correction for im- perfect compensation is made by raising or lower- ing the cylinder of mercury by means of a screw. 252. Compensation Balance- Wheel. If the bal- ance-wheel of a chronometer be formed, as in 250 HEAT. Figure 176, not with one continuous rim, but with a broken rim of several separate pieces, all of which are fixed at one end and free at the other, the free ends being loaded ; and further, if each piece be composed of two metals, of which the most expansible is placed without ; then it is evident Fi : 6 that on a rise of temperature the loaded ends will approach the centre. This may be so arranged as to coun- teract the effect produced on the rate of the chronometer by the expansion of the wheel, which carries the cir- cumference farther from the centre. 253. Other Effects of Expansion. It requires very intense pressure to produce the same change of volume in a solid or liquid body as that which is occasioned by a very small change of temperature. It follows from this that the force exerted by solids in con- tracting or expanding, or by liquids in expanding, must be very great. If a strong vessel be entirely filled with a liquid and then sealed tightly, the vessel will burst if there be a considerable rise of temperature. In like manner it has been calculated, that a bar of wrought iron whose temperature is 15 F. above that of the surrounding medium, if tightly secured at its ex- tremities, will draw these together, with a force of one ton for each square inch of section, on cooling down to the surrounding temperature. In the arts it is of great importance to bear in mind the intensity of this force, sometimes with the view of guarding against its action, and sometimes in order to make it useful. Thus, bars of furnaces must not be fitted tightly at their extremities, but must at least be free at one end. In making railways, also, a small space must be left between the successive rails. For a similar reason water-pipes and gas-pipes are fitted to each other by telescopic joints. HEAT. 251 As an instance of the advantage which may be derived from the force of contraction, we may mention the fa- miliar method by which tires are secured on wheels. The tire is put on hot, when it fits loosely, but as it cools it contracts and grasps the wheel with very great force. 254. DanieWs Dew-point Hygrometer. A hygrometer is an instrument for measuring the amount of moisture in the air. The one invented by Daniell is shown in Figure 177. It is composed of two glass bulbs. The bulb A is more than half filled with ether, and contains a delicate thermometer ^ plunged in the ether ; the space above is void of air and of every- thing but the vapor of ether. The bulb B is covered with some fine fabric, such as muslin, upon which ether is dropped ; the evaporation of the ether produces intense cold, in consequence of which the ether vapor inside B is rapidly con- densed, and of course the ether in A as rapidly evaporates. The evaporation of the ether at A cools the bulb until the air in contact with it sinks below the dew-point ; that is, the temperature at which the moisture in the air begins to be deposited as dew. The bulb A is made of black glass in order that this deposition may be more readily observed. At the moment of deposition the thermometer in A is read. When the dew disappears, as the temperature rises, the same thermometer is also read, and the mean of these two readings is taken to indicate the dew-point. The ther- mometer C gives the temperature of the air. The nearer the dew-point is to the temperature of the air, the nearer the air is to being saturated with vapor. 255. Wet and Dry Bulb Hygrometer. This instrument was devised by Mason, and consists of two thermometers 2 5 2 HEAT. Fig. 178. (Figure 178) placed side by side, one having a dry bulb and the other a bulb covered with muslin, kept moist by means of a string dipping in water. The wet bulb is chilled by the evaporation of the water from it, since this evaporation renders some of its heat latent. The drier the air, the more rapid the evaporation, and the greater the difference between the readings of the wet and dry bulb thermom- eters. When we speak of the hu- midity of the air, we do not mean the absolute amount of vapor which it holds, but the degree of its saturation. Thus, a cubic foot of air at 32 is saturated by two grains of water ; but at 68 it requires 7.5 grains to saturate it. When the air is com- pletely saturated, its humidity is said to be 100 ; when half saturated, 50; when three fourths saturated, 7 5 ; and so on. 256. Edsoris Hygrodeik. This is shown in Figure 179, and is an improved form of Mason's hygrometer. It dif- fers from all other hygrometers in having a dial, over which moves a pointer, showing at a glance the temper- ature, the degree of humidity, the absolute amount of vapor in each cubic foot of air, and the dew-point. 253 SUMMARY. One of the most important thermal instruments is the thermometer. The thermometer scales most used are Fahren- heit's, the Centigrade, and Reaumur's. (245 - 247.) Breguefs thermometer indicates changes of temperature by the unequal expansion of metallic ribbons. (249.) The differential thermometer serves to measure the dif- ference of temperature at two places. The most delicate differential thermometer is the thermopile. (248.) The expansive power of heat may be made to regulate the rate of clocks and watches. (250-252.) The hygrometer is an instrument for measuring the amount of moisture in the air. (254-256.) 254 HEAT. CONCLUSION. There are two kinds of heat, luminous and obscure ; and each is radiated, reflected, refracted, dispersed, ab- sorbed, and polarized, in the same way as light. They are both radiated from an incandescent body, but luminous heat is more refrangible than obscure heat. As the tem- perature of a body is raised, it at first radiates only the less refrangible rays, but as it grows hotter it begins to send out more and more refrangible rays, until it becomes white-hot, when it emits all the rays of the spectrum. At the same time the obscure radiations become more intense. The ordinary spectrum is made up of a luminous portion, which is prolonged at one end by an obscure chemical, and at the other by an obscure thermal portion. Each part is crossed by blank lines, which, being equally devoid of luminous, thermal, and chemical power, show that the three kinds of radiations are essentially the same, differing only in refrangibility, or in the rate of vibration. The periods of these vibrations may be so changed that the obscure thermal and chemical radiations become luminous, as in calorescence and fluorescence. Heat originates in the vibrations of the molecules of bodies, and is transmitted by imparting these vibrations to the ether. It is absorbed when these vibrations are again taken up by the molecules of gross matter. As the mole- cules of any body can vibrate only in certain periods, a body can radiate or absorb only certain qualities of heat. The heat which a body absorbs raises its temperature, changes its state, and causes it to expand. It is also com- municated from molecule to molecule by conduction, and, in gases and liquids, by currents, or convection. IV. ELECTRICITY ELECTRI CITY. MAGNETISM. 257. Magnets. In studying Electricity it is necessary to know a few things about magnets. Bring one end of an ordinary bar magnet into contact with a pile of iron tacks ; on removing it, a number of the tacks are carried away with it. This illustrates one of the leading characteristics of a magnet ; namely, that it attracts iron. The force residing in a magnet and shown by its at- tracting iron is called magnetism. There is a certain iron ore which has the power of at- tracting iron. This ore seems to have been first found near Magnesia, a city of Asia Minor. Hence the name magnet. Natural magnets are called loadstones (more prop- erly lodestones}, that is, stones that lead or draw iron. 258. The Power of a Magnet resides chiefly at the Ends. If a small iron ball is fastened to a string, and moved alongside a bar magnet, it is scarcely attracted at the mid- dle of the bar. As it approaches either end it is attracted more and more strongly, until it is brought near the end, where attraction is found much the strongest. The force of a magnet,' then, resides chiefly at the ends. Put a piece of stiff drawing-paper over a strong magnetic bar, and strew fine iron-filings over it. Not only is the position of the magnet below shown on the paper, but the Q 258 ELECTRICITY. particles of iron arrange themselves in lines radiating from the poles. These lines are called lines of magnetic force, or magnetic curves. Fig. 180. 259. The Forces at the Opposite Ends of a Magnet act in Opposite Directions. Suspend a bar Ing. iSi. w * t * magnet by a string so that it can turn freely. Bring one end of a bar mag- net near one end of the suspended magnet, and the latter is drawn to- 8 wards it. Reverse the ends of the bar magnet, and the end of the sus- pended magnet is repelled. This shows that the forces at the ends of a magnet act in opposite directions. 260. The Poles of the Magnet. The ends of the magnet, where the opposite forces reside, are called poles. When a bar magnet is poised so that it can move freely, it takes a nearly north and south direction. One of its poles will always point to the north, and is called the north pole. The opposite pole is called the south pole. A bar magnet thus poised so as to turn freely is called a magnetic needle. 261. The Earth acts like a Magnet. If a small needle which is free to move in a horizontal plane is placed upon a bar magnet, its south pole will always point towards the north pole of the latter. If a small dipping needle, that is, a ELECTRICITY. 259 needle which is free to move in a vertical plane, is placed above the middle of a bar magnet, it stands parallel with the bar magnet. If it is moved towards the north pole of the magnet, the south pole begins to dip towards the magnet ; and the farther it is moved towards this pole, the more it dips. If it is moved from the centre of the bar magnet towards the south pole, its north pole dips in the same way. We have already seen that a magnetic needle free to move in a horizontal plane points north and south when held above the earth. It is also found that a dipping needle in the vicinity of the equator stands parallel with the plane of the horizon, and that, when carried north from the equator, its north pole dips towards the horizon ; while, if it is carried south from the equator, its south pole dips towards the horizon. It is thus found that the earth acts upon a magnetic needle like a magnet whose poles are near the poles of the earth ; its south pole near the north pole of the earth, and its r orth pole near the south pole of the earth. The French regard the magnetic pole of the earth near the north pole as a north pole, and the pole of the magnetic needle which points towards this pole as the south pole. The pole of the magnet, therefore, which we call the north pole, the French call the south pole, and vice versa. 262. Like' Poles of Magnets repel and unlike Poles attract. This has already been shown by the action of a bar mag- net upon a dipping needle. It may be further shown by bringing the north pole of a bar magnet near the north pole of a needle, which will be repelled. On bringing the south pole of this magnet near the north pole of the needle, it will be attracted. 263. Magnetism is developed in Iron or Steel by Induc- tion. When a piece of soft iron is brought into contact with the pole of a magnet, it will attract other pieces of 200 ELECTRICITY. iron, showing that magnetism has been developed in the iron by contact with the magnet. Magnetism can be de- veloped in a piece of steel in the same way. The iron however, loses its magnetism as soon as it is taken away from the magnet, while the steel retains it. It is not neces- sary that a piece of iron should be brought into actual contact with the pole of a magnet in order that magnetism may be developed in it, but merely that it be brought very near the pole. Magnetism developed in this way in a piece of iron or steel is said to be induced. 264. Forms of Magnets. Ordinary magnets are made Fig. 182. f steel. When straight they are called bar magnets; when bent into the shape of the letter U they are called horseshoe mag- nets. When several bar or horseshoe mag- nets (see Figure 182) are connected, they constitute a magnetic battery. 265. The Making of Magnets. Mag- nets are often made by contact with per- manent magnets by a process of single or double touch. In the former case, the steel bar to be magnetized is laid on a table, and the pole of a powerful magnet is rubbed from ten to twenty times along its length, always in the same direction. If the magnetizing pole be north, the end of the bar it first touches each time becomes north, and the end where it is taken off becomes south. The same thing may be done by putting one pole of the magnet, say the north, first on the middle of the bar, then giving it a few passes from the middle to the end, returning always in an arch from the end to the middle. The other half of the bar is then rubbed in the same way with the south pole of the magnet. The first end rubbed becomes the south, and the other the north pole of the new magnet. ELECTRICITY. 26l Fig. 183. The method by double touch is shown in Figure 183. The bar s n to be magnetized is placed on a piece of wood, W, with its ends resting on the extremities of two powerful magnets NS and SN. Two ^_ _ -\\^ rt '^ rubbing magnets are placed with their poles near, but not touch- ing, on the middle of sn, inclined to it at an angle of 10 or 15. The two magnets are then drawn along from the middle to one end and then back to the other, and so backwards and forwards from ten to twenty times, and lifted from the magnetized bar again at the middle. Care must be taken that both ends are rubbed the same number of times, and that the lower poles of the rubbing magnets do not go beyond the ends of the bar. Both the upper and lower surfaces of the bar must be rubbed in this way, in order to magnetize it fully. A small piece of wood may be placed between the poles of the rubbing magnets to prevent contact. The position of the poles is shown in the figure by the letters ; JV or n meaning a north, and S or s a south pole. For horseshoe magnets Hof- =// fer's method is generally fol- lowed. The inducing magnet (see Figure 184) is placed vertically on the magnet to be formed, and moved from the ends to the bend, or in the op- posite way, and brought round again in an arch to the starting-point. A piece of soft iron is placed at the poles of the induced magnet. Both magnets should be of the same width. Fig. 184. 262 ELECTRICITY. SUMMARY. Any substance which will attract iron is called a magnet. The force which enables it to attract iron is called magnet- ism. (257.) This force resides chiefly at the ends of a magnet, which are called its poles. It radiates from these poles in curved lines, called lines of magnetic force, or magnetic curves. (258, 2^0.) The forces residing at the opposite poles of a magnet act in opposite directions. (259.) The north pole of a dipping needle always points to- wards the south pole of a bar magnet, when held over it. The earth acts upon a needle like a magnet. Its mag- netic poles are situated near the poles of its axis. As we name the poles of a magnet, the magnetic pole of the earth north of the equator is a south pole, and the one south of the equator is a north pole. The French call the magnetic pole north of the equator a north pole, and the end of the nee- dle which points towards it a south pole. (261.) Like poles of magnets repel, and unlike poles attract each other. (262.) A magnet can develop magnetism in iron or steel by in- duction. Soft iron loses its magnetism as soon as it is with- drawn from the influence of the magnet, while steel retains its magnetism permanently. (263.) Ordinary magnets are made of steel. They are called, from their shape, bar magnets, or horseshoe magnets. (264.) Magnets may be made by contact with other magnets, by a process of single or double touch. (265.) ELECTRICITY. 263 Fig. 185. Zn NATURE AND SOURCES OF ELECTRICITY. VOLTAIC ELECTRICITY. 266. The Voltaic Pair. If in a vessel of dilute sul- phuric acid we suspend a plate of zinc and a plate of platinum opposite to each other, and not in contact, we find that no chemical action whatever takes place, provided the zinc and the acid are perfectly pure. As soon, however, as the plates are united by a cop- per wire, as shown in Figure 185, chem- ical action begins. Bubbles of hydrogen gas rise from the surface of the platinum, and the zinc slowly dissolves, zincic sulphate being formed and dissolved in the liquid. The acid does not act at all upon the platinum. Such an arrangement is called a voltaic pair or cell. If the wire connecting the plates of the pair be held over a small magnetic needle and parallel with it, the needle turns aside, and seeks to place itself at right angles to the wire, showing that a new force is developed in the wire. This force is called electricity. 267. The Electric Current. If the vessel just used be filled with dilute muriatic acid, similar effects are produced, except that we get zincic chloride instead of zincic sulphate. "In this case the space between the plates is filled with molecules consisting of hydrogen and chlorine atoms, as indicated in Figure 186, where we have at- tempted to represent by symbols a single one of the innumerable lines of molecules which we may conceive of as uniting the two plates. The zinc plate, in virtue of the Dowerful affinity of zinc for chlorine, Fig. 1 86. 264 ELECTRICITY. attracts the chlorine atoms, which rush towards it with immense velocity ; and the sudden arrest of motion which attends the union of the chlorine with the zinc has the effect of an incessant volley of atomic shot against the face of the plate. Each of the atomic blows must give an impulse to the molecules of the metal itself, which will be transmitted from molecule to molecule through the material of the plate and the connecting wire, in the same way that a shock is transmitted along a line of ivory balls." * From the fact that the electric motion is thus transmitted from molecule to molecule, it is called a current. It must be borne in mind, however, that the electric current is not a fluid flowing through the wire, but it is merely "a wire or other conductor filled with innumerable lines of oscillating molecules." But these very impulses which impart motion to the metallic molecules react upon the liquid, and force back the hydrogen atoms towards the platinum plate ; so that, for every atom of chlorine which unites with the zinc plate, an atom of hydrogen is set free at the platinum plate. Thus we have two atomic currents in the same liquid mass : one of chlorine atoms setting towards the zinc plate, and one of hydrogen atoms flowing in the opposite direc- tion towards the platinum plate. Corresponding to this motion in the liquid is the peculiar atomic motion in the metallic conductor. The two are mutually dependent. The moment the connection is broken so that the motion can no longer flow through the conductor, the motion in the liquid ceases. We know nothing of the mode of the molecular motion in the metallic conductor. It is appar- ently allied to heat, but is capable of producing very different effects. Since we are ignorant of its nature, we * First Principles of Chemical Philosophy, by Prof. Josiah P. Cooke, Jr., page 121. The remainder of 267, together with 271 - 274, is mainly condensed from the same work. ELECTRICITY. 265 cannot be sure of the direction in which the current flows. It is possible that there may be a double current in the wire as well as in the liquid. It is always assumed, how- ever, as a matter of convenience, that the current flows from the platinum plate through the wire to the zinc, and thence back through the liquid to the platinum. 268. The Galvanometer. We have seen that the elec- tric current has power to deflect a magnetic needle. If the wire is wound once round a needle, it is found that the deflection is greater than when it passes merely over or under it. When the wire is wound a number of times around the needle in the form of a coil, the deflection is greater still. In this case we get virtually as many cur- rents to act upon the needle as there are turns in the coil. A needle placed within or above such a coil gives by its deflection a ready means of measuring the strength of the current. Such an arrangement is called a galvanometer. 269. The Astatic Needle. A needle may be rendered still more sensitive to the action of the current by combining it with a Flg> l87 ' second needle of the same strength, with its poles reversed. The second J. .y |i' i ? needle serves to neutralize the directive power of the earth, so that the needles ^ == ^s will have no tendency to point north and south. Such a combination is shown in Figure 187, and is called an astatic needle (from a Greek word meaning unsteady), that is, one having no directive power. A galvanometer in which an astatic needle is used is called an astatic galvanometer. One needle is always placed within the coil, and the other above it. A very delicate instrument of this kind is shown in Fig- ure 1 88. The astatic needle is placed within a coil of fine copper wire carefully insulated with silk, and is sus- pended by a cocoon thread to a hook supported by a brass 12 266 ELECTRICITY. Fig. 1 88. frame. It hangs freely without touching the coil, and the upper needle moves on a graduated circle. The whole is enclosed in a glass case, and rests on a stand supported by three levelling-screws. When the direction of the current is changed, the needle of the galvanometer turns the opposite way ; hence the gal- vanometer serves to ascertain the direction of the current, as well as its strength. 270. Electrical Conducting Power or Resistance. Some materials transmit the electric current more readily than others, since their molecules yield more readily to this peculiar form of molecular motion. An instrument used to measure the relative conducting power of different substances is called a rheostat (that is, an instrument for making the current steady, or of uniform strength). Wheatstone's rheostat is represented in Figure 189. It is constructed so as to introduce into or withdraw from the circuit a considerable amount of highly resist- ing wire, without stopping the current. If consists of two cylinders, one of brass, the other of well-dried wood, turning on their axes by a crank. The wooden cylinder has a spiral groove cut into it, in which is placed a fine metallic wire ; the brass cylinder is smooth. The end of the wire attached to the wooden cylinder is connected by means of a brass ring with a binding-screw for the attach- ment of a battery wire. A metallic spring pressing against the brass cylinder is connected with the other binding- screw. If now a current be sent through the wire, it will pass through all that portion of it which is wound at the ELECTRICITY. 267 time upon the wooden cyl- inder, but it will not pass through the portion wound upon the brass cylinder, but through the cylinder instead, since the latter is a better conductor than the fine wire. The wire wound upon the brass, then, is withdrawn from the circuit. When the rheostat is to be used, all the wire is wound upon the wooden cylinder, and put into the circuit along with a galvanometer. If now the resistances of two wires are to be tested, the galvan- ometer is read before the first is put into the circuit. After it is introduced, the needle falls back in consequence of the increased resistance, and then as much of the rheo- stat wire is withdrawn from the circuit as will bring the needle back to its former place. The quantity thus with- drawn is shown by a scale, and is obviously equal in re- sistance to the wire introduced. The first wire is then removed, and the second wire is tested in the same way as the first. If 40 inches were withdrawn in the first case, and 60 inches in the second, the resistance offered to the current by the first wire is to that offered by the second as 40 is to 60 ; or, in other words, the former is two thirds of the latter. By means of the rheostat it has been proved that the resistances of wires of the same material and of uniform thickness are in the direct ratio of their lengths, and in the inverse ratio of the squares of their diameters. Thus a wire of a certain length offers twice the resistance of its half, thrice that of its third, and so forth. Again, wires of the same metal, whose diameters are in the ratio of i, 2, 3, etc., offer resistances which are to each other as i, , \, 268 ELECTRICITY. etc. Therefore, the longer the wire, the greater the resist- ance ; the thicker the wire, the less the resistance. The same holds true of liquids, but not with the same exact- ness. The following, according to Becquerel, are the specific resistances of some of the more common substances, or the resistance which a wire of each, so to speak, of the same dimensions, offers at the temperature of 54 F. : Copper, i ; silver, 0.9 ; gold, 1.4 ; zinc, 3.7 ; tin, 6.6 ; iron, 7.5 ; lead, n ; platinum, 11.3 ; mercury (at 57), 50.7. For liquids, the resistances are enormous compared with metals. With copper at 32 F. as i, the following liquids stand thus : saturated solution of blue vitriol at 48, 16,885,520 ; ditto of common salt at 56, 2,903,538 ; white vitriol, 15,861,267 ; sulphuric acid, diluted to T J T , at 68, 1,032,020 ; nitric acid at 55, 976,000 ; distilled water at 59, 6,754,208,000. Gases offer even greater resistance to the current, so that they are virtually non-conductors. 271. Ohm's Law. The force of the current must de- pend upon the power which the moving atoms exert against the zinc plate. The effect of these atomic blows must be determined, in the first place, by the chemical force which draws the atoms towards the plate. This force is called the electro-motive force of the voltaic pair. But, in the second place, each moving atom is but one of a long line of similar atoms which it drags along behind it, while an equal line of dissimilar atoms is pushed back in the opposite direction. These lines of atoms act as so much dead weight to resist the atomic motion, and to lessen the effect of the atomic blows. In the third place, each line of moving molecules in the liquid is connected with a line of vibrating molecules in the wire, and forms with it a con- tinuous chain so connected that the amount of motion must be equal at all points. Thus the resistance in the con- ducting wire reacts upon the whole chain, and lessens the effect of the atomic blows upon the zinc plate. What is ELECTRICITY. 269 true of each line is true of all the lines in the electric cur- rent. This current is kept up by the chemical activity at the zinc plate. This activity is sustained by the electro- motive force, but impeded by the resistance of the liquid and the wire. Evidently then the power of the current is directly proportional to the electro-motive force which sustains the motion, and inversely proportional to the sum of the resist- ances throughout the circuit. If we represent the power of the current by P, the electro-motive force by E, the resist- ance in the conducting wire by R, and the resistance in the liquid by r, we shall have The principle embodied in this formula is known as Ohnts law. 272. Quantity and Intensity. If we increase the size of the plates in the voltaic pair, we shall increase the num- ber of lines of moving molecules in the current. When these plates are connected by a thick metallic conductor, so that there shall be little resistance outside the liquid, all the lines of moving molecules will be excited to the great- est activity which the pair can give. We thus obtain a current of very great volume, and flowing with all the force which a single pair is capable of maintaining. The mo- ment, however, we attempt to force this current through a great length of wire, we interpose a resistance to the atomic motion which tends to reduce the chemical activity ; and as this resistance must increase with the volume of the motion, it will reduce the chemical activity to what it would be with a plate of much smaller size and giving a current of much less volume. By increasing the size of the plate, then, we increase the power of the current only when there is little resistance outside the liquid. We thus obtain a current composed of many moving lines of molecules, 270 ELECTRICITY. that is, of great volume, or quantity, but the molecular mo- tion has little intensity, or power of overcoming resist- ance. The quantity of the current, then, is the volume of the molecular motion ; while the intensity is the energy of this motion. It is evident that we can increase the intensity of the current only by increasing the chemical activity, or the electro-motive force. This may be done to a certain ex- tent by using pairs in which there are more powerful affinities between the plate and the liquid. The electro- motive force may, however, be increased to almost any extent by using a number of pairs, and connecting them as shown in Figure 190. The platinum plate of the first cell is united with the zinc of the second, and so on to the last, whose plat- inum plate is united with the zinc of the first. Such a combination is called a gal- vanic or voltaic battery, and the current from such a battery has a much greater power of overcoming resistance than that from any single cell, however large. In a single cell the motion throughout any single line of molecules is sus- tained by the chemical energy at only one point, but in the battery it is reinforced at several points, that is, at every zinc plate. Where before we had a single atomic : " blow, we have now a number which send their united energy along one and the same line. The electro-motive force, then, is increased in proportion to the number of cells; and the power of the current would be increased in the same proportion, were it not for the fact that the current has to traverse a greater extent of liquid. If we use n cells, both the electro-motive force, E, and the liquid re- sistance, r, become n times as great, while the resistance ELECTRICITY. 2 J 1 in the wire, R, remains the same. Ohm's formula then becomes n E This formula shows at once that when the exterior resist- ance, R, is little or nothing, we gain little or nothing by n E E increasing the number of cells, for is equal to -. If, on the contrary, R is very large, there is great gain in using a number of cells, for we increase the numerator of the fraction much more rapidly than the denominator. 273. The Construction of Cells. A voltaic pair may be constructed of any two metals, provided they are unequally acted upon by the liquid used. The greater the difference in this respect, the better. Practically, sulphuric acid is found to be the best liquid, and zinc the best material for the active plate. The zinc of commerce, however, contains impurities, which give rise to what is called local action, and cause the zinc to dissolve in the acid when the battery is not in action. This local action can be prevented by amalgamat- ing the zinc, that is, coating its surface with mercury. " The mercury on the surface of the zinc plate acts as a solvent, and gives a certain freedom of motion to the par- ticles of the metal. These, by the action of the chemical process, are brought to the surface of the plate, while the impurities are forced back towards the interior, so that the plate constantly exposes a surface of pure zinc to the action of the acid." (See Appendix, Note 7.) In the second place, "the hydrogen gas, which, by the action of the current, is evolved at the platinum plate, ad- heres strongly to its surface, and with its powerful affinities draws back the lines of atoms moving towards the zinc plate, and thus diminishes the effective electro-motive force. Moreover, after the battery has been working for some time, 272 ELECTRICITY. Fig. 191. the water becomes charged with zincic sulphate ; and then the zinc, following the course of the hydrogen, is also de- posited on the surface of the platinum, which after a while becomes, to all intents and purposes, a second zinc plate, and then, of course, the electric current ceases." 274. Grove's Cefi. Both these difficulties are overcome in Groves Cell, shown in Figure 191. It consists of a hollow cylinder of zinc immersed in a vessel of dilute sul- phuric acid. Within the zinc cylinder is put a small cylindrical vessel of porous earthen-ware, filled with the strongest nitric acid, and in this hangs the platinum plate. "The walls of the porous cell allow both the hydrogen and the zinc atoms to pass freely on their way to the platinum plate, but the moment they reach the nitric acid they are oxidized, and thus the surface of the platinum is kept clean, and the cell in condition to exert its maximum electro-motive power." 275. Bunseris Cell. If in Grove's cell we substitute for the platinum a plate of dense coke, such as forms in the interior of gas retorts, we get a very much cheaper cell of nearly equal power. The use of gas-coke was first suggested by Prof. Bunsen, and this cell is therefore called Bunserfs Cell. It is represented in Figure 192. 276. Danieirs Cell. This cell is shown in Figure 193. The outer ves- sel is of copper, and serves as the pas- sive plate. Inside this is a vessel of porous earthen-ware, containing a rod of zinc. The space between the copper and the porous cup is filled with a solu- Fig. 192. ELECTRICITY. 273 Fig. 193. tion of blue vitriol, which is kept saturated by crystals of the salt lying on a perforated shelf. The porous cup is filled with dilute sulphuric acid. The porous partition keeps the fluids from mingling, but does not hinder the passage of the current. The blue vitriol which is in contact with the passive plate serves to take up the hydrogen. There are two other reasons for putting the sul- phuric acid within the porous cup : (i.) if the sulphuric acid came in contact with the copper, it would tend to act upon it as well as upon the zinc, and thus to diminish the electro-motive force; (2.) the zincic sul- phate formed is thus kept from coming in contact with the copper. If it were allowed to come in contact with the copper, it would be decom- posed by the current passing through the cell, and zinc would be deposited on the copper ; and both plates would soon be virtually of the same metal. Fig. 194. Fig. 195- Figure 194 shows the way in which the cells of a bat. tery are connected in order to get the greatest possible in- tensity of the elect'ic force ; Figure 195 the way in which they are connected to get the greatest quantity. In the latter case, since the zincs are all connected together, 12* R 274 ELECTRICITY. - X 9 6 - they form virtually one large plate ; and the same is true of the plati- nums. When considerable intensity as well as quantity is desired, the two forms are combined, as shown in Fig- ure 196. 277. Electrolysis. If two strips of platinum be hung opposite each other in a cup filled with muriatic acid, and one of them be connected with the negative pole (that is, the zinc end) of the battery, and the other with the positive pole (the platinum end), the muriatic acid will be decom- posed, the hydrogen passing towards the negative pole, and the chlorine towards the positive pole. Here are two atomic currents flowing in opposite directions, just as in the liquid between the plates in the voltaic pair. It is found to be true, in general, that when any compound liquid, which is a conductor of electricity, is introduced into the circuit, it is similarly decomposed. This decom- position of a substance by electricity is called electrolysis. The literal meaning of the word is loosening by electricity. The substance decomposed by the electricity is called the electrolyte. The metallic conductors through which the current passes into and out of the electrolyte are called electrodes (roads of electricity]. That through which the electricity passes into the electrolyte is termed the anode (road up], and that through which the current passes out is termed the cathode (road down}. The electrolyte is always decomposed into two parts, one of which appears at the anode and the other at the cathode. The former is called the anion (going up, or to the anode) ; the latter, the cation (going down, or to the cathode}. 278. The Electrolysis of Cupric Sulphate. If two elec- trodes of platinum (Figure 197) be introduced into a solu- tion of cupric sulphate (blue vitriol), bubbles of gas rise ELECTRICITY. 275 from the anode. This gas may be collected by filling a test-tube with the solution of cupric sulphate, and inverting it over the anode. On testing Fi s- '97- the gas, we find it to be oxygen. On remov- ing the cathode from the solution, we find it to be coated with copper. If one of the elec- trodes be of platinum and the other of cop- per, and the platinum be made the anode, the result is the same. If, however, the cop- per be made the anode, the cathode is still coated with copper, but no gas escapes from the anode. The most probable explanation of the above facts is as follows. The electric current decomposes the cupric sulphate into copper and SO 4 . This action may be expressed by an equation thus : Copper, appearing at the cathode, is the cation ; and SO 4 , appearing at the anode, is the anion. When the anode is platinum, the anion acts upon the water of the solution, uniting with its hydrogen and setting its oxygen free. H 2 O + SO 4 = H 2 SO 4 (sulphuric acid) + O. So that the escape of the oxygen gas in this case is due to a secondary action, which is purely chemical. .When the anode is of copper, the anion, instead of act- ing upon the water, acts upon the anode itself. Cu + SO 4 = CuSO 4 . Hence no oxygen escapes in this case, but cupric sulphate is formed as rapidly as it is decomposed ; so that the solu- tion always remains of the same strength. The anode is gradually eaten away and transferred to the cathode. 276 ELECTRICITY. When any compound containing a metal is decomposed by electricity, the metal always appears at the cathode ; and if the anode is of the same metal, the solution always remains of the same strength, while the anode is gradually transferred to the cathode. 279. The Voltameter. This instrument was invented by Faraday for testing the strength of a current. It is shown in Figure 198. Two platinum plates, each about half a square inch in size, are placed in a bottle containing water acidulated with sulphuric acid ; the plates are soldered to wires which pass up through the cork of the bottle and terminate in binding-screws ; a glass tube fixed into the cork serves to discharge the gas formed within. When the binding-screws are connected with the poles of a bat- tery, the water in the bottle begins to be de- composed, and hydrogen and oxygen are set free. If now the outer end of the discharging tube be placed in a trough of mercury, and a small graduated bell-glass, like- wise filled with mercury, be placed over it, the mixed gases rise into the bell-glass. The quantity of gas given off in a given time measures the strength of the current. SUMMARY. The electric current is a line of oscillating molecules, set in motion in the voltaic cell by the chemical activity at the zinc plate. (258.) The galvanometer measures the strength of this current ; and the rheostat, the resistance of the conductor. (259, 261.) ELECTRICITY. 277 The power of the current equals the electro-motive force divided by the sum of the resistances throughout the cir- cuit. (271.) The quantity of the current is the volume of the molecu- lar motion ; its intensity is the energy of this motion. (272.) In a voltaic cell it is necessary to have two plates, and a liquid which acts upon one more strongly than upon the other. The most powerful cells are Grove's and Bunseris. When any compound liquid, which is a conductor of electricity, forms a part of the circuit, it is decomposed. This decomposition by electricity is called electrolysis. It is usually attended by a secondary action, which is purely chemical. (277.) RELATIONS OF ELECTRICITY TO MAGNETISM. 280. The Current can make Iron Magnetic. If a part of the wire of the circuit be wound into a coil, and a piece of soft iron be placed inside this coil, it becomes strongly magnetic while the current is passing ; as may be shown by bringing bits of iron near the ends of the iron inside the coil. Such a magnet is called an electro-magnet.. The coil is called a helix. If the coil is a left-hand coil (see Figure 199), the end at which the current enters the coil will be Fig. 199- found by means of the magnetic needle to be the north pole ; so that, by reversing the current, the poles of the electro-magnet will be reversed. If the coil is a right-hand one (see Figure 200), the end at which the current enters is found to be the south pole. 2 7 8 ELECTRICITY. Fig. 200. When the current is broken, the soft iron instantly loses its magnetism, and the bits of iron no longer cling to it. If a steel rod is used, instead of a soft iron one, it retains its magnetism after the current is broken. If the wire is wound around the iron in several layers, the strength of the magnet is greatly increased. F i g . 20I . The strongest electro-magnets are of the horseshoe form. They far ex- ceed ordinary magnets in power. Small electro-magnets have been made which support 3500 times their own weight, and large ones which hold up a weight of 2500 pounds. These magnets are much stronger when pro- vided with a keeper, or armature, that is, a piece of soft iron which connects the two poles, as shown in Figure 201. 281. The Wire through which a Current is passing is a Magnet. If the current be sent through a coil such as is shown in Figure 202, and the end of a rod of soft iron be brought near the opening in the centre, it is at once drawn into the coil. Coils have been constructed powerful enough to draw up and sustain a weight of 600 pounds. The electric current, then, not only de- velops magnetism in soft iron, but the coil itself, through whicli the current is pass- ing, is magnetic. Fine iron-filings will ad- Fig. 202. ELECTRICITY. 279 here to the wire which joins the poles of a battery, show ing that any wire through which the current is flowing is magnetic. 282. Magneto-electricity. We have now seen that the electric current has power to move a magnet. Excite an electro-magnet, hang the rod of a lifting-coil to one of its poles, attach the lifting-coil to the galvan- ometer, and quickly slip it over the rod, which is now a magnet. The needle promptly turns aside, but soon comes back to its former position. Now quickly slip the coil off from the rod, and the needle turns in the opposite direc- tion. This experiment shows that an electric current is de- veloped when a continuous conductor is moved near a magnet. A current thus originated by a magnet is said to be induced by it, and the electric force thus induced is called magneto-electricity. We have seen that the electric current renders a piece of soft iron placed inside a helix temporarily magnetic. Attach the lifting-coil to the galvanometer, place the rod within the coil, and bring it quickly in contact with the pole of an excited electro-magnet. Magnetism is devel- oped in the rod, and a current in the wire of the coil, as is shown by the galvanometer. The needle soon returns to its former position. Now quickly detach the rod and coil from the magnet. The rod loses its magnetism, and a current is developed in the coil. The galvanometer shows that its direction is the opposite of that of the former cur- rent. It appears, then, that a current may be developed in a conductor by using either a constant or a variable magnet. When a constant magnet is used, the current is developed by changing the relative positions of the rmgnet and the conductor ; when a variable magnet is used, by changing the strength of its magnetism. 280 ELECTRICITY. SUMMARY. The wire through which a current flows is magnetic. When a piece of soft iron is placed inside a helix, and a current sent through the wire, magnetism is developed in the iron. A magnet made in this way is called an electro- magnet^ and is much stronger than an ordinary magnet. (280, 281.) Electricity can be developed by magnetism, either by moving a conductor near a constant magnet, or the magnet near the conductor ; or by changing the strength of the magnetism in a magnet which is near a conductor. Electricity developed by magnetism is called magneto- electricity. (282.) THE RELATION OF ELECTRICITY TO HEAT. 283. Heat developed by the Current. When a current passes through fine wire, an intense heat is produced, suf- ficient in some cases to bring it to a white heat, and even to fuse platinum wire. Experiments upon the heating effects of the current may be made by the apparatus shown in Figure 203. The bottle is filled with alcohol, which is a non-conductor. The thick wires n and / are connected with a battery, and within the bot- tle they are joined with a fine spiral wire, surrounding the bulb of a delicate thermom- eter, /. When the circuit is closed, the heat developed is communicated to the alcohol, and thus to the thermometer. It is found that if the wire be kept the same, or of the same resist- ance, the heat is in proportion to the square of the strength of the current. Thus, if a current of a certain strength ELECTRICITY. 28 1 raises the thermometer i in a minute, a current of twice the strength will raise it 4 in a minute. Again, if by means of a rheostat the strength of the cur- rent be kept at the same point, and wires of different resist- ance be put into the bottle, the heat developed is in pro- portion to the resistance of the wire. Thus, if with a wire of a certain resistance the thermometer be raised i per minute, it will be raised 2 per minute with a wire of double the resistance. Hence the heat developed in a conducting wire by an elec- tric current is proportional to the square of the strength oj the current, and to the resistance offered by the wire. A very pretty illustration of the fact that the heat is pro- portional to the resistance is furnished by a chain, the alternate links of which are made of silver and platinum. When a current of sufficient strength is sent through the chain, the silver links remain black, while the platinum links become red hot. 284. The Voltaic Arc. When the ends of two wires which form the poles of a powerful battery are made to touch, and then are separated for a short distance, the current does not cease with the separation, but forces its way through the intervening air, with an intense evolution of light and heat. The heat is sufficient to melt the most o refractory metals, and therefore some substance rivalling the metals in conducting power, but much more infusible, must be found to act as the poles under such circumstan- ces. The various forms of carbon are well suited to this purpose ; but the best, both for conducting power and dura- bility, is the coke formed in the retorts in the distillation of coal-gas. Figure 204 represents a simple arrangement for producing the electric light. The carbon points. P, N, are fixed into hollow brass rods, which slide in the heads of the glass pillars, A, A, and are connected with the bat- tery by binding-screws, s, s. The points are made to 282 ELECTRICITY. touch, and the current is sent through the rods ; the points are then separated a little, when a light appears Fig. 204. between them rivalling that of the sun in purity and splen- dor. On examination this light is found to arise chiefly from the intense whiteness of the tips of the carbon points, and partially from an arch of flame extending from one to the other. The positive pole is the brighter and hotter, as is shown by the fact that, on intercepting the current, it continues to glow for some time after the negative pole has become dark. While the light is kept up, a visible change takes place in the condition of the poles. The positive pole suffers a loss of matter; particles of carbon pass from it to the negative pole, some reaching it, and some being burned by the oxygen of the air on the way. There is a similar loss, though to a much less extent, at the negative pole. The positive pole becomes hollowed or blunted, and the nega- tive remains pointed. The heat of this arch of flame, or voltaic arc, as it is called, is the most intense that can be produced, and is due to the great resistance the current meets in traversin \ the air. Platinum melts in it like wax in the flame of a candle. Quartz, the sapphire, magnesia, lime, and other substances equally refractory, are readily fused by it. The diamond becomes white hot, swells up, fuses, and is re- duced to a black mass resembling coke. The electric light is caused, not by the combustion of ELECTRICITY. Fig. 205. the carbon, but by its incandescence. The light can con- sequently be produced in a vacuum, and below the surface of water, oils, and other non-conducting liquids. It is thus quite independent of the action of the air. With a battery of some fifty Bunsen's cells, a light is produced of very great brilliancy ; but when very great power is to be obtained, twice or thrice that number must be employed. 285. Thermo-electricity. When the point of junction of any two metals is heated, a current is always produced. When a bar of antimony, A, is soldered to a bar of bismuth, B (see Fig- ure 205), and their free ends are connected with a galvanometer, G, a current passes from the bismuth to the antimony when the junction is heated. When S is cooled by applying ice, or otherwise, a current in the opposite direction is produced. Such a combination of metals is called a thermo-electric pair. The electricity so developed is called thermo-electricity (heat electricity). Metals like antimony and bismuth, which have a crystal- line structure, are best suited for a thermo-electric pair. Farmer's alloy (of zinc and antimony) forms a much more powerful pair with bismuth than antimony itself does. 286. Thermo-eltctric Battery. One bismuth-antimony pair has very little power. To obtain a stronger current, several pairs are united, as shown in Figure 206. The heat in this case must be applied only to one row of sol- dered faces. The strength of the cur- rent depends on the difference of tem- perature of the two sides ; and to in- crease it to the maximum the one series must be kept in ice or in a freezing mix- Fig. 206. 284 ELECTRICITY. ture, whilst the other is exposed to an intense heat. As in the galvanic battery, the electric force is proportionate to the number of pairs. At best, however, it is small, and the galvanometer used to measure it must be a very deli- cate one. When a great many pairs are formed into a battery, they are usually arranged as shown in Figure 207, which repre- sents one of thirty pairs. The odd Fig. 207. laces, i, 3, 5, etc., are exposed on one side, and the even faces, 2, 4, 6, etc., on the other. The terminal bars are connected with the bind- ing-screws. The interstices of the bars are filled with gypsum to keep them separate, and the whole is put in a frame of non-conducting material. Such a battery, in connection with a sensitive galvan- ometer, forms the most delicate differential thermometer (248) which has yet been constructed. So long as the opposite faces are exposed to the same temperature, no current is produced ; but if the temperature of one side becomes higher than that of the other, a current is at once indicated. If the hand, for instance, be brought near one side, the needle shows a current ; or if a piece of ice be held near, a current is also shown, but moving in the op- posite direction. SUMMARY. When the current passes through a conductor, heat is developed. The heat is proportional to the square of the strength of the current, and to the resistance offered by the conductor. (283.) Advantage is taken of the same fact in the development of the electric light. (284.) ELECTRICITY. 285 Heat has power to develop electricity in a combination of different metals. Electricity thus generated is called thermo-electricity. (285.) The thermo-electric pile is a very sensitive differential thermometer, since a current is developed by the slightest difference of temperature between the two faces. (286.) FRICTIONAL ELECTRICITY. 287. Electricity developed by Friction. When a cat's back is stroked on a cold, dry day, in a darkened room, sparks are obtained which at once indicate the develop- ment of electricity. If a well-dried rod of glass or gutta- percha be rubbed with a piece of siik or flannel, similar sparks appear. Hence electricity may be developed by friction. Such electricity is called frictional electricity. It is found by experiment that, when any two dissimilar bodies are rubbed together, electricity is developed ; but when the substances are conductors of electricity, the force thus de- veloped passes off silently through the hands and body. In order to detect it, the substances rubbed together must be held by insulating handles, that is, handles which do not conduct electricity. 288. The Electrical Machine. An apparatus for gener- ating frictional electricity is called an electrical machine. The one shown in Figure 208 consists of a thick plate of glass turned by a crank. At one end there is a glass standard surmounted by a brass ball. From this standard project two brass strips in the form of a clamp, which hold the rubbers against the glass plate. These rubbers are pieces of wash-leather or woollen cloth, covered with an amalgam of mercury, lead, and tin. At the opposite end, on a glass support, is a long cylinder of brass with rounded ends. This cylinder is the prime or positive conductor. The brass ball connected with the rubber is the negative 286 ELECTRICITY. conductor. The plate and conductors of the machine must be well insulated. In dry and frosty weather glass Fig. 208. insulates very well ; at all other times it becomes covered with a scarcely visible layer of moisture, which very much impairs its insulating power. The deposition of moisture is greatly lessened by coating the glass with shellac. 289. Quantity and Intensity of Frictional Electricity. With a medium-sized electrical machine of this kind, sparks are readily obtained two inches long by presenting a con- ducting substance to the ball of the prime conductor. Very large machines will give a spark two feet in length. Frictional electricity, then, must have great intensity, in order to traverse so great a distance of a non-conducting substance like the air. Its quantity, on the other hand, is next to nothing. This is shown by connecting the positive conductor with one end of the wire of a moderately delicate galvanometer, and the negative conductor with the other end, and working the machine. The needle will be de- flected only one or two degrees. The great tension (or intensity) and the small quantity of friction il electricity place it in striking contrast with voltaic electricity. ELECTRICITY. 287 The positive conductor of an electrical machine answers to the positive pole of a galvanic battery, and the negative conductor to the negative pole, and the friction on the plates to the chemical action in the cells. With the gal- vanic battery an enormous quantity of electricity is obtained of slight tension ; with the electrical machine, a small quantity of enormous tension. 290. The Electroscope, If a pith ball hung by a silk thread from a glass rod be brought near the ball of a prime conductor, it is at first attracted and then repelled. This power of attracting light bodies is one of the most striking features of friclional electricity. It grows out of its high ten- sion, and it furnishes the most ready means of detecting the presence of this electricity, as the needle furnishes the most ready means of detecting the presence of voltaic electricity. An instrument constructed on this principle Fig. 209. for the detection of frictional electricity is called an electroscope. The pith-ball electroscope (Figure 209) consists of a brass conducting-rod supporting a gradu- ated semicircle, in the centre of which is a movable index made of very light wood, with a pith ball at the end. When it is attached to the prime conductor of the machine, the pith ball is repelled as soon as the plate is turned. Fi , ria The gold-leaf electroscope (Figure 210) is a more delicate instrument. It consists of a hollow glass ball, the neck of which is covered by a brass cap. Through this cap, but insulated from it, passes a brass rod having a brass ball at its upper end and two narrow strips of gold-leaf suspended from its lower end. If the brass ball be brought near a body charged with elec- tricity, the strips of gold-leaf repel each other, as in the figure. 288 ELECTRICITY. 291. The Electrical Forces on the Positive ana Negativt Conductors act in Opposite Directions. Insulate both con- ductors of the machine, and charge them with electricity by turning the plate. Bring a pith ball suspended by a silk thread in contact with the positive conductor, and it is soon repelled. Take it now to the negative conductor, and it is strongly attracted. Discharge now the pith ball by taking it in the hand, and again bring it in contact with the negative conductor, and it is repelled ; but on taking it to the positive conductor it is attracted. We see then that a ball which is repelled by the force on one conductor is attracted by the force on the other. In other words, the forces on the two conductors act in opposite directions. These opposite electrical forces are called positive and negative forces. 292. Both Electrical Forces are always developed together. It is found to be impossible to develop one of these forces without at the same time developing both. The positive force always appears upon one of the substances rubbed together, and the negative force always appears upon the other. The force that acts in the same way as that upon the prime conductor of an ordinary electrical machine is called positive electricity ', and the opposite force is called negative electricity. Of course, in order that both *he forces should be detected, both of the substances rubbed together must be insulated. 293. Induction. If an insulated copper ball be connect- ed with the prime conductor of the Fig. 211. machine, and a small insulated con- C ., -j) \J ductor be placed near it (see Figure ^ 211), on developing electricity and examining the condition of the insu- lated conductor, opposite electrical forces will be found to be developed upon its ends. On the end next the ball, negative force ELECTRICITY. 289 will be found ; on the end farthest from the ball, positive force. This action of a charged body upon a body near it is called induction. The insulated conductor is said to be Polarized. When an insulated conductor is brought near a charged body, it is first polarized, and the nearer it is brought, the higher the polarization rises. If the conductor is so situ- ated that it can discharge its force at the end nearest the polarizing body, it becomes charged with the same electric force as the polarizing body ; if it discharges from the op- posite end, it becomes charged with the force opposite to that on the polarizing body. If the conductor is so situ- ated that it can discharge quite readily at both ends, but more readily at one end than at the other, there will be three steps in the process. It will first become polarized, then charged, and finally neutralized. If the conductor can discharge quite readily, and with equal readiness at each end, there will be only two steps in the process : it will be first polarized, and then neutral- ized. 294. The Polarization of the Insulated Conductor depends on the Non- Conducting Medium which separates it from the Charged Body. Charge a metallic disc, and bring it near the ball of the gold-leaf electroscope ; the leaves diverge, owing to the electricity induced upon them. Put a thick cake of shellac between the disc and the ball, and the leaves diverge still more, showing that the polarization has risen higher. The polarization of a body changes when- ever a different non-conductor occupies the space between it and the charged body. The polarized condition of a body then depends upon the non-conducting medium which separates it from the charged body. 295. The Charge on a Solid Insulated Conductor is always on the Surface. To an insulated copper ball are care- 13 s 2QO ELECTRICITY. fully fitted two hemispherical metallic caps provided with insulating handles. The caps are placed upon the ball, and the whole apparatus is charged. The caps are then removed and examined, and are found to be charged, while not the slightest trace of a charge is found on the ball. 296. Distribution of the Charge on the Surface. It is found by experiment that, when a spherical conductor is charged and placed in the centre of a room, the charge is distributed uniformly over its surface ; and that, when an oblong conductor is charged and placed in a similar situa- tion, the charge accumulates at the ends. 297. The Charge which any Body can receive depends upon its Facilities for carrying on Polarization. This fact is illustrated by a simple piece of apparatus. It con- sists of three cups made to fit closely within one another. The outer and inner ones are of tin ; the middle one, which is higher than the others, is of glass. In the centre of the inside tin cup there is an upright glass tube, within which is a brass chain attached to the bottom of the cup, and having a brass ball at the other end. Remove the outside tin cup, place the glass cup on an insulating stand, and bring the brass ball of the inner cup near the prime conductor of the machine. Few sparks will pass, showing that the cup receives but a small charge. Discharge the cup, replace the outside tin cup, connect the latter with one of the conductors of the machine, and bring the ball of the inside cup near the other conductor of the machine. A large number of sparks can now be made to pass, show- ing that the cup can receive a much larger charge. In the first case polarization has to be carried on through the glass and the air outside, to the nearest conductors ; while, in the second case, it is carried on merely through the glass which separates the two coats. Hence there is much less resistance to polarization in the second case ; and, as we have seen, the cup receives much the greater charge. ELECTRICITY. 291 Remove the inner cup by taking hold of the glass tube, and then the glass cup. Very little electricity will be found on the tin cups, but on rubbing the hand over the glass cup we find that cup to be charged. 298. The Ley den Jar. Replace the two metallic cups with tinfoil, and the apparatus just described becomes a Ley den jar. This jar is charged by connecting its outer coating with one conductor of an electrical machine, and the inner coating with the other, and developing electricity. The jar may be discharged by means of the discharger, which consists of two bent brass arms connected by a movable joint and having brass balls at their ends. It is fastened at the joint to a glass handle. To discharge the jar, hold the discharger by the glass handle, and bring one ball in contact with the outer coating and the other ball near the knob connected with the inner coating. 299. The Ley den Battery. The amount of charge which a Leyden jar can receive, other things being equal, evi- dently increases with the size of the coatings. The area of the coatings can be increased, either by making the jar larger, or by connecting together several smaller jars. The latter arrangement constitutes a Leyden battery. Like the cells of the voltaic battery, the jars can be connected in two ways : (i.) the outer coating of one may be connected with the inner coating of the next, and so on throughout the series ; or, (2.) the outer coatings may all be con- nected together, and also the inner coatings. In the first case, the battery is discharged by bringing the inner coat- ing of the first jar in contact with the outer coating of the last , in the second case, by bringing the connected outer coatings in contact with the connected inner coatings. Like the voltaic battery, when the Leyden battery is arranged in the first way, it gives electricity of the greatest intensity ; and, in the second way, electricity of the greatest quantity. 292 ELECTRICITY. The spark obtained from a powerful Leyden battery can be made to imitate on a small scale all the effects of light- ning. It can be made to split tough bits of wood, shiver glass, and ihe like. 300. The Effect of Points on a Conductor. It is found to be impossible to charge a conductor when a sharp point projects from it, or is held near it. The point conveys away the electric force silently. If the hand is held in front of the point when the electricity is developed, a cur- rent of air is distinctly felt setting off from the point. If a lighted taper is held near the point, the flame is blown away from it. The electric force is then evidently carried off by the molecules of the air which form the current, and hence it is called convective discharge. Since in a darkened room a star of light is seen upon a point held near a powerful electrical machine while in action, this silent discharge is also called glow discharge. The charge rises so high at the point that the molecules of air just about it are strongly polarized. They then seem to act like little pith balls. The molecules directly in front of the point are first attracted and then repelled ; while those just behind are in turn drawn to the point and then driven from it, giving rise to a current of air from the point. 301. The Electric Wheel. As each molecule is repelled from the point, it also repels the point itself, which, if free to move, ought to move as well as the molecules of air. Fig. 212. This explains the action of the electric ivheel, which consists of a number of points all bent round in the same direction, as shown in Figure 212. The wheel is poised so as to turn easily, and when connected with the prime conductor of the machine in action, it rotates rapidly, each point moving backwards. ELECTRICITY. 293 SUMMARY. When unlike substances are rubbed together, frictional electricity is developed. (288.) Frictional electricity has slight quantity but enormous tension ; while voltaic electricity has slight tension but enormous quantity. (289.) Two opposite electrical forces are developed on the two conductors of the electrical machine ; and one cannot be developed without at the same time developing the other. (291, 292.) A body is polarized when it has opposite electrical forces developed on opposite parts ; it is charged when it has only one electrical force upon it. A body charged with either electrical force polarizes an insulated conductor near it, inducing upon the face nearest itself the opposite electrical force. The polarized condi- tion of such a conductor depends upon the non-conducting medium between the two bodies. (293, 294.) The charge which a body can receive depends upon the readiness with which it can carry on polarization, as is shown in the case of the Leyden jar. (297, 298.) The action of points on charged bodies is to convey the charge off silently by convective discharge. (300.) ELECTRICAL MACHINES AND APPLICATIONS OF ELECTRICITY. MACHINES FOR DEVELOPING ELECTRICITY. 302. Magneto-electric Machines. The batteries for de- veloping voltaic electricity have already been described. An instrument for developing electricity by means of mag- netism is called a magneto-electric machine. In ordinary ma- 294 ELECTRICITY. Fig. 213. chines of this kind the electricity is induced by means of a variable magnet : there must, therefore, be some means of developing and destroying magnetism in a piece of soft iron. The iron is placed inside a helix, which serves as a conductor for the current induced. The magnetism may be developed and destroyed by means either of a perma- nent magnet or of an electric current. The former method is illustrated by Figure 213. JVS is a permanent horseshoe magnet C D is a bar of soft iron with coils, A and B, wound round its ends, and may be viewed as the armature of the magnet. C D is capable of rotation round the axis E F. So long as CD remains at rest, no currents are induced in the coils, for no change takes place in the magnetism induced in it by the action of N S. But if the poles of C D leave N S, the magnetism of the soft iron diminishes as its distance from N S increases, and when it stands at right angles to its former position, the magnetism has disappeared. During the first quarter-revolution, there- fore, the magnetism of the soft iron diminishes, and an electric current is induced in the coils. During the second quarter-revolution the magnetism of the armature increases till it reaches a maximum when its poles are in a line with those of IV S. A current also marks this increase, and moves in the same direction as before ; for though the magnetism, increases instead of diminishing, which of itself would reverse the induced current, the poles of the arma- ture, having changed their position with relation to those of the permanent magnet, have also been reversed, and ELECTRICITY. 295 Fig. 214. this double reversal leaves the current to move as before. For the second halt-revolution the current also moves in one direction, but opposite to that of the first half-revolution, since the position of the arma- ture is reversed. Thus in one revolution of a soft iron armature in front of the poles of a perma- nent magnet, two currents are in- duced in the coils encircling //, each lasting half 'a revolution, starting from the line joining the poles. The manner in which the armature may be made to ro- tate, and the current to flow constantly in one direction, is shown in Figure 214, which represents a common form of magneto-electric machine. NS is a fixed permanent magnet. B B is a soft iron plate, to which are attached two cylin- ders of soft iron, round which the coils Cand D are wound. C B B D is thus the revolving armature, corresponding to CD in Figure 213. A A is a brass rod attached to the armature, and serving as its axle. ./MS a cylinder fastened to A, and is pressed upon by two fork-like springs, Zf and K, which are also the poles of the machine. The ends m and n of the coil are soldered to two metal rings on F, in- sulated from each other. When the armature revolves, A A and F move with it. F, H, and ^are so constructed as to reverse the current at each half-revolution. By this arrangement, the opposite currents proceeding from the coil at each half-revolution are so transmitted to Zf and K> that these retain their polarity unchanged. When the armature is made to revolve rapidly, a very energetic and steady 296 ELECTRICITY. current is generated, which has all the properties of the gal- vanic current. Compared with the galvanic battery, the magneto-electric machine is a readier, steadier, and clean- lier ource of electricity, and has come to be extensively used instead of it. Magneto-electric machines may be made of any strength by increasing the number of magnets and the mechanical force employed. In large machines, several magnetic batteries are em- ployed. The coils may be arranged, like the cells of a gal- vanic battery, for tension or for quantity. For giving shocks, or for electrol- ysis, the wire used must be long and fine ; for heating platinum wire, thicker and short- er. The electric force increases with the ra- pidity of rotation. 215. c 303. Wilde's Mag- neto-electric Machine, A magneto-electric ma- chine of great power has been recently in- vented by Mr. Wilde, of Manchester, Eng- land. A front view of the machine is shown in Figure 215. M is the foremost of a se- ries of sixteen power- ful steel magnets of horseshoe form, placed one behind another in a horizontal row. These magnets are fixed be- ELECTRICITY. 2Q7 low to the magnet cylinder, shown on a larger scale in Figure 216. This is made partly of iron, partly of brass. The sides / / are of iron, and the brass bars b b lie be- tween them. In the centre is a circular hole extending the whole way through. The magnets are firmly fastened to the iron sides / /, so that the latter form the poles of the magnetic battery, the brass bars between them insulat- ing them from each other. A cylindrical armature a a of cast iron is made to re- volve within the magnet cylinder. Its diameter is a little less than that of the cylindrical hole, so that it can revolve without friction very close Fig . 2l6 . to the polar surfaces. It is shown in section in Fig- ure 216. Two rectangu- lar grooves are cut in it, as there represented, and in these about fifty feet of insulated copper wire is wound lengthwise in three coils. The coil thus formed is shut in by wooden packing, c c. Two caps of brass are fitted to the ends of the arma- ture, and to these are attached the steel axes of rotation. The rear axis is connected by means of a pulley and belt with the engine which rotates the armature. On the front axis are two metallic pieces, one connected with the arma- ture, and the other insulated from it. One end of the armature coil is connected with the armature, and thus with one of these metallic pieces, and the other end is insulated from the armature and connected with the other piece ; so that these metallic pieces are the terminals of the coil. Two steel springs press against these pieces, each spring against one piece during half a rotation. In the position shown in Figure 216, the armature is magnet- ized, since the parts a a are facing the poles of the per- 13* 298 ELECTRICITY. manent magnets. On performing a quarter-revolution, the armature loses its magnetism, since its poles are carried away from the poles of the magnets. After another quar- ter-revolution, it again becomes magnetic, and so on ; so that in one revolution the armature induces two opposite currents in the coil, one in each half-revolution. The springs act in such a way that the current passes through them always in the same direction. The armature is made to revolve some 2,500 times per minute, sending 5,000 waves or currents of electricity to the wires o o. One advantage of the position of the armature in this machine is that its motion is not resisted by the air. In the ordinary magneto-electric machines (see Figure 214) much of the mechanical force applied to the rotation is wasted in beating the air. Another advantage is that the inductive action of the magnet is exerted directly on the coil, as well as through the intervention of the armature. If the coil were made to rotate without the armature, currents would be induced in it of the same kind as that induced by the armature, though of feebler intensity ; and these currents would be strongest when the coil was moving through the line join- ing the poles, and weakest when it was at right angles to that position. The currents induced by the armature are strongest when those just mentioned are weakest, and weakest when those are strongest ; so that armature and coil combine to make the current uniform. But the chief peculiarity and merit of Wilde's machine is that the current got from the magneto-electric apparatus is not directly made use of, but is employed to magnetize an electro-magnet, E E (Figure 215), some hundreds of times more powerful than the magnetic battery originally employed, and this electro-magnet is made to induce an- other and proportionally more powerful current by means of a second rotating armature. The upper and lower ELECTRICITY. 299 machine are in action precisely alike ; only the upper magnet is a permanent magnet, and the lower one an electro-magnet. We have the same magnet cylinder, the same armature, springs, and poles. This armature is made to rotate some 1,800 times per minute. A machine intended for a three-horse power steam- engine, and worked with that power, will consume carbon sticks three eighths of an inch square, and evolve a light of surpassing brilliancy. With a machine consuming car- bons half an inch square, the light is of sufficient intensity to cast shadows from the flames of street-lamps a quarter of a mile off. The same light, at two feet from the re- flector, darkened photographic paper as much in twenty seconds as the direct rays of the sun at noon in one minute. Wilde's machine enables us to convert any amount of mechanical force into electricity by increasing the size of the electro-magnet, or by using a second electro-magnet induced by the first ; so that a magnet indefinitely weak can be made to induce a current or a magnet of indefinite strength. The size and weight of the apparatus are also small. 304. Induction Coils. When the magnetism is devel- oped and destroyed by means of a current, the soft iron must be placed inside a coil through which the current is sent. This is called the/;7- mary coil, and must be placed inside an- other coil, called the secondary coil, which serves as a conductor of the induced elec- tricity. Such a machine is commonly called an 300 ELECTRICITY. induction coil. In the one shown in Figure 217, the primary coil is of coarse wire wound with wool, and is attached to the wooden base of the instrument. The secondary coil is of finer silk-wound wire, much longer than the primary wire. Within the primary coil is a bundle of iron wires, which are sufficiently insulated by the rust that gathers on them. The developing of mag- netism in these wires is the chief aim of the primary coil, and, as a strong current is necessary for that purpose, coarse wire is used in that coil. In the secondary coil, the tension of the induced current alone is aimed at, and fine wire is used, so that as many turns as possible may be brought within the influence of the primary coil and its core ; for it is found that the tension of the induced cur- rent is proportional to the strength of the primary cur- rent, and to the square of the resistance in the secondary coil. In order, however, to obtain the greatest effect from the secondary coil, it is necessary to have some means of rap- idly completing and breaking the primary current. This is effected in the instrument under consideration, either by means of the rasp seen behind the coils, or by the self- acting rheotome (that is, 'current-cutter] at the left hand. When the former is used, one of the battery wires is at- tached to one of the binding-screws, and thereby to one end of the primary coil ; and the other battery wire is drawn along the teeth of the rasp, which is connected with the other end of the coil. The current is stopped and started again every time the wire passes from one tooth to another ; and every time it is stopped or started, an inverse or a direct current is excited in the secondary wire. The rheotome breaks the current in the same way, but more regularly and rapidly. When it is used, both battery wires are attached to the binding-screws, bringing the rheotome and the primary coil into the circuit. ELECTRICITY. 3 OI 305. The Inductorium, or Ruhmkorff 's Induction Coil. The essential parts of this apparatus, like those of the one described in the last section, are a primary coil, with its core of iron wire, and a secondary coil outside the primary and insulated from it. The primary coil is connected with a galvanic battery, and a rheotome is used to interrupt the current, as already explained. A RuhmkorrT's coil of moderate size readily yields sparks of from four to five inches, with a battery of six Bunsen's cells. The power of the induced current to de- flect the needle of the galvanometer, and to effect electrol- ysis, is very insignificant. This shows that it is very much inferior to the inducing current in quantity, however much it may be superior in tension. The physiological effect, however, is tremendous, and the experimenter must take care not to allow any part of his body to form the medium of communication between the poles, as the shock might be dangerous, if not fatal. 306. Foucaulfs Self-acting Rheotome. The best rheo- tome for use with the inductorium is Foucault's. This instrument is shown in Figure 218, and illustrates one of Fig. 218. 3O2 ELECTRICITY. the many applications of the electric force to doing me- chanical work. It consists of a beam, a d, supported by a standard C G, which acts as a spring. At one end of the beam there is a keeper of soft iron; at the other end, two iron rods, which plunge into cups A, B, partially filled with mercury. Under the iron keeper is an electro-magnet, D. One end of the wire of the helix of this magnet connects with one pole of a Bunsen's cell. The other pole of this cell is connected with the mercury cup, B. The other end of the wire of the helix is connected with the beam by means of the standard ; so that the circuit of the Bunsen's cell is closed when the iron rod dips into the mercury, and is open when it is out of the mercury. It is best to cover the mercury with alcohol, which is a non-con- ductor. When the rheotome is to be worked, the iron rod is so adjusted that its end is just above the surface of the mer- cury. That end of the beam is then depressed by the hand so as to bring the rod into the mercury. This closes the circuit, and renders the electro-magnet active, and the keeper at the end of the beam is drawn down upon it. This carries the other end of the beam up and the rod out of the mercury, opens the circuit, and renders the electro- magnet inactive. The elasticity of the standard throws this end of the beam back and lowers the rod into the mercury, closing the circuit again, and the same succession of movements is repeated indefinitely. This instrument is made to open and close a second circuit in the following manner. One pole of the battery of this circuit is connected with the beam, and so with the iron rod, which dips into the second cup of mercury, A, which is connected with the other pole of the battery ; so that this circuit is closed when the rod dips into the mercury, and open when it is out of the mercury. But if the point of the rod is so adjusted as to be just above the ELECTRICITY. 303 surface of the mercury, it is drawn out of it every time that the keeper is drawn down to the electro-magnet, and is plunged into it every time that the keeper is thrown back by the spring. 307. Geissler's Tubes. A variety of forms of apparatus are used for showing the electric light in rarefied air and in other gases.* Geissler's tubes, so called from the in- ventor, are combinations of bulbs and tubes, filled with rarefied gases and liquids, and then sealed air-tight, so as to be ready for use at any time. One of them is shown in Figure 219. When the current is sent through these tubes, they exhibit lights of various tints according to the gases contained in them. SUMMARY. IN ordinary magneto-electrical machines electricity is induced by developing and destroying magnetism in soft iron placed inside a helix. This may be done by using a permanent magnet, or, as in the various forms of induction coils, by means of the current. (302, 304, 305.) In Wilde's machine, the electricity obtained by means of permanent magnets is made to develop much more power- ful magnetism in a large electro-magnet, which in turn is made to develop electricity. In this way a magnet in- definitely weak may be made to develop a current in- definitely strong. (303.) * All the experiments with the electric light usually performed by means of Frictional Electricity can be better performed with the /- ductoriitm. See Appendix, Note 8. 3 c>4 ELECTRICITY. APPLICATIONS OF ELECTRICITY. 308. Electrotyping. When the solution of cupric sul- phate is decomposed slowly, the copper is deposited on the cathode in a coherent mass, which may be stripped off when it has become sufficiently thick. The sheet of copper stripped off is found to present a perfect reverse image of the face of the cathode, the faintest lines being copied with perfect distinctness. If this reverse image be now made the cathode, and another sheet of copper be deposited upon it, an exact copy of the original electrode is obtained. Any conducting substance, of whatever size and shape, may be made a cathode by simply connecting it with the negative pole of the battery. Hence coins, medals, and engraved plates may be copied with perfect accuracy, and with but slight trouble and expense. This process of copying by means of electricity is called electrotyping. The face of a medal may be copied by making it the cathode and depositing a sheet of copper upon it, and then depositing another sheet of copper upon this sheet after it has been separated from the medal. In practice, however, a mould of the thing to be copied is first taken in some soft substance, such as plaster, gutta-percha, or wax, and this mould is made the cathode. If the mould is made of non- conducting material, as is usually the case, its surface must be covered with some conducting substance, as powdered graphite. The mould may be covered by means of a hair brush with a film of graphite sufficient to make it a con- ductor, without obliterating the finest lines. One of the chief uses of electrotyping is in copying printer's type after it has been set up, and in copying wood engravings. An impression is taken of the type or of the engraving in wax. This wax is then brushed over with ELECTRICITY. 3^5 powdered graphite, and made the cathode ; the electrolyte is cupric sulphate, and the anode a piece of copper. A large bath is used (see Figure 220), so that several Fig. 220. pieces may be electrotyped at the same time. These are all hung by wires to a metallic rod which is connected with the negative pole of the battery. Upon another metallic rod pieces of copper are hung opposite to the pieces to be copied. The electric current is sometimes generated in the bath itself. The object to be coated serves as one of the plates of the battery, and a piece of zinc as the other, the wire connecting the two being coated with insulating varnish. 309. Electro-plating. This is the art of coating the baser metals with silver by the electric current. Articles to be electro-plated are generally made of brass, bronze, copper, or nickel silver, this last being the best material. The bath is a large trough of earthen-ware or other non- conducting substance. It contains a weak solution of argentic cyanide (cyanide of silver) and potassic cyanide (cyanide of potassium). A plate of silver forms the anode ; and the articles to be plated, hung by wires to a metal rod lying across the trough, constitute the cathode. When the former is connected with the positive pole of a bat- tery, and the latter with the negative pole, the silver of T 306 ELECTRICITY. the cyanide begins to deposit itself on the suspended articles, and the cyanogen, set free at the plate, dissolves it, forming argentic cyanide. The thickness of the plat- ing depends on the length of time the articles are im- mersed. 310. Electro-gilding. This process is essentially the same as electro-plating, except that the articles are coated with gold instead of silver. The electrolyte in this case is the cyanide or some other salt of gold, and the anode is a lump of gold. If it is not intended to gild the whole sur- face of the article, the parts not to be gilded must be coated with some non-conducting substance. 311. Electro-metallurgy. Many other metals besides copper, silver and gold may be deposited by electrolysis. The art of depositing, by electro-chemical action, a metal on any surface prepared to receive it, is called electro- metallurgy. All processes of the kind may be classified in two divisions, one of which is illustrated by electrotyping, and the other by electro-plating. The former includes all those cases in which the coating of metal is to be re- moved from the surface on which it is deposited ; and the latter all cases where the coating remains permanently fixed. Gold, platinum, silver, copper, zinc, tin, lead, cobalt, and nickel can be deposited by electrolysis. 312. Electric Clocks. The elec- tric force has also been used to reg- ulate the movements of clocks, called copying clocks. They are of the usual construction, except that the pendu- lum balls are hollow coils of copper wire, so that they become magnetic when a current is sent through them. In Figure 221, represents a part of the rod, and B the ball, of such a pendulum. Permanent magnets, ELECTRICITY. 307 N S and S JV, are fastened against the sides of the clock- case opposite the ends of the coil B, with like poles to- wards the coil. The hollow of the coil, as it swings, can pass a little way up the length of each magnet. If the south poles of the magnets are turned towards the coil, as in the figure, and a current is sent through the wire, one end of the coil becomes a north pole, which is attracted by the magnet near it, and the other end a south pole, which is repelled by the magnet near it. This attraction and repulsion both tend to send the coil in one direction. If, now, at the instant that B is drawn to one side, the di- rection of the current is changed, the poles of the coil are reversed, and it is carried to the other side. The pendu- lum thus vibrates every time the current is reversed. This is done by means of a standard or regulating clock. Every time the pendulum of this clock vibrates, the direction of the current is reversed ; so that the pendulums of all the copying clocks vibrate exactly at the same rate as the pen- dulum of the regulating clock. In this way, by means of one accurate clock, any number of copying clocks, of the most ordinary construction, can be made to keep accurate time. Fig. 222. ..I... Figure 222 shows one of the ways in which the pendulum, A, of the regulating clock can change the direction of the current. The spring e is connected with the negative pole 308 ELECTRICITY. of the battery G, and the spring d with the positive pole of the battery F. The other poles of these batteries are con- nected with the plates m and ;z, buried in the earth. B and C are the pendulums of the copying clocks. When the regulating pendulum touches the spring d, the current flows through the wire from A to B and C ; when u v touches the spring e, the current flows first through the eartH from 11 to o, and then through the wire from C to A. The Der- manent magnets connected with the pendulums B and , , the record- ing instrument, then to earth. When 7/is pressed down, the key is in the sending position, and transmits the bat- tery current by c, a, m, A, Z, to the distant station. 316. The Earth. One wire is quite sufficient to con- nect two telegraph stations, if its terminations be formed by two large plates sunk in the earth. The plates are gener- ally of copper, and should have a surface of not less than twenty square feet ; and they must be buried so deep that the earth about them never gets dry. The gas and water pipes in a town make an excellent earth, or earth-connec- tion. When the earths are good, the current passes through the earth between the two stations, no matter what may be the nature of the region it has to pass, plain or mountain, sea or land. The resistance of the earth to the current, compared with that of a long line, is next to nothing. The earth serves the purpose, not only of a second wire, but of one so thick that its resistance may be left out of account. In conducting power, for equal dimensions, the earth stands much inferior to the wire ; but then its thickness, so to speak, is indefinitely greater, and hence its conduct- ing power, on the whole, is superior. 317. The Relay. It is only on short circuits, generally of less than fifty miles, that the receiving instrument is worked directly by the line current. On long circuits, direct working could only be accomplished by an enor- mous sending battery. The loss by leakage on the way is very considerable, so that a current strong at starting be- comes very weak before it reaches the station to which it is sent. Besides, the leakage is the greater, the greater the number of cells employed, or the greater the tension of the battery. It is found a much better arrangement to work the receiving instrument by a local current, and to include in the line circuit a very delicate instrument, which has only to make or break the local circuit. Such an instru- 312 ELECTRICITY. ment is called a relay ^ and is shown in Figure 225. The electro-magnet, , of the relay is included in the line cir- cuit, instead of the electro-magnet of the receiving instru^ Fig . 22S . ment. The coil is long, and of very fine wire ; and a very faint current is sufficient to develop magnetism in the core. The keeper, A, of the relay is attached to a lever, when the low grounds are sandy or dry, mist is less frequently produced. When an oceanic current meets a shoal in its course, the cold water of the lower depths is brought to the surface, and in all cases where its temperature is lower than the dew-point of the air, fogs are formed over the shoal. For a similar reason icebergs are frequently enveloped in fogs. In like manner mist is sometimes seen to rise from rivers whose temperature 'is lower than that of the air. Thus the waters of the Swiss rivers which issue from the cold glaciers cool the air in contact with them below the point of saturation, and mist is thereby often produced. So, also, such rivers as the Mississippi, which flow directly into warmer latitudes, and are therefore colder than the air above them, are often covered with mist or fogs. When rivers are considerably warmer than the air, they give rise to fogs, because the more rapid evaporation from the warm water pours more vapor into the atmosphere than it can hold, and the surplus is condensed into mist by the colder air through which it rises. Thus deep lakes, and rivers flowing out of them, are in winter generally much warmer than the air, and hence when the air is cold and its humidity great they are covered with fogs. When Sir Humphrey Davy descended the Danube in 1818, he observed that mist was always formed during the night, when the temperature of the air on shore was from 3 to 6 lower than that of the stream ; but when the sun rose, and the temperatures became equal, the mist rapidly disappeared. The densest fogs occur during the cold months in large towns built on rivers, the causes which produce fogs being then at the maximum. The peculiar denseness of the London Novem- ber fogs is caused by the warmth of the river-bed, and it is in- creased by the sources of artificial heat which London affords ; and since the temperature is falling everywhere, and the humid- ity is then great, the vapor of the atmosphere is quickly and copiously condensed by the gently flowing cold easterly winds which generally prevail in November. In all these cases the fogs are confined to the basin of the river or lake where they are formed, and do not extend far up into the atmosphere. There are, however, other fogs that spread over large districts, like the fogs which often accompa- APPENDIX. 337 ny the breaking up of frosts in winter. When the humid south- west wind has gained the ascendency, and is now advancing over the earth's surface as a " light air," it is chilled by contact with the cold ground, and its abundant vapor thereby condensed into a wide-spread mist. Mountains are frequently covered with mist. Since the pres- sure and consequently the temperature of the air falls with the height, it follows that as warm air is driven up the slopes of the mountain by the wind, it becomes gradually colder, and its ca- pacity for moisture is diminished until condensation takes place, and the mountain is swathed in mist. Mists often appear sooner on the parts of hills covered with trees than elsewhere. This happens especially when the mist begins to form after midday, because then the temperature of the trees is lower than that of the grassy slopes. Mists also linger longer over forests, proba- bly on account of the increased cold arising from the large ex- tent of evaporating surface presented by their leaves when drenched with mist. Occasionally the summit of a hill or an isolated peak is wrapped in mist, while elsewhere the atmos- phere is clear ; and though a breeze be blowing over the hill, still " Overhead The light cloud smoulders on the summer crag," apparently motionless and unchanged. This phenomenon is easily explained. The temperature at the top is below the dew- point of the atmospheric current. Hence when the air rises to this region its moisture is condensed into mist, which is borne forward over the top of the hill and down the other side, acquir- ing heat as it descends, till it is again dissolved and disappears. Meanwhile its place is constantly supplied by fresh condensa- tions which take place as the current, rising to the height of the mist, falls below the temperature of saturation. Thus, though the mist on the top of the hill appears to remain motionless aad unchanged, the watery particles of which it is composed are con- tinually undergoing renewal. 25. Clouds. Clouds are visible vapors floating in the air at a considerable height ; thus differing from mists and fogs, which float near the surface. Both arise from the same causes. During the warmest part of the day, when evaporation is '5 V 338 APPENDIX. greatest, warm, moist air-currents are constantly ascending from the earth. As they rise in succession, the moist air is pushed high up into the atmosphere, and, losing heat by expansion, a point is at length reached when it can no longer retain the moisture with which it is charged ; hence condensation takes place, and a cloud is formed, which increases in bulk as long as the air continues to ascend. But as the day declines, and evap- oration is checked, the ascending current ceases, and, the tem- perature falling from the earth's surface upwards, the lower stratum of air contracts, and consequently the whole mass of dir begins to descend, and the clouds are then dissolved by the warmth they acquire in falling to lower levels. The whole of Jhis process is frequently seen on a warm summer day. In the morning the sky is cloudless, or nearly so ; as the* heat becomes greater, clouds begin to form before noon and gradually increase in numbers and size ; but, as the heat diminishes, they contract their dimensions, and gather round the setting sun, lit up with the fiery splendors of his beams. In a short time they disap- pear, and the stars come out, shining in a cloudless sky. Balloon ascents, as well as observations of the clouds, have shown that the whole atmosphere, to a great height, is constantly traversed by many aerial currents, one above another, and flow- ing in different and frequently in opposite directions. Masses of air of different temperatures thus frequently combine togeth- er ; and since the several portions when mingled cannot hold the same quantity of vapor that each could retain before they were united, the excess is condensed and appears as cloud. But again, when a dry and heavy wind begins to set in, or take the place of a moist and light wind, it generally does so by edging itself beneath the moist wind and forcing it, as with a wedge, into the upper regions of the atmosphere, where con- densation rapidly follows, and dense black clouds, often heavily charged with rain, are formed. This is a frequent cause of cloud and rain in Great Britain, when the cold, heavy east wind, or polar current, thrusts high up into the air the rain-bring- ing southwest wind, causing it to darken the sky and pour its surplus moisture in torrents of rain. Currents of air driven up the sloping sides of hills and moun tains by the winds often cause the formation of clouds (24). APPENDIX. 339 26. How Clouds are suspended in the Air. The example of a cloud appearing to rest on the top of a hill though a strong wind be blowing at the time (24) suggests how clouds are sus- pended in the air. The cloud itself may appear stationary or suspended, but the particles of which it is composed are under- going constant renewal or change. The particles are upheld by the force of the ascending current in which they are formed ; but when that current ceases to rise, or when they become sep- arated from it, they begin to fall through the air by their own weight, till they melt away and are dissolved in the higher tem- perature into which they fall. Hence, as Espy has reasoned, every cloud is either a forming cloud or a dissolving cloud. While it is connected with an ascending current, it increases in size, is dense at the top, and well defined in its outlines ; but when the ascending current ceases, the cloud diminishes in size and density. When a cloud overspreads the sky, its lower surface is for the most part horizontal, or more generally it seems as if it was an impression taken from the contour of the earth's surface beneath it. This arises from the high temperature of the air below the cloud, which is sufficient to dissolve the particles as they descend below its level. 27. Classification of Clouds. Clouds are divided into seven kinds ; three being simple, the cirrus, the cumulus, and the stratus ; and four intermediate or compound, the cirro-cumulus, the cirro-stratus, the cumulo-stratus, and the cumulo-cirro-stra- tus or nimbus. These forms of clouds, with the exception of the nimbus, are represented in the plate on page 341. The one marked by one bird is the cirrus ; by two birds, the cirro-cumulus ; by three, the cirro-stratus; by four, the cumulus; by five, the cumulo-stratus ; by six, the stratus. 28. Cirrus Cloud. The cirrus (or curl) cloud consists of parallel, wavy, or diverging fibres which may increase in any or in all directions. Of all clouds it has the least density, the greatest elevation, and the greatest variety of extent and direc- tion, or figure. It is the cloud first seen after serene weather, appearing as slender filaments stretching like white lines pen- cilled across the blue sky, and thence propagated in one or 340 APPENDIX. more directions, laterally, or upward, or downward. Sometimes the thin lines of cloud are arranged parallel to each other, the lines lying in the northern hemisphere from north to south, or from southwest to northeast; sometimes they diverge from each other in the form of the tail of a horse ; while at other times they cross each other in different ways, like rich, delicate lace-work. It is probable that the fine particles of which this cloud is composed are minute crystals of ice or snow-flakes. The duration of the cirrus varies from a few minutes to many hours. It remains for a short time when formed in the lower parts of the atmosphere and near other clouds, and longest when it appears alone in the sky, and at a great height. The cirrus, though apparently motionless, is closely connect- ed with the movements of the great atmospheric currents, and is therefore a most valuable prognostic of stormy weather. 29. Cumulus. This name is applied to convex or conical heaps of clouds increasing upwards from a horizontal base. They are usually of a very dense structure ; are formed in the lower regions of the atmosphere ; and are carried along in the current next the earth. The cumulus has been well called the cloud of the day, being caused by the ascending currents of warm air which rise from the heated ground. Its beginning is the little cloud not bigger than a man's hand, which is the nu- cleus round which it increases. The lower surface remains roughly horizontal, while the upper rises into towering heaps, which may continue comparatively small, or swell into a size far exceeding that of mountains. When these clouds are of moderate height and size, of a well- defined curved outline, and appear only during the heat of the day, they indicate a continuance of fair weather. But when they increase with great rapidity, sink down into the lower parts of the atmosphere, and do not disappear towards evening, rain may be expected. If loose fleecy patches of cloud begin to ap- pear thrown out from their surfaces, the rain is near at hand. 30. Stratus. The stratus, as its name implies, is a widely- extended, continuous layer or sheet of cloud, increasing from below upwards. It is, besides, the lowest sort of cloud, its lower surface commonly resting on the earth. The stratus may be called the cloud of night, since it generally forms about sun- APPENDIX. 341 H CLOUDS. 342 APPENDIX. set, grows denser during the night, and disappears about sun- rise. It is caused by the vapors which rise during the day, but towards evening fall to the earth with the falling temperature. Since during night the cooling of the air begins on the ground, the stratus first appears like a thin mist floating near the surface of the earth ; it thence increases upwards as successive layers of the air are cooled below the point of saturation. It includes all those mists already described, which in the calm evening of a warm summer day form in the bottom of valleys and over low- lying grounds, and then spread upwards over the surrounding country like an inundation. When the morning sun shines on the upper surface of the stratus cloud, it begins to be agitated and to heave up in dif- ferent places into the rounded forms of the cumulus, and the whole of its lower surface begins to rise from the ground. As the heat increases, it continues to ascend, breaks up into de- tached masses, and soon disappears. This indicates a continu- ance of fine weather. 31. Cirro-cumulus. This cloud is composed of well-defined, small, roundish masses, lying near each other, and quite sepa- rated by intervals of sky. It is formed from the cirrus cloud, the fibres of which break, and gather into these small masses. It is commonly known among sailors as a mackerel sky. 32. Cirro-stratus. The cirro-stratus partakes partly of the characteristics of the cirrus and stratus. It consists of long, thin, horizontal clouds, with bent 'or undulated edges, and either separate or in groups. It is a marked precursor of storms. 33. Cumulo-stratus. T\i\* cloud is formed by the blending of the cirro-stratus with the cumulus, either among its piled-up heaps, or spreading underneath its base as a horizontal layer. It is formed when the cumulus becomes surrounded with small fleecy clouds just before rain begins to fall, and also on the approach of thunder-storms. 34. Cumulo-cirro- stratus, or Nimbus. This is the well-known rain-cloud, consisting of a cloud, or system of clouds, from which rain is falling. It sometimes has its origin in the cumulo- stratus, which increases till it overspreads the sky, and becomes black or bluish-black in color ; but, this soon changing to gray, the nimbus is formed, and rain begins to fall. APPENDIX. 343 Its name, cumulo-cirro-stratus, suggests the way in which it is usually formed. At a considerable height, a sheet of cirro- stratus cloud is spread out, under which cumulus clouds drift from the windward ; these rapidly increase and unite into a continuous gray mass, from which the rain falls. The breaking up of this gray mass indicates that the rain will soon cease. When a rain-cloud is seen approaching at a distance, cirri appear to shoot out from its top in all directions ; and the more copious the rain-fall, the greater is the number of these cirri. RAIN, SNOW, AND HAIL. 35. Rain. Whatever lowers the temperature of the air may be considered as a cause of rain. It is chiefly brought about by the ascent of air into the higher regions of the atmosphere. Moist air-currents are forced up into the higher parts of the atmosphere by colder, drier, and therefore heavier, wind-cur- rents which get beneath them. Ranges of mountains also oppose their masses to the winds, so that the air forced up their slopes is cooled, and its vapor condensed into showers of rain or snow. Moist air-currents are also drawn up into the higher regions of the atmosphere over the area of least pressure at the centre of storms ; and in such cases the rain-fall is gen- erally very heavy. The temperature of the air is lowered, and the amount of the rain-fall increased, by those winds which convey the air to higher latitudes. This occurs in temperate regions, or in those tracts traversed by the return trade-winds, which in the north temperate zone blow from the southwest, and in the south temperate zone from the northwest. The meeting and mixing of winds of different temperatures is also a cause of rain, since the several portions, when combined into one, cannot hold as much vapor as before. The rain-fall is also increased if the prevailing winds are directly from the sea, and are therefore moist; but it is diminished if they have passed over large tracts of land, particularly mountain-ranges, and are therefore dry. The quantity of rain is influenced by sandy deserts, which allow radiation, by day or night, to take im- mediate effect in raising or depressing the temperature ; and also by forests, which retard or counteract radiation. 344 APPENDIX. Rain rarely or never falls in certain places, which are, on that account, called rainless regions ; as, for example, the coast of Peru, in South America, the Sahara in Africa, and the desert of Gobi, in Asia. The Sahara is bounded on the north and on the south by ranges of mountains. When the northeast trade-wind strikes the northern range, a part of its vapor is condensed. As it moves southward, it reaches warmer latitudes, where there is a greater capacity for moisture. Since there are no opposing winds to force it upwards, it sweeps on across the vast sandy plain until it arrives at the southern mountains, where its vapor is precipitated in abundant rains. In the few spots in the desert where hills or mountains occur, there are occasional rains. On the desert of Gobi, the prevailing winds are from the southeast, and are very dry, because they have precipitated nearly all their moisture in passing over the Himalaya Moun- tains. The rainless district in Peru is caused by the Andes, which condense nearly all the vapor of the southeast trade-wind in copious rains on their eastern slopes. On the other hand, in such places as Chili and Patagonia, it rains almost every day. 36. Rain-fall within the Tropics. At places within the tropics, where the trade-winds blow regularly and steadily, the rain-fall is small. Since these winds come from higher lati- tudes, the temperature is increasing, and they are thus more likely to take up moisture than to paft with it. Where, how- ever, the trade-winds are forced up the slopes of mountain ranges, they bring rain in copious showers. The tropical belt, known as the region of calms (see page 326) is the region of constant rains. Here the sun almost invariably rises in a clear sky ; but about midday clouds gather, and the whole face of the sky is soon covered with black clouds, which pour down prodigious quantities of rain. Towards evening the clouds disappear, the sun sets in a clear sky, and the nights are serene and fine. The reason of this is, that the air, being greatly heated by the vertical rays of the sun, ascends, drawing with it all the vapor which the trade-winds have brought with APPENDIX. 345 them, and which has been largely increased by the rapid evap- oration from the belt of calms ; and this vapor is condensed as it rises. The rain is sometimes so copious that fresh water has been collected from the surface of the sea. As evening sets in, the surface of the earth and the air near it being cooled, the ascending currents cease, and the cooled air descends ; the clouds are thus dissolved, and the sky continues clear till the returning heat of the following day. Over a great part of the tropics disturbing influences draw the trade-winds out of their course, and sometimes, as in the case of the monsoons, give rise to winds which blow from the opposite point of the compass. These winds affect the rain-fall of India, and but for them the eastern districts of Hindostan would be constantly deluged with rain, and the western districts constantly dry and arid. As it is, each part of India has its dry and wet seasons, summer being the wet season of the west and interior as far as the Himalaya, and winter the wet season of the east, and especially the southeast. So far as known, the heaviest annual rain-fall at any place on the globe is 600 inches on the Khasia Hills. About 500 inches of this fall in seven months, during the southwest mon- soons. These hills face the Bay of Bengal, from which they are separated by only 200 miles of swamps and marshes. Hence the southerly winds not only arrive heavily laden with vapor from the Indian Ocean, but they get more moisture in passing over the 200 miles of swamp. They are, therefore, ready to burst in torrents, even before they are suddenly raised, by the hills they encounter, into the cooler regions of the atmos- phere. 37. Snow. Snow is the frozen moisture which falls from the clouds when the temperature is 32 or lower. The particles of which snow is composed are crystals, which are usually in the form of six-pointed stars. About 1,000 different kinds of snow-crystals have been already observed, a few of which are shown in Figure 229. The forms of the crystals of the same fall of snow are generally similar to each other. Snow-flakes vary from an inch to .07 of an inch in diameter, the largest being observed when the temperature is near 32, and the smallest at very low temperatures. 15* 346 APPENDIX. The limit of the fall of snow at any time of the year coincides nearly with 30 N. latitude, which includes almost the whole of Europe. On traversing the Atlantic, this line rises to 45, but on nearing the American continent it descends to 33 ; it rises in the west of America to 47, and again falls to 40 in the Pacific. Snow is unknown at Gibraltar; at Paris, it falls 12 days on an average annually, and, at St. Petersburg, 170 days. The white color of snow is caused by the combining of the different prismatic rays which issue from the minute snow- crystals. When the crystals are looked at separately, some Fig. 229. appear red, others green, purple, and, in short, all the colors of the spectrum ; but when a mass of snow is looked at, the different colors blend into white. Red snow and green snow have been occasionally met with in the arctic regions and in other parts of the world. These colors are due to the presence of vegetable organisms, about .001 of an inch in diameter, which grow and flourish in the region of eternal snow. From its loose texture, and from its containing about ten times its bulk of air, snow is a very bad conductor of heat ; and thus is an admirable covering to preserve the earth from the effects of its own radiation. It not unfrequently happens in times of great cold, that the soil is 40 warmer than the surface of the snow which covers it. The flooding of rivers, from the melting of the snow on mountains in spring and summer, carries fertility into regions which would otherwise remain barren wastes. 38. Hail. Hailstones are generally of a conical or of a round shape, and, when cut across, are found to be composed of alternate layers of clear and opaque ice, enveloping a white snowy nucleus. Less frequently they are composed of crystals APPENDIX. 347 radiating from the centre outwards. They vary much in size, some being as small as the smallest shot, while others are several inches in diameter. In August, 1813, hailstones the size of eggs fell upon the British army among the Pyrenees ; the storm lasted twenty minutes, and was not accompanied with thunder or lightning. June 4th, 1814, hail, from 13 to 15 inches in diameter, fell in Ohio. In the Orkney Islands, July 24th, 1818, during thunder, a very remarkable shower of hail took place ; the stones were as large as a goose's egg, and mixed with large masses of ice. The origin of hail is not fully understood ; but it appears to be formed by a cold current of air forcing its way into a mass of air much warmer and nearly saturated, the temperature ot the united mass being below the freezing-point. The warm, moist air is easily accounted for, since hail generally falls in summer and during the day ; but it is difficult to account for the intensely cold current which is sufficient to reduce the warm saturated mass below 32. In mountainous regions, cold currents from the fields of snow, rushing down the sides of the mountains and mixing with the heated air of the valleys, are no doubt frequent causes of hail ; and such places are peculiarly subject to hailstorms. The sudden ascent of moist warm air into the upper regions of the atmosphere, where a cold current prevails at the time, is, in all probability, a common cause of hail. This is confirmed by the sultry, close weather which generally precedes hail- storms, the slight but sudden fall of the barometer, the whirl- winds and ascending currents which accompany them, and the fall in the temperature which follows after the storm has passed. ATMOSPHERIC ELECTRICITY. 39. Electricity in the Air. The identity of lightning and electricity was first suspected by Wall in 1708, but it was re- served to Franklin to prove it. In 1749, he suggested, as the mode of proof, the erection of pointed metallic conductors prop- erly insulated. Acting on this suggestion, Dalibard erected near Paris a pointed iron rod, 40 feet in length, and insulated ; and, on the loth of May, 1752, obtained electrical sparks from 348 APPENDIX. it. In June of the same year, Franklin, impatient at the delay in erecting the spire for his pointed conductor, tried the experi- ment of obtaining electricity from the clouds by flying a kite. The kite was held by a hempen string, to the lower end of which a key was attached ; and the whole was insulated by tying a silk ribbon to the key, the other end of the ribbon being attached to a post. On the approach of the thunder- cloud, he raised the kite, and soon the fibres of the hempen string began to repel each other ; and, at last, when the rain had moistened the string, he had the satisfaction of drawing sparks from the key. When the sky is cloudless, the electricity is always positive; but the intensity increases with the height. When the sky is clouded, the electricity is sometimes positive and sometimes negative, according to the electrified condition of the clouds. In relation to the air, the earth's surface is always negative. The electricity of the atmosphere is stronger in winter than in summer, increasing from June to January, and decreasing from January to June. It is subject to a double maximum and minimum each day. . 40. Sources of Atmospheric Electricity. (i) Evaporation. Electricity is produced when impure water is evaporating, or water in which chemical decomposition is going on ; none whatever being produced by the evaporation of pure water. Evaporation from water containing an alkali or a salt gives off negative electricity to the air, and leaves positive electricity behind ; but when the water contains acid, positive electricity is given off, and negative is left behind. Hence it is supposed that seas, lakes, and rivers are abundant sources of electricity, particularly of the positive sort. (2) Vegetation. The vege- table kingdom is also a source of electricity ; (a) from the evap- oration going on by which water is separated from the sap of the plants, and (b) from the giving off of oxygen gas during the day, and carbonic gas during the night. In these cases, positive electricity arises from the plants, and negative is left behind. (3) Combustion. During the process of burning, bodies give off positive electricity, and become themselves neg- atively electrified. This is frequently seen on a grand scale APPENDIX. 349 during volcanic eruptions. (4) Friction. Wind, by the fric- tion it produces upon terrestrial objects, the particles of dust, and the watery particles which it carries with it, contributes to the electricity of the air. Electricity is not generated if the moisture be in the form of pure vapor. 41. Effect of the Condensation of Vapor. When a great mul- titude of molecules of vapor are condensed by cold into a drop, or snow-spangle, that drop probably collects and retains on its surface the whole electricity of the molecules from which it is formed. If a thousand such globules coalesce into one, the electricity will be increased a thousand-fold, and, being spread entirely over the surface, will have a tenfold tension. This view (which is Sir John Herschel's) explains the electricity observed in the lower stratum of air when dew is being de- posited, and the highly electrical state of fogs and clouds. It also explains the annual fluctuation ; for, since in winter the condensation of vapor is greater and more frequent than in summer, the average quantity of electricity will be greater in winter. 42. Thunder-storms. The thunder-storm probably originates, like cloud and rain, in the condensation of vapor ; but the con- densation is more copious and more rapid, so as to bring about an accumulation of a sufficient quantity of electricity. If the condensation is not copious, the electricity will be too weak ; and if not sudden, it escapes before enough collects for a dis- charge. Thunder-storms occur most frequently within the tropics, and diminish in frequency towards the poles. They are also more frequent in summer than in winter ; during day than during night ; after midday than before it ; and in mountainous countries than in plains. Within the tropics they prevail most in the region of calms and during the rainy season ; and least in arid deserts and during the dry season. 43. Lightning. Arago has divided lightning into three kinds ; zigzag lightning, sheet lightning, and ball lightning. When the electric flash darts through the air, it takes the path of least resistance; and, since the conducting power of different portions of the atmosphere is unequal, the lightning frequently appears zigzag. When branches are given off at different 350 APPENDIX. points of its course, the lightning is said to be forked. Sheet- lightning is the most common, appearing as a glow of light illuminating the sky. The flashes often follow each other in quick succession, and the thunder which accompanies them is low and at a considerable distance. Analogous to this is silent lightning, frequently termed heal lightning, which generally occurs during serene summer evenings, lighting up the sky fit- fully for hours, with repeated faint flashes ; it is not attended with thunder. It is probable that this kind of lightning is al- most always the reflection of the lightning of distant storms from the vapor of the upper regions of the atmosphere, the storms themselves being so far off that their thunder cannot be heard. Ball lightning is the least common. It appears as a globular mass, moving slowly or sometimes remaining station- ary, and in a short time explodes with violence. It has not yet been satisfactorily explained. Professor Wheatstone has shown that the duration of a flash of lightning is less than the thousandth part of a second. A wheel was made to rotate so rapidly that the spokes were invisible ; on being lighted up with the electric flash, the duration of the flash was so brief that the wheel appeared quite stationary, even though rotating with the utmost speed possible. 44. Thunder. Thunder is probably the noise produced by the instantaneous rushing of the air to fill the vacuum left by the lightning along the path of the discharge. The sound emitted by flames is a familiar illustration of a similar phenom- enon. Flashes of lightning frequently extend two or three miles in length ; and since the thunder is produced at every point along its course nearly at the same instant, the prolonged rolling noise of thunder arises from the different intervals of time it takes the sound to reach the ear. For since sound travels at the rate of 1,090 feet per second, it is first heard from the near- est point of the flash, later and later from points more distant, so that the combined effect is a continued peal of thunder. The direction and character of the peal will depend on the length of the flash, and the greater or less obliquity of its course in rela- tion to the observer. Reverberations from clouds and from mountains frequently heighten the effect and prolong the peal. From the rate at which sound travels, if the thunder is not APPENDIX. 351 heard till five seconds after the flash, the distance is about a mile. Thunder has not been heard at a greater distance than 14 miles from the flash. 45. Effects of Lightning. The great proportion of electrical discharges pass into the air, or into other clouds less highly electrified ; a very few only take place between the cloud and the earth. The destructive effects of this latter class are known to all. By the electric discharge innumerable lives have been destroyed, the strongest trees rent to pieces, heavy bodies dis- placed, iron and steel magnetized, metals and rocks softened and fused, and combustible substances set on fire. When the thunderbolt falls upon sand it usually produces fulgurites or fulminary tubes, which are silicious tubes of various sizes vitri- fied internally. 46. Return Shock. This shock sometimes proves fatal to living beings, even at great distances from the place where the electric discharge takes place. It is caused by the inductive action of the electrified cloud on bodies within the sphere of its influence, by which they become charged with the electricity opposite to that of the cloud. Hence, when the cloud has dis- charged its electricity into the ground, the induction ceases and a rapid change takes place in bodies from the electrified to the neutral state, thus causing the concussion of the return shock. 47. Lightning- Rods. The lightning-rod was introduced by Franklin in 1755 as a means of protecting buildings from the destructive effects of electricity. The advantage gained by it consists not in protecting the building in case of a discharge by allowing a free passage for the electric fluid to escape to the earth, for it is but a poor protection in such a case ; but, by quietly and gradually keeping up the communication, it tends to maintain the electric equilibrium, and thus prevent the oc- currence of a discharge. The best rods are made of copper not less than three quarters of an inch thick, and pointed at the upper end. They should be of one piece throughout, fastened vertically to the roof of the building, and thence carried down into the ground. The lower extremity should part into two or three branches bent away from the house, and carried suffi- ciently far into the soil to meet water or permanently moist earth. The conductor should be connected with all metallic 352 APPENDIX. surfaces on the roof or other parts of the building, in order to prevent the occurrence of lateral discharges, or discharges from the conductor to these surfaces, which are often very destruc- tive. 48. St. Elmo's Fire. This meteor is the Castor and Pollux of the ancients, and is frequently mentioned in classic writings, from the Argonautic expedition downwards. Caesar notices its appearance after a storm of hail in these words : " Eadem nocte legionis quintae cacumina sua sponte arserunt." The finest and most beautiful displays occur at sea during storms, when it appears as a light resting on the masts. The light which is seen on a point held near the conductor of an electric ma- chine explains St. Elmo's fire, which takes place when the elec- tricity of a cloud and that of the earth combine, not in flashes of lightning, but slowly and continuously from different points. 49. The Aurora Borealis. The aurora borealis is the lumi- nous appearance in the northern sky, which forms, in its most vivid displays, spectacles of surpassing beauty. The aurora is observed also in the neighborhood of the south pole, and is there called aurora australis. When fully developed, the au- rora consists of a dark segment of a hazy or slaty appearance surmounted by an arch of light, from which luminous streamers quiver and dart upwards. Several auroral arches are some- times seen at once. Sometimes the streamers appear to unite near the zenith, forming what is called the corona of the aurora, towards which the dipping needle at the time points. Auroras are very unequally distributed over the earth's sur- face. At Havana but six have been recorded within a hundred years. As we travel northwards from Cuba, they increase in frequency and brilliancy ; they rise higher in the heavens, and oftener attain the zenith. If we travel northwards along the meridian of Washington, we find on an average near the par- allel of 40 only ten auroras annually. Near the parallel of 42, the average number is twenty annually ; near 45, it is forty ; and near 50, it is eighty. Between this point and the parallel of 62 auroras are seen almost every night, high in the heavens, and as often to the south as the north. Farther north they are seldom seen except in the south, and from this point they diminish in frequency and brilliancy as we advance towards APPENDIX. 353 the pole. If we make a like comparison for the meridian of St. Petersburg, we shall find a similar result, except that the auroral region is situated farther northward than it is in America. Au- roras are more frequent in the United States than they are in the same latitudes of Europe. The aurora is of great extent, having been sometimes ob- served simultaneously in Europe and America. From obser- vations made in the two hemispheres, Professor Loomis thinks it probable that an exhibition of auroral light about one mag- netic pole of the earth is uniformly attended by a simultaneous exhibition of auroral light about the opposite magnetic pole.* The height varies from about 45 to 500 miles above the earth. 50. Relations of the A^trora to Magnetism. Many facts point out an evident connection between the aurora and terres- trial magnetism. The magnetic needle is much agitated when the aurora is visible. When the arch is motionless, so is the needle ; but as soon as streamers are shot out, its declination changes every moment, and this happens though the aurora does not appear at the place of observation, but is seen near the pole. Captain M'Clintock, when in the arctic regions, observed that the aurora in all cases appeared to come from the surface of open water, and not in any case from the fields of ice. This favors the idea that it is caused by electrical discharges between the earth and the air, and that these are interrupted by the fields of non-conducting ice. General Sabine has discovered that magnetic disturbances of the earth are due to the sun, but not to his heat and light ; and are invariably accompanied by the aurora and by electric cur- rents on the surface of the earth. The secular periods of the sun's spots, of the variation of the magnetic needle, and of the frequency of auroras, coincide in a remarkable way, indicating that these phenomena are regulated by astronomical causes.f OPTICAL PHENOMENA. 51. The Rainbow. For the description and explanation of the rainbow, see pages 144- 147. * Treatise on Meteorology, p. 188. t See Handbook of the Stars, p. 91. 354 APPENDIX. Since rainbows in the morning are always seen in the west, they indicate the advance of the rain-cloud from the west at the lime that it is clear and bright in the east ; and since the fall of rain at this time of the day when the temperature should be ris- ing is an additional evidence of increasing moisture, a morning rainbow is regarded as a prognostic of a change to wet, stormy weather. On the contrary, the conditions under which a rain- bow can appear in the evening are, the passing of the rain-cloud to the east, and a clearing up in the west at the time of day when the temperature has begun to fall, thus further indicat- ing a change from wet to dry weather. Hence the popular rhyme : " A rainbow in the morning, Sailors take warning ; A rainbow at night Is the sailor's delight." 52. Lunar Rainbows. Rainbows are also produced by the light of the moon falling on rain-drops, exactly in the same way as solar rainbows. They are by no means of rare occurrence. Owing to the feeble light of the moon the bow is generally with- out colors ; but when the sky is very clear and the moon at the full, the prismatic colors appear, but in subdued splendor. 53. Coronas. The corona is an appearance of faintly-colored rings encircling the moon when seen behind the light, fleecy cloud of the cirro-cumulus. When the corona is perfect, the rings form several concentric circles, the blue prism-itic color being nearer the centre than the red. When of large dimen- sions the ring has generally a whitish, nebulous appearance. Coronas are also very frequently formed round the sun ; but to see them it is necessary to look through smoked glass, or at the image of the sun reflected from still water. 54. Anthelia. Glories of light, otherwise called anthelia, because formed opposite the sun, are sometimes seen when the shadow of an observer is cast on fog ; and the shadow of his head is surrounded with the prismatic circles. On one occa- sion Scoresby saw four colored concentric circles around his shadow, and he observed that the phenomenon was always seen in the polar regions whenever sunshine and fog occurred at the same time. APPENDIX. 355 55. Halos. Halos are circles of prismatic colors around the sun (Figures 230-233) or the moon (Figures 234 and 235). Fig. 230. Fig. 231. Fig. 232. Fig- 233. Fig. 235- but they are perfectly distinct from coronas, with which they should not be confounded. Halos are of comparatively rare 356 APPENDIX. occurrence ; coronas, on the contrary, may be seen every time a light, fleecy cloud comes between us and the sun or moon. The structure of halos, as seen from the figures, is often very complicated, circle cutting circle with mathematical exactness, the circles being generally very large. The structure of the corona, on the other hand, is simple, the circles concentric, the inner one small, the diameter of the second being double, and that of the third treble, the diameter of the first. In halos, the red prismatic color is next the centre ; in coronas, the blue. Halos are formed from the refraction and reflection of the rays of light by the minute snow-crystals of the cirrus cloud ; while coronas arise from the interference of the rays passing on each side of the globules of vapor. 56. Parhelia and Paraselene. At the points where the cir- cles of the halo intersect, images of the sun or moon generally appear from the light concentrated at these points. The images of the sun are called parhelia, or mock-suns; and those of the moon, paraselenes, or mock-moons. These also exhibit the prismatic colors of the halo. 57. Colors of Clouds. Every one has observed and admired the red and golden clouds which fire the western sky at sunset, and make " the day's dying glory." They are observed to be the accompaniment of cumulus clouds as they slowly sink, while dissolving, down into the lower and warmer parts of the atmos- phere ; and consequently they disappear from the sky shortly after sunset. Such sunsets are therefore universally regarded as prophetic of fine weather. A green or yellowish-green tinted sky, on the other hand, is one of the surest prognostics of rain in summer, and snow in winter. The changing tints of the evening sky after stormy weather supply valuable help in forecasting the weather ; for, if the yellow tint becomes of a sickly green, more rain and stormy weather may be expected ; but if it deepens into orange and red, the atmosphere is getting drier, and fine weather may be looked for. Some years ago, Forbes showed from experiments that high- pressure steam, while transparent, and in the act of expansion, readily absorbs the violet, blue, and part of the green rays, thus letting the yellow, orange, and red pass. Dr. E. Lommel has APPENDIX. 357 shown that successive layers of air with visible vapor diffused through them act, so to speak, like sieves, which continually separate the transmitted light more and more perfectly from its more refrangible rays. Hence, in passing through different thicknesses of vapor, the blue rays are first absorbed, then the yellow rays, and finally the red rays. It is in the lower layers of the atmosphere that dust, smoke, watery vapor, and small rain-drops are chiefly suspended. When the sun is high in the heavens, the thickness of the vapor-screen between the sun and the eye is not sufficient to produce any perceptible action on the rays of light, which consequently appear white ; but as the sun descends to the horizon the thickness of the vapor is greatly increased, and at sunset it is calculated that the light of the sun has to pass through 200 miles of the air in illuminat- ing a cloud a mile above the earth. Hence, as the rays fall more and more obliquely on the clouds, they appear succes- sively yellow, orange, and finally red. The varied colors often seen at sunset are due to the fact that the clouds appear at dif- ferent heights and in different parts of the sky, so that various thicknesses of vapor are interposed between them and the sun. At dawn the clouds first appear red ; but, as the sun rises high- er, the yellow light ceases to be absorbed, and they appear orange, yellow, and finally white. These successive stages of a perfect dawn are well described in Dante's Purgatorio : " The dawn was vanquishing the matin hour, Which fled before it, so that from afar I recognized the trembling of the sea Already had the sun the horizon reached So that the white and the vermilion cheeks Of beautiful Aurora, where I was, By too great age were changing into orange." Longfellow's translation. Milton has accurately described the last stage of dawn in U Allegro: " . . . . the great sun begins his state, Robed in flames and amber light, The clouds in thousand liveries dight." It is evident that a high red dawn may be regarded as a prog- nostic of settled weather, because the redness seen in clouds at 358 APPENDIX. a great height while the sun is yet below the horizon may be occasioned by the great thickness of the vapor-screen through which the illuminating rays must pass before reaching the clouds, and not. to any excess of vapor in the air itself. But if the clouds be red and lowering in the morning, it may be ac- cepted as a sign of rain, since, the thickness traversed by the illuminating rays being now much less, the red color must arise from an unusual amount of vapor in that stage of partial con- densation, when, according to Forbes, the blue rays are ab- sorbed, and the yellow and red pass. SOURCES AND CONVERSION OF^ENERGY. IgiP" This Abridgment of the chapter in the ''''Astronomy'" on "Energy" u inserted for the convenience of teachers who may not use both books. 1. Kinds of Energy. Every moving body is said to have a dynamical energy ; and every body which is so situated that it can be moved by the forces acting upon it is said to have a pos- sible or potential energy. The energy of a visible mass in mo- tion is called mechanical. The energy of a moving molecule or atom is called molecular or atomic. The energy manifested in the bodies of animals is called nerve force or nmscular energy. 2. Affinity, Cohesion, and Gravity are the Forces which tend to convert Potential into Dynamical Energy. When visible masses are separated, gravity tends to pull them together, and to convert their potential into dynamical energy. When the molecules of a body are separated by melting and boiling, cohe- sion tends to draw them together again, and thus to convert their potential into dynamical energy, which appears as heat. Again, when the elements of a compound are separated, chemi- cal affinity tends to pull them together, and to convert their potential into dynamical energy, which appeals, in ordinary chemical action, as heat and electricity, or, in respiration, as heat and muscular force. 3. Mechanical Energy may be converted inf~* Heat. We APPENDIX. 359 have a familiar illustration of this in the lighting of a friction match. A portion of the energy employed in rubbing the match is converted by the friction into heat, which ignites the phosphorus. Here there is a double transfer of energy. The muscular energy of the arm is converted into mechanical en- ergy in the moving match, and a part of this into heat by the friction. Before matches were invented, the flint and steel were used for the same purpose. The steel was struck against the flint, and the spark obtained was caught in tinder. A part of the mechanical energy of the steel appeared as heat in the spark. Indians are said to obtain fire by vigorously rubbing to- gether two pieces of dry wood. In this case, too, the heat is nothing but mechanical energy appearing in a new form. Iron can be heated red-hot by hammering it. And, gen- erally, heat is developed by friction and percussion. 4. A II Mechanical Energy is ultimately converted into Heat. When a falling body strikes the earth, it becomes heated. In this case the whole energy of the body is converted into heat. When bodies are rubbed together, their energy, as we have seen, is converted into heat. The energy of a running stream is gradually converted into heat by the friction against its banks and bed and among its particles. If it is made to turn the wheels of a factory on its way, the rubbing of the parts of the machinery against each other and against the air, together with the various kinds of work done by the machinery, converts the mechanical energy of the water-wheel into heat. A railway train is really stopped by the conversion of its motion into heat. When this has to be done quickly, the change is hastened by increasing the friction by means of the brakes. On the other hand, in order to prevent the loss of energy while the train is in motion, the axles of the wheels are kept carefully oiled, that they may turn with as little friction as possible. When unlike substances are rubbed together, a part of the energy is first converted into electricity, but ultimately into heat. 5. When Mechanical Energy is converted into Heat, the Same Amount of Energy always gives rise to the Same Amount of 360 APPENDIX. Heat, This was first shown by Joule, who began his experi- ments in 1843 and continued them till 1849. He converted mechanical energy into heat by means of friction. He first ex- amined cases of the friction of solids against liquids. The ap- paratus used for this purpose is shown in Figure 236. B is a cylindrical box holding the liquid. In the centre of the box is Fig. 236. an upright axis, to which are attached eight paddles like the one shown in the figure. These revolve between four station- ary vanes, which prevent the liquid from being carried round. The paddles are turned by means of the cord r and the weight W. The size of the weight is such that it descends without acquiring any velocity, and hence all its energy is expended in the friction of the paddles. The degree to which the liquid becomes heated by the friction is shown by a thermometer at /. Knowing the weight of the liquid, its specific heat, and the rise of temperature during the experiment, the amount of heat generated can be readily calculated. With this machine Joule found that, whatever the liquid he used, a weight of one pound falling through 772 feet, or 772 pounds falling one foot, generated heat enough to raise one pound of water one degree Fahrenheit in temperature, or one unit of heat, as it is called. APPENDIX. 361 He also found that, when solids were rubbed together by the action of a falling weight, one pound falling through 772 feet generated a unit of heat. In this experiment iron discs were made to rotate together, one against the other, in a vessel of mercury. If a metallic disc be put into rapid rotation and then brought between the poles of a powerful electro-magnet, it soon comes to rest. It will now be found very difficult to turn it, and it becomes heated as it rotates. Joule found in this case, as in the others, that, if the disc is turned by a falling weight, one pound descending 772 feet generates a unit of heat. The force necessary to raise one pound one foot is called a foot-pound; and this is the same force- which a pound acquires in falling one foot from a state of rest. We see, then, that when mechanical energy is converted into heat, the same amount of energy always gives rise to the same amount of heat, and that 772 foot-pounds of mechanical force are equivalent to one unit of heat. For this reason, we call 772 foot-pounds the mechanical equivalent of heat. 6. Heat may be converted into Mechanical Energy. The steam-engine is a contrivance for converting heat into mechan- ical energy. The heat converts the water into steam, and gives to this steam an expansive force ; and this expansive force is made to move a piston, as has already been explained (Part I., pages loo- 102). The animal body is a machine for converting the molecular energy developed by affinity into mechanical energy. 7. The Same Amount of Heat always gives rise to the Same Amount of Mechanical Energy. In Figure 237, C is a box a Fig 237 * ot S( l uare> Suppose a a to be a partition one i foot from the bottom, so as to shut in a cubic foot of air. Suppose this partition to be immov- able, and the air beneath to be heated. Its elastic force will be increased, but it cannot ex- pand. We will next suppose that a a is mov- able, but without weight, and that the air beneath is heated as before. On raising its temperature 490 its volume will be doubled, and a a will of course be raised one foot to b b. In raising a a 3 62 APPENDIX. one foot it has had to raise the air above it. Now this air presses with a force of 15 pounds upon every square inch, or 15 X 144 = 2,160 pounds upon the whole surface. From the specific heat of air, we know that to raise the temperature of a cubic foot of air 490, when it is free to expand, 9.5 units of heat are required. But we have seen that a part of the heat which enters a body is used in expanding it, and a part in raising its temperature. In the above experiment, how much heat is used in raising the temperature ? This is equivalent to asking how much heat is required to raise the cubic foot of air 490 when it is not allowed to expand. We have learned that the computed ve- locity of sound in air is less than its observed velocity, and that this is owing to the heat developed in the compressed portion of the sound-wave. From the ratio between the observed and the computed velocity, it is found that the specific heat of air when free to expand must be 1.42 of its heat when not allowed to expand. Hence the heat required to raise the temperature of the cubic foot of air 490, when it is not allowed to expand, is found by the following proportion to be 6.7 units : 1.42 : i = 9.5 : 6.7. The amount of heat, then, used in expanding the air that is, in raising 2,160 pounds one foot high is 2.8 units. Divid- ing 2,160 by 2.8, we get 772, nearly. Since there is no cohesion among the particles of air, the whole expansive force is used in raising the weight. We see, then, that 772 foot-pounds of mechanical force are equivalent to a unit of heat, and that a unit of heat is equivalent to 772 foot-pounds of mechanical force. We have seen that merely to melt a pound of ice at a temperature of 32 Fahrenheit requires 143 units of heat, which is equivalent to the force required to lift 110,396 pounds, or about 55 tons, a foot high. And to convert a pound of boiling water into steam requires 967 units of heat, equivalent to the force required to lift 746,524 pounds, or about 373 tons, a foot high. The force of gravity is almost as nothing compared with this molecular force. The strength of affinity is shown by the amount of heat de- APPENDIX. 363 veloped by the combination of oxygen and hydrogen. It is found that, when oxygen unites with one pound of hydrogen, 61,000 units of heat are generated. Hence the force which has combined the two gases is equal to 61,000 X 7?2 = 47,092,000 foot-pounds, or the force necessary to raise 23,546 tons a foot high, or to throw one ton to a height of more than four miles. A pound of carbon, in combining with oxygen, gives out about 14,500 units of heat, equivalent to 11.194,000 foot-pounds. We see, then, that the force even of cohesion is insignificant compared with that of affinity. 8. Energy may be transmuted, but not destroyed. We have now seen that mechanical motion may be converted into the molecular motions of heat and electricity, and that these molec- ular motions may be converted into mechanical motion. Energy, like matter, may assume a great variety of forms ; but, like matter, it is wholly indestructible. 9. Source of Energy. If left to itself, affinity would soon bring all dissimilar atoms together, and lock them up in com- pounds ; cohesion would bring all the molecules of these com- pounds together, and lock them up in -solids ; and gravity would bring all these solids together, and hold them in its iron grasp ; while the heat developed by these forces would be radiated into space, and our earth become one dreary waste, void of all signs of life and activity. What, then, is the source of the energy which is thus manifesting itself in Protean forms ? Let us consider, first, the energy developed by gravity. This energy is seen in the winds, the falling rain, and running streams. The atmosphere on each side of the equator is an immense wheel. The side of this wheel next the equator is continually expanded, and thus made lighter, by the heat of the sun. Hence gravity pulls down the colder and heavier side in the polar regions, and thus the wheel is made to turn. Were it not for the sun's heat, it would soon come to rest. Again, the heat of the sun evaporates the waters of the ocean, and in their gaseous state they are swept round with the atmospheric wheel till they come to colder regions, where they are condensed, and fall to the earth as rain, and flow to the ocean in rivers. It is due, then, to the heat which comes to the earth in the sunbeam, that gravity cap thus unceasingly manifest its energy. 364 APPENDIX. The energy of chemical affinity which is manifested in heat, light, and muscular force is developed by its action between oxygen and carbon. How are these elements separated from carbonic acid, so that they may be reunited by affinity ? Place a leafy plant in a glass vessel, and let a current of car- bonic acid stream over it in the dark, and no change takes place. Let the same gas stream over the plant in the sunshine, and a part of it will disappear, and be replaced by oxygen. When acted upon by the sunbeams, leaves of plants remove carbonic acid from the air, separate its carbon and oxygen, retain the former, and give the latter back to the air. When plants are consumed by combustion in our furnaces, and by respiration in our bodies, this oxygen combines with carbon and develops energy, which appears as mechanical force in our engines, and as muscular force in our bodies. In the summer, when more sunshine than we need is poured upon the earth, a part of it is absorbed by the leaves of plants, and used to decompose carbonic acid, to build up the varied forms of vegetable life. In this way, the forests and the fields become vast storehouses of force which has been gathered from the sunbeam. When, therefore, we burn fuel in our stoves and food in our bodies, the light, heat, and muscular force de- veloped are only the reappearance in another form of the sun- beams stored up in plants. But this process of gathering force from the sunlight has been going on for ages ; and when we burn anthracite or bituminous coal, we are merely releasing the sunbeams im- prisoned in plants which grew upon the earth before it became the dwelling-place of man. The energy of affinity, then, like that of gravity, is nothing but transmuted sunshine. The only form of energy known to us which does not come to the earth in the sunbeam is that developed by the ebb and flow of the tidal wave. This wave is dragged round the earth mainly by the attraction of the moon ; and it acts as a brake upon the earth's rotation, since it is drawn from east to west while the earth is turning from west to east. The energy of this wave, then, is developed at the expense of the earth's motion on its axis ; and it must tend to retard this motion, APPENDIX. 365 though to so slight a degree that the observations of thou- sands of years have not served to make it appreciable. 10. The Amount of Heat given out by the Sim. Making allowance for the heat absorbed by the atmosphere, it has been calculated that the amount received by the earth during a year would be sufficient to melt a layer of ice 100 feet thick and cov- ering the whole earth. But the sun radiates heat into space in every other direction as well as towards the earth ; and if we conceive a hollow sphere to surround the sun at the distance of the earth, our planet would cover only ^Locoo of its surface. Hence the sun radiates into space 2,300,000,000 times as much heat as the earth receives. Sir John Herschel has calculated that if a cylinder of ice 45 miles thick were darted into the sun with the velocity of light (190,000 miles a second), it might be melted by the heat radiated by the sun, without lowering the temperature of the sun itself. 11. Source of the Surfs Heat. It has been supposed by some that the materials of the sun are undergoing combustion, and that this combustion develops the light and heat which it sends forth. There are, however, no substances known to us whose burning would produce so much heat for so long a time as we know the sun has been shining. Carbon is one of the most combustible substances with which we are acquainted ; but if the sun, large as he is, were a mass of pure carbon, and were burning at a rate sufficient to produce the light and heat that he is giving out, he would be utterly consumed in 5,000 years. It seems hardly possible, then, that the solar light and heat can be generated by ordinary combustion. One of the most satisfactory theories of the origin of the solar heat is that developed in 1848 by a German physician, Mayer, and known as the meteoric theory. We have seen that a pound-weight which has fallen through 772 feet will, when its motion is arrested, generate a unit of heat. Now, we know that a body falling that distance will acquire a velocity of about 223 feet a second. Hence a pound ball moving with a velocity of 223 feet a second will generate a unit of heat when its motion is arrested. We know, too, that the velocity with which a falling body strikes the ground is in proportion to the square root of the height from which it falls ; 3 66 APPENDIX. that is, in order to double or treble its velocity, a body must fall from four or nine times the height. A pound ball, then, moving with a velocity of twice 223 feet a second will be able to generate 4 units of heat ; one moving with thrice this velocity, 9 units of heat ; and so on. When, therefore, we know the weight of a body and the speed with which it is moving, we can easily calculate how much heat will be gen- erated on stopping it. Were tfie earth's motion arrested, its elements would melt with fervent heat, and most of them would be converted into v'apor. Were the earth to fall into the sun, the heat generated by the shock would be sufficient to keep up the solar light and heat for 95 years. We know that countless swarms of meteoric bodies are revolving in rings about the sun, and that they must be moving in a resisting medium. If so, they must eventually be drawn into the sun, and, from the velocity with which they must strike, it has been shown that they could fall in sufficient numbers to generate all the light and heat of the sun, without increasing his magnitude enough to be detected, since accurate measures of his diameter were first made. " Solar light and solar heat lie latent in the force which pulls an apple to the ground. The potential energy of gravitation was the original form of all the energy in the universe. As surely as the weights of a clock run down to their lowest posi- tion, from which they can never rise again unless fresh energy is communicated to them from some source not yet exhausted, so surely must planet after planet creep in, age by age, towards the sun. When each comes within a few hundred thousand miles of his surface, if he is still incandescent, it must be melted and driven into vapor by radiant heat. Nor, if he be crusted over and become dark and cool externally, can the doomed planet escape its fiery end. If it does not become in- candescent, like a shooting-star, by friction in its passage through his atmosphere, its first graze on his surface must pro- duce a stupendous flash of light and heat. It may be at once, or it may be after two or three bounds like a cannon-shot ricochetting on a surface of earth or water, the whole mass must be crushed, melted, and evaporated by a crash, generat- ing in a moment some thousands of times as much heat as a coal of the same size would produce by burning." (Tyndall.) APPENDIX. 367 12. The Nebular Hypothesis. According to Laplace, the material of our solar system was once a nebulous mass of ex- treme tenuity, and the sun, moon, and planets were formed by its gradual condensation. Let us suppose such a nebulous mass slowly rotating, and gradually cooling by radiation into space. As it cools, it must begin to contract ; and as it con- tracts, its rotation must be quickened, since the matter at the surface must be moving faster than nearer the centre. It thus goes on contracting and rotating faster and faster, until the centrifugal tendency becomes so great that cohesion and grav- ity can no longer hold it together. A ring is then detached from the circumference, which continues to rotate by itself. The central mass goes on contracting and rotating with ever- increasing velocity, until a second ring is thrown off. In this way, ring after ring is detached, and all these rings continue to rotate round the central mass in the same direction. But the rings themselves would go on condensing, and at last they would be likely to break up, each forming one or several glob- ular masses. These would, of course, all revolve about the central mass in the same direction, and their condensation would cause them to rotate on their axes ; and it has been proved that, with the exception of one or two of the outer ones, they must all rotate on their axes in the same direction in which they revolve in their orbits. But as these masses condensed, their rotation would be ac- celerated, and they would be very likely to throw off rings, which would either .remain as rings, or be condensed into globes. The central mass, of course, forms the sun ; the rings which it throws off, the planets ; and the rings thrown off by the planets, the moons. In the case of Saturn, a part of the rings still remain uncondensed, while a part appear as moons. The rings thrown off by the central mass usually condensed into one body, but, in the case of the minor planets and the meteoric rings, into many. 13. Helmholtz's Theory of Solar Heat. Helmholtz has made the nebular hypothesis the basis of his theory of solar heat, an account of which is given by Tyndall as follows : " He starts from tne nebular hypothesis of Laplace, and, 368 APPENDIX. assuming the nebulous matter in the first instance to have been of extreme tenuity, he determines the amount of heat generated by its condensation to the present solar system. Supposing the specific heat of the condensing mass to be the same as that of water, then the heat of condensation would be sufficient to raise their temperature 28,000,000 Centigrade. By far the greater part of this heat was wasted ages ago in space Helmholtz supposes this condensation to continue ; that a vir- tual falling down of the superficial portions of the sun towards the centre still takes place, a continual development of heat being the result. However this may be, he shows by calcula- tion that the shrinking of the sun's diameter by .0001 of its present length would generate an amount of heat competent to cover the solar emission for 2,000 years ; while the shrinking of the sun from its present mean density to that of the earth would have its equivalent in an amount of heat competent to cover the present solar emission for 17,000,000 of years. "'But,' continues Helmholtz, 'though the store of our planetary system is so .immense that it has not been sensibly diminished by the incessant emission which has gone on during the period of man's history, and though the time which must elapse before a sensible change in the condition of our plane- tary system can occur is totally beyond our comprehension, the inexorable laws of mechanics show that this store, which can only suffer loss and not gain, must finally be exhausted. Shall we terrify ourselves by this thought? We are in the habit of measuring the greatness of the universe, and the wisdom dis- played in it, by the duration and the profit which it promises to our own race ; but the past history of the earth shows the insig- nificance of the interval during which man has had his dwelling here. What the museums of Europe show us of the remains of Egypt and Assyria we gaze upon with silent wonder, in despair of being able to carry back our thoughts to a period so remote. Still, the human race must have existed and multi- plied for ages before the Pyramids could have been erected. We estimate the duration of human history at 6,000 years ; but, vast as this time may appear to us, what is it in comparison with the period during which the earth bore successive series of rank plants and mighty animals, but no men ? periods APPENDIX. 369 during which, in our own neighborhood (Konigsberg), the am- ber-tree bloomed, and dropped its costly gum on the earth and in the sea ; when in Europe and North America groves of tropical palms flourished, in which gigantic lizards, and, after them, elephants, whose mighty remains are still buried in the earth, found a home. Different geologists, proceeding from different premises, have sought to estimate the length of the above period, and they set it down from one to nine millions of years. The time during which the earth has generated organic beings is again small compared with the ages during which the world was a mass of molten rocks. The experiments of Bischof upon basalt show that our globe would require 350 millions of years to cool down from 2,000 to 200 Centigrade. And with regard to the period during which the first nebulous masses condensed, to form our planetary system, conjecture must entirely cease. The history of man, therefore, is but a minute ripple in the infinite ocean of time. For a much longer period than that during which he has already occupied this world, the existence of a state of inorganic nature, favorable to man's continuance here, seems to be secured ; so that for ourselves, and for long generations after us, we have nothing to fear. But the same forces of air and water, and of the volcanic interior, which produced former geologic revolutions, burying one series of living forms after another, still act upon the earth's crust. They, rather than those distant cosmical changes of which we have spoken, will put an end to the human race, and perhaps compel us to make way for new and more complete forms of life, as the lizard and the mammoth have given way to us and our contemporaries.' " Mayer's theory is evidently not inconsistent with that of Helmholtz, but supplementary to it. The former merely as- sumes that the meteors and planets, which were thrown off from the nebulous mass as it condensed, are slowly falling into it again. When these shall all have fallen into it and the con- densation shall have ceased, our sun will cease to shine, like many other stars which have disappeared from the heavens. 16* x NOTES. PART FIRST. I. ANOTHER way to find the specific gravity of a liquid is the following. Fill a small bottle accurately with water, and then with the liquid, and find the weight of each ; then divide the weight of the liquid by the weight of the water, and the quotient will be the specific gravity required. A specific gravity bottle is a bottle which is made to hold a definite weight of water, as 1,000 grains. If it holds 790 grains of alcohol, the specific gravity of the alcohol is evidently .79 ; if it holds i, 860 grains of sulphuric acid, the specific gravity of the acid is 1.86 ; and so on. Again, since the weight which a body loses when immersed in a liquid is equal to the weight of its own bulk of that liquid (23), we can find the specific gravity of a liquid by dividing the weight which a body loses in that liquid by the weight which :.t loses in water. Thus, if a piece of copper loses 200 grains when weighed in water, and 158 grains when weighed in alco- hol, the specific gravity of the alcohol is equal to 158 divided :- 200, or .79. II. WHEN we know the velocity a body acquires in falling through a certain distance a, and we wish to know what velocity it will acquire in falling through any other distance b, divide the dis- tance b by a, extract the square root of the quotient, and mul- tiply the velocity the body acquires in falling through the APPENDIX. 371 distance a by the number thus obtained. If, on the other hand, we wish to know how far the body must fall to acquire any velocity c, divide the velocity c by the velocity a body acquires in falling through the distance #, square the quotient, and mul- tiply the distance a by this number. PROBLEMS. 1. A body in falling from a state of rest through 4.9 metres acquires a velocity of 9.8 metres. Through what distance must it fall to acquire a velocity of 39.2 metres ? 2. To acquire a velocity of 88.2 metres ? 3. To acquire a velocity of 125 metres ? 4. To acquire a velocity of 396 metres ? 5. What velocity does a body acquire in falling from a state of rest through 19.6 metres? 6. In falling through 44.1 metres ? 7. In falling through 340 metres ? 8. A body falls from a height of 60 metres. With what ve- locity does it reach the earth ? 9. How long is the body in falling to the earth ? 10. How long will it take a body to fall from a state of rest through i, 1 88 metres? 11. A cannon ball is fired horizontally from the top of a tower 60 metres high. How long will the ball remain in the air? FRENCH WEIGHTS AND MEASURES. gg=" The English equivalents given below are those which were established by Congress, in July, 1866, and are sufficient- ly accurate for all practical purposes. TABLE OF LINEAR MEASURE. 10 millimetres = i centimetre = 0-3937 inch. 10 centimetres = I decimetre = 3-937 " 10 decimetres = i metre = 39-37 " 10 metres = i decametre = 393-7 10 decametres = i hectometre = 328 ft. i inch. 10 hectometres = I kilometre = 3280 " 10 " 37 2 APPENDIX. TABLE OF MEASURES OF SURFACE. = 1 19.6 square yards. = 2.471 acres. The centiare is a square metre, and is equal to 1,550 square inches. 100 centiares 100 ares = I are = i hectare TABLE OF MEASURES OF CAPACITY. 10 millilitres = 10 centilitres = 10 decilitres = 10 litres = 10 decalitres = 10 hectolitres = The kilolitre is a cubic metre, and is also called a stere. decastere= 10 steres. centilitre = 0.6102 cubic inches. decilitre = 6.1022 " " litre = 1.0567 wine quarts. decalitre = 2.6417 " gallons. hectolitre = 26.417 kilolitre = 264.17 " " The TABLE OF WEIGHTS. i o milligrammes = I centigramme = 0.1543 grains. 10 centigrammes = I decigramme = 1.5432 " 10 decigrammes = i gramme =15.432 " 10 grammes = i decagramme = 0.3527 oz. avoirdupois. 10 decagrammes = i hectogramme = 3-5274 " " 10 hectogrammes = i kilogramme = 2.2046 pounds " The millier or tonneau is equal to 1,000,000 grammes, or 2204.6 pounds avoirdupois. NOTE. The names of the higher orders of units, or the multiples of the standard unit, are formed from the name of the standard unit, (the metre, litre, etc.) by means of prefixes taken from the Greek numerals ; namely, deca- (10), hecto- (100), kilo- (1,000). The names of the lower orders of units, or the subdivisions of the standard unit, are formed in a similar manner by means of prefixes taken from th>' Latin numerals ; namely, deci- (10), centi- (100), milli- (1,000). PART SECOND. 1. (page 23.) For other methods of illustrating the forma- tion of nodes see TyndalFs Lectures on " Sound." 2. (page 79.) Sensitive Naked Flames. Professor Leconte of this country was the first to observe that ordinary gas-flames, even when not enclosed in tubes, are sensitive to sound. He gives the following account of his observations at a musical party : " Soon after the music commenced, I observed that the flame exhibited pulsations which were exactly synchronous with the audible beats. This phenomenon was very striking to every one in the room, and especially so when the strong notes of the violoncello came in. It was exceedingly interesting to observe how perfectly even the trills of this instrument were reflected on the sheet of flame. A deaf man might have seen the harmony. As the evening advanced, and the diminished consumption of gas in the city increased the pressure, the phe- nomenon became more conspicuous. The jumping of the flame gradually increased, became somewhat irregular, and, finally, it began to flare continuously, emitting the character- istic sound indicating the escape of a greater amount of gas than could be properly consumed. I then ascertained by experiment, that the phenomenon did not take place unless the discharge of gas was so regulated that the flame approximated to the condition of flaring. I likewise determined, by experi- ment, that the effects were not produced by jarring or shaking the floor and walls of the room by means of repeated concus- sions. Hence it is obvious that the pulsations of the flame were not owing to indirect vibrations propagated through the medium of the walls of the room to the burning apparatus, but must have been produced by the direct influence of aerial sono- rous pulses on the burning jet." * * Philosophical Magazine, March, 1858. 3 74 APPENDIX. The significant remark, that the jumping of the flame was not observed until it was near flaring, suggests t]?e means of repeating the experiments of Dr. Leconte ; while a more inti- mate knowledge of the conditions of success enable us to yary and exalt them in a striking manner. It will be noticed in the above account that the flame be- comes more sensitive when it is near flaring. Figure 238 represents the flame of a common fish-tail burner. Fig. 238. Fig. 239. When this flame is not near flaring it is not at all sensitive to sound. If, however, we turn on the gas until the flame is on the point of flaring, and sound a whistle near it, the flame takes the form shown in Figure 239. With a bat's-wing burner the result is the same. By using burners of suitable forms, flames may be obtained which are much more sensitive than ordinary gas-flames. The simplest burners, and those which show the sensitiveness of the flame best, can be made by drawing out small glass tubes into a fine jet. Tyndall gives the following account of his experiments with a tall slender flame such as is shown in Figure 240: " The flame reaches a height of 24 inches. The slightest tap APPENDIX. 375 on a distant anvil reduces its height to 7- inches. When I shake this bunch of keys the flame is violently agitated, and emits a loud roar. The dropping of a sixpence into a hand already containing coin, at a distance of 20 yards, knocks the flame down. I cannot walk across the floor without Fig. 240. a gitating the flame. The creaking of my boots sets it in violent commotion. The crumpling or tearing of a bit of paper, or the rustle of a silk dress, does the same. It is startled by the patter of a rain-drop. I hold a watch near the flame ; nobody hears its ticks ; but you all see their effect upon the flame. At every tick it falls. The winding up of the watch also pro- duces tumult. The twitter of a distant sparrow shakes the flame down ; the note of a cricket would do the same. From a distance of 30 yards I have chirruped to this flame, and caused it to fall and roar. I repeat a passage from Spenser : ' Her ivory forehead, full of bounty brave, Like a broad table did itself dispread, For Love his lofty triumphs to engrave, And write the battles of his great godhead. All truth and goodness might therein be read, Fig. 241. jr or there their dwelling was, and when she * spake, II, Sweet words, like dropping honey she did shed ; IJIII And through the pearls and rubies softly brake A silver sound, which heavenly music seemed to make.' The flame picks out certain sounds from my utterance; it notices some by the slightest nod, to others it bows more distinctly, to some its obeisance is very profound, while to many sounds it turns an entirely deaf ear. " In Figure 240 this tall, straight, and bril- liant flame is represented. On chirruping to it, or on shaking a bunch of keys within a few yards of it, it falls to the size shown in Figure 241, the whole length, a b, of the flame being suddenly abolished. The light at the same time is practically destroyed, a pale and almost non-luminous residue of it alone remaining. 376 APPENDIX. " We have called this the vowel flame, because the different vowel sounds affect it differently. We have already learned how these sounds are formed ; that they differ from each other through the admixture of higher tones with the fundamental one. It is to these tones, and not to the fundamental one, that our flame is sensitive. I utter a loud and sonorous u, the flame remains steady ; I change the sound to o, the flame quiv- ers ; I sound E, and now the flame is strongly affected. I utter the words boot, boat, and beat in succession. To the first there is no response ; to the second, the flame starts ; but by the third it is thrown into greater commotion ; the sound Ah ! is still more powerful. Did we not know the constitution of vowel sounds this deportment would be an insoluble enigma. As it is, however, the flame is a demonstrator of the theory of vowel sounds. It is most sensitive to sounds of high pitch ; hence we should infer that the sound Ah ! contains higher notes than the sound E ; that E contains higher notes than o ; and o higher notes than u. I need not say that this agrees perfectly with the analysis of Helmholtz. " This flame is peculiarly sensitive to the utterance of the letter s. If the most distant person in the room were to favor me with a hiss, the flame would instantly sympathize with him. A hiss contains the elements that most forcibly affect this flame. The gas issues from its burner with a hiss, and an external sound of this character is therefore exceedingly effec- tive. I hold in my hand a metal box, containing compressed air. I turn the cock for a moment, so as to allow a puff to escape, the flame instantly ducks down, not by any transfer of air from the box to the flame, for I stand at a distance which utterly excludes this idea ; it is the sound that affects the flame. I send a man to the most distant part of the gallery, where he permits the compressed air to issue in puffs from the box ; at every puff the flame suddenly falls. Thus the hiss of the issu- ing air at the one orifice precipitates the tumult of the flame at the other. " Finally, I place this musical box upon the table, and permit it to play. The flame behaves like a sentient creature ; bow- ing slightly to some tones, but courtesying deeply to others." What now is the explanation of these phenomena ? APPENDIX. 377 If we use a burner with a single circular orifice of such a size that it requires a great pressure to make the flame flare, we may, by turning on the gas, obtain a flame 15 or 20 inches long. If we make it longer and larger, it will at length begin to quiver and finally to flare, shortening considerably at the same time. If we diminish the pressure a little, so as to bring the flame just below its point of flaring, it shortens on sounding a whistle near it, exactly as it did when the pressure was in- creased. Like the singing flame which was started by the voice (78), it stands on the brink of a precipice, and the proper sound pushes it over. We see, then, that the effect of sound upon a naked flame is the same as that of an increase in the pressure of the gas. The gas in escaping from the ori- fice of the burner encounters friction, and when the pressure of the gas is sufficient, the stream as it issues is thrown into vibra- tion. It is this vibration which causes the flame to flare. Sonorous pulses of the proper period may also throw the stream of gas into vibration, and thus cause the flame to flare. In a word, then, the flame flares because the gas as it escapes from the burner is thrown into vibration, and it may thus be thrown into vibration by increasing the pressure of the gas or by the action of sonorous pulses of the proper period. It has been found that liquid jets, as well as gas jets, are sensitive to sound. 3. (page 1 01.) Total reflection in a liquid may be elegantly illustrated by the following experiment. Near the bottom of a tall vessel a round hole is made for water to run out ; opposite this hole is a glass plate, through which a beam of solar or electric light is admitted. The vessel is filled with water, and the outlet opened. The beam of light is totally reflected from the inner surfaces of the liquid jet, and is therefore carried down with it, lighting it up throughout its whole extent. To produce the best effect the vessel should be set high enough to give a jet of considerable length. 4. (page 116.) M. Plateau gives the following directions for preparing the liquid for these soap-bubbles : i. Dissolve one part by weight of white soap, cut into thin slices, in forty parts 37 APPENDIX. of distilled water, and filter. 2. Mix two parts by measure of pure glycerine with one part of the filtered solution, in a tem- perature of 66 F., and, after shaking them together long and violently, leave them at rest for some days. A clear liquid will settle, with a turbid one above. The lower is to be sucked out from beneath the upper with a siphon, taking the utmost care not to carry down any of the latter to mix with the clear liquid. A bubble blown with this will last several hours in the open air. Or, the mixed liquid, after standing twenty-four hours, may be filtered. 5. (page 126.) The simplest and most satisfactory way of see- ing diffraction fringes is to place wire gauze of various coarse- ness over the object-glass of an ordinary telescope, and then to look at some brilliant point of light, as a star, or the image of the sun reflected from a flask filled with water. The fringes will vary with the coarseness of the gauze used. They may be seen even when the meshes are a quarter of an inch across. The experiment is very easy and is well worth trying. 6. (page 195.) The laws of the reflection and refraction of luminous and obscure heat are best illustrated with the lime light and the iodine cell. Let the light pass through the largest aperture of the diaphragm, and concentrate it by a lens. Let the pencil thus concentrated fall upon the small mirror placed so near that it is not brought to a focus till after reflection. Place the blackened bulb of a differential thermometer at this focus, and the reflection of the luminous heat is proved. Place the iodine cell behind the lens so as to cut off all luminous radi- ation, and again place the bulb of the thermometer at the focus previously marked, and the reflection of the obscure heat is proved. For refraction, use the refracting prism instead of the mirror, placed so near that the light is not brought to a focus till after refraction. Of course it is easy to form invisible foci with any lens or concave mirror. These experiments are in every way satisfactory. Care must be taken in using the iodine solution, as it is very inflammable. After use it should be re- moved from the cell and kept in a well-corked bottle. APPENDIX. 379 7. (page 271.) The zinc used for battery purposes should in all cases be amalgamated. This may be done either by im- mersing the zinc in mercury, or by rubbing its surface with that vnetal. In either case the zinc should first be cleaned with dilute sulphuric acid. It is well to amalgamate the zinc plates of a battery every time it is used, and the best time for doing this is when the battery is taken down after being used, as the zincs then need no cleaning. For amalgamating the zincs of a large Bunsen's battery, a cylindrical vessel of soapstone, made with a core and just large enough for immersing the zincs in the mercury, will be found convenient. With such a vessel, not more than forty pounds of mercury will be needed. After immersion in the mercury the zincs should be set to drain in an iron sink, the surplus mercury being caught in a vessel below. 8. (page 300.) Here, as elsewhere, we have described only one or two experiments, which serve to illustrate the principles. If the teacher has the apparatus for a larger number of experi- ments, he will of course make use of it at the proper point ; if he has not, it is hardly worth while that the pupil should learn descriptions of experiments which he never witnesses. A very pleasing illustration of the electric light in rarefied air is afforded by the " guinea and feather tube " used in pneumatic experiments. If the ends of the tube are connected with the poles of the inductorium (or with the electrical machine) purple flashes of auroral light mark the passage of the current through the tube when the air is exhausted. In all experiments of this kind, the room should be darkened. Gassiofs cascade is a simple and inexpensive piece of appara- tus for showing the electric light in a vacuum. It consists of a large glass goblet (uranium glass is best), the inside of which is coated nearly to the top with tinfoil. Place the vessel on the plate of the air-pump, cover it with a receiver which has a slid- ing rod through the top, bring the sliding rod in contact with the tinfoil coating, and connect one pole of the inductorium (or one conductor of the electrical machine) with the rod, and the other with the pump-plate. When the air is exhausted, and the current sent through the receiver, streams of blue light flow 380 APPENDIX. from the tinfoil over the side of the vessel to the pump-plate. A variety of beautiful effects are produced by different degrees of exhaustion, and by changing the direction of the current. The apparatus known as the Abb Nolle fs Globe also fur- nishes very pretty displays of the electric light in rarefied air. It consists of a glass globe suspended in the upper part of a glass bell-jar, and arranged so that it can be partially filled with water, and connected with the inductorium or the electrical machine by means of a chain dipping into the water. The light in this case flows in lambent streams from the globe to the pump-plate. A variety of pieces of apparatus for showing the electric light are made by pasting bits of tinfoil about ^ of an inch apart on glass, oiled silk, or other non-conducting substance. Letters, outline figures, etc., may thus be formed, which appear in lines of scintillating light when the current is sent through them. The pieces of tinfoil may be pasted in a spiral on the inside of a long glass tube, and lighted up in the same way. The diamond jar, as it is sometimes called, is a Leyden jar, the coatings of which are composed of small pieces of tinfoil, separated from one another. Brilliant sparks pass between these pieces when the jar is charged or discharged. If the knob of a common Leyden jar is connected with one pole of the inductorium, and a wire from the other pole is brought near the outer coating of the jar, bright sparks pass in most rapid succession between the pole and the jar. The elec- trical machine may be used instead of the inductorium in this experiment, but the effect is much less striking. The teacher will find many other experiments in the works on Electricity mentioned in the Preface, especially in the little book of Ferguson's. To those who have Ruhmkorff's oil, we commend a little volume by Noad, entitled " The Inductorium," (London, John Churchill and Sons, 1866) which describes 3 large number of beautiful and instructive experiments with that instrument. QUESTIONS FOR REVIEW AND EXAMINATION. PART FIRST. \. WHAT is true of the parts of a stone or a piece of wood } 2. What are such bodies called ? 3. When is a body called a solid ? 4. What substances are called liquids ? 3. Give an il- lustration. 6. Show that a vessel cannot be filled with water until the air is removed from it. 7. What are substances like air called ? 8. How many states of matter are there ? 9. What are they called ? 10. Show that there is a force drawing bodies toward the earth. 11. What is this force called? 12. What is weight? 13. Show that all bodies do not have the same weight. 14. How can we find how much heavier one body is than another? 15. Describe the spring balance. 16. Explain how bodies may be weighed by it. 17. Show how we can find the weight of bodies by means of a rod poised at its centre. 1 8. Describe the balance. 19. Show how we can find the weight of a body by means of a rod poised at a point near one of its ends. 20. Describe the steelyard. 21. When a rod is alike throughout its whole length, where must it be supported in order to have the force of .gravity acting upon one arm bal- ance that acting upon the other ? 22. When a weight is hung to one end of the arm just twice as heavy as that hung to the other, where must the rod be supported in order to have the force of gravity acting upon one arm just balance that acting upon the other ? 23. What is true of a disc of wood when supported at its centre ? 24. What is true of the same disc when one side of it is loaded with lead ? 25. What point may be found for every body ? 26. What is this point called ? 27. Define the centre of gravity of a body. 28. Show that the centre of gravity is not always in the body itself. 29. What is true of the centre of gravity of two balls connected by a rod ? 30. When a loaded disc which is supported at its centre is 382 QUESTIONS FOR REVIEW AND EXAMINATION. placed in different positions, what is true of it ? 31. When is a body said to be in equilibrium ? 32. When, in stable equilib- rium ? 33. When, in unstable equilibrium ? 34. When, in in- different equilibrium ? 35. Show that the centre of gravity seeks the lowest point it can reach. 36. Illustrate the different kinds of equilibrium by means of spheres. 37. What is true of the centre of gravity in each kind of equilibrium ? 38. Show that the broader the base of a body compared with its height, the greater the stability of its equilibrium. 39. Show that a body with a broad base may be in unstable equilibrium. 40. When may a leaning body be in stable equilibrium ? 41. Show that a body having a very narrow base may be in stable equilibrium. 42. Show how the centre of gravity of a body may be found. 43. How do we know that liquids have weight ? 44. Are all liquids equally heavy ? 45. Show that liquids when acted upon by gravity press not only downward, but also upward and sideways. 46. Show that the upward, downward, and lateral pressures are equal for the same depth of liquid. 47. Show that these pressures increase with the depth. 48. Show that these pressures do not depend at all upon the form or size of the vessel which holds the liquid. 49. Show what takes place when different vessels are connect- ed, and one of them filled with a liquid. 50. Show that a press- ure of -gL of a pound upon a particle of water in a closed vessel causes every particle of water at the surface to exert an upward pressure of -$ of a pound. 51.. Show that a pressure of -$ of a pound upon a particle of water in a closed vessel causes the particles of different depths to exert the same upward press- ure as those at the surface. 52. Show that when any pressure is brought to bear upon any particle of a liquid, each particle is made to exert the same pressure upward, downward, and side- ways. 53- What is true when any pressure is brought to bear upon any particle of a liquid in a closed vessel ? 54. How by means of a liquid may a small pressure be made to exert a great one ? 55. Describe the hydrostatic press, and explain its action. 56. What do all natural collections of water illustrate ? 57. Give an example. 58. Explain the formation of springs. 59. Why are Artesian wells so named ? 60. Explain their ac- tion. 61. What is true of a body when placed in water? QUESTIONS FOR REVIEW AND EXAMINATION. 383 62. Show this. 63. How much is a body buoyed up in water ? 64. Show this. 65. When will a body sink in water ? 66. When float ? 67. When a body floats in a liquid, how much of the liquid does it displace ? 68. Why do iron ships float? 69. When is one body said to be more dense than another ? 70. What is specific gravity ? 71. What must be known to find the specific gravity of a solid or liquid ? 72. How can we find the weight of a bulk of water equal to that of a solid ? 73. Describe the hydrometer in Figure 23, and show how the specific gravity of a liquid is found by means of it. 74. Describe the hydrom- eter in Figure 24, and explain how it is used in finding the specific gravity of a liquid. 75. Show that gases have weight. 76. How do gases press ? 77. Show that they press in this way. 78. Tell what you can about the hand-glass. 79. About the Magdeburg hemispheres. 80. About the weight- lifter. 81. Show that gases have an expansive force. 82. De- scribe the air-pump, and explain its action. 83. Show that a body is buoyed up in the air. 84. When will a body rise in the air ? 85. When will it sink in the air ? 86. Why do balloons rise ? 87. With what must they be filled ? 88. How are paper balloons sometimes made to rise ? 89. Show that the atmos- pheric pressure will hold up a column of liquid in an inverted vessel. 90. How high a column of mercury will the atmos- pheric pressure hold up in a tube ? 91. Show this. 92. The atmospheric pressure is equal to how many pounds to the square inch ? 93. Show this. 94. Show what is true of the atmospheric pressure from day to day. 95. Show what is true of the atmospheric pressure as we go away from the earth. 96. Describe the barometer. 97. Give an account of its uses. 98. How high a column of water will the pressure of the atmos- phere sustain ? 99. How do we know ? 100. What is a pump ? 101. Describe the lifting pump, and explain its action. 102. De- scribe the force-pump. 103. What pumps are there in the fire- engine ? 104. What is a siphon ? 105. Explain the action of a siphon. 106. Explain Tantalus's Cup. 107. Explain inter- mittent springs. 108. What increases the expansive force of gases? 109. Explain the air-gun. 110. Describe the conden- ser, in. State Mariotte's law. 112. Illustrate this law. 113. What is a manometer? 114. Describe a manometer. 384 QUESTIONS FOR REVIEW AND EXAMINATION. 115. Describe the spirit-level, and explain its use. 116. Sho\? that gravity may put a body in motion, as well as cause it to exert pressure. 117. Will a body begin to move or come to rest of itself? 118. State the first law of motion. 119. How do we know that a body will move in this way? 120. Show that an unbalanced force must act upon a body in order to put it in motion. 121. What is necessary to change the speed or direction of a moving body? 122. Why does it seem to us more natural for a body to be at rest than in motion? 123. What is the effect of a force acting upon a body for a moment only ? 124. What is the effect of a force acting upon a body continuously? 125. Show that the resistance a body meets increases as the square of its velocity. 126. Show that a moving body may be in equilibrium. 127. State the second law of motion. 128. Illustrate this law in the case of a body thrown forward. 129. In the case of a body thrown upward. 130. In the case of a body thrown downward. 131. When does a moving body acted upon by gravity describe a curved path ? 132. Illustrate this. 133. What is true of the speed with which all bodies would fall were it not for the air? 134. Show that this is so. 135. At what rate does gravity increase the speed of a body falling directly downward ? 136. Show that this is so. 137. Show how we find the dis- tance a body falls in a given time. 138. Show at what rate gravity retards the velocity of a body moving directly upward. 139. Show how we find the distance a body rises in a given time. 140. What is true of the velocity a body always acquires in falling the same distance ? 141. Show that this is so. 142. Through what distance must a body fall, in order to double its velocity? 143. With how many times greater velocity must a body start, in order to rise to double the height ? 144^ How does the velocity which a falling body acquires compare with the height from which it falls. 145. How does the height to which a body will rise compare with the velocity with which it starts ? 146. Show that the same force acting upon different quantities of matter does not impart to them the same velocity. 147. What do we mean by the mass of a body ? 148. By its momentum ? 149. Does the same force always give the same momentum t 371- compound, 76. simple machines, 91. law of, 74. third law of motion, 64. mechanical advantage of, 75. three kinds of, 73. Pulley, the, 83, 92. 93, 94. the law of, 83. Liquids, 3. Pumps, 37. buoy up bodies, 20. air, 31. how to find the weight of, 13. press equally in afl directions, force, 37. lifting, 37. jo 07. pressure of, not affected by shape R. of vessel, 14. on sides of vessel, 26 Rack and pinion, the, 77. (foot-note). Ratchet, the, 80. transmitted equally in Reaction, 60. all directions, 15. water wheels, 1 1 1. specific gravity of, 22, 25. Reflected motion, 62. Resistance to motion, 49. M. S. Machines, 73. law of, 75. Safety-valve, the, 106. Magdeburg hemispheres, 30. Manometer, the, 48, 100. Screw, the, 87. differential, or Hunter's, 88. Marcet's globe, too. endless, 89. Mariotte's law, 47. Ships, iron, 21. Mass defined. 58. sails of, 95. Matter, 4. Siphon, the, 39. acted upon by gravity, 4. Solids. 3. states of, 4. Measures, tables of French, 370. Momentum, 58. Specific gravity, 22. of a gas, 45. liquid, 22, 25. Motion, 47. solid, 22. first law of, 47. quantity of, 58. Spirit level, the, 43. Spring balance, the, 4. reciprocating, 102. Springs, 19. reflected, 62. Steam engine, the, 100. resistance to, 49. high and low pressure, rotary, 102. 105. second law of, 50. locomotive, 108. third law of, 58. power, 100. Steelyard, the, 5. P. T. Parabola, motion in a, 52. Tantalus's Cup, 40. Pendulum, the, 47, 55, 65. V. compound, 67. laws of, 65. Vacuum defined, 33. reversible, 78. Velocity of falling bodies, 53, 55. used for measuring time, 68. gravity, W. 70. virtual length of, 68. Pisa, the Leaning Tower of, u. Plane, the inclined, 85. Water-power, 96. wheels, 96. breast, 96. horizontal, 97. INDEX. 4OI Water (continued) wheel overshot, 97. reaction, in. turbine, 98. undershot, 97. vertical, 96. Wedge, the, 86. Weight, 4. of bodies in air, 33. liquids, 21. Weight-lifter, the, 31- Weights, 5. Wells, Artesian, 19. Wheel and axle, the, 77, 92. Wheels, belted, 82. bevel, 82. cog, 81. crown, 82. friction, 81. spur, 82. Wheel-work, 80. Windlass, the, 78, 92. Windmills, 95. Wind-power, 95. PART SECOND. Abbe* Nollet's Globe, 380. Adiatnermancy, 210. Aldebaran, spectrum of, 115. Amplitude of vibrations in sounding bod- ies, 7. Analysis, spectrum, 112. Analyzer, the, 135. Anion, 274. Anode, 274. Anthelia, 354. Atmosphere, composition of the, 321. electricity in the, 347. heating of the, 321. moisture of the, 332. pressure of the, 32. Aurora Borealis, the, 352. Axis, the optical, 162. Balance-wheel, the compensation, 249. Battery, Bunsen's, 272. Daniell's, 272. electric, 270. Grove's, 272. Leyden, 291. magnetic, 258. thermo-electric, 283. Beats, 39. Boiling, 226. Boiling-point, the, 226. of water affected by cohe- sion, 228. of water affected by pres- sure, 227. of water affected by the vessel, 229. Brocken, the spectre of the, 164. Bunsen's cell, 272. Calms, region of, 326. " rain in, 344. Calorescence, 200. Calorimeter, the, 219. Camera obscura, the, 152. the water, 153. Carbonic acid, condensation of, 2 v- Cathode, 274. Cation, 274. Cells, construction of voltaic, 271 Charge, distribution of electric, 290. Chords, 44. Clang-tint, 26. Clocks, electric, 306. Clouds, 337. cirro-cumulus, 342. cirro-stratus, 342. cirrus, 339. colors of, 356. cumulo-cirro-stratus, 342. cumulo-stratus, 342. cumulus, 340. nimbus, 342. stratus, 340. Coils, induction, 299. Collodion process, the, 184. Color of bodies, in. Color-blindness, 161. Colors, analysis of, 112. complementary, no. in crystalline plates, 139. of soap : bubbles, 116. prismatic, 106. Condensation, 231. Coronas, 354. Crystals, biaxial and uniaxial, 128. Cupric sulphate, electrolysis of, 274, Current, heat developed by, 280. induction, 288, 299. intensity of, 269. light developed by, 282. makes iron magnetic, 277. quantity of, 269. resistance to, 266. Curves, magnetic, 256. D. Daguerreotype, the, 183. 402 INDEX. Dew, 334- Diathermancy, 193, 210. Diffraction fringes, 125, 377. Discharge, convective, 292. glow, 292. Discharger, the, 291. Discords, 45. Dispersion of light, 106. Dissonance, cause of, 46. Distance, estimated by the eye, 163. Duboscq's electric lamp, 317. E. Ear, the human, 83. range of, 84. Earth, telegraphic, 311. Echoes, 12. Electric battery, 270, clocks, 306. current, 263. lamp, 317. light, 282. telegraph, 308. wheel, 292. Electrical machine, 285. Electricity, a source of mechanical power, atmospheric, 318, 347. conductors of, 268. developed by friction, 285. " heat, 283. " magnetism, 279. positive and negative, 288. voltaic, 263. Electrodes, 274. Electro-gilding, 306. Electrolysis, 274. Electrolyte, 274. Electro-magnets, 277. strength of, 278. Electro-metallurgy, 306. Electro-plating, 305. Electroscope, 287. gold-leaf, 287. Electrotyping, 304. Energy, actual, 358. mechanical, 358. converted into heat, 358, 359- molecular or atomic, 358. " converted into heat, 358, 362. , converted into elec- tricity, 358. muscular, 358. of affinity, 358, 363. cohesion, 358. " gravity, 358, 363. potential, 358. source of, 363. transmuted, not destroyed, 363. Engines, electro-magnetic, 317. Evaporation, 231, 333. Expansion by heat, 234. coefficient of, 235. effects of, 250. Expansion of gases, 238. " liquids, 236. " solids, 237. Eye, the, 153. adjustment of, 155. affected by age, 168. normal, 167. F. Farmer's alloy, 283. Far-sightedness, 166. Flames, naked sensitive, 373. sensitive, 78. sounding, 74. Fluorescence, 200. Foci, invisible, 199. Fogs, 335. Foucault's rheotome, 301. Fraunhofer's lines, 115, 197. Freezing-mixtures, 233. Friction, always rhythmic, 74. electricity developed by, 285. a Galvanometer, the, 265. the astatic, 265. Gases, absorption of heat by, 205. " light by, 114. >ound in velocity of sound in, 68. Gassiot's cascade, 379. Geissler's tubes, 303. Graham's pendulum, 249. Gulf Stream, the, 241. H. Hail, 346. Heat, 'absorbed by gases, 205. " solids and liquids, 204 " vapors, 208. causes liquids to boil, 226. solids to melt, 223. conduction of, 213, 214. convection of, 240. converted into mechanical energy, 361. developed by electricity, 280. dispersion of, 196. electricity developed by, 283. expansion by, 234. from affinity, 363. latent, of gases, 226. " fiquids, 224. " steam, 244. luminous, 193. makes gases more elastic, 239. mechanical equivalent of, 361. obscure, 193, 199. of the atmosphere, 321. polarization of, 197. quality of, 204. radiation of, 193, 321. " " explained, 210. INDEX. 43 Heat, reflection of, 194, 378. refraction of, 195, 378. solar, amount of, 365. ' Helmholtz's theory of, 367. " meteoric theory of, 365. specific, 216. found by melting, 217. " mixture, 217. of gases, 220. " liquids, 219. the same as light, 197. unit of, 216, 360. Heating by steam, 244. Helix, 277. Hygrodeik, the, 252. Hygrometers, 251. Iceland spar, 128. Induction coils, 299. electrical, 288. Inductorium, the, 301, 380. Instruments, musical, 51. stringed, 51. wind, 55, 72. Intensity of electricity, 269. Interference of light, 118. " polarized light, 136. " sound, 35. Invisible foci, 199. Irradiation, 159. Kaleidoscope, the, 178. Lamp, electric, 317. the platinum, 207. Lenses, 148. achromatic, 173. images formed by, 149. Leyden battery, 291. jar, 291, 380. Light, absorption of, in. chemical action of, 182. composition of white, 108. diffused, 99. dispersion of, 106. intensity of, 94, 98. interference of, 118, 126. length of waves of, 123. origin of, 124. polarization of, 130. polarized by reflection and refrac- tion, 134, propagated by the ether, 122. radiation of, 91. reflection of, 96, 1 19. refraction of, 96, 99. total reflection of, 101, 377. undulatory theory of, 118. velocity of, 93. Lightning, 349, 351. rods, 351. M. Magic lantern, the, 174. Magnetic battery, 258. curves, 256. induction, 257. Magnetism, 255, 353. developed by electricity, 277. of the earth, 256. of wire carrying a current, 278. Magneto-electricity, 279, Magneto-electric machines, 293. Magnets, forms of, 258. making of, 258, 259. natural, 257. poles of, 256. Melting-point, the, 223. Microscope, the compound, 170. " simple, 170. " solar, 176. Mirage, 102. Mirrors, concave, 178. convex, 180. parabolic, 181. plane, 177. Mists, 335. Molecules of bodies are in motion, 212. Monsoons, 327. Musical sounds, 18. pitch of, 1 8. transmission or, 28, 29. N. Near-sightedness, 166. Nebular hypothesis, the, 366. Needle, astatic, 265. dipping, 256. telegraph, 308. Nodal lines, 26. Nodes formed in plates, 25. " strings, 23. Noise, defined, 18. O. Octave, defined, 22. Ohm's law, 268. Opacity, 91. Opera-glass, the, 174. Optic nerve, action of light upon the, 157. Optical axis, the, 162. Organ-pipes, 64. reed, 70. Overtones, or harmonics, 26. P. Parhelia and paraselene, 356. Pendulum, Graham's, 249. Penumbra of shadow, 93. Phosphorescence, 201. 404 INDEX. Photographic printing, 184. Photography, 182. Photometers, 95. Pincette, the tourmaline, 142. Pitch, defined, 18. Polarization of electricity, 289. " light, 130. circular and ellipti- cal, 136. rotatory, 137. Polarizer, the, 135. Prisms, 96. achromatic, 107. double-refracting, 129. for total reflection, 101. Nicol's, 135. path of rays through, 104. Purkinje's figures, 158. Q. Quantity and intensity of electricity, 269, 286. Rain, 343- in India, 345. in the tropics, 344, Rainbow, the, 144, 354. Rays, 93. Reed pipes, 70. Refraction, double, 129, 131. effects of, 103. index of, 101. Relay, 311. Resonance, 58. cause of, 61. Resultant tones, 40. Retina, duration of impression on, 159. exhaustion of, 161. structure of, 156. Rheostat, the; 266. Rheotome, the, 300. Foucault's, 301. Rods, longitudinal vibrations of, 56. Ruhiakorff s coil, 301. Saccharometer, the, 138. Saint Elmo's fire, 352. Scale, the musical, 49. Shadows, 91. Siren, the, 19. Sirius, spectrum of, 115. Soap-bubbles, colors of, no, 377. Sonometer, the, 22. Sound, caused by vibrations, 3. coincidence of, 35. intensity of, 7. interference of, 35. passes through gases, liquids, and solids, 4. propagated by vibrations, 5. Sound, quality of, 26. reflected, 10. refracted, 14. velocity of, in air, 8. " gases, 68. " liquids, 69. " solids, 10, 59. " " water, 9. * " " wires of different kinds, 56. will not pass through a vacuum, 3. Sounding-boards, 51. Sound-waves, length of, 21. superposition of, 34. Speaking-tubes, 7. Spectre of the Brocken, the, 164. Spectroscope, the, 112. Spectrum, the solar, 105. analysis of, 1 12. chemical action of, 185. reversed, 114. Spheroidal state, the, 230. Steam, heating by, 244. latent heat of, 244. Stereoscope, the, 165. Storms, 328. Strings, vibrations of, 22. " laws of the, 53. T. Telegraph, Bain's, 308. combination printing, 308, 31 fire-alarm, 315. four things essential to, 308. House's printing, 312. Hughes's " 3x3. Morse s, 308. needle, 308. submarine, 316. Telegraphic alphabet, Morse's, 310. earth, 311. Telescope, the, 172. " reflecting, 181. " refracting, 181. " terrestrial, 173. Temperature, 215. affected by drainage, 334. affects time-pieces, 249. of the atmosphere, 321. Thaumatrope, the, 159. Thermo-electricity, 283. Thermometer, the alcohol, 247. " air, 247. Breguet s, 248. differential, 247, 284. mercurial, 245. scales, 246. Thunder, 350. Thunder-storms, 349. Tones, resultant, 40. summation, 42. Tornadoes, 329. Tourmaline, and its action on light, 133. pincette, the, 142. Trade-winds, 325. INDEX. 405 Transparency, 91. Tubes, vibrations in, 63, 64. Tuning-fork, the, 18. U. Umbra of shadow, 93. Undulatory theory of light, the, 118. V. Vibrations, longitudinal, 55. of columns of air, 63. sympathetic, 31. Vision, laws of, 166. near and far point of, 166. single, 161. Visual angle, the, 162. Voice, the human, 80. Voltaic arc, the, 281. electricity, 363. Voltaic pair, the, 263. Voltameter, the, 276. Vowel sounds, 81. W. Water, irregular expansion of, 243. specific and latent heat of, 242. Water-spouts, 332. Water-waves, superposition of, 33. Watery vapor in the air, 332. elastic force of, 335. Weights and measures, French, 370. Wheel, the electric, 292. Whirlwinds, 329. dust, 330. Wilde's magneto-electric machine, 296. Wind instruments, 55, 72. Winds, 324. of Asia and North America, 327 " middle latitudes, 326. " northern Atlantic, 339. i'HE END. o o o o &../ 541762 UNIVERSITY OF CALIFORNIA LIBRARY "Q