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Principal London Normal School HAMILTON PUBLIC LIBRARY TORONTO THE COPP, CLARK COMPANY, LIMITED Entered according to Act of the Parliament of Canada, in the year one thousand nine hundred and six, by TuR Copp, Clark Compant, LmiTiD, Toronto, Cntario, in the Office of the Minister of Ag^rioulture. MiHK ^ i. nf^\ l>e-p . \ HAMILTSN PUiLlG L18RARY PREFACE The revised edition of the High School Physical Science, Part ^I., is designed to cover the courses in Sound, Light, Magnetism and Electricity prescribed for the Middle School. To make the treatment continuous, references are inserted wherever articles from Part I. are to be read in connection with this work. A few topics not named in the Departmental Course of Study have been included on account of their practical interest or their bearing on the present reconstruction of physical ard chemical theories. The student who desires to confine iiimself strictly to the curriculum may omit pages 223-232, and pages 244, 245. I am indebted to Mr. F. W. C. McCutcheon and Mr. A. W. Keith, of the* London Collegiate Institute, for assistances in reading the proof sheets. F. W. Merchant. London, 10th Aijril, 1906. mmtmmmmmm CONTENTS. ♦ 4 CHAPTER I. ' PAOK Origin and Transmission of Sound 1 CHAPTER II. Intensity, Reflection, Refraction and Interference of Sound- Waves. 19 CHAPTER III. Pitch of Sounds — Musical Scales 33 CHAPTER IV. Transverse Vibrations of Strings 41 CHAPTER V. Vibration of Air in Tubes 45 CHAPTER VI. Nature and Propagation of Light 59 CHAPTER VII, Photometry 66 CHAPTER VIII. ' Reflection of Light 75 CHAPTER IX. Refraction of Light 96 CHAPTER X. Dispersion of Light— Colour 124 V VI CONTKNTS. CHAPTKR Xr. PAQK Magnetism . 134 CHAPTER XII. The El«ctric Current 150 CHAPTKR XIII. The Chemical Kfreets of the Electric Current 169 CHAPTER XIV. The Magnetic Effects of the Current 185 CHAPTER XV. Current Induction 210 CHAPTER XVI. Heating and Lighting Effects of the Electric Current 251 CHAPTER XVII. Electrical Measurements 259 ji PHYSICAL SCIENCE PART II. CHAPTER I. ORIOIX AND TRANSMISSION OF SOUND. We have learned, Chaptera xii. and xiii., Part I., that sound has its orit^in in the vibrations of some vibrating body and is transmitted from the centre at which it originates by some material medium, which may be a solid, a liquid or a gas. We shall now examine more closely the nature of this vibratory movement and the theory of its transmission by an elastic medium. 1. Simple Hannonic Motion. Experiment 1. Suspend a small heavy hall (a lead bullet answers well) by a thread, which should ba as long as practicable. 8et it revolving in a circle (Fig. 1). Is the number of times which it revolves the same during equal intervals of time ? Bring the eye on a level with the ball, when it will appear to move to and fro in a straight line. Study the motion carefully. When does the ball appear to be at rest? When does its speed appear to })e greatest ? When does its speed appear to be increasing ? When decreasing ? 1 Fio. 1. PHYSICAL SCIENCE. Draw a circle (Fig. 2) to represent tlie path of the ball, and divide the circumference into any nuinl)er of equal parts, say twelve, abf be, cd, etc. Through the points of division draw perpendiculars to the line AG, *ilie distances AB, BC, CD, etc., being the projections on AG of the equal arcs ab, be, cd, etc. If the hall makes a complete revolution in one second, (1) How long does it take it to pass from a ioh, h to c, etc. ? (2) How long does it take it in appearing to pass from A to B, B to C, etc. ? When a body vibrates alon^ a straight line, as the ball in the above experiment appears to do, in such a manner that its position at any moment is the same as the pro- jection on that line of a point moving uniformly in a circle whose diameter is the length of the line, it is said to move with simple harmonic motion. The motion is so named because all musical sounds are caused by bodies vibrating in this way. % • Motion from left to right is regarded as positive, and from right to left negative. The extent of the excursion of the vibrating body on either side of its middle point is called its amplitude. It corresponds to the radius of the circle of reference. The interval of time between two successive passages of the vibrating body through a given point in its path in the same direction is called its period. The fraction of a whole period which has elapsed since the particle OUKJIN AND THAN8MI8810N OF SOUND. last pHMsefl tlirougli the luiddlo point ol:' its range in the positive direction is called the phase. 2. Wave-Motion. Before proceeamg to consider the theory of the trans- mission of sound by elastic lx)die8, it will be necessary for the student to become familiar with the phenomena of wave-motion in general. Let a pebble drop into a body of water at rest, and observe the motion of the water. Observe (1) That a depression is produced at the point where the stone touches the water. (2) That this depression travels outward from this point as a circular trough. (3) That the depression of the water at the point where the stone dropped is followed by an upward movement of the water at this point, causing a ridge or crest. (4) That this crest travels after the depression, moving at the same rate in a circle concentric with it, (5) That this crest is followed by another depres- sion, and the depression by another crest, and so on, thus producing a series of ripples or waves. Throw a piece of wood on the water, and note that it moves up and down, thus show- ing that, while the waves move outward in a horizontal direction, the particles vibrate vertically. Ezperiment 2. Fasten one end of a light chain about eight feet long to the ceiling (Fig. 3). By giving the lower end of the chain a number of quick jerks, send a series of pulses along the chain. Fio. 3. ■■■■■■I I i r I ! ' 4 PHYSICAL SCIENCE. 1. In what direction are the waves in the chain propagated? 2. In what direction do the individual links of the chain move ? Tlie transmissions of the disturbances in the water and the chain furnish examples of wave-motion. A wave in its simplest form consists of a series of par- ticles all vibrating in simple harmonic motion and having between tliem a uniform diflerence of phase. Consider, for example, a number of particles all made to vibrate witlv simple harmonic motion along the vertical lines A, B, C, etc. (Fig. 4), so that each succeeding particle begins to move yV ^^ ^ period behind the other. To determine the posi- A B CPE FG H JKLMNOPQRS n Fia. 4. tions of the particles at equal intervals of time draw a circle whose radius is the amplitude of vibration, divide it into twelve equal parls, and through the points of division draw lines perpendicular to the lines A, B, C, etc. Then these lines will mark off on the lines A, B, C, D, etc., spaces which the vibrating particles traverse in i\ of a period. Suppose tlie particle in A to be at a, corresponding to ^ in the circle, then as the particle in B is iV of a period behind, it will be at 6, corresponding to 3 in the circle, and the particle in C, which is ^-^ ^^ * period behind that in A, will be at c, corresponding to ^ io. the circle. Similarly the positions of the particles in the other lines are determined to be at d, e, / etc. ORIGIN AND TRANSMISSION OF SOUND. Tlirough the.se points trace a smooth curve, representing tlie wave form. Trace curves to sliow the positions of tliese particles, iV» i%> tV ^^^ 11 ^^ '^ period later, and interpret them. The distance from any particle in the wave to the next one in the same phase, for example from e to q, c to o, or a to ni, is called the wave-length. In other words, the wave-length is the distance traversed by the wave during one vibration period. 3. Transverse Waves. Waves, like those of the water or the chain, which are produced by the vibratory motion of particles at right angles to the direction in which the wave is propagated, are called transverse, or crest-and- hoUow, waves. 4. Longitudinal Waves. Experiment 3. Make a " wave machine " similar to that illustrated in Fio, 6. Fig. 5. The spiral should be 2 metres long and 7cm. in diameter, and be made of 72 turns of No. 12 copper wire. "^ h \ ! ^i 6 PHYSICAL SCIENCE. The spiral may be made by winding the wire uniformly around a cylindrical rod, and then removing the rod. The threads by which the spiral is suspended should be 60cm. long. The frame should be made light and stiff. Take hold of the end of the spiral and give it a quick jerk outward in the direction of the axis, and then let go. Observe the pulse as it moves along the spiral. How do the separate coils move ? Take hold of the end of the spiral again, push it inward, . let go quickly, and again observe the pulse as it moves alon^ the spiral. How do the separate coils now move ? Insert the blade of a knife between the coils near one end of the spiral, rake it quickly towards the other end across a few turns of the wire, and observe the motion of the wave along the spiral. In tlie first case, when the spiral was jerked outward, the coils appeared to move backward in a direction opposite to that in which the pulse is moving, thus forming what is called a pulse of rarefaction. In the second case, when the spiral was pushed inward, the coils appeared to move forward in the direction in which the pulse was moving, forming a pulse of condensation. In the third case a pulse of condensation (Fig. 6 B) is B Fig. 6. followed by a pulse of rarefaction (Fig. 6 C), and a double pulse, or wave, is formed. i :1 ORIGIN AND TRANSMISSION OF SOUND. 7 It will be observed that while the wave moves along the spiral, each individual turn of wire simply moves backward and forward in the line of direction of the wave. . . Waves which are produced by the vibratory moliion of particles along the lines in which the waves are propagated are called longitudinal waves. The wave-length in this case is the distance between two successive centres of condensation or between two successive centres of rarefaction. 5- Theory of the Transmission of Sound by an Elastic Medium. Experiment 4. Take a tin tube about 3 metres long and 10 cm. in diameter one end of which tapers to a diameter of about 2.5 cm. (Fig. 7) Fig. 7. Tie over the large end a paper membrane and in front of the small end place the ilarae of a lighted candle. Strike two books together in front of the membrane. Tap the membrane. 1. How is the flame affected ? 2. How do you know that the effect is not due to a current of air? 3. What is the cause of the effect noted ? To answer the last question compare the air as an elastic medium with the coil spring (Experiment 3) and consider the following questions : — M : ' i { I, i: 11 ; \-\ f- 8 PHYSICAL SCIENCE. (a) How will the sudden forward motion of the membrane affect the air in the tube immediately in front of it ? (h) Will this air remain in its changed condition ? If not, why will its condition be again changed, and how, in changing its condi- tion, will it affect the air beyond it ? (c) How does the motion of the individual particles of air within the tube differ from the movement of the disturbance as it passes from one end of the tube to the other ? Experiment 5. Wet a piece of linen paper and paste it over the nriouth of a tumbler. When tlie paper has become dry, cut away a part of it, as shown in Fig. 8, making a small opening at first and Fio. 8. gradually increasing its size until the tumbler gives forth a loud sound when a vibrating tuning-fork is held over the opening. Sprinkle fine sand on the paper, mount the fork on a resonance-box, and sound it at a distance from the tumbler. 1. What effect has the sounding of the fork on the sand placed on the paper ? ORIGIN AND TRANSMISSION OF SOUND. 9 2. What evidence have you that the paper is vibrating? 3. How are the vibrations of the fork transmitted to the i)aper ? It is evident from the foregoin|^ experiments tluit the vibrations of a sounding body are transmitted by the air in a species of wave-motion. The waves are believed to be of a form similar to those which pass along the spiral spring (Experiment 3, page 5), when one of the coils is disturbed. Take, for example, the nature of the disturbances set up in the air by a tuning-fork. As one of the prongs of the vibrating fork swings swiftly forward, it compresses the air immediately in front of it (Fig. 9). This air, on account of its elas- ticity, resists the compression, and its tendency to Pio. 9. expand causes the air in front of it to oe compressed. This air in turn compresses that in front of it, and thus a pulse of condensation travels forward through the air from the prong of the fork. In the meantime the prong of tlie fork swings backward, and tlie air behind it is rarefied. A pulse of rarefaction is thus produced, which follows immediately the pulse of condensation. This in turn is followed by a pulse of condensation, which again is followed by one of rarefaction, and so on. 1' 10 PHYSICAL SCIENCE. These alternate pulses of condensation and rarefaction constitute a regular series of sound-waves, which pass in succession through the air, and, falling upon the ear, are the condition of the sensation of sound. The vibration of all other sonorous bodies set up similar waves, which pass outward in every direction from the body, like a series of ever-enlarging concentric spherical shells (Fig. 10). Fio. 10. The student must be careful not to confound the. motion of the wave with the motion of the air particles which constitute it at any instant. While the wave moves constantly forward, the air particles simply move backward and forward in the direction of the wave. Since a single wave is made up of a pulse of conden- sation and a pulse of rarefaction, each aerial particle makes one complete vibration while the wave pro- gresses one wave-length. To get a clear conception of the propagation of sound- waves and the motion of the individual particles which compose them, repeat the experiment with the coil spring. Also perform the following experiment. ORIOIN AND TRANSMISSION OF SOUND. 11 Experiment 6. Cut a slit AB ill a piece of black cardboard as shown in Fig. 11a. Place the slit over the dotted line in Fig. ll/>, and draw tlie book from under it in the direction of the arrow, keeping the slit always at right angles to the side of the page. Fig. iio. " Observe the propagation of the waves of condensation and rarefaction as they appear at one end of the slit and pass along in the direction of the other. Also observe the to-and-f ro motion of the individual small white dashes in the direction of the slit. no. 116. Liquids and gases are believed to transmit sound by waves of condensation and rarefaction in exactly the same way as an*. 12 PHYSICAL SCIENCE. 1 ; 6 Upon what does the Velocity of Transmission of a Wave in an Elastic Medium Depend ? Experiment 7. Stretch side by side with equal tension two similar rubber tubes, about 3 metres long. Strike the tubes with a ruler a short distance from one end, causing a depression in each. Compare the velocities of the transmission of the depression along the tube. Increase the tension of one of the tubes and strike the tubes as before. Compare the velocities of transmission. Remove one of the tubes, fill it with sand and stretch it beside the other with equal tension. Strike the tubes again with the ruler, and again compare the velocities of trans- mission. Upon what properties of the tube does the velocity of trans- mission of wave-motion depend ? 7. Velocity of Sound Dependent on the Elasticity and the Density of the Medium- Newton demonstrated that the velocity of propagation of a wave through any medium varies directly as the square root of the coefficient of elasticity of volume, and inversely as the square root of the density. According to this law the velocity of sound-waves will be given by the equation wliere V denotes the velocity of the sound, E the co- efficient of elasticity, and D the density of the medium. The greater the elasticity and the less the density of the medium, therefore, the more rapidly is sound trans- mitted by it. ,y ORIGIN AND TRANSMISSION OF SOUND. 13 )ressioii Since the density of a solid or a liquid is greater than that of a gas, sound would naturally travel more slowly through these forms of matter than through gases, were it not that the increase in velocity due to their greater elasticities more than compensates for the decrease in velocity due to increase in density. Hence sound-waves generally travel faster in solids and in lic^'iids than in gases. 8. How do changes in the Temperature and in the Pressure of the Atmosphere affect the Velocity of the Trans- mission of Sound by it ? 1. If a given mass of gas is confined within an enclosed space and then heated, what change will take place in (a) the density, (b) the elasticity of the gas ? What effect will these cha^^ges have upon the velo(;ity with which the gas transmits sound ? 2. If the same gas is heated when it is free to expand, what changes in density and elasticity will take place, and what difference in its conducting power will be observed ? Explain. 3. How does an increase in the temperature of the air, the pressure remaining constant, affect the velocity with which sound is trans- mitted by it? Explain. 4. If a given mass of gas is confined within an enclosed space and its volume is (1) decreased, (2) increased, while the temperature is kept constant, what change will take place in (a) the density, (6) the elasticity of the gas in each case 'i What is the relation between the change in elasticity and the change in density ? (See Part I., page 119.) What changes, if any, will take place in the velocity of sound transmitted by the gas? 5. What changes in the velocity of sound transmitted by the air accoiu})any (1) a rise in the barometer, (2) a fall in the barometer, the temperature of the air remaining constant ? Explain. If the above questions are carefully considered it will be understood that a change in the height of the barometer, the temperature remaining constant, is not :. I I I 14 t>HYSICAL dCIBNCi^. accompanied by a change in the v^^locity of the trans- mission of sound by the atmosphere, because the elasti- city and the density change in the same ratio, but that a change in the temperature of the atmosphere, the height of the barometer remaining constant, affects tlie velocity of the transmission of sound, because the elasticity remains constant while the density varies inversely as the absolute temperature. (See Charles' Law, Part I., page 203.) For example, if the temperature of the atmosphere changes from 17°C to 27°C, the density decreases in the ratio (273 + 27) : (273 : 17), or 30 : 29. Hence the velocity of sound increases in the ratio |/29 : t/30. « 9. Determinationof the Velocity of Sound in Air. The velocity of sound in the air may be approximately determined in the following manner. The distance between two stations is measured. A gun is fired at one station, and the interval of time elapsed between the seeing of the flash and the hearing of the report at the other station is observed. The distance between the stations and the time taken by the souiid to travel between them being known, the velocity of sound in the air can be determined. It is assumed that the time taken by the light to pass from one station to the other is so short that it may be neglected. To allow for the action of the wind, the firing should be done at alternate stations, and the average of several results taken. The above method will at best give but an approximate result. The method devised by Regnault for determining the velocity of transmission by gases enclosed in tubes gives a much more accurate determination. OitlOIN AND TRANSMISSION OF SOUND. 15 A pistol is fired at one end of a long tube of known length, and an electrical recording apparatus registers automatically the time that elapses between the pulling of the trigger of the pistol and the making of a mark by a pointer attached to a membrane, which, placed at the other end of the tube, vibrates when the sound-pulse reaches it. Data are thus furnished for calculating the velDcity of the sound trarjsmitted by the air in the tube. The velocity of sound In any other gas may be deter- mined in the same manner with this apparatus. The air is exhausted and the tube filled with the gas. When the temperature is 0°C, the velocity of sound in the air is about 1090 feet per second, and the velocity increases about two feet per second for each increase in one degree centigrade in temperature. 10. Determination of the Velocity of Sound in a Liquid and in a Solid- Since the coefficients of elasticity and the densities of liquids and solids can be determined experimentally, the velocity of sound in these forms of matter can be deter- mined theoretically from the equation. v=Vi The results are found to agree closely with experi- mental determinations when these are possible. The velocity of sound in water is about 4J times its velocity in air. 11. Relation among Velocity, Vibration-Number, and Wave- Length. The particles composing a sound-wave make one com- plete vibration while the sound-wave travels one wave- 1 I I 16 PHYSICAL SCIKNCK. Icn^tli ; tliereforc, if n ck'HotoH tlio nunibor of vibrations ill a unit of tiinl fired at one end of the tulje will pass to the other, if the density of oxygen is 16 times that of hydrogen, and the velocity of sound in hydrogen is 4200 feet per second, when the pressure of the hydrogen is the same as that of the oxygen. 3. At which place has sound the greater speed — at the foot of a mountain or at the top ? Why ? 4. If the velocity of sound in the air at 0°C is 1090 feet per second, find : (1) The speed in air at a temperature of (a) 7°, (b) 10°, (c) 20°. (2) The velocity in carbon dioxide at 0°C if its density is 1.5 times the density of air. (3) The velocity in hydrogen at 0°C if the density of air is 14.5 that of hydrogen. (4) How long it will take sound to traverse a distance of one mile in air when the temperature is 16°C. ORIGIN AND TKANSMISSION OF SOUND. 17 5. What must ho tho tuinporaturo of llio air in onlur that Hound may have a veh)city douhlo that at if (J ? 6. If tho Hpood of Houiul in tho air is 340 metres |)er second at 16°C, what will the speed he at a tompe) iture of 1()8°C if tho pressure uf the gas is doubled ? 7. How long will it take the sound of a signal gun to reach an observer 3.2 miles away when the temperature of the air is 18°C ? 8. Two stations are 61045 foot apart, and tho report of a gun fired at one station is heard at tho other 54.0 seconds a/ter the flash is seen. What is the velocity of the sound in the air? Fid. 12. 9. Two boats were stationed on Lake Geneva, 51700 feet apart. One boat was supplied with a bell B placed under water (Fig. 12), and so arranged as to be struck by a hammer H at the same instant that a torch M turns over and lights the gunpowder P. The sound of the bell was heard at the other boat, by means of trumpet T placed in the water, just 11 seconds after the flash of the gunpowder was seen. What was the velocity of sound in the water ? 10. A report of a cannon is heard 6 seconds after the flash is seen. If the temperature of the air is 15C., what is the distance of the observer from the cannon ? 11. How do you account for the fact that the time reipiired for a sound to travel a certain distance difters from day to day ? 12. If all the soldiers in a long column keep time to the music of a band, will they step together ? ijB \ 18 PHYSICAL SCIENCE. 13. A number of soldiers are drawn up in the form of a circle, and each man fires his gun at tlie instant a signal is given by a man placed at the centre of the circle. Will the sound appear as a single report to any of the men? Explain. 14. If a tuning-fork which vibrates 256 times per second sets up in the air sound-waves the wave-length of which is 52 inches, what is the velocity of sound in the air ? 15. It is observed that the volocity of a sound produced by a tuning-fork whose vibration-number is 436, is 1100 feet per second, what is tho wave-length of the sound-waves ? CHAPTER II. INTENSITY, REFLECTION, REFRACTION AND INTERFERENCE OF SOUND-WAVES. I.— Intensity of Sound. 1- Intensity and Amplitude of Vibration. Experiment 1. Repeat Experiment 1, page 160, Part I. Observe the string, and note the changes in the amplitude of its vibrations. What change takes place in the amplitude of the vibration of the string as the sound grows weaker ? Experiment 2. Repeat Experiment 5, page 162, Part I. Observe the tracing on the smoked glass. What evidence have you that the intensity of the sound increases with the amplitude of vibration of the sonorous body ? The intensity of a sound-wave is measured by the energy of the vibrating particles. When the vibration- number remains constant, the velocity varies as the amplitude of vibration; for example, if the vibrating particles have twice as far to swing in the same time, the velocity must be doubled ; but the energy var^'es as the square of the velocity (Part I., page 78), therefore the intensity of a sound-wave varies as the square of the amplitude of vibration. 2. Intensity and Density of the Medium. Experiment 3. Repeat Experiment 1, page 167, Part I. 1. What change takes place in the density of the air in the receiver as the exhaustion proceeds ? 19 r ' 20 PHYSICAL SCIENCE. ik "ll! 2. What change in intensity of the sound accompanies this change in density? The intensity of sound-waves increases with the density of the medium in which they originate. If the intensity of the sound-wave is nie.isured by the energy of vibrating particles, why should its intensity be affected by changes in the density of the medium in which it originates ? 3. Intensity and Distance. It is a matter of common experience that the intensity of a sound decreases with an increase in the distance from the point at wliich it originates. The exact law will be learned from tlie following considerations. As we have seen (page 10), a sound-wave is spherical in form. When the radius is unity, the surface is 4nr. 2 « IGtt. (( t( (C ) how this change in velocity of different portions of the waves atl'ects their form. 2. If the balloon were filled with liydrogen instead of carbon dioxide how would it dispose of the sound-waves falling upon it? Why? 7. Refraction by Wind. The observation th.'it sounds lieard witli the wind are louder than tliose lieard against it, is explained by the fact that the velocity of sound in the direction of the wind is increased by an inci'ease in its velocity, while the velocity of sound in the opposite direction is retarded by an increase in its velocity. Since the velocity of the wind is less near the earth's surface than a little above it, the portions of sound-waves touching the earth's surface travel more slowly than those immediately above it; hence the waves are deflected downwards and the sound is condensed along the earth's surface if the sound is travelling in the direction of the wind, and are deflected upwards if the sound is travelling in the opposite direction. IV.— Forced and Sympathetic Vibrations. 8. Forced Vibrations. > Experiment 1. Suspend a heavy Aveight by a long cord. From this weight suspend a small weight, say a bullet, by a short thread. Set the system vibrating. RKPRACTION OP SOUND-WAVE;!. n Set 1. Duserihu tlu! motion of the sysfiun, ooinpariii^ tlio jR-riods of vibration of tho two peii/•'/, (Fifr. 20), where the opposite })ulses meet and nentraliz(i each other. Experiment 2. /• Fid. 20. A B Pake two brass U-tuhes, A nrid I>, ooiniectcd bv teli^scophiijf joints as show II in W^. -1, short tuh(»s being insorted at (J .*inI>. Coimect D with your ear by means of a ])i(!co of rubl)er tubing, and place a vibrating tuning- fork at the opening ('. Note that the sound of the fork is heard, the sound-waves reaching the ear through botii ])ranches togetlier. A Kio. 21, Now draw A out until the intensity of the sound is a minimum. If A is propeily adjusted, the sound will ahnost, or altogether, disappear. !i ii i 30 Piivsr. Pulses of rai'(!factioii at 1) are always met \>y pulses of condensation, and the sound-waves are conseijuently destroyed. [n this case the distance around the tube in the direction CAD differs from the distance in the direction (*li|) l)y one- luilf a wave-lengtli, tlwft is, the distance m/i is one-quarter of the length of the wave produced by the fork. When two sound-waves interfere and thus destroy each other either wholly or partially, the effect is known as interference. 10. Determination of Wave-Length. The iiistrninent described in the experiment above may bo used for y the tuiilii;^^-t'oiUH in K.\|M'ri- niont .S, calculate the approximate speed ot* sound in the air. 12. Beats. Experiment 4. Take two tuning-forks of the siune vihnitioii number, hold one in each hand and make them sound together. Note that the sounds blend perfectly. Load one of the forks by sticking a piece of wax to the end of one of the prongs. Excite the forks and place each on its .esonance-hox. Note that tliere is now no continuous flow of sound, but that the intensity is alternately increased and diminished. Tliis effect is tlie result of interference, and is called beating. Tlie loading of the fork causes it to vibrate more slonly and to originate soundrwaves which are of greater wave- length than those produced by the other fork. Since the sound-waves proceeding from the forks are equal in Fio. 22. velocity and unequal in length, they periodically coin- cide, the condensation of the one with the condensation of the other (Fig. 22 A), or the rarefaction of the one 32 PHYSICAL SCIENCE. witli rare f cacti on of the otlier (Fii^^ 22 C); .aiifl periodi- cally interfere, the condensation of the one coincidin<^ with the rarefaction of tlie other (Fi<^. 22 B). Thus alternate re-inforcenients and dimiinitions of sound are produced. nf QUESTIONS. 1. If a circular plate is made to vibrate in four sectors, as in Exp. 7, page 164, Part I., and if a cone-shaped funnel is connected with the ear])y a rubber tu])e, and the other ear is stopped with soft wax, no sound is heard when the centre of the mouth of the cone is placed over the centre of the plate ; but if it is moved outward along the middle of a vibrating sector, a sound is heard. Explain the reasons. Try the ex[)eriment. The mouth of the funnel should bo about 2V inches in diameter, if the diameter of the plnte is (5 inches. / 2. A sounding tuning-fork, mounted on a resonance-box, is carried slowly toward the wall of a room. Why is it that the sound becomes wavy, rising and sinking at regular intervals \ 3. A vibrating fork is placed before the o[>ening C in the tubes (Fig. 21), and the ol)Herver at D notes that com[)lete interference takes place when A is drawn out l.'J inches. What is the length of the sound-wave which originates with the fork ? If the vibration- number of the fork is 256, what is the velocity f)f sound in air? 4. A fork, whose vibration-nuni})er is 256, is made to vibrate before the opening C (Fig. 21), and perfect interference takes place when 'iC tube A is drawn out 33 cm. What is the velocity of sound in the air ? 5. When two tuning-forks are beating, show that the number of beats per second is always etpial to the difference between the vibration-numbers of the forks. p : I' !l CHAPTER III. PITCH OF SOUNDS — MUSICAL SCALES. 1. Determination of the Fitch of a Note. We have lecanied (paoje 175, Part I.) tliat the pitcli of a musical note depends upon the rapidity of tlie vibrations wliich enter tlie ear. To determine the number of vibrations corresponding to any note, an instrument called a siren is used. Fit^. 23 shows t'.io construction of a simple form of this instrument. C is a cylindricjil air-chambei", upon the upper end of which is mounted a circular rotatinjj^ disc B, whicii almost touches the upper surface of tlie cylinder. The disc is perforated at ecpial intervals along a circle nesir its circumference. The upper end of the air-chamber is also perforated, the holes cori'esponding Mo in number, position, and size with those •'">». -iii. in the disc above. The holes in both the disc and the end of the chamber are drilled oblitjuely, those in the disc sloping in one diiection and those in the end of the chandjer in the opposite. The tube D at the lower end of the chamber is connected with a bellows or blower. When air is forced into the chamber and passes up througli the holes, the disc is made to rotate by the pressure of the air against the sides of the holes, the rapidity of rotation depending on the force with wiiich the air is sent into the chamber. I? li li 34 PHYSICAL SCIENCE. As the disc rotates, vibrations will bo set up in the external air by the putts of air which pass out of the chamber when the holes in the disc are opposite those in the end of the chamber. A note will thus be produced, the pitch of which will depend on the rapidity with which the disc is rotated. By controlling the blower any note can be produced at will. Its number of vibrations per second can be determined by reading from the dial of a mechanical recorder attached to the spindle A, on which the disc is mounted, the number of revolu- tions made in any observed interval, multiplying this by the number of holes in the disc and dividing by the number of seconds in the interval. Experiment 1. * ' " If your laboratory is supplied with a siren, determine with it the number of vibrations per second of a tuning-fork. Excite the tuning-fork with a violin-bow, and at the same time press air through the siren, gradually increasing 4he speed of the rotating disc. ' When distinct " beats," which indicate that the two notes are nearly alike in pitch, are heard, cautiously increase the speed until the beats disappear and the two notes blend. Now set the clockwork of the recorder in motion and keep the disc revolving at a uniform rate for an interval of time, sav one-half minute. Read from the dial the number of revolutions, and calculate the vibration-frequency of the fork. Experiment 2. If the laboratory is not supplied with a siren, determine approximately the vibration-frequency of the tuning-fork in the following manner : — Take a glass tube about 15 inches long and | inches in diameter, and select a cork that will just slide up and down PITCH OF SOUNDS -MI'SICAL SCALES. 35 within the tube, toiicliing its sides. Attach a wire to the cork to serve as a Ijandle. Insert the cork into one end of the tube, excite the fork and liold it over the other end of the tube. By means of the wire move the cork up or down until the position of the cork which causes the tube to give out its loudest sound is found. Now place the tube in a horizontal position in a support with its open end close to the disc used in Experiment 3, page 174, Part I., and facing the ring of holes (Fig. 24). Hold the tube through which the air is blown on the other side of the disc as shown in the figure, force air through the tube and turn the disc, gradually increasing or decreasing its speed until the velocity at which the tube gives out the loudest sound is found. Continue to revolve the disc at this rate for half a minute, and count the number of turns made by the handle in that time. Multiply the number of turns made by the handle by the number of times wliich the disc revolves for every turn of the handle, and this by the number Fia. 24. of holes in circle. Divide the product by 30, the number of seconds. The result will be the number of vibrations per second which the disc sends into the tulje ; but, since the tube is sounding its loudest, this is the numl)er of vibrations made by the tuning-fork. The average of several results should be taken. J 36 PHYSICAL SCIENCE. QUESTIONS. 1. When a sounding body approaches the ear, or recedes from it, the pitch of the tone appears to cliange. Explain the cause. 2. A person carries a vibrating tuning-fork. Will the pitch of the note appear the same to a [)erson going before him as to a person foUowing him, all three moving at the s;ime rate ? Give reasons for your answer. 3. If A carries a vilmating tuning-fork from B to C, will the pitch of the fork ai)pear the same to A, B and C. If not, what will be the difference in their observations ? 2. Musical Scales. To produce an effect agreeable to the ear the notes cannot be used arbitrarily or at hazard. When once a note is chosen to begin a piece of music the notes which are to accompany or follow it must be selected according to well-defined law*?. In the music of all nations changes in pitch take place by definite intervals, and not by continuous transitions. Music, therefore, proceeds by notes clearly separated from one another. A collection of notes whose vibration-numbers bear definite ratios to one another forms a musical scale. The notes of a musical scale are selected according to this fundamental law. Simultaneous or successive notes are agreeable to the ear only when their vibration-numbers bear simple ratios to one another. When the ratios are not simple, audible beats occur and dissonance results. 3. Harmonic Scale. The harmonic scale is composed of a series of notes whose vibration-numbers are proportional to the natural numbers Xf^ifOf 4, O . • • • PITCH OP SOUNDS — MUSICAL SCALES. 37 Tlie first six afc least of tlioso form agreeable harmonies wit) I tlie first. The first is called tlie fundamental note, and the others when heard as auxiliaries to it are called har- monics. The latio between the vibration-number of one note and that of its antecedent note is called a musical interval. The interval between two notes, therefore, is obtained by dividing the vibration-number of the one note by that of the other. Since the intervals between the notes are very great, music in wdiich the notes used form a harmonic series is restricted and monotonous. Following the principle that the less complicated the ratios of the vibration-numbers of the notes the more perfect the harmonies, physicists have constructed a natural scale in which the intervals are much smaller. 4. Diatonic Scale. The interval between tw^o notes whose vibration- numbers are in the ratio 1:2 is called an octave. The sound produced by the simultaneous production of more than two separate notes is called a chord. It is found that any three notes, X, Y, Z, whose vibra- tion numbers are p, q, r respectively, are concordant if 2^ :q :r::4>\ o :6 Three such notes are called a harmonic triad, and if sounded \vith a fourth, which is the octave of the first, they form what is called a major chord, the most con- sonant chord found in music, tlie ratios of the vibration- numbers being the simplest possible. s\l 88 PHYSICAL SCIICNCE. 1 The letters C, D, E, F, G, A, B, are used to denote notes connected in liarnionic triads as follows : — C G F E : G :: 4 : 5 : c B : 2 D : : 4 : 5 : 6 A : 2 c : : 4 : 5 6. Therefore, The vibration-number of Fi = | thai of C. G = $or i^lhatof C. u tt « a Or, ♦ * B = ^ that of G = J X 3 or -'/ that of C. • • D = $ that of G = J X ij or | that of C. F-J that of C. A = |thatofC. the notes, C D, E, F, G, A, B, C, have the ?ibi.at.ion-raMos i, I, h t, ^, s. V. 2 and the intervals » 10 Ifl 9 10 10 The above scale is called the natural or diatonic scale. The first, or lowest note, is called the key-note, and the last is taken as the key-note of another set of eight notes, and so on until a sufficiently extended scale is obtained. 5. Intervals of the Diatonic Scale. An inspection of the scale shows that the intervals in this scale are not equal. Three are represented by f, tw'o by -V", and two by |f. The intervals f , -V- are known as tones, the first being a major-tone and the second a minor-tone. The interval ^| is called a major semi-tone. Other important intervals in the scale are the major third (C . . . E), the numerical value of whicli is | ; the fourth (C . . . F), value, i ; the fifth (C . . . G> value, ^; and the minor third (Ai . . . Cg), value, |. PITCH OF SOUNDS — MUSICAL SCALES. 39 6. Designation of Octaves. The letters C, D, E; etc., distinguish the notes of an octave from one another. It is also necessary to have a means of designating tlie different octaves of any musical instrument. This is done in various ways. One of the best is to write the letter desimiatinsr the note with a subscript figure which indicates the octave. For example, the C's of the eight octaves of the organ are written thus : — C_2, C-i, Ci, C.J, C3, C4, C5, Co, C7. 7. Standard of Pitch. When once the vibration-number of any note is fixed, the vibration-ratios given above may be used to deter- mine the vibration-numbers of the other notes. The pitch usually adopted by writers on acoustics and by makers of acoustical apparatus is C.j = 256 double, or 512 single vibrations per steond. The vibration-number of the C's of the different octaves will then be C-2, 0-1, Ox, Co, C3, G4, Or,, C,;, C-. 16 32 64 128 256 512 1024 204S 4096 This pitch has the advantage of simplicity, the vibration- number of each C being a power of 2. The standard is a tuning-fork made to vibrate 25G times per second. The international concert pitch adopted by nmsicians is A3 = 435 double, or 870 single vibrations per second, and the standard is a tuning-fork made to vibrate 435 times per second. ' 1. Determine the vibration-number of each note in an octave when the vibration-number of A is 435. 2. Wliiit is the measure of the interval between the acoustic and the musical standard of [)itch ? 40 PHYSICAL SCIENCE. I K 8. Transposition of Scales— Scale of Equal Temperament. If C wore always taken as the point of departure, tlie notes of tlie diatonic scale would be sufficient for all purposes except for minor chords ; but since any note of the scale may be used as the key-note, it is obvious that to maintain the same succession of intervals, that is, H. V'' 11' ^tc, new and intermediate notes must be intro- duced. For example, comparing the scales tabulated below : — C.J, Dj, E.J, F.J, G.J, A.J, B.J, C4, D^, E^, F^, G4 Key of C. . . . 2r)6 28S .S20 341^ 384 426g 480 512 576 640 6S2§ 768 Key of G.... 256 2S8 320 360 384 432 480 512 576 640 720 768, it will be noted that the As of the two scales differ by an interval of ^^- and the F's by an interval of |f|. Similarly every transition from one key to another adds extra tones. It has been calculated that with all the naturals as key-notes the scale would consist of at least 72 notes to the octave. Clearly it would be impracticable to construct instruments with fixed tones, like pianos or organs, to play in different keys. The difficulty is overcome by tempering the scale, that is, by reducing the number of notes by changing slightly the values of the intervals to ecjualize them. In the scale of equal temperament commonly adopted the octave is divided into twelve oiiujil intervals, each of which is called a semi-tone, two intervals forming a tone. There are, therefore, twelve notes, and the pitch of each is obtained from the next lower by multiplying it by i/2 ; that is, the vibration- ratios of the notes in the octave are 1, 2'-^ 2.\ 2v^ .' . . . 2 and each interval is 2i'2. CHAPTER IV. TRANSVERSE VIBRATIONS OF STRINGS. 1. Laws of Vibration. We have learned, Art. 3, page 175, Part I., that the vibration-frequency of a stretched string or wire depends on its length, its diameter, its tension and its density. Let us examine the subject more closely to determine the exact laws of vibration. Experiment 1. Stretch two piano wires A and B on a sonometer, tune them in unison, and place a movable bridge under the centre of B. Pluck wire A at it» centre and B at the centre of one of its halves. Compare the notes. It will be found that the note given by the short wire is just one octave above that given by the wire vibrating as a whole. 1. How does the vibration-number of a note given by a wire compare with the vibration-number of the note given by the same wire when its length is decreased by one-balf ? Repeat the experiment, shortening B with the movable bridge successively to f, f, f, f, §, and -^^ of its length. 2. What will be the successive intervals between the notes emitted by wires A and B ? 3. What then is the relation between t! e length of a wire and the number of vibrations which it makes per second. Experiment 2. Place a wire B on a sonometer, let it pass over the pulley and hang a weight from its end. Tune anotlier wire A in unison with it. Note the weight that is hung from B 41 42 PHYSICAL SCIENCE. and add other weights until it vi))r;ites in unison with (1) one- half of A, (2) on(^third of A, (.']) one-fourth of A, etc. It will be found that the weight is in (1) 4 times, in (2) 9 tinjes, in (3) 16 times the original weight. 1. How does the nuiii})er of vibrations per second made by the wire B when it vibrates in unison with (1) ^ A, (2) .\ A, (.']) ] A compare with the lunuber of vibrations made by the same wire when it vibrates in unison with A ? 2. What caused the difference ? 3. What then is the relation between the tension of the wire and the number of vibrations which it makes per second ? Experiment 3. Measure with a micrometer caliper the diameters of several wires B, C, D, E, etc., and stretch them successively by the same weight on a sonometer. Tune a wire A to vil)rate in unison with the largest wire, say B, and, using a movable bridge, determine what fraction of As length will vibrate in unison with each of the other wires. It will be found that the ratio of the length will be. inversely as that of the diameters. Experiment 4. Stretch with equal tension on the sonometer a steel wire and a brass one of the same diameter. Place a movable bi'idge under each, adjust the bridges until lengths of the wires are found which vibrate in unison, and measure these lengths. It will be found that the length of the steel wire is to the length of the brass wire as the square root of the density of the steel is the square root of the density of the brass ; but the vibration-numbers of wires are inversely proportional to their lengths, therefore their vibration-numbers are inversely proportional to the square roots of their densities. The same is found to be true of wires of other materials. The above expei-iments, .and ofchoi's of a more general character, carefully performed, verify the following laws: 19 TRANSVERSE VIBRATIONS OF STRINGS. 43 1. When the tension is constant the number of vibrations per second varies inversely as the length. 2. The number of vibrations per second varies as the square root of the tension. 3. The number of vibrations per second varies inversely as the diameter. 4. The number of vibrations per second varies inversely as the square root of the density of the material of which the string is composed. QUESTIONS. 1. Wliat are the proportionate lon^'ths of a Rtretched striiijj which gives, when vi]>rating, a harmonic series of notes ? 2. Stretch a wire on the .sonometer, and, taking the note which it gives when it vibrates as a wholo as a fnndajuental note, shift the movable bridge to the ])roper position to produce in order the otlier notes of a harmonic series. 3. What are tlie proportionate lengtlis of a stretched string which gives the notes of the diatonic scale '( 4. Stretch a wire on a sonometer, and tune it to vibrate .as a whole in unison with a C-fork. Determine the positions where the movable bridge must be placed to give each of the other notes in the octave. Place the bridge in the proper positions and produce the notes. 5. A wire stretched on a sonometer l)y hanging a weight W from one of its ends gives the note C. What weights must be hung in succession from its end that the string may give in order the notes of the diatonic scale ? 6. A string stretched on a sonometer gives a certain note. What must be the diameters of wires of tiie same material and the same length that will, when stretched to the same tension, give notes which will be in a harmonic series with the first ? 7. A and B are two wires of the same material and thickness. A is two feet long, and is stretched by a weight of 8| pounds. B is t 44 PHYSICAL SCIRNCB. four feet long, and is stretched by a weight of 34 pounds. How are tlio notes which the wires yield when struck related to each other? 8. A steel wire one yard long, and stretched by a weight of 6 pounds, vibrates 100 times per second when i)lucked. What must be the tension of two yards of the same wire that it may vibrate twice as fast ? 9. Two precisely similar strings A and B have the same tension. If the tension of A is doubled, and the length of B is halved, how must the tension of B be altered to give the same note as A ? 10. Two similar wires of the same length are stretched, the one by a weight of 4 pounds and the other by a weight of 9 pounds. What is the interval between the notes which they produce ? 11. A stretched string 3 feet long gives the note C when vibrating transversely. What note will be given by a string one-quarter the thickness and one foot long, made of the same material and stretched by the same weight ? 12. Four exactly similar strings, stretched with the same tensi are vibrating side by side. How will the note emitted be afiecteu if they are fastened together so as to form one string, by winding around them an extremely thin piece of silk ? 13. A. silver and an iron wire of the same diameter are stretched by weights of 4 and 36 pounds respectively. When plucked they give the same note. If the density of silver is 10.5, and that of iron 7.8, find the relative lengths of the wires. CIIAP^rKU V. VIHUATIOX OK AIR IN Tl'ISKS. I.— Resonance. Experiment 1. Repeat Experiment 5, p.'ige 180, Part T. The cause of tlie plienoiiuMui ob.sorved in tliis cxpcii- ment can be best understood by perroniiiiii;- soiiir simple experiments witli the wave nuichine used in ExpeiiuKint 3, page 5. Experiment 2. Fix the left-hand end of tlie spiral by pushing a cork into it and fastening the cork in an immovable olamj). Take hold of the right-hand end, and, by pushing it in, send a pulse of condensation along the spiral. Watch it as it is relli'clcd from the fixed end, and the instant it reaches the free etui pull the coil outward, producing a pulse of rarefaction, When this is reflected and returns to the fice vm\, push tlie coil inward, and so on until the spiral vibi'ates as a whole steadily. You will then observe : 1. That at the fixed end the coils are alternately crowde*! together and then draw?! apart. 2. That the amplitude of vibration of the coils at the free end is greater than at any other part of the spiral, but that they roniuin at about the same distance apart. 3. That to form a complete wave of condensation and rarefaction, a pulse of condensation travels from the free end to the fixed end, and back again to the free end ; and is then followed by a pulse oi iw" ■i 46 PHYSICAL SCIKNCE. ■ a B Fig. 25. i'.v! .?f{vctioti, wliich also tr.avels from tlie free eml to the lixetl end, r.'ul if. reflected back to the free end. ^tmftr:"::""'^ ^^^^ wave-length is therefore four times ■^ - the length of the spiral. The motion of tlie coil spring furnishes .an illustration of the maimer in vhich tlie air-colunm in the tube is believed to vibrate. The movement of a prong of tlie fork in tlie direction a to b (Fig. 25) pro- duces in the air a pulse of condensation, which runs down to the bottom of the jar and is reflected back. Now, if the distance AB is sucli that this pulse of condensation reaches tlie prong of the fork at the instant that it is on the point of returning from b to a, a pulse of rare- faction will be produced, which will run to the bottom of the jar and back, and, overtaking the prong when it reaches its limit a, will again be changed by it to a pulse of condensation. The vibrations of the tuning-fork will therefore be re-inforced by synchronous vibrations of the air-column in the tube, and the intensity of the sound thus increased. It is evident that the distance AB must be just one- quarter of the wave-length of the wave produced by the fork, and since the wave-length depends upon the vibration-frequency of the fork, the distance AB must vary with different forks. Since there can be no gain in energy, the increase in the intensity of the note when a resonator is used nmsfc be accompanied by a decrease in the length of time durinff which it sounds. VIBKATION OF AIU IN TUBES. 47 1. Resonators. / Resonators are used for analyzing composite sounds. Fig. 26 shows two common forms of tlie instrument. Tliey are made in various sizes, and each is carefully tuned to a definite pitch. The small opening a is placed in the ear, and if the sound to which the resonator is tuned exist in the air, it is re-inforced by the vibration of ^the air within the cavity, and its presence is thus made known to the observer. By applying successively different resonators to the ear, the simple notes which make up a composite tone may be determined. Fio. 26. 2. Determination of the Velocity of Sound by Resonance. Since AB (Fig. 25) is just one-quarter the wave- length of the sound-wave produced by the fork, the wave-length is kno^vn when AB is measured ; and if the vibration-number of the fork is known, the vehjcity of sound in air can be calculated from the equation V — nk (Art. 11, page 16.) The velocity in other gasos may be determined in the same way. 48 PHYSICAL SCIENCE. I I '1\ ■ I II. —Vibration of Air in Tubes. 3. Vibration of Air in Closed Tnbes. Experiment 1. Take a glacs tube, about 30 inches long and three quarters of an incli in diameter, insert by means of a stiff wire a cork which will slide up and down in the tube, just touching the sides (Fig. 27). Adjust the cork so that the air within the upper end of the tube will vibrate in unison with a tuning-fork. With a piece of brass tubing flattened at one end, blow across the end of the tube. 1. How does the note produced compare with that given when the fork is placed above it ? 2. The blowing across the mouth of the tube causes a mixture of vibrations of dif- ferent frequencies. Why is it that the tube causes one note to become dominant ? Experiment 2. Adjust the cork in the tube used in the last experiment so that the air- column will be 24 inches in length. Blow across the end of the tube. Repeat the experiment, making the length of the air-column (a) 1 2 inches, (b) G inches. 1. What is the relation between the vibration-numbers of the notes given by (1) the 24-inch and the 12-incli air-columns, (2) the 12-inch and the Cinch air-columns ? " 2. Determine by trial the different lengths of the tube necessary to give the notes of the diatonic scale. When a flutter, caused by the co-mingling of a number of vibrations of different frequencies, is made at the Pia. 27. VIBRATION OP AIR IN TUBES. 49 montli of a tube, the air-column within the tube selects the vibrations which are in synchronism with itself, vibrates in unison w ith them, and re-inforces them, thus producing a musical note. The vibration-number of the note produced by a vibrating air-column within a tube varies inversely as the length of the tube. 4. Vibration of Air in Open Pipes. Experiment 3. Blow a puff of air across the end of a glass tube open at both ends. Now close one end and blow a puff of air across the open end. How does the pitch of the note in the first case couniare with that in the second case ? Experiment 4. Select two glass tubes of the same bore, one of whicli is twice the length of the other, close one end of the short tube, and blow a puff of air across an open end of each. What is the relation }>et\veen the vibration-numbers of the notas produced by the two pipes ? A tube open at both ends gives a note whose vibra- tion-number is double that given by a tube of the same length which is closed at one end. A tube closed at one end will, therefore, give the same note as an open one of twice the leng-th ; but the wave- length of the sound-wave is four times the length of a stopped tube, therefore the length of the open tube is one-half the wave-length of the sound-wave produced by it. The vibration of the air in an open tube may also be illustrated by a coil-spring wave-machine. Experiment 5. Push both ends inward at once, thus sending two pulses of condensation towards the centre. Watch them as they cross 50 PHYSICAL SCIENCE in the centre, and wlien they reach the ends, pull })oih ends outwards. Repeat this process until the two halves of the coil vibrate stea«Uly in and out. Now observe : — 1. That wlien a pulse reaches the end of the spiral its type is changed, and if it is a pulse of condensation it is rettucted as a pulse of rarefaction, and vice versa. 2. That the centre remains stationary. 3. That the condensations and the rarefactions are not uniformly distributed along the spiral, but are greatest at the centre and least at the ends. 4. That at the ends where the coils remain always about the same distance apart the amplitude of vibration is the greatest. 5. That the rate of vibration is twice as great as when one end of the spiral was fixed (Exp. 2, page 45). Wluit is the reason ? ' The air-colnnin in the open tube is be- »J lieved to vibrate in niucli the same way as the coil-spring was made to vibrate in the last experiment. The movement of the prong of the fork in the direction a to h (Fig. 28) produces in the air a pulse of condensation, which runs down to the end of the jar. Its type is then changed, and it is reflected back as a pulse of rarefaction. When it readies the upper end, its ty2)e is again changed, and it is reflected as a pulse of condensation. Now if the distance AB is such that the prong of the fork is just starting to move again from a to h at the instant that this pulse of condensation starts down the tube, the vibration of the fork will be re-inforced Fio. 28. lyy ^]^^ vibration of the air-colunni. This evidently can take place only when the distance AB is one-half the wtwe-lenirth of the note. VIBRATION OP AIR IN TUBE8. 51 n 5. Nodes and Loops in Pipes- Since the layer of air at tlie closed end of a stopped pipe is necessarily at rest, and since rapid alternations of condensation and rarefaction take place there, the density of the air at this point, like the relative positions of the coils at the fixed end of the spiral (Exp. 2, l)a<;e 45), is constantly changing. At the open end of a tube the air has a constant density, that of the atmosphere ; consequently the air particles, like the coils at il»e free end of the coil-spring, remain at about the same distance apart. The amplitude of the vibration of the air particles at this point is, there- fore, at a maxinnim. A node in an air-column of a pipe is a section of the column where the particles of air are at rest, but where the changes of density are the greatest. A loop is a section of the air-column where the vibrations of the particles of air have the greatest amplitudes, but where there is no change of density. In a stopped pipe th( re is a loop at the open end and a node at the closed end. In an open pipe there is a loop at each end, and a node nt the centre. The existence oF nodes and loops may be shown experimentally by placing a light powder in a horizontal tube (Exp. 9, page 1G5, Part I). When a note is sounded the powder accunmlates at the points of rest. Their existence may also be shown as in Experiment 0, page 52. 6. Organ Pipes. Fi'^ 29 shows the construction < I' a common UrJl organ pipe. Air is forced throu^jli the tube T fio. 29. i t It i^ 52 PHYSICAL SCIENCE. into tlie chamber C. The compressed air escapes from this chamber by a narrow slit ed, and, striking against the narrow bevelled edge, or lip ab, produces a fluttering noise. The vibrations of the flutter which are in syn- chronism with the air-column of the tube are re-inforced by it, and a musical note, the pitch of which depends upon the length of the tube, results. .7. To Show the Existence of Nodes and Loops in an Organ Pipe. Experiment 6. . ' Make a small tambourine by stretching a mem- brane over a circular hoop. Scatter fine sand on the membrane and by means of a string lower it slowly into an organ pipe which is producing a musical note (Fig. 30). Observe the sand. What evidence have you of the existence of loops and nodes ? Repeat the experiment sev'eral times, varying the force of the current of air passing tlirough tlie tube. Is there a node at the centre of the tuhe in each Fio. 30. case ? Are there other nodes ? If so, where ? 8. Overtones of Pipes. Repeat the experiments on nodes and loops in strings, Part I., pages 181, 182. Experiment 7. Blow a strons: blast across the end of the tube used in experiment 2, page 34. Note the overtones which mingle with the fundamental note emitted by the pipe. VIBRATION OP AIR IN TUBES. 53 When a pipe is blown gently it yields its fundamental note. By gradually increasing the force of the current of air the air-column is made to break up into vibrating segments, and hence to yield overtones. Upon what does the quality of the note omitted by a pipe depend ? See Part I., page 182. The series of overtones given by a stopped pipe differs from that given by an open one, as will be seen from a consideration of the following conditions : — (1) There must be a loop at the open end of a tube, and a node at the closed end. (2) Nodes and loops recur alternately. On these conditions the following will be the simplest possible divisions of air-columns in pipes. 9. In Stopped Pipes. The open end remains always a loop and the closed end a node (Fig. 31). If there are no other nodes and loops, the pipe yields its fundamental note only. n H N' N" L' c L'" l' N N i:' N ••-■ L' N N : N • t( L' M y I ir L Ir L y I it 1 4 Via. 31. Fig. 32. Fig. 33. Fig. 34. Fig. 35. Fio. 36. When the pressure of the air is increased, the air- column divides into three equal parts, and an additional Hi, ^ 54 PHYSICAL SCIENCE. node and loop are formed (Fig. 32). If the air pressure is still increased, the air-column divides into 5, 7, 9, etc., equal parts (Fig. 33). Hence the vibration-numbers of the possible notes given by a stopped pipe are in the proportion 1, 3, 5, etc., and odd harmonics only are, therefore, present in the overtones of a stopped pipe. 10. In Open Pipes. A loop remains always at each end of the pipe. When the fundamental note is sounded there is but one node, that at the centre (Fig. 34). When the first overtone is produced there will be a loop at the centre, and the air-column divides as shown in Fig. 35. Fig. 37. When the second overtone is produced the column will divide as shown in Fitj. 36. The other overtones are L .1 lU I uumnwaEsaoui VIBRATION OF AIll IN TUBES. 55 formed by siiiiibir divisions. Hnice tlie vibration- numbers of tlie possible notes given by an open pipe are in tlie proportion, 1, 2, 3, 4, etc., and, therefore, the over- tones together with the fundamental note form a complete harmonic series. The quality of tlie musical sounds j^iven by the pipes will depend upon the degree of complexity of the vibration of the air-columns (Art. 10, page 182, Part I). 11. Manometric Flames. Koenig has devised a means of showing the complex, nature of sound-vibrations by means of a vibrating gas flame. Fig. 37 shows the construction of the apparatus. A box or capsule A is divided into two compartments by a thin membrane B. Gas is admitted into one of the compartments by a tap G, and is lit at the nozzle D. The other compartment is connected by means of a rubber tube with a funnel-shaped mouth-piece. A rotating mirror is placed in front of the gas flame. When sound- waves enter the capsule by the mouth-piece, the mem- brane, gas and flame are set in vibration. By revolving the mirror the image is drawn out into a band of light. If the flame is burning steadily, the band will be con- tinuous; but if the flame is vibrating, it will have a Fio. 38. wavy appearance. The complexity of the vibrations is shown by the succession of images which appear on the mirror (Fig. 38). • li iji' !i!: ^■1 ', 56 PHYSICAL SCIENCE. Fig. 39 showK the iinaoo wlien tlie vowel E is sung in front of the mouth-piece on the note C. t'lo. au. Experiment 8. * Revolve the mirror and sing into the mouth-piece the vowel A (1) on the note F, (2) on the note C. Make a driiwing of tlie image made hy the flame in each case. Vary the experiment hy singing diiferent vowel sounds on different notes, by blowing a toy trumpet and by making sounds of various kinds in front of the mouth-piece. Instead of connecting the capsule with the mouth- piece, it may be comiected with organ pipes, resonators, etc., aud the character of the vibrations of air-columns Fio. 40. VIBRATION OF AIR IN TUBES. 67 observed. Fi^r. 40 shows a method of comparin*; the vibrations of two air-columns in or^an pipes. Let two different persons repeat in succession the above experiments. Are the images uhko ? If not, exphvin tlie ruason. iSl 111 QUESTIONS. 1. Calculate the depth of a resonant jar for a fork whose vihration-nuuiber is 440, when the velocity of sound in air is 1,100 feet per sec. 2. It is found tliat the depth of a resonant jar wliich gives the loudest sound with a fork whose vibration-number is 250 is 13.2 inches. What is the velocity of sound in air ? 3. A tuning-fork, making 384 vibrations per second, is held over a cylindrical jar in which the velocity of sound is 1,100 feet per second. What must be the length of the jar in order that it may be best adapted to resound to the fork ? What is the length of the wave sent out by the fork ? 4. When a tuning-fork is set in vibration, .and held close to one end of a glass tube 20 inches long and open at both ends, an augmentation of sound takes place. If the tube is longer or shorter thau 20 inches, the increase of sound is not so great. How do you explain these facts, and how could you a calculate from them the pitch of the tuning-fork ? 5. A stopped organ pipe 4 feet long, and an open organ pipe 12 feet long, are sounded. How are the notes related to eachc other ? Do they differ from each other in quality, and, if so, why ? 6. Give the lengths of the three shortest closed tubes, and of the three shortest open tubes, which will resound to a tuning-fork making 200 vibrations per second, the velocity of sound being 33,240 cm. per second. Fio. 41. 7. If a pipe is constructed with holes bored in one of its sides, and these covered with little doors, as shown in Fig. 41, 6 6 '! ifi^! 58 PIIY8ICAL SCIENCE. wimt off(!ct will ho iiroilucid on tlio vilnntioiis of tlio Hir-column within tlio tubu by opening A, 15, and C in Huccussion i 8. What otFoct is producotl by tlio opening and the closing with the fingers of the lateral orifices of a Hute '( Exi>lain. {). A stojiped pipe 2 feet long and an open pipe 4 feet long give tho Hanie fundamental notes. How do these two notes difier in quality? • . rl^ l!! ^1 CHAPTER VI. NATURE AND PHOPAr.ATIOX OF-^ LIGHT. 1. Theory of the Nature and Propagation of Light. Before proceeding' witli tin's cli.-ipter, tlie student should repeat the experiments descrilxMl in Chapter xxi., Part T., and make liimself familiar with the theory of the nature and propagation of light. 2. Sources of Light for the Laboratory. For most experiments in light, it is necessary to darken the laboratory. Close wooden shutters, either liinged or supported by weights and made to slide up and down, are the best, but blinds made of the cloth used by carriage makers for covering buggy tops answer well. If blinds are used, 'they should be mounted on spring rollers, and the light should l)e shut out at the edges by having tlie blinds run in grooves not less than 6 inches deep. It is convenient to have some ready means of con- trolling and directing fairly powerful beams and pencils of light for experimental purposes. If the sun is the source of light, a porte lumiere is used to transmit the light into the laboratory. This consists of a mirror A, which can be so adjusted that direct sunlight is reflected through the tubular opening B (Fig. 42). A double-convex lens should be mounted in a brass ring made to slip easily into the tube B. This lens is called the condenser. A lantern objective C 59 - . '. - - I': ■J' ^ , , 'If'- . ' '"'11 f I •*; i»! 60 PHYSICAL SCIENCE. sliould be supported in front of the condenser on a metal bar 1), which can be (juickly adjusted or removed. Fig. 42. Caps E, E, witli circular openings and slits, are made to tit over the tube B. A slide-iiolder F, which also can be attached to the tube B, as shown in the figure, should be provided. I .;i I ; I ) I: Ffq. 43. To introduce a beam of light into the laboratory, attach the porie lumiere to a shutter in a window facing south, remove all the lenses and adjust the mii-ror (Fig. 43). The size of the beam may be regulated by using caps with apertures of various sizes. I' ' NATURE AND PROPAGATION OF LIGHT. 61 To iiitrofUice a convergent or a diverf^enfc pencil, slide tlie condensing lens into the tnbe (Fig. 44). Tlip pencil will be convergent to a focus, and divergent beyond the focus. ^ • Fio. 44. To project lantern slides, place the condensing lens and the objective in position, attach tlie slide-holder to the tube, place the slide in position, and move the objective backward or forward until the picture is focused on w FiO. 45. a wliite screen placed in front of tlu^ objective (Fig. 45). A plaster wall makes the best screen. Pieces of appa- ratus, and experiments that can be pertormed on a small scale, may also be projected in the same manner by ])lacing tlie apparatus between the condenser and the objective. If it is not convenient to use a lantern 62 PHYSICAL SCIENCE. liii i! I I I! li :t objective, an ordinary double-convex lens mounted on a stand infiy be used for this purpose. If the sun is not used as the source of light, a box for shutting in the radiant must be provided. The ap- paratus then becomes a projection lantern. The simplest form of the lantern is that which most nearly resembles B^SJ^ Fio. 46. the porte lumiere described above. The tube for holding the condensing lens, the objective, the support, the caps, the slide-holder, etc., ave the same. The lantern differs from the porte luuiic e simply in substituting a venti- lated box to enclose the radiant for the adjustable mirror which reflects the sunliglit. Fig. 4G shows a projection lantern with an electric arc lamp as the source of light. This is the best radiant for experimental purposes; but an oxy-hydrogen lamp, an acetylene gas flame or a good coal-oil lamp will give sufficient light if the room is well darkened and the screen is not placed at too great a distance. The ordinary closed front lanterns, sold for pro- jecting slides alone, are not adapted for physical work. NATURE AND PlKiPAOATION 01' LIGHT. 63 To obtain a beam of liobt vvitli tbc lantern, remove the objective, place a single plano-convex lens in the Fig. 47. tube, and draw the radiant back until the light becomes parallel (Fig. 47). - {: - ^ FiQ. 48. To obtain a convergent or a divergent pencil, place two plano-convex lenses in the tube (Fig. 48). s ! I: 64 PHYSICAL SCIKNCE. To project slidcH, place the two plano-convex lenses in the tube, rest the slide in position, and focus on the screen with t'.ie objective (Fig. 40). 3. Rectilinear Propagation of Light. Repeat Experniieiit 2, page 253, Part T. Experiment 1. By means of a porto lumiere or projection lantern introduce a beam of liuht into a darkened room, and burn some touch- paper in its path. 1. Whut uvidonco liivvo you that light travels in straight lines. 2. Is it th'j light whicii is mado visible to you })y the hurning of the paper ? 4. Images by Means of Small Apertures. Repeat Experiment 4, page 254, Part J. Experiment 2. Remove all the lenses from the porte lumiere, or projection lantern,, cover the front with a sheet of tin-foil, and prick a pin-hole in it. A round image of the sun, or an inverted image of the lantern radiant appears on the screen. Make several pin- holes near the first. Observe the number of the images increasing and overlapping as the pin lioles are made. The more the tin-foil is removed by prickiujij holes in it, the more the images overlap iMid become confused. Remove the tin-foil altogether. The light on the screen m.ay be regarded as the overlapping of an infinite number of images of the radiant. Why is it that a single image is produced only hy a very small aportme ( NAT« RT. AND PROPAGATION OF LIGHT. 65 5. Shadows. Repeat Experiments 6 and 7, page 256, Part I. Experiment 3. - Place a blackened ball three or four inches in diameter at various positions in tlie path of the light between a porte lumiere or lantern and a screen, when the light is (a) divergent, (b) parallel, (c) convergent. Make diagrams to show (a) the characters of the umbral and penunibi-al cones, (h) the distri])uti<)n of light and sliade on the screen, for the different positions. (I ' CHAPTER VII. PHOTOMETRY. 1. Illuminating Power. Since liglit is a form of energy it is a measurable quantity. It is a matter of common observation tliat tlie quantity of lij^lit given out by one luminous body may differ widely from that given out b}^ another. A candle, for example, gives out less light than a coal-oil lamp, and a coal-oil lamp much less than an electric arc lamp. The illuminating power of a source of light is usually measured by a unit quantity, which is the light given out by a candle of a certain weight burning at a certain rate. The illuminating power is then measured in candle-powers. 2- Intensity of Illumination. The illuminating power of a source of light must not be confounded with the intensity of the illumination which it produces. A candle and a coal-oil lamp, although differing in illuminating power, or the quantity of light given out by them, may illuminate the same surface to the same extent, if their distances from the surface be different. The intensity of illumination on a given surface is the quantity of light received on a unit surface. This is mnnifestly dependi it on : — 1. The illuminating power of the source of light, the intensity of illumination bei -j directly .proportional to illuminating power. 66 PHOTOMETRY. 67 2. The distance of the surfjice from tlie source of lij-ht. Since li screen (tii wliicli the candle shadow falls is illuininatcd by tin; lamp only, aiul the part of the surface on wliich the lamp shadow falls is illuminated by the candle only, and the shadows are of ecpial dt'i)th ; hence the intensity of illumination produced l)y the candle when at a distance D^ equals the intensity of the illumination pioduced by the lamp at a distance D.,. If Ij and lo denote the illuminatin*,' powers of the candle and the lamp respectively, I^ and I., will be proportional to the intensities of the illuminations produced by the candle and by the himp respectively at a unit distance. When T^ is the intensity of illumination produced 1)y the candle at a unit distance, I _^;, .— the intensity of illumination at a distance of D^ ; ^ (l.aw of Inverse S(juares), and when I^ is the intensity of illumination produced ])y th(; lamp at a unit distance, lo distance I).,. But tlie intensity of the illumination produced l)y candle at the distance D, = the inl(Misity of illumination produced by the lamp j^t a distance D^. That is, h ^ '^ -—- = the intensity of the illumination of the lamp at a or. i>i Il = ? If the candle is a standard candle, the illuminating power of the Ipmp ■^' 11 = r. can(lle-i)owei". ■iliPlllMBil ■! •;:;! I'' ■ r, 1 1 70 PHYSICAL SCIKNCE. 5. Bunsen's Grease-Spot Photometer. It will bo (jl).sefV(Ml that il' a oreaso-spot ia mad*; on a slieet of wliite paper, and a ll) 100 cm., (c) 120 cm. fiom the sciven, and in each case adjust the sliding i)iece caiiyin_t( tht; sini,'!*^ candle to cause the grease-spot to disapjxar. What is the distance of tho cantllc llumc from the screen in each case 1 i-i ; i ■! :' s! ^ ii QUESTIONS. 1. A candle is placed at a distance of 2 feot from a screen, and then removed to a distance of 3 feet. Compare tl .e intensities of illumination of the screen in the two cases. 2. A candle is placed at a distance of 10 inches from a screen and a lamp of 10 candle-power is placed on tlie other side of the screen at a distance of 10 feet from it. Compare the intensities of illumination on the two sides of the screen. 3. In a Rumford's photometer, it is found that the shadows are of equal depth when one of the lights is at a distance of 110 cm. from the screen, and the other at a distance of 200 cm. from it. Compare the illuminating powers of the lights. 4. How can you make use of a Bunsen photometer to prove tho law of inverse sipiares ? 5. In measuring the illunnnating powers of an incandescent lamp with a Bunsen photometer, it is found that the distance from the disc to a standard candle is 25 centimetres, and the distance from the disc to the lamp 100 cm. What is the candle-power of the lamp 'i G. A standard candle and a gas-tlame of 4 candle-power are placed 6 feet npart. Where would a I'nnsen disc have to he placed between them to cause the grease-spot t«» disappear? chap'ii^:r viit. REFLECTIOX OF LIGHT. 1 Laws of Reflection. Repeat tlie expei-iineiits described in Part I. wliicli lead lip to tlio deteniiiiiatioii ot* tlie laws ol' reliection. See paoes 2()0 -262, Part I. Experiment 1. Arrange api)afatiis as shown in Fig. HG. The nurror is mounted so that it can rotate on an axis. The protractor is attaciied to the mirror, and st.ands at right angles to its plane, the line drawn from tlie axis of the mirror to the zero of the protractor being a normal to the mirror, Pli ice tl le mirror so that V( ry small beam of liglit from a {)orte lumiere or lantern will 1)6 close to the protractor, parallel to if.s plane, and fall upon tlie mirror at its axis. I *urn touch 1 paper m tn P'-^l th ith of tl'.e l)eam of light, and by | | turning the mirror on its axis B'lo. 56. make it take different positions. T»ead on the graduated arc of the protractor the angles which the incident and the Lcilected ])eams make with the normal for each position of the mirror. 1. Are these .'nglcs altvays e(|iial as the mirror is rotated ? The incident boam was matli' parallel to the j)l;ine of the pro- tractor. Is tJie retiected beam also in the same plane/ 9 (1 ii) 18r- w PHYSICAL SCIENCE. \i i j: it i . ,j : I i ! 2. Geometrical Construction to Find the Image of a Point Formed by a Plane Mirror- We have (leterinhied experinientally (Experiment 5, pa<5fe 2()4, Part I.), tliat the image of a point formed by a plane mirror is behind the mirror at a distance equal to that of the point from the mirror, and on the perpei^dicular let fall from this point on the mirror. Tliis proposition follows directly from the laws of refieetioii of light. The rays of liolit from any luminous point A in front of a mirror MN (Fig. 57) proceed from A in all direc- tions, and any ray AB incident upon the mirror is reflected by it in the direction BE, the angle of incidence ABD being equal to the angle of reflection DBE ; and, to an observer whose eye is in the line BE, the light will appear to come from a point behind the mirror in the line EB produced. If a perpendicular AC is drawni to the mirror and produced to meet EB produced in Aj, the triangle ABC will eipial the triangle A,BC, because tlie side CB is common to the two triangles, and the angle ACB=()0°^A,CIi, also the angle ABC = 90° - ABO = 90" -DBE = EBN = AiBC, therefore the triangles are ether. W'liat is the relative [)ositi(m of the Hrst incident ray and the last retlected one ? 8. Find, by construction, the number of images formed of a luminous point by two plane mirrors inclined to each other at an angle of 40^ («) when the i)oint is on the bisector of the. angle {b) when it is to one side of the bisector. 0. A person is equidistant from two plane njirrors which meet in the corner of a S(iu:»re room. In what way dctes the image of himself which he sees when looking toward the corner of the room differ from the image which he sees when looking toward one side of the room ? 10. A ray of light is incident on one mirror in a directiim parallel to a second, and after reflection at the second retraces its own course. What was the angle between the mirrors? If the ray after reflection from the second h!>d been parallel to the first, what would have l)een the anyle between the mirrors ? Ill— Concave and Convex Spherical Mirrors. 7. To Determine How a Concave Mirror Disposes of Incident Light. Experiment 1- Cause a beam of light from a porte lumiero or lantern to be incident perpendicularly on a concave mirror, and burn some touch paper in front of the mirror. REFLECTION OF MCHT. 83 Fio. 61. 1. TTow 7')). Hut hefore pro- ceed in o- to consider tins (|Uestion it will be necessary t(j explain some of tlie terms applied to concave and con- \ex min'ors. A spiierical mirror ^IN (Fig. Gl) is a very small segment of a spherical surface. It is described as COncave or convex, according as the reflection takes place from the internal or the external surface. The centre of curvature C, is the centre of the sphere of wliich thc^ mirror is the segment. Tlie centre of figure A, is the centre of the mirror itself. An axis is any line passing through the centre of curv^ature and incident upon the nn'nor. The principal axis CA, is a line passing tiu'ough the centre of curvature, and the centre of figure. Other axes are called secondary. The radius of curvature is any line passing from the centre of curvature to the mirror. To explain the phenomenon ol)servearallel ^vith H and the principal axis, are reflected in the same way and brought practi- cally U) the same point F. This 2>oint F is called the principal focus of the mirivji*, and the distance AF is called the principal focal distance. 8 Position of Principal Focus An incid;!nt i-ay HB, pai'allel witli the principal axis, is reflected and j^asses through the focus F (Fig. 62). Fia. 62. The angle FBC = the angle HBC = the angle KCB ; tlieirfore, FB = FC. When AH is very small, FB is approximately equal to FA ; therefore AF=FC = J AC, approximately. Hence The principal focal distance for rays incident oh a small portion of the surface of a spherical mirror surrounding the centre of figure equals half the radius of curvature of the mirror. RKFLKCTION OF LIGHT. 85 9. To Find Experimentally the Principal Focus, and Hence the Centre of Curvature of a Concave Mirror. Experiment 2. Mount the mirror on a slidini,' piece of an optical licncli (Fi<^. 03), and causo a small heam of light from a lantern or S I'O I'S 2'0 z's I'O 3i -i'O Hb SO Fio. 63. porte luniiere to be incident peii)endicularly ujion the mirror; attach a vertical wire to another sliding piece placed in front of the mirror, biii-n touch })apor in the path of the light, and move the wire up to the point where the rays are brought to a focus. Observe the distance on the scale between the wire and the centre of figuie of the mirror. 1. What is the principal focal distance of the mirror i 2. What, therefore, is the radius of curvature of the mirror? Make a record of these numbers. They will be reipiired in some of the experiments which follow. 10. To Locate Experimentally the Position of the Focus for Light Diverging from a Centre and Incident upon a Concave Mirror. Experiment 3- Arrange apparatus as in the last* experiment Place in the path C)f the beam of light near the tube of the lantern or [)orte lumieie a lens, the focal distance of which is about 30 or ^, IMAGE EVALUATION TEST TARGET (MT-3) ^O /^A^ ^o 1.0 1.1 U&t2A |Z5 |50 "^ ■■■ ■^ ^ 12.2 1.8 1:25 1 1.4 1.6 ' ^ 6" ► "9 Vi /. Photographic Sciences Corporation 33 WEST MAIN STREET WEBSTER, N.Y. I4SS0 (716) B73-4S03 ,^ <- **>^ ■4^^ ^\$' ¥ k 86 PHYSICAL SCIENCE. 40 cm. (Fig. 64), and attach the mirror to another sliding piece placed a distance beyond the focus of the lens. The light which is incident on the mirror will be divergent. Wiiiiilji: LI I I '. U I I 1 1 - 1 1 1 1 1 1 Z5 ■3'd"'3V"yo"'V5- Fig. 64. Burn touch-paper, and gradually move the mirror up toward the focus of the lens. Mark the foci with wires, as in Experiment 2. 1. Where is the focus of the reflected rays when the light diverges from (1) ? point beyond tlie centre of curvature of the uiirror, (2) the centre of curvature, (3) a point between the centre of curvature r.iid the principal focus, (4) the principal focus, (5) a point between the principal focus and the mirror 1 Bring the mirror up between the lens and its focus — that is, let convergent light fall upon it. What is the course of the light after reflection 1 11. Conjugate Foci. Can the point from which light diverges and the focus to which it is brought by reflection be interchanged ? Try. Two points 30 related that the light diverging from either is brought by reflection from a mirror to a focus at the other, are called the conjugate foci of the mirror. r REFLECTION OF LIGHT. 87 Repeat Experiment 3 above and sliow that if n and v are respectively the distances AP and AQ (Fig. G5) of the con- Fio. 65. jugate foci from the centre of figure^ and r is the radius of curvature of the mirror 112 , , 4- - = - approxnimtely. n V 12- To Determine How a Convex Mirror Disposes of Incident LigVt. Experiment 4. Repeat Experiments 2 and 3 above, using a convex mirror instead of a concave one. 1. What changes in the direction of the ruys t.iko place hy reflec- tion when a convex mirror is ))lHced in the })!ith of (1) a heaiu of light, (2) in a divergent pencil, (3) in a convergent pencil. 'This proposition may be demonstrated geometrically as follows .— Since BC bisects the angle PBQ, PB _ PC . But when AB is very small PB - ['A and C^B == l^A approximately. • Hence, If .. ''-^I. I 'i m ill or h 1 1 u V r 88 PHYSICAL SCIENCE. IV.— Images Formed by Concave and Convex Mirrors. 13. To Determine Experimentally the Character of the Images Formed by a Concave Mirror. Experiment 1 Support the concave mirror at one end of the optical bench and place a lighted candle on a sliding piece at a distance Fig. 66. greater than the centre of curvature from the mirror. Support on another sliding piece a small paper or ground glass sen en, placed between the candle and the mirror (Fig. 66). Slide the screen backward or forward until a sharply defined image of the candle is formed on it. 1. Is the image real or virtual ? How do you know ? 2. Is it larger or smaller than the candle ? 3. Is the image erect or inverted ? - 4. At what point with respect to the centre of curvature and the principal focus is the image found ? • Move tlie candle gradually toward the mirror, adjusting the screen to receive the image. . , , . , 1. What change takes place in the position and the size of the image ? 2. Where is the image when the candle is at the centre of curvature ? Explain. REFLECTION OF LIGHT. 89 3. Where is the image wlien the caiullc is between the centre of curvature and the principal focus ? What are its characteristics ? 4. Where is the image when the candle is at the principal focus ? Explain. 5. Where is the image when the candle is between the principal focus and the mirror ? To answer this question look in the mirror. What are the characteristics of the image ? The above experiments sliow that in concave mirrors : — (1) The image of an object placed beyond the centre of curvature is Teal, inverted, smaller than the object, and placed between the centre of curvature and the principal focus. (2) The image of an object placed between the centre of curvature and the principal focus is real, inverted, larger than the object, and placed beyond the centre of curvature. (3) The image of an object placed between the principal focus and the mirror is virtual, erect, larger than the object, and placed back of the mirror. (4) The image of a luminous point placed at the centre of curvature of the mirror is coincident with the point, because the rays of light from the object return to it after reflection. (5) No image of a luminous point placed at the focus is formed because the rays of light from it after reflection become parallel with the principal axis, and consequently are not brought again to a focus and an image formed. 1. How can number (4) above ]>e used to determine experi- mentally the centre of curvature of a concave mirror ? 2. Does the formula r 1 + 1 u V which gives the relation of the distances of a luminous point and its image from the mirror, hold approximately for the candle and its image ? To answer this question repeat Experiment 1, placing the candle beyond the centre of curvature, and ivioving m 90 PHYSICAL SCIENCE. it by stage.«i towardw tlie mirror. Adjust the screen to receive tlie iina<(o, and measure the distances u of tlie candle and v of tlie imaj^e from the mirror for each position of the candle. Tabulate the results as follows : — Value of 1 1 Value of u « V i+l=^ r tt « r Compare the results recorded in the last column with the value of r determined in Experiment 2 page £ a 11 be the 15. Drawing of Images I ormed by Mirrors. In loc{itin<^ by a ^^coinotrical construct ion (be points wbich determine tbe form and tbe position of an image, tlie following principles sbould be observed : — 1. The image of a luminous point is located where any two rays after reflection intersect. 2. The rays of which the direction after reflection can usually most easily be determined Jire : {a) a ray parallel with the principal axis, and {h) a ray passing in the direction of the centre of curvature. The first is reflected through the principal focus, and the second returns along the same line. To locate the image of my luminous point, therefore, draw from the point a line parallel to the principal axis of the mirror, and from the point wdiere this line meets the mirror draw a line through the principal focus. The image of the point will be in this line. Again, draw from the luminous point a line througli the centre of curvature and produce it to meet the mirror. Since the light is reflected back along this line, the image will be in it also. Hence the image will be located at the point where these two lines intersect Fio. 67. Fig. 67 shows the position and the character of the image HiKj of an object HK placed beyond the centre of %\ i^ SSBBmOm ! 92 PHYSICAL SCIENCE. cnrvaturo oF a concave mirror and Fij^^ G8 sliows the position and tlio character of the iniai^c of tlie ohject phiced before a convex mirror. Fig. 68. Make drawings showing the position and the character of the image of an object placed (1) between the centre of curvature and the [)rincipal focus, (2) between the principal focus and the mirror, (3) at the centre of curvature, (4) at the principal focus of a concave mirror. 16- Caustics— Spherical Aberration. Experiment 3. Take a strip of bright polished metal and bend it into senii-eircular form. Stand it on a siieet of white paper and place a lighted eandle in front of its concave .surface as shown in Fig. 69. Make a sketch on the paper showing the way in which the light is focused. Experiment 4. Project the image of a lighted cand)? on a screen with a concave spherical mirror. Observe the brightness and the Now cover the outer edge of the sharpness of the image. REFLKCTION OF LKSIIT. 93 mirror witli black papor, leaving only a small roflocting surface near its centre, ami again project the image of the candle on the screen. Fio. (19. How dots the ini;igo differ from tho f(»rnior one in (n) brightness, (b) sharpness of duHnition ? How do you account for the ditFerence ? The ef1[bcts noted in tho preceding experiments are due to the fact tliat all rays falling on tho surface of a larj^e concave spherical reflector do not after reflection 'cross the principal axis at the same point, rays incident near the margin of the mirror crossing nearer the mirror than those which ai*e incident upon it nearer its centre. The Fio. 70. Intersections of the reflected ray\s with one another form a curve known as the caustic. Fig. 70 shows the form I 94 PHYSICAL SCIENCE. of ctiustic produced by luyH parallel to the principal axis. Allow Huiilight to fall on the side of a l)»Hin nearly filled with milk, ol)Horve the cauutic on the Hurfaee. The non-coincidence of foci i)rodnced hy rays reflected from diflerent sections of the surface of a mirror cause an indistinctness in the iumjijes formed by it This is due to what is called the spherical aberration of the njirror. It is corrected by making the aperture of the mirror very small, not more than 10°, or by decreasing the curvature of the mirror from the centre outwards as is done in the parabolic reflectors in common use for head-lights, search-lights, etc. QUESTIONS.' 1. Determine by drawing accurately the paths of four rays, two proceeding from each end of an object 2 inches high, placed symmetrically on the axis of a concave mirror of 4 inches focal length at inches from it, the height and the position of the image. 2. The radius of curvature of a concave spherical mirror is 20 cm. If the rays diverge fr fl ^1 m i ■ri: ;f'ii ■Fil 102 PHYSICAL SCIENCE. II.— Total Reflection. Experiment 1. Arrange apparatus as shown in Fig. 75. The movable strip is placed against the end of the tank used in Experiment 1, Fig. 75. page 96. By means of two mirrors cause a thin beam of light to enter a slit placed at the bottom of the tank and to pass through the water to the centre of the circle. 1. What is the course of the light after it reaches the surface of the water ? 2. What is the measure of the angle which the incident beam makes with the normal ? 3. The light is refracted in passing from the denser to the rarer medimn ; which is the greater, the angle of incidence or the angle of refraction ? Make the angle between the incident beam and the normal greater by moving the slit upward and adjusting the mirrors. rkfra(;tiox of li(;iit. 103 of bo of III Br le Observe that the refracted beam approaches nearer and nearer the surface of the water, and finally passes out ;doii<4 the surface, and then into the water. 1. What angle does the incident beam nwiko with tho normal when this takes place I When the angle of incidence is made i,'reater than this an<,de, the light does not leave the water, but is reflected from its upper surface- as from a mirror. 7. Explanation of Phenomena of Total Reflection. To exphiiii the plienoineiia, consider Fi^. 70. Siuce the angle of incidence is gi'cater than the angle of refraction when a ray passes from a rarer to a denser medium, the refracted rav OH will still make an angle HOB, which is less than a rioht ano-le, with the normal, and will then be within the denser mediur i when the angle of incidence is 90\ that is, when the incident Fiq. 76. ray just grazes the surface sepai'ating the two media. Now it is evident that if the process is reversed and the light is sent back from the denser to the rarer medium along the line HO, the refracted beam will just graze tin; surface separating the media, and that, if the angle of incidence is less than the angle HOB, it will pass up into the rarer medium according to the laws o\' I'efractioii. If the an ill e of incidence 1M)B becomes oi-cater than H015 the incident ray on reaching tin.' point () ])asses into the denser medium again, or is reflected in the direction OQ, from the surface separating the media. I 1 I ?^emiBsammaa 104 PHYSICAL SCIENCE. 1- The limiting angle of incidence, HOB, which allows a ray travelling in a denser medium just to escape into a rarer one, is called the critical angle. The reflection of light from the surface of separation of two media wlien the incident ray is in the denser medium and the angle of incidence is greater than the critical angle, is called total reflection. From water to air the critical angle is 48° 35'. 8- To Construct the Critical Angle- Let CD (Fig. 77) be the surface separating the media, say air and water. With O as a centre and with radii in the ratio 4:3 de- scribe two conce itric circles. The ray issuing from the water must be in OD. From S, the point of intersec- tion of 01) with the smaller circle, draw the line SE parallel with the normal AB. Join E and O and produce the line EO to H. Then HO will be the incident ray and the angle HOB will be the critical angle. (Art. 6, page 100). Fig. 77. REFRACTION OF LIGHT. QUESTIONS 105 1. Construct tlic critical angle for : (1) crown glass, (2) diamond, (3) carbon disulpliide. 2. If a beam of light is passed into a right-angled glass prism, ABC (Fig. 78), in the direction OH, it passes out in the direction HI at right angles to OH, and tlie image (►f any luminous object placed at O appears at Oi. Ex- plain. If you have a prism, place it in the path of a beam of light from a lantern and observe the change in the direction of the beam. Fio. 78. 3. If a thick rectangular piece of glass (a paper weight answers well) is placed on a printed page, the print can be read when the eye is directly above it, but if the position of the eye is gradually changed, and the page is viewed more and more obli(|uely, a point is reached wlien the jjrint suddenly becomes invisible. Explain. 4. If an empty test-tube is thrust into water and placed in an inclined position, the inu)iersed part appears, when viewed from above, as if tilled with mercury. If the tube is now filled with water the brilliant re- flection disappears. Explain the phenomena. 5. If you hold a glass of water with a spoon in i^ above the level of the eye and look upward at the under surface of the water, you are unable to se(i the ir.ivt of the spoon above water, and the surface of the water appears burnished, like silver. Explain. 6. If a lighted candle is held oblicjuely before a piece of thick plate glass several images of the caudle (Fig. 79) are i"'io. 7y. 11 'I 1 m 'id • it ■i *v. 106 PHYSICAL SCIENCE. seen. Explain, by ineaii.s of a diagram, how theso images are formed. Fio. 80. 7. If a pencil of strong light is brought to a focus at the point where water is issuing in a thin stream from a vessel (Fig. 80), the* light instead of escaping into the room remains within the stream and illuminates it intensely. Explain. Try the ex[)eriment. The vessel is an ordinary receiver used with retorts. All its outer surface except the circle at which the Fig. 81. light enters is painted black. The water fron) any source of supply filters by the rubber tube, and passes out in a stream through a, nt le m led le 5iy 1^ RRFnACTION OF Lir.TIt. 107 glass tube inst'rto«l in a c<»ik. Tho vessel is ]»lace«l in such a [)()si- tion beforo the lantern or poite luniiere th;it the light is brought to a focus at the point where the water leaves the vessel. 8. Why does an o})server at the bottom of a pond in looking upwards through the water see all objects outside as if they were cr(»wded within a cone, while beyond this cone he sees by reHection objects lying on the bottom of the pond ? (See Fig. 81). III.— Refraction in Media Bounded b> Plane Inclined Surfaces — Prisms. Experiment 1. Slide the condensers into the tube of the lantern or porte lumiere, and over the tube place a cap with u narrow vertical slit. By means of the lantern objective or a single lens, focus the slit oil the screen. Fig. 82. Now support .a glass prism of 60° angle close to the ol^joc- tive lens, between it and the screen, and turii it around until the light is seen to pass through it (Fig. 82). 1. What change in direction in the light takes place in passing into and out of the prism ? ii I* 1 is a i t fib , •("'1 r f i^-'i 108 PHYSICAL SCIENCE. 2. Give a reason for this change in direction ? To answer this question refer to Fig. 83, j,nd read again Art. 5, page 99. ina. 83. 3. Why does the light emerge from this prism, while it is reflected from a side of a right-angled prism, as shown in Fig. 185? Experiment 2. Place a bright object opposite one face of the 60*^ prism and look at it through the prism. How must the eye be placed to see the object i Why ? 9. To find by a geometrical construction the path of a ray of light through a triangular glass prism. Fig. 84 sliows how the path of a ray of light DE may be traced tlirough a prism by the method described in Art. 6, page 100. Fia. 84. E m is the normal to the surface of the lens, and OP is drawn parallel to it from tlie point of intersection of the ray and the circumference of the smaller circle. REFRACTION OP LIOIIT. 109 OE, therefore, repre.sentH tlie directioii of the my tlirougli the j^hiss. Simihirly FIT is foiuul to be the patli of the ray on emertrinjr froni the gljis.s. 1. Draw accuriitely tho path of a ray of liglit, through a 45° prism of glass, wh(»se iiidox «»f rufraction is 8 5, drawing tho ray incidunt on ono face in a direction porpendicuhir to tlio other face. 2. The angles, of a glass [trisni are (K)°, 70°, and 20°, and a ray of light enters the prism normally at the face bounded by tho angles JK)° and 70°. If the refractive index w the (»tli«'r farms «»f h'nses with spherical surfaces are foriiu'd. The point on the principal axis of a convex lens to which rays parallel with the axis eonver^je niter passin<^ thron^h the lens, is called tin; principal focus. Since the rays actually converl i Ml 'Mi ■ 1 ffji •I m ^i 114 PHYSICAL Sf'lF-NCE. It- i I. ■• index oC rofniction of tlii; inatorial coiiipoHi'n<:j tlie lens is known. It' ilie index of I'efniction is f), it will be found to be at the centre of curvature. Fi<;. 94 sliows a Fro. 94. similar construction for a plano-convex lens. In this case if the index of refraction is {?, the focal length will be twice the radius of curvature. 14. To Ascertain How a Convex Lens Disposes of a Pencil of Light. Experiment 2. Repeat Exp. 3, page 85, using a converging lens instead of a concave mirror. 1. Where do the rays focus wlion tlie liglit diverges (1) from a p()int l)eyoiid twice the focal distance, (2) at, twice th;^ focal distance, (li) at less than twice tlie focal distance, (4) at the focus, (5) from a point between the focus and the lens? 2, \\'hat is the course of the li,i,'ht when the lens is placed in the path of convergent light ? 15. Conjugate Foci. Can the point from which light diverges and the focus to which it is brought be interchanged '( Try. Two points so related that the light diverging from either is brought by a lens to a focus at the other, are called the conjugate foci of the lens. UKFUA(TION OF LKWIT. 115 If the position of one of the foei is known tiie position of the other can be (h't«'rnnne(l h\' ji (^comctrienl con- stniction as shown in FliZ- 90, if the refnielive index of the lens is known. Fi<^. 95 shows tluit wlien tlie rays diveri^^e fi'oni a point between tlie princi}>al focus and the lens tht-y are not brought to a focus on tlie opposite side of tlic lens, but are I'endered less divergent, an;:,.A«.£->kW>xv:l. ^A-'«g\ I I)':. h 116 PHYSICAL SCIENCE. optical bench, and cause a beam of light to be incident perpen- dicularly on the lens, the covered face of the lens being turned away from the light. Mount a cardboard screen on another sliding piece, placed on the side of the lens opposite to the source of light. Move the screen backward or forward until the disc of Hglit on the screen is just 4 cm. in diameter. Observe the distance on the scale between the lens and the screen. This will be equal to the principal focal distance of the lens, as will be seen from the following considerations. The rays which were parallel before reaching the lens diverge after passing through the circular opening BC (Fig. 96), and apparently come from a focus F in front of the lens. The focus is thercfoie virtual, and the principal focal length of the lens is AF ; but when BiC, = 2 BO neglecting the thicknuss of the lens, FD = 2FA or FA = AD Fio. 9G. 17. To Ascertain How a. Concave Lens Disposes of Incident Light. Experiment 4- Repeat Experiment 2, page 114, using a concave lens instead of a convex one. What change is produced in the direction of the rays when a concave lens is placed in the path of (1) a beam of light, (2) a divergent pencil, (3) a convergent pencil ? ■.-awK MnuXtt^ w REFIIACTION OF LIGHT. 117 a a 18. Summary. The above experiments sliow that when rays from a luminous point on tlie principal axis ot* a lens fall upon it, the transmitted rays (l) converge to another point on the principal axis, or (2) are rendered parallel with the principal axis, or (3) appear to diverge from a point on it. When the rays transmitted actually j)ass through a point the focus is real; when they only appear to diverge from a point the focus is virtual. With the convex lens the focus is real when the source of light is beyond the principal focus, and virtual when it is between the principal focus and the lens. Show how you would, find ]»y a geonietriciil construction tlie princiiJi.i focus of a ccjncavo lens whoso index of refraction is known. v.— Images formed by Convex and Concave Lenses. 19- To Determine Experimentally the Character of Images formed by Convex Lenses. Experiment 1. Support on a sliding piece of an optical l)eiu'h a candle, a Fio. 97. convex lens, and a cardboard screen in the order shown in Fig. 97, their centres being in the same liorizontal line. it' M W' 3 '•* r mP' I r Jf il 118 PHYSICAL SCIENCE. Place the candle at more than twice the focal distance from the lens. Move the screen backward, or forward, until a sharply defined image of the candle is formed on it. 1. Is the image real or virtual ? 2. Is it larger or smaller than the candle ? Is there any relation between the relative sizes of the candle and the image and the relative distances from the lens ? 3. Is the image erect or inverted ? Move the candle gradually toward the lens, adjusting the screen as before. 1. What changes take i)lace in the position and the size of the image? 2. Where is the image when the candle "is at twice the principal focal distance ? Where, when it is at the focus of the lens ? 3. Where is the image when the candle is between the principal focus and the lens ? To answer this question, place the eye on the side of the lens opposite to the candle, and look through the lens at the candle. The above experiments show that with convex lenses : 1. The image of an object placed more than twice the principal focal distance from the lens is real, inverted, and smaller than the object. ' 2. When the object is moved up toward the lens the image becomes larger, being equal in size to the object when it is at twice the focal distance, but remains real and inverted until the object reaches the focus, when the rays are rendered parallel and the image is at an infinite distance. 'I When the object is between the focus and the lens, thQ image is virtual, erect, and enlarged. . w 01 ill. !■■ REFRACTION OF i'.lCJHT. 119 .Does the fornuila^ hold Jipproxinwitely, when u und v aio rospectivoly tlio distancoH of the candlo and its image from a convex lens whoso principal focal length is/ ? To answer tliis (inestion repeat Experiment 1, page 117, takino- earel'nl measurements, ami tabulatino- the results, as in Art. 18, paoe 90. How may the formida - 4- - = - he made use of to H V f determine experimentally the focal length of a convex lens ? » This proposition may be demonstrated geometrically as follows :— The parallel rays BD and CE may be regarded as being approximately refracted as shown in Fig. 98, where I5C - DE. Since the triangles BAG" and BAC are similar BXI' ^ IIA ^ V BC GA u Again, since the triangles B'FC and DFE are similar But DE = BC B'q J HF DE AF ■^1 If M le Therefore Fio. 98. B C _ HF ^ « - / B(; AF 7 Hence, equating the two values of we have B'C or BC V V - / u J 1 + u I V = 1 7 a .1 120 PHYSICAL SCIENCE. 20. To Determine Experimentally the Character of the Ima^e Formed by a Concave Lens. Experiment 2. Look ill- ;i candle through a concave lens. It will b(! found tliafc iha imag^e is always virtual, erect and smaller than the object. 21. Drawing Images Formed by a Lens. The iina<^(3s formed by lenses are located in a geomet- rical coMstruction in tlie same way as the images formed by mirrors, by locating the images of certain points whicli determine the form and the position of the image. The image of a point is located by finding tlie point of intersection after refraction of two rays proceeding from tlie point. The rays of wbicli the direction after refrac- tion are usually most easily determined are (a) a ray parallel^ with the principal axis, which after refraction passes tln'ough the principal focus; and (h) a ray through the optical centre, which passes on through the lens without change in direction. (Art. 9, page 111.) Fig. 99 shows the image formed by a convex lens Fio. 39. nEFRACTION OF LKJHT. 121 when tho o])joct is beyond tlie focns ; and Kij^. 100 allows tlie image formed by a concave lens. Fio. loa Make a similar drawing; to show tho imago formed by a convex lens when the object is placed between the principul focus and the lens. 22. Spherical Aberration by Refraction. It can bo seen by a geoMieti'ical consti'uction tliat tlu^ rays from a luminous point incident on the margin of a convex lens cross after refraction the })rincipal axis nearer the lens than those incident upon it nearer its centre. This non-coincidence of foci causes, as in the case of the sjdierical mirror, a blurrintj^ of the imai^^e. It is corrected by the use of an aimular stop or diaphra(»iiit situated voiticiilly over a VoshdI of water is foniiod <>ii thu l.ittoin of tlu; vcssi'l l>y a convex lens iimnei".se (»l»ji'ct from tlio ct'iitit' of tlic Ifiis is to the distanco of the iniii''o from tlu' cnitii' of flu- K«iih. 12. Tf the disc, ((uestion '.), is \ inch in rojecte,i,'otl!er, and mounted centrally on tlu? axle of an electric motor or whirling machine, exposing any pro})ortional parts of each (Fig. 106j. Select s(!vcn discs representing as nearly as possible the sevfui prismatic colours, and mount tluMU on the spindle of the whirling machine or motor, expos- ing equal portions of the colours. ^^^^ ^^^ What is the colour of the disc when it is rot;ited rapidly in a strong light ? Fio. 106. * Repeat the experiment, using in succession discs of the following colours, exposing equal portions: — (1) Red, green and blue. . (2) Orange and light blue. (3) Green and pur[)le. (4) Yellow and indigo. t i ..,41 130 PHYSICAL SCIENCE. RED The iiKitliod of inixiiiii' eoloui's illustrated in tlio {ibove experiment depends on the l*;ict that when the colour disc is rotsited rapidly, the sensations of colour ex- perienced by the observer persist after the impressions which w^ere their occasion liave ceased, and while new impressions are fallincj upon the retina. This lajj^ging of the colour sensations behind their stinnili produces an effect e/piivalent to the superposinijf of colours U[)on one another, as in the re-composition of white liuht (Experi- ments 3 and 4, page 125). The experiments show tliat white light not only results from a combination of the prismatic colours, but that it is produced by a cond)ination of certain colours selected from tliem. For example, it will be found that any two colours opposite e;ieh otlier in the colour circh; (Fig. 107) gives, when -< mixed, gray, that is, § white of low luminosit3^ Two colours whose mix- ture results in gray aie said to be complemen- tary. Eveiy colour has some complementarj^ in tlie spectral series, except green, whose complementary is purple, a mixture of red and blue. 8. Mixing of Pigments. Experiment 11. Mix chronn^ yellow and ultramarine blue pigments. What is the colour of the mixture'? Tiie experiment evidently Fio. 107. : DISPKUSIO.V OF LIGHT — COLOUR. 131 1 - indicates that a iiiixturo of pigments ami a mixture of spectral colouis iniiy proiluce different results. Experiment 12. To discover the cause of the efF(!ct produced by tlui mixing of the pigments, project a spectrum on the screen as in Ex- periment 1, page 121, and })lace in the patii of the light l)etween the slit and the prism, first, a Hat glass llask or cell containing a solution of copper sulphate, and then a similar cell containing a solution of })ichromate of potash. What parts of the spectrum are absorhed by each solution ? What part remains unabsorbed by either ? It is evident from the experiments that green is a constituent of both the yellow and blue pigments whicli survives the absorption of the other elements anolariti/. When the liody ((s />areH^^j/ j)o.sscs.st's no mmjnetic itropcv- ties, the opposite poles of adjacent molecules tieutrtdize one another (Kig. llO(t); Imt when At is magnetized, the greater nnmher of the molecules are turned into lines, with their N-seeking jxdes turned in, one direction and their S-seeking poles in the opposite direction. Fig. llOo. Fig. 1106. When, therefore, the magnet is broken at any point, one face of the fracture is a N-seeking and the other a S-seeking pole. If the magnetization were equal at all points of the magnet, and the molecules were all arranged in line Mnth their magnetic axes parallel to the axis of the magnet, with like poles all pointing in one direction (Fig. llOh), 134 ! MAGVETISM. 135 freo poles would 1)0 found only at the end surfaces; but this is not the ease, because we have found that complete neutralization takes place only near the centre of tiie , magnet. The intensity of magnetization must, conse- quently, be greatest at the middle of a bar of steel, and less toward its ends. The theory of molecular polarity may liij illustrated by the following experiment: — • Experiment 1. Fill a test-tube nearly full with steel filings (Fig. 11 la); magnetise it by drawing one pole of a strong magnet over ' the tube repeatedly in the same direction. Observe that the filings set themselves end-ways (Fig. 1116). Fig. 111. Without disturbing the arrangement, bring one end of the tube near (1) the N-seeking pole, (2) the S-seeking pole of a suspended magnetic needle. What evidence have you that tlie tube tilled with steel filings acts as a bar magnet ? Disturb the arrangement of the filings by shaking the tube, and again present one end of the ♦^ube to each pole of a maijnetic needle. 1. Does the tube now act as a bar magnet ? How do you know ? The tube filled with steel tiliny mcuis of a wiic stiniip .ind fihro a har <>t' soft iron over it. (I'lg. 1 1^"'). 1. Whut position tlous it tuki* '. W'liy ! "Tl Ki >. n; 2. Wluit hiippons wlion (1) the N-sockiii<^ polo, (2) llio S-scrkinj^ pole of niiotlu'r inagiiet is ])l!ico(I, as shown in the ti/ mft iron, the ait r((('t ions and rejndslouH hi'ticcni it and the miujio'tic mole- cules of tit e soft iron cause these tnohvules to turn around and arratxie themselvs with their S-seck'nuj jtoles turned toward the N-st'vl:in(j pole of the maijnet. The har, lii.e the tulm eotifainiiKj the slrel Jilimjs (Fi(j. Ill), then sh.ous polaritti, its S-scrlitai pole hcintj at the end of the rod nearest the N-seckintj jmle of the uuujuet. if 4' n ii i3 m 140 PHYSICAL SCIENCE. When the iniKincl Is rcniorcd, the mutual attrartums and repulsions inunuj the niolecides of the soft iron cause the poles to turn ayuin in jvrious directions, und thus to neutrali::e one another s action. The rod, therefore, no longer appears a magnet. In the case of steel, which possesses greater molecular rigidity, greater difficult}^ is found in causing the mole- cules to set themselves with one class of poles pointing in one direction ; but when the poles have once set them- selves in this way, they retain their relative positions for a long time. For this reason, the steel remains permanently a magnet, while the soft iron possesses magnetic properties only wliile under the direct iniluence of the inducing magnet. Steel is usually magnetized in one of the following ways: — ^ • 6. Methods of Magnetization. 1. Single Touch. This method consists in rubbing the bar of steel to be magnetized repeatedly in the same direction with one pole of canother magnet Fio. 116, placed as shown in Fig. 116. 2. Double Touch. The biir AB to be magnetized is usually supported on two magnets arranged as shown in Fig. 117, and is Fic. 117. ''' MAGNETISM. 141 stroked first in one direction and tlieti in the otlier by two bar ma<:^nets the opposite poles of wliicli are kept at a constant distance from each other by means of a piece of wood, as sliown in the figure. 3. Separate Touch. The bar to be magnetized is supported on tlie opposite poles of two magnets as in the last case. The inducing magnets are placed as shown in Fig. 118, and are drawn m ni h!I - aiiii A liiiiiiiiiMiiiiiiiiiiiiiiiiiiiiiimiiiiMiii B Sj 11 Fio. 118. away from each other to the two ends of the bar, lifted up. carried back in a wide curve through the air, placed again at the middle, and again drawn away from each other to the two ends. This process is repeated several times. Experiment 2. Magnetize a needle by single touch. Prove t!:afc it is mag- netic by rolling it in iron filings. Heat it red hot, allow it to cool, and agaiii test its magnetic power. 1. What do you observe? 2. Explain the change. 7. Magnetic Field. The space surrounding^ a magnet pervaded by the magnetic forces is called the field of the magnet. At every point in the field the magnetic force has a definite strength, depending, as we have seen, on the distance of the point from the poles. i1 I n h 142 PHYSICAL SCFENCB. 8. Magnetic Lines of Force Experiment 3. Lay a sheet of heavy paper or cardboard on a short bar magnet, and sprinkle iron filings over the paper by sifting them through a piece of nnislin. Gently tap the paper, nnd observe the manner in which the filiiiirs anaiii^e themselves under magnetic induction (Fig. 1 10). Fig. 119. Tbe experiment sliows that maii^ni'tic induction takes place along certain lines. The directions in the field of a magnet along which magnetic induction takes place are called the lines of magnetic induction, or lines of magnetic force. They are connnonly spoken of simply as "lines of force." Since eacli piece of iron takes its particular direction on account of the action of the two poles of the magnet 'upon it, the direction of the curve of the filings at any point represents the direction of the resultant of the forces at that point. The lines of force can represent not only by their posi- tion the direction of the magnetic force, but also by their MAONETIRM. 143 iiuinber its intensity. Jnst as we st)(';ik of nieasnrin*^ tlie intensity of the illuinination ol* a surface hy tlie number of imaginary rays of light falling upon it, so we speak of estimating the sti'ength of a pai't of a magnetic field in terms of the number of imaginary lines of mag- "netic force present in it. l>ut it shouKl be carefully borne in mind that, like the rays of light, the lines of force have no real existence. The actual forces do not act along a set nund^er of lines, but pervade the whole mairnetic held. Experiment 4. * Repeat E.xporiinent 3, placing a suspended magnc^tic needle in different positions over the card on which the iron filings are placed. 1. How does the magnetic needle in its diU'erent ])ositions set itself with regard to the direction of the lines of force? Explain. Experiment 5. Magnetize a needle and suspend it, not by a stirrup, hut by a silk fil)re tied around it in such a position that it will rest horizontally. Now bring the needle within the field of a bar magnet, placing it at various points around, above, and below the magnet. Remembering that the magnetic needle always tends to set itself parallel with the lines of force of the magnet, note the direction of the lines of force at the different points at which the needle is placed (Fig. 120). 9 / It ■W"«!!' J n s n >s n E • J 158 PHYSICAL SCIENCE. ii I !f IE 11. How Does tke Film of Hydrogen on the Copper Plate Cause the Weakening of the Current ? To partially answer this question perform the follow- ing experiment : — Experiment 6. Place three plates in dilute sulphuric acid, two copper plates, Cj and Cg, and a zinc plate, Z (Fig. 125). Connect the Fig. 125. two copper plates with the galvanoscope, using the mercury cups so that the connections can be made and unmade rapidly. Does the galvanoscope indicate a current ? Leaving C^ connected with the galvanoscope, disconnect C^ and connect the zinc plate with a mercury cup. Allow the cell to stand for a few minutes until C^ becomes covered with a film of hydrogen, and the current grows weak. Now dis- connect the zinc plate and at once connect the two copper plates with the galvanoscope as at first. 1. Does the galvanoscope now indicate a current ? ' 2. If so, does it flow in the same direction as the current given byZandCi? 3. Which is of the higher potential, C^ or C.j ? THE ELECTRIC CURRENT. 159 y r. h 4. Does the film of hydrogen on the copper plate, therefore, increase or :>'■ .■ft ji 162 PHYSICAL SCIENCE. Chemical Action. Tlie chemical actions in the cell are somewhat compli- cated, but the following are the leading ones. The sulphuric acid acts upon the potassic bichromate, forming chromic acid. When the circuit is completed, the zinc displaces the hydrogen of the sulphuric acid, forming zinc sulphate, and the hydrogen in the nascent state reduces the chromic acid. Polarization is thus prevented. Current, Etc. The E.M.F. remains constant at about 2 volts for a short time, but soon decreases rapidly. The cell is con- sequently capable of giving a strong current for a few minutes. 3. Grove's Cell. Construction. The construction of Grove's cell is shown in Fig. 128. It consists of a zinc plate immersed in dilute sulphuric uii/re SULPHURIC ACio ■POROUS CUP PLATINUM Nirnic Acio ,, Fio. 128. acid in an outer vessel, and a platinum plate immersed in nitric acid placed in an inner porous cup. I! THE ELECTRIC CURRENT. 163 !i Chemical Action. The zinc displaces the liydrogjen of tlie sulplmric acid, forming zinc sulpliate, and tlie nascent liydrogen reduces the nitric acid, thus preventing polarization. Current, Etc. The E.M.F. of the cell is about 1.9 volts, and remains nearly constant for some time. One of these cells will furnish an energetic continuous current for three or four hours. 4. Bunsen's Cell. Bunsen's cell differs from Grove's cell in substituting a carbon plate for a platinum one. Fig. 129 shows a common form of it. The chemical action is the same as in the Grove cell. The character of the current given by it is also very much the same, the E.M.F. being slightly higher. i/1 DILUTE SULPHURIC ACID ZINC P0H0U5 CUP CMBON SOLUTION OF BICHMMATE Of POTASSIUM Fig. 129. 5. Ledanche Cell. Construction. The construction of the Leclanchd cell is shown in Fig. 130. It consists of a zinc rod immersed in a solution of ammonic chloride in an outer vessel and a carbon plate ■'fivj Mn »■ ':1 164 PHYSICAL SCIENCE. 111 lit surrounded by a mixture of small pieces of carbon and powdered manganese dioxide in an inner porous cup. Chemical Action. The solution of ammonic chloride acts upon the zinc, forming a double chloride of zinc and ammonium, and liberating ammonia and hydrogen. The hydrogen is oxidized by the mangfinese dioxide. As the reduction of the manganese dioxide goes on very slowly, the cell soon becomes polarized, but recovers itself when allowed to stand for a few minutes. The E.M.F. is about 1.4 volts at first. As the zinc does not waste away when the circuit is not complete, it does not require renewing for several months, when used intermittently for a minute or two at a time. It is, consequently, specially adapted for use with electric bells, telephones, etc. CAftBON POttOUS CUP ZINC mancaucse aomc ^MIXCD YIITH CAIfBOU SOLUTION OF MUMOmC CHtOBIDf F^G. 130. 6, Dry CeUs. Dry cells are now commonly used in open circuit work for electric bells, telephones, gas-engine ignition, i THK ELECTKIC CURRKNT. 05 it 't etc. There is a ^reat variety of forms of these cells, h»ifc most of them are modifications of tlie Leclaiichd cell ill which a paste is substituted for the tluid. A paste with the following constituents makes a very effective cell : — Charcoal - - - 3 pprts by weight. Graphite - ... 1 part Manganese dioxide - - 3 parts (( <« (( (( Slaked lirae - - - - 1 part Arsenic trioxide - - - 1 Mixture of glucose and starch 1 << (( (( (( (( (( (( (( These should be intimately mixed when dry, and then worked into a smooth paste, with equal parts of a saturated solution of anniionic chloride, and a similar solution of common salt, to which one-tenth by volume of a saturated solution of corrosive sublimate and one- tenth by volume of hydrochloric acid have been added. The carbon plate is supported at the centre of a zinc vessel, which acts as the positive plate, and the unoccupied space is packed with the paste. The vessel is then sealed with a non-conducting cement, leaving a small aperture for the escape of gas. » 7.— Gravity Cell. Construction. Fig. 131 shows a common form of the cell. A copper plate is placed, at the bottom of a vessel, and a zinc plate suspended near the top. Crystals of copper sulphate are placed at the bottom of the vessel around the copper plate, and the vessel is nearly filled with water. The liquid at the lower part of the vessel is, therefore, a saturated solution of copper sulphate. m ifil M m r\ ■ IL 166 PHYSICAL HriKNCE. 1.; Ohemical Action. Wlien a little dilnto sulphuric acid is added, tlio zinc displaces tho hydroj^on of the acid, fori niiif^ zinc sulphate; the displaced hydrogen in turn displaces the copper of tlio copper sulphate, forming more sulpliuric acid, and copper instead of the hydrogen is deposited on the copper plate. The zinc displaces the hydrogen of the sulphuric acid formed, and so on ; hence the zinc wastes away, copper is deposited on the copper plate and zinc sulphate dissolves in the water. The zinc sulphate solution, being much less dense than the copper sulphate solution floats on the top of it, leaving a sharp line of demarkation between the solutions when the cell is undisturbed. IINC "^Zlfte SVLPHATt SOIUTION y^SoiUTIOMOFCOPPCIt SOLPtUTt CHYSTALSOF COPKR SUIPMATI FiO. 131. Current, Etc. Since nothing but copper is deposited on the copper plate, the cell is never polarized ; consequently it is capable of giving a continuous current for an indefinite period, if the materials are renewed at regular intervals. For this reason it is adapted for use with telegraph instruments, or for other closed circuit work. The E.M.F. is about 1.07 volts. THK KLRCTHIC CUUKKNT. 167 nT£ )er is ite Lis. )h 8. Danleirs Cell. Fiir. 132 showH the construction of tlio Daiiicll ct^ll. It coiiHists of a copper plate, which is friMjuently the outer vessel, immersed in a concentrated solution of copper sulphate, and a zinc plate immersed in dilute sulphuric acid in an imier porous vessel. Chvstals ercoppta suiPHATt -^oiuTioH or eopput sulpn/^tc OiLurc suiPHumcMD Porous ct//> Zinc COPPfR Fio. 132. Chemical Action. The zinc displaces the hydrogen forming zinc sulphate, and the displaced hydrogen in turn disphices the copper from the copper sulphate, forming sulphuric acid ; and the displaced copper, instead of the hydrogen, is deposited on the copper plate. Hence polarization is altogether done away with. Current, Etc. Since the cell is not subject to polarization, it, like the Gravity cell, may be used for continuous closed circuit work. Its E.M.F. is the same as that of the Gravity cell. 1. How would the action of a Daiiiell's cell be modified if the solution of copper suli)hate were replaced by dilute sulphuric acid ? 2. The platinum plate of a Grove's cell is connected with the copper plate of a Daniell's cell. Would there be 'a current if the zinc plates were also connected, and if so, in which direction would it flow ? What reasons have you for your answer ? ' »■ ) ^! • .1l i I II ■iMBiiiiiiiiiviiiiini 168 PHYSICAL SCIENCE. 14. Uses of Cells. DynamoH and storage cells have altogether displaced primary cells whenever a pcjwerful current is required for commercial purposes. Some form of the Gravity or the Daniell cell is gener- ally employeh.serve the colour of the gases liberated. Test each with a riling splinter. 2: What is the anion, and what the cation ? 3. Electrolysis of Salts. Experiment 2. Uepeat Experiment 1, attaching platinum strips, instead of carbon pencils, to the ends of the wires, and filling the U-tube with a solution of copper sulphate. Collect the gas which is liberated at one of the electrodes by the displacement of water. 1. What is deposited on the cathode ? 2. What gas is liberated at the anode ? To answer this question insert a 8[)1 inter, at the end of which is a glowing ember, into the test-tube when tilled with the gas. Experiment 3. Repeat Experiment 2, allow the current to pass until a deposit is fornuid on tlie cathode and then reverse the direction of the current by changing the wires at the poles of the cell. 1. Upon which [)ole is the deposit now formed? 2. Does the deposit remain on the plate which was at first the cathode ? 3. Is gas liberated at either electrode while the change in the deposit is taking place ? If not, explain. Experiment 4. Weigh two strips of coppei", attacli each to the pole of a voltaic cell, aiul, without allowing them to touch, dip them into a solution of copper sulphate. Is any change observed to take place at either pl.itc ? If so, describe it. I THE CHEMICAL EFFECTS OP THE ELECTRIC CURRENT. 171 When tlie strips have remained a few minutos in (lie solution, reniov^e them, and, roiuemberin<:{ wliicli was the anode and which the catliode, weigh tlu ni again. 1. What chiinge huH taken place in the weight of (1) the anode, (2) the cathode 'i 2. How do you account for these changes? Experiment 5. Set up apparatus as for the electrolysis of wati-r (Fig. 246, page 305, Part I.) Fill the vessel and jest-tubes witli a strong solution of connnon salt (NaCl), to which has been added suthcient red litmus solution to colour it distinctly. 1. What gases fill the tubes ? 2. Account for the change in colour around one of the electrodes. Experiment 6. Repeat the last experiment, using a soli tion of sodium sulphate instead of sod '.mi chloride, and making the litmus purple in colour by exacu neutralization. 1. What gases are now liberated ? 2. Account for the ch.ange in colour around eacli electrode. 4. Summary. The prccedintr experiments show : 1. That electrolytes are — (a) Dilute acids. (h) Solutions of metallic salts. Certain fused salts are also capable of electi'ical decomposition. 2. That when electi-olysis takes place the substances resultin<^ from the decomposition of tlu"; electrolyte are ^'ound at the electrodes. Hydrogen and the metals are cations, vldle oxygen, chlorine, iodine, etc., and electro-negative radicals are anions. m ■m ' »ii $1 i,\ ' jS*| 172 PHYSICAL SCIENCE. : i"l 8. That in most cases of electrical decomposition, secondary actions, depending on the chemical affinities of the elements involved, take, place. For example : — (a) In Experiment 2, the radical sulphion (SO^) combines with the hydrogen of the water, forming sulphuric acid (H^SO^) and liberating oxygen. (h) In Experiment 4, the radical sulphion (SO4) combines with the copper of the anode, forming more of the copper sulphate (CuSOJ. (c) In Experiment 5, the sodium re-acts upon the water forming sodium hydroxide and liberating hydrogen. (d) Even in the case of the electrolysis of water, it is probable that the radical sulphion (SO4) of the sulphuric acid combinies with the hydrogen of the water, thus liberating the oxygen and foiming more of the acid. The quantity of the acid, therefore, remains cons- tant, and the water only is decomposed. 1. Wliiit are the chemical changes which take place in Experi- ment 6 ? 2. Write equations representing the chemical actions which take place in Experiments 3-5. 5. Theory of Electrolysis. The following is the theory at present most commonly accepted as explaining the phenomena of electrolysis : — h I -, ! THE CHEMICAL EPPECtS OP THE ELKCTRtC CURRENT. l73 1. A)i electrolytic, salt or add when in Hobitinn, or frhcn, melted, becomes more or less completely dissociated^ the respective 2>arts into which its m,oleci: one metal witli a thin layer of another. The process is known as electroplating. The metallic object to be plated is connected by a conductor with the negative pole of a battery or dynamo, and immersed in a bath containing a solution of a salt of the metal with which it is to be plated. A plate of this metal is also immersed in the bath and is connected by a conductor with the positive pole of the battery or dynamo; that is, the object to be plated is made the cathode, the metal with which it is to be plated is made the anode, and the electrolyte is a salt of this metal. When the current passes through the solution from the plate to the object, the salt is decomposed and the me*:al is deposited on the object ; but as the radical of the salt combines with the metal forming the anode, the strength of the solution remains constant. The metal is thus transferred from tl plate object. For copper plating, the bath is usually a solution of copper sulphate ; for gold and silver plating, a solution of cyanides of these metals is commonly used. THR CHEMICAL EFFECTS OP THE ELECTRIC CURRENT. 175 ti Fig. i;^4 sliows a bath and the connections for silver plating. ml Fig. 134. > M f 2.. Electrotyping. Books are now usually printed from electrotype plates instead of from type. These are made as follows : — An impression of the type is made in a wax mould. This is covered with powdered plumbago to provide a conducting service upon which the metal can be deposited. The mould is flowed with a solution of copper sulphate, and iron filings are sprinkled over it. The iron displaces copper from the sulphate, and the plumbago surface is thus covered with a thin film of copper. The iron filings are washed off", and the mould immersed in a bath of nearly concentrated copper sulphate solution slightly acidulated with sulphuric acid. The copper surl'aee is then connected by a conductor with the negative polo of a battery or dynanu), and a copper ])latr wliich is connected with the positive pole is immersed in the bath. ill!'' li ' 1 il 176 PHYSICAL SCIENCE. When tlie current pjiHscs, the copper sulphate is decomposed and a layiT of copper is deposited uni- formly on the mould, while the copper anode combines with the sulphion (SO^) groups to form more of the copper sulphate. When the layer of copper has become sufficiently thick it is removed from the bath, backed with melted type-metal and mounted on a wooden block. The face is an exact reproduction of the type or engraving. 3.— Reduction of Ores.— Electricity applied in Manufactures. Electrical decomposition is sometimes resorted to for reducing metals from their ores. A soluble or fusible salt is formed by the action of chemical re-agents, and the metal is deposited from this by electrolysis. For example, copper is now produced on a large scale by electro-deposition. Aluminium is also reduced in large quantities from a fused mixture of electrolytes.* A current of electricity is now frequently employed for preparing chemical products for commercial purposes. Caustic soda, chlorate of potassium, and bleaching liquors are manufactured extensively by electrolytic processes. 4. Secondary or Storage Cells. 6. Polarization of Electrodes. Experiment 1. Connect by means of wires two platinum strips with the poles of two Bichromate or Bunsen cells, placing a galvanoscope in the circuit. Keep the strips from touching, and immerse them in water acidulated with sulphuric acid. Observe the direction of the deflection of the needle of the } THE CHEMICAL EFFECTS OP THE ELECTRIC CURRENT. 177 galvanoscopp, and as soon as tlie gases are given oflF freely from the sti'ips, disconnect the wires from the pf)h\s of the battery, and at once join them together, as shown in Fig. 135. Fio. 135. 1. What evidence have you that a current of electricity flows through the wires when they are disconnected from the battery and joined ? • 2. Does the current flow in the same direction as the battery current, or in a direction t>pposite to it 'i 3. How long does the current continue to flow ? When a film of hydrogen surrounds one platinum strip in the dilute sulphuric acid and a film of oxygen the other, there is a difference in potential between the strips, which causes a current to flow from one to the other when they are joined by a conductor. The electrodes are then said to be polarized. As the hydrogen is of higher potential than the oxygen, the direction of the current in the conductor joining the electrodes will be opposite to the direction of the current which deposited the oxygen and hydrogen. Hence, in order to overcome this diflference in potential and to decompose water, the E.M.F. of the battery used ♦•, > i 4 -' i m ■ *i^ fl 178 PHYSICAL SCIENCE. I must be j^rcalor tliJiii tlie opposite E.M.F. caused by tins pottnitijil-diH'erence between the electrodes. This is about L47 volts. Experiment 2. Repeat the last experimc.it, using two lead strips instead of platinum ones. The}' should be an inch or more in width. Allow the current to pass from one strip to the other through the dilute acid for a few minutes. Observe the direction of the deflection of the needle of the galvanoscope and an}' changes which take place in the appearance of the surface of either strip. Discorniect the wires from the poles of the battery, and join their ends as in the last experiment. Agaiii observe the direction of the deflection of the needle of the galvanoscope, and any changes in the appearance of the surface of either strip of lead. 1. What changes are oljserved to take pl;ice in either lead strip (1) when the batteiy is in the circuit, (2) when the battery is disconnected and the ends of the wires joined ? 2. What is the cause of the current which flows through the wires when the battery is disconnected and the circuit completed ? 3. How does the direction of the battery current compare with that given by the lead strips immersed in the dilute acid ? 4. Can the latter current be used to ring an electric bell ? Try. 7. Secondary or Storage Cells. The last experiment illustrates the principle of action of all secondary, or storage, cells. When the current is passed through the dilute acid from one plate to the other the oxygen freed at the anode unites with the lead, forming an oxide of lead. The composition of the anode is thus made to differ from the cathode, and in consequence there is a difference in THE CHEMICAL EFFECTS OP THE ELECTRIC CURRENT. 179 Fio, 136. potential between them, whicli caus(»s a current to flow in the opposite direction when the pbites are joined by a conductor. Tliis current will continue to flow until the plates become again alike in composition, and hence in potential. Instead of using solid lead plates, perforated plates, or " grids," made of lead or some alloy cf lead, are frequently employed. The holes in the plates are filled with a paste of lead oxides, which form the "active material" (Fig. 186). When the plates are immersed in dilute sulphuric acid and the current passed through, the cell, these oxides are changed into peroxide (PbO^,) in the positive plates and reduced to spongy lead in the negative. The chemical changes which go on in the storage cell are very complex, and, to a certain extent, undetermined. The following equations represent approximately the re-actions which, according to the latest investigations, are believed to take place. Charged cell PbO,, a-H,, SO,, yR.p, Pb, (Hjuals Discharged cell PdSO,, {x~2) H,S0„ (y + 2) H,0, PbSO,. " . During the process of discharge both plates are con- verted into lead sulphate, and a part of the sulphuric acid disappears thus lowering tlie density of the elec- trolyte. When the cell is being chai'gcd the sulphion ions combine with lead sulphate and water to form the t It ii ■ m 'm 1 I ii'i m liar IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I LiyjS 125 ,^1^ 12.2 i 2.0 L25 |II_U 11.6 ^^ '/l 'y,. V '/ z!^ Photographic Sciences Corporation 23 WIST MAIN STRUT WEBSTER, N.Y. 14SS0 (716)873-4503 in ^V^ i^ ■' '■-■'■■• ' i 180 PHYSICAL SCIENCE. lead peroxide and sulphuric acid, and the hydrogen ions re-act upon the lead sulphate forming spongy lead and sulphuric acid. 1. What transformations of energy take place in (1) charging a secondary cell, (2) discharging it. 2. Is anything " stored up " in a storage cell ? If so, what ? 6. Measurement of the Current— Voltameters. 8. Laws ot Electrolysis. Carefully repeated quantitative experiments have verified the following laws of electrolysis. Law I.— The amount of an ion liberated at an elec- trode in a given time is proportional to the strength of the current. Law II.— The weights of the elements separated from an electrolyte by the same electric current are in the proportion of their chemical equivalents. These laws furnish a means of comparing the strength of one electric current with that of another, and hence of measuring a current when a unit current is adopted. 9. Unit Current. The practical unit of current commonly adopted Is the ampere, which may be defined to be a current which deposits silver at the rate of 0.001118 grams per second. The same current deposits per second 0.000328 , grams of copJ)er, and liberates 0.000010386 grams. The weight of an element liberated in one second by a current of one ampere is called the electro-chemical equivalent of the element. > An electrolytic cell used for the purpose of comparing the strengths of different currents is called a voltameter. THE CHEMICAL EFFECTS OF THE ELECTRIC CURRENT. 181 10. Silver Voltameter. • The silver voltameter consists of a light platinum bowl partially filled with a solution of silver nitrate in which is suspended a silver disc. When the voltameter is placed in the circuit, the platinum bowl is made the cathode, the silver disc the anode, and the current to be measured is passed through the silver nitrate solution for a specified time. The silver disc is then removed, the solution of nitrate poured off, and the silver deposited in the bottom of the bowl washed, dried, and weighed. The rate in grams per second, at which it is deposited is then calculated, and this divided by 0.001118 gives the measure of the current in amperes, or W C = The current to be measured is passed through the water until the liquid in the tube stands on a level with the liquid in the vessel, and the time during which the current is passing is noted. The temperature of the gas and the barometric pressure are also noted. The volume of the hydrogen liberated is read from the graduated tube, reduced to standard temperature and pressure, and the mass corresponding to this volume calculated. Then, if the current is passing for t seconds, and W grams is the weight of the hydrogen liberated, W ^""^x. 000010386 wh ?re is the measure of the current in amperes. THE CHEMICAL KFPKCTS OF THK ELECTRIC CURRENT. 183 W QUESTIONS. 1. Can !i single Gravity cell be used to decompose water? If not, why i 2. When a plate of zinc and a plate of platinum connected by a wire are both dipped into the same vessel of dilute sulphuric acitl, an electric current i)asses through the wire. State and account for the etfect of moving one of the plates into a separate vessel of acid. 3. Two copper wires, one connected with one terminal of a voltaic battery and the other connected with the other terminal, dip side by side, but without touching each other, into a solution of sulphate of copper. What happens to the inunersed part of each wire ? 4. Plates of copper and platinum are dipped into a solution of copper sulphate, and a current is passed through the cell from the copper to the platinum. Describe the 'effects produced ; also what happens when the current is reversed. 5. A vertical partition of porous earthenware is fitted into a tumbler, and dilute sulphuric acid is poured into each compartment. Rods of common zinc and coj)per are placed respectively in the two compartments, and connected by a wire. Stjite what will be observed with regard to the evolution of gas, and how the observed phenomena will be modified when copper sulphate is poured into the compartment containing the copper rod. 6. A piece of zinc and a piece of copper are each carefully weighed ; they are then connected by a copper wire and dipped side by side into dilute sulphuric acid contained in an earthenware jar. After, say, half an hour, the pieces of zinc and copper are taken out of the acid^ washed and dried, and weighed again. Would the weights be the same as at first ? If not, how, and why, would they diflfer ? 7. A vessel containing a solution of salt, coloured with v ittlo litmus or indigo, is divided into two parts by a partition formed by stitching together severjil layers of blotting paper. The wires coming from the poles of a (irove's battery are dipjjcd into the liquid on opposite sides of this partition. On one side the colour i'fl ■'! I » •'111 m m m w wmmmm wm» 184 PHYSICAL SCIENCE. is observed to disappear. Explain its disappearance, and mention the pole of the battery from which the wire that destroys the colour proceeds. 8. The same current is passed through three electrolytic cells, the first containing acidulated water, the second a solution of copper culphate, and the third a solution of silver nitrate. What weight of hydrogen and what weight of oxygen will be liberated in the first cell, and what weight of copper deposited on the cathode of the second cell when 11.18 grams of silver are deposited on the cathode of the third cell ? 9. Is there polarization of the electrodes in (1) the water volt- ameter, (2) the copper voltameter, (3) the silver voltameter ? Give reasons for your answer. < 10. Obtain two copper plates, make a copper voltameter, and measure witli it the current given by any cell. I';;! m CHAPTER XTV THE MAGNETIC EFFECTS OF THE CURRENT. I.— Electricity and Magnetism. 1. Magnetic Field Due to an Electric Current. Experiment 1. ' Pass a strong current from a battery* thi-oug}i a coj)i)er wire, dip the wire into iron filings, and lift it out. 1. What is observed ? Break the circuit. 2. What now takes place ? Why ? Experiment 2. Arrange apparatus as shown in Fig. 138. Drop a magnet- ized needle on the surface of • the water near the vertical wire (See Experiment 1, page 89, Part I.), and connect the ends of the wire with the poles of a battery. How did the needle set itselt (a) before, (b) after the wire was connected with the battery ? Reverse the direction of the current. How does the needle behave? Fio. 138. ,'( in ' F| > t.if i^S I'M i i , * If a storage battery is used for experiments of this class, care should be taken to keep from "short-circuitinff " it, that is, using it with a resistance so low that the battery discharges at too high a rate. To prevent this, a resistance coil should he permanently attached io one of the poles of the battery. A suitable coil of iron telegraph wire will answer well. The rate of discharge will depend upon the niunlier and the size of the plates in the cell. The rate should be ascertained from the maker. 185 !W i ■i I 15 186 PHYSICAL SCIENCE. Experiment 3. PfiMH a tliick wire vertically through a liolo in the centre of a card. Sprinkle iron filings from a niuslin bag over the card, Fig. 139. Now connect the ends of the wire with the jtoles of a battery, and gently taj) the caid. fy ''^^^>^^''^^^^:^1r^-:^ 1. How do the iron filings arrange lliuinselves around tlio wire i 2, What does this prove ? Fio. 139. • Experiment 4. Repeat Experiment 1, page 150. The above expcrimeiits sliow that a wire through which an electric current is flowing is surrounded by a magnetic field, the lines of force of which pass in circles around it ; that is, the wire thron<>hout its whole length is surrounded by a " sort of enveloping magnetic whirl." The poles of a magnetic needle placed in this field are apparently urged with equal force in opposite directions around the wire, and it, therefore, remains at a tangent to it. Experiments 3 and 4 show that the direction in which each pole of the magnetic needle tends to turn around the wire depends on the direction of the current. If we imagine a current to flow through a wire from an observer to the face of a clock, the N-seeking pole of a magnetic needle placed in its field tends to turn in the direction of the hands of the clock, while the S-seeking pole is urged ''n the opposite direction. If there were but one pole to the magnet it would apparently revolve around the wire continuously. THE MAGNETIC EFFECTS OF THE CIUUENT. 187 2. Magnetic Field about a Circular Conductor. Experiment 5. Take a piece of copper wire, No. IG, and bend it into the form shown in Fi<;,'. 110, mnkinj,' the ciicle about 20 cm. in diameter. Suspend tin' win? by a long thread, and allow its ends to dip into mercury held in recc^ptades made in a wooden block of the form shown in the figures The inner receptack^ should be about 2 cm. in ('iam(^ter and the outer one 2 cm. wide, with a space of 1 cm. of wood between them. Pass a current thi'f)ugh the circular conductor by connecting the poles of a l)att(uy with the mercury in the re- ceptacles. For convenience in making the connections the receptacles should be conne(;ted by iron wir(\s with binding posts screwed into the block. Fig. 140. When the current is passing, bring a magnet near the face of the circular conductor. Wlijifc position relative to the poles of the magnet does the conductor take ? The experiment shows that a circular conductor acts as a disc magnet whose poles are its faces. The lines of force surround the conductor as shown in Fig. 141. Which is (a) the N-seeking face, {h) the S-seeking face of the circular conductor (Figs. 140-141) ? Fio. 141. ■'l| •i 1 'A '1' I %> '1* i' 1: Ih! 188 PHYSICAL SCIENCE. 3. The Magnet and the Solenoid. Experiment 6. Mak(^ a helix, f)r coil, of wire two or three inches lon<^ by windin*^ insulated copper wire No. '20 around a lead pencil. Conn(?ct the ends of the wire to the poles of a battery, and pass a magnetic needle around the coil. 1. How doos the niagnotic needle set itself when placed (1) near each end of the spiral, (2) midway between the ends? 2. In what particulars does the helix resemble a bar magnet ? 3. What ])()le of the helix is the observer in front of when the current in the coils facing him is passing in the direction of the hands of a clock ? Experiment 7. Make a helix of insulated wire, No. 16 or 18, about | inch in diameter and three inches long, and place it in a rect- angular opening made in a sheet of cardboard, so that its axis will be in the plane of the cardboard (Fig. 142). This can be done by cutting but the three sides of a rectangle of the proper size, and then passing the free end of the strip through the FiQ. 142. - . centre of the helix, and replacing the strip in position. Sprinkle iron filings from a muslin bag on the cardboard around the helix and within it. Attach the ends of the wire to the poles of a battery, and gently tap the cardboard. How do you account for the , way in which the iron filings arrange themselves? . THE MAONRTIO EFFECTS OF THE CURRENT. 189 The above experiments sliovv that a helix of wire through which an electric current is passing acts exactly like a magnet, having two poles and a neutral equatorial region. The field which surrounds it re- sembles that of a bar magnet. Such a coil is sometimes called a SOlenoid. 4. Electro-Magnets. Experiment 8. Repeat Experiment 4, passirig a small soft iron rod through the helix before the current is passed through the wire. 1. What effect has the iiitroductiun of the iron upon the magnetic power of the helix 1 2. Are the N-seeking and S-seeking poles at the same ends of the helix as before the insertion of the core ? Will the end of the rod lift up a small piece of iron, say a tack, (1) when the current is passing through the wire, (2) when the circuit is not completed ? A soft iron core surrounded by a helix of insulated wire, through which an electric current can be passed, is called an electro-magnet. Why is an electro-magnet a more powerful magnet than a solenoid? To answer this question repeat Experiment 6, placing a soft iron core in a helix of wire. 1. How does the arrangement of the iron filings on the card differ from that observed when the core was not inserted ? When the helix is used without the core the greater number of the lines of force pass in circles around the individual turns of wire, and but a few run through the helix from end to end, and back again outside the coil ; but when the iron core is inserted the greater number of 190 PHYSICAL SCIRNCB. the lines of force pasH in this way, hecaiise tlie perme- ability of iron is very much ^rruter than tliat of air, and whenever a coil passes near the core, the lines of force, instead of passing in closiid curves around the wire, chanjije their shape and pass from v\u\ to end of the core. The effect of the cor«*, therefore, is to inei'easethe number of lines of force which are concentrated at definite poles, and conse(piently to increase the power of the masfiiet. 5. Polarity of an Electro-Magnet and Direction of the Current. Looking at the S-seeking pole of an electro-magnet, the magnetizing current is passing through the coils in the direction of the hands of a clock, and, looking at the N-seeking pole, the current is circulating in the opposite direction (Fig. 143). i-'io. 143. 6. Use of Solenoid. Experiment 9. Make a solenoid about 4 inches long by winding four or five layers of No. 20 insulated wire around a glass or cardboard tube. Connect the ends of the wire with a battery, hold the tube in a vertical position, and take a short soft iron rod which will just slip easily into the bore of the tube, and insert it part way into the tube. How does the rod tend to set itself within the helix ? . THE MAONKTIC KFI'F.rTS or Til 11 ClUltKNT. 191 I A .solenoid witli a inovablo iron j)luii;;«'r is ficinicntly used in.stcaid ol* an uluctro-ninj^iMl, \\\{\\ a pninMiicnt coiv, when the ina<;net is iviiuiivd to o^'wv a pull thioiijrh a long range. 7. Laws of 71agnets. Experiment 10. Take a soft iron rod 1 Ji inches in dianiet(M' and two or three inches lonyf, and wind around it one layer of insulated wire No. 20. Connect the ends of tlu! wire with the j)oles of a battery, and test th(^ lifting' power of the n)a;L,'net hy tryinj^ to lift Hiiiall pieces of iron with it. Repeat the experiment, winding' two, three, four, etc., layers of wire on th<^ rod. 1. Wliut etruct liHS iiicreasing the ninubcr of Inyers of wire upon tho power of the lu.'ignot ? Wliy ? 2. If tho same diflerenco in potontial is always maintained between the ends of the wire, will the power of tlie magnet always continue to be atfected in the same way l)y increasing the num1>er of turns of wire ? If not, why ? 3. If the same current is maintained in the wire, will the power of the magnet always continue to be affected in the same way by increasing the number of turns of wire? Give reasons for your answer. Experiment 11. Connect in a circuit with a battery an electro-nia^gnet and a rheostat, or series of resistance coils. Test the lifting })ower of the magnet. By lessening the number of the coils of the rheostat in the circuit, increase the curi-ent. Again test the lifting power of the magnet. What effect has increasing the current (m the lifting })owcr of the magnet ? Repeat the experiment, decreasing the current by increasing the resistance. 192 PHYSICAL SCIENCE. ■1 h 1. What change now takes place in the strength of the magnet? 2. What is the relation between the current and the strength of the magnet ' Why ? These experiments illustrate the following laws : 8. Law3 of Magnets. 1- The strength of an electro-magnet is proportional to the strength of the current. 2. The strength of an electro-magnet is proportional to the number of turns of wire, if the current is kept constant. These laws are true only when the iron core is not near the point of bein<^ magnetized to saturation. It should also be observed that when an electro- matrni't is used M'ith a battery, or other source of cuirent where the ends of the wire are kept at a constant differ- ence in potential, an increase in the number of turns of the wire may not necessarily adjj to the strength of the magnet, because the loss in powc^r through loss in current caused by increased resistance may more than counter- balance the o-ain throuiih the increased number of turns of wire. In what circuit should a " long coil " electro-magnet (one with a great number of turns of fine wire) be used, one in which the remaining resistance is great or small as compared with the resist- ance of the magnet ? 9. Laws of Currents. Experiment 12. Wind insulatod ma<^iiot wire, No. 20, into coils of the forms A and I> in Fig. 144. A is about 25 cm. square and contains five convolutions of tlie wire. It may be made by winding the wire around the edge of a square bt)ai'd, tying the strands together at a numbei- of points with thread, and removing the THE MAGNETIC EFFECTS OF THE CURRENT. 193 board. I » may bo made in a similar manner. It is reetanf^ular, 20 cm. X 10 cm., and contains also five convolutions. FlO. 144. Suspend A by a long thread and allow the ends of the wire to dip into the mercury receptacles as in Experiment 5, page 187. Connect the wires as shown in Fig. 144, so that a current from a battery of three or four cells will pass by one continuous circuit through the two coils. Bring one edge of B near one of the vertical edges of A with the planes of the coils at right angles to each other in i I Fio. 145. 194 PHYSICAL SCIKNCE. such a position that tlie curroiit in tiie adjacent portions of the two coils will tlow (1) In the same direction (Fig. 144) ; (2) In opposite directions (Fig. 145). Wh.'it h.'ippens in each case ? Hold J> within A as shown in Fig. 14G, arranging the connecting wu'cs in such a way that A is free to turn around. How does the coil A tend to get itself relatively to B ? The above Experiments illustrate the following laws of currents : — Fi(». 146. 1. Parallel currents in the same directions attract each other ; parallel currents in opposite directions repel each other. 2. Angular currents tend to become parallel and to flow in the same direction. Wlieii the curroMts flow in tlie same direction, their magnetic fields tend to mer^^e, and the stress in the medium which surrounds the wires tends to draw them together, but when the currents liow in opposite direc- tions the stresses tend to push tlie wires further apart. Show how the second law results from the doctrine of stresses in till) medium surrounding the wires. To show the directions of tlie lines of force in the fields rep it Experiment 8, page 18C, passing two wires through the card and causing the current to pass (1) in THE MAGNETIC EFFECTS OF THE CURRENT. 195 the same direction tlirouoli each wire (Fig. 147), (2) in opposite directions (Fig. 148). et be r ; - ' ■ " r. n r e n r n e s n liG. 147. Fio. ua. II— Practical Applications of the Magnetic Effects of the Current. 1. The Electric Telegraph. The telegraph instruments are the key the sounder and the relay. I'm. 149, The Key. Tlie key is an instrument for closing and hrcaking the circuit. Fig. 149 shows its construction. Two 2>ljitinum !! ill m 1 H 196 PHYSICAL SCIENCE. contact posts P, P, are connected with tlie biiirling posts A and B, tlie lower one being coiniected by a bolt C insulated from the frame, and the upper being mounted on the lever L wliich is coiniected with the binding post B by means of the frame. The key is placed in the circuit by connecting the ends of the wire to the binding posts. When the lever is pressed down the platinum points are brought into contact and the circuit is completed. When the lever is not depressed a spring N, keeps the points apart. A switch S, is used to connect tlie binding posts, and close the circuit when the instrument is not in use. The Sounder- Fig. 150 shows the construction of the sounder. It consists of an electro-magnet E, above the poles of which is a soft iron armature A, mounted on a pivoted beam B, the beam being raised and the armature held by a Fio. loO. spring S, above the poles of the magnet at a distance regulated by the screws C and D. The ends of the wire of the magnet are connected with the binding posts. THE MAGNETIC EFFECTS OF THE CURRENT. 197 The Belay. The relay is tin instrument for closin<^ mitoniatically a local circuit in an office when the cunent in the main circuit, on account of the great resistance in the line, is too weak to work the sounder. It is a key worked by an electro-magnet instead of by hand. ¥\ nd = nb cos bnd = nb cos na sin but and therefore or or rm cos = tan nb — na tan . THB MAGNETIC EFFECTS OF THE CURRENT. 207 But nh represents C, and na represents H, therefore C = H tan ^, but H is constant. Hence C varies as tan <^. That is, the intensity of the current varies as the tangent of the angle of deflection of the needle- If the current correspondintr to any an<;'lo of deflection is known, the current corresponding to any other angle of deflection can be determined by referring to a table for the tangent of the angle, and making the necessary calculations. Experiment 1. Place in a circuit with a constant battery a tangent galvano- meter and a copper voltameter, observe the reading of the galvanometer, and determine, as described in Art. 11, page 181, the current in amperes passing through the coil of the galvanometer. Make a record of the result and keep it for futui-e experi- ments. l\ 4 'd, QUESTIONS. 1. If you were given a voltaic cell, wire with an insulating covering, and a bar of soft iron, one end of which was marked, state exactly what arrangements you would make in order to magnetize the iron so that the marked end miglit be a north- seeking pole. Give a diagram. 2. A current is flowing through a rigid copper rod. How would you place a small piece of iron wire with respect to it, so what the iron may be magnetized in the direction of its lengtii ? Assuming the direction of the current, state which end of the iron will be a north pole. V, 208 PHYSICAL SCIENCE. I 3. A .stroll*^ cloctric curroiih flows Mirougli a coj)per wire, which passes through the ceiitie of an iron riiij^, and is at riglit angles to the plane of the ring. Describe the magnetic state of the ring. 4. A telegraph wire runs north and south along the magnetic meridian. A magnetic needle free to turn in all directions is placed beside the wire, and on the same level with it. How will this needle act when a current is sent through the wire from south to north ? Supposing the wire to run east and west, how would you detect the direction of a current passing through it ? 5. A gutta-percha covered copper wire is wound round a wooden cylinder, AB, from A to 15. How would you wind it ])ack from B to A, (I) so as to increase, (2) so as to diminish the magnetic effects which it produces when a current is passed through it ? Illustrate your answer by a di.igrani drawn on the assumption that you are looking at the end B. G. An insulated copper wire is wound round a glass tube, AB, from end to end, and a current is sent through it, which to an observer looking at the end A, appears to go round in the same direction as the hands of a watch. A rod of soft iron is held (1) inside the tube ; (2) outside but parallel to the tube. What will be the magnetic pole at that end of the bar which is nearest to the observer in each case ? 7. Two parallel covered wires are traversed by ecpial currents in the same direction : what is the joint effect of the currents upon a bar of soft iron () withdrawing the magnet from the coil, does it flow in tho same direction in each .IS' ' 212 PHYSICAL SCIENCE. case, and ia there any relation between tlio E.M.F. of these cur- rents and the rapidity with which tlie magnet is inserted or with- drawn ? Fio. KiJ. 4. Does the inserting of the magnet increase' or diminish the number of magnetic lines of force which pass across the space en- closed by the coil ? What effect has withdrawing it ujjon the number of lines of force passing across the space ? Experiment 2. Make an electro-magnet by placing the soft iron rod within the small coil of fine wire prepared as described above and connecting the ends of the wire with a battery. Place the <;alvanometer in the circuit for an instant and observe the direction of the dellection of the needle. Now remove the galvanometer from this circuit and connect it with the large coil, as shown in Fig. 163, taking care to connect each binding post with the end of the wire of the large coil which corres- ponds to the end of the small coil with which it was connected. CUURKNT INDUCTION. 213 the en- tile bin and the the the Li-ge mg When the small coil is conncH-tcMl with the battery, thrust it (|uickly iiito'the large coil, allow it to stand a few seconds and then withdraw it (luickly. llepeat the experiment several times, changing the rapidity with which tiie coil is inserted and withdrawn. Fig. 163. 1. When does the galvanometer indicate that a current is flowing through the coil connected with it ? 2. When does this current How in the same direction as the battery cm-rent, when the coils are approaching or when they are receding from each otlier ? 3. What is the relation between the rai)i(lity wiMi which the coils are brouglit together, or separated, and the K M.F. of the cm-rent produced in the coil connected with the galvanometer? 3. Explanation cf Terms. The coil connected with the batteiy is calKnl the primary coil, and the current wbicb tbjw.s tbrouob it is I, II lit!-' f •I f 1 % i ! 214 PHYSICAL SCIENCE. I called tlie primary current ; the coil connecter] with the galvanometer is called the secondary COil, and the momentary currents made to flow in it, secondary currents. When the secondary currents flow in the same direction as the primary, tliey are said to be "direct," or to flow in a positive direction; but when the secondary currents flow in the opposite direction, they are said to be "inverse," or to flow in a negative direction. Is the secondary current direct or inverse wlien the nnmher of lines of force passing tlirt)Ugh the 8[)ace enclosed by the secondary coil is (1) increasing, (2) decreasing ? 4. Laws of Induction. Experiments 1 and 2 show : — 1. Whenever a decrease in the number of lines offeree which pass through a closed circuit takes place, a current is induced in this circuit flowing in the same direction as that which would be required to produce this magnetic field, that is, a direct current is produced. Whenever an increase in the number of lines of force takes place, the current induced is such as would by itself produce a field opposite in direction to that acting ; that is, an inverse current is produced. 2. The total electromotive-force induced in any circuit at a given instant is equal to the time-rate of the variation of the flow of magnetic lines of force across this circuit. 5. Lenz's Law. We have found (a) that parallel currents in the same direction attract each other (Art. 9, page 194), (h) that on moving a current from a conducting circuit, an induced current is produced in the secondary in the same direction as in the primary (Experiment 2, page 212). We have also found (a) that parallel currents in opposite directions repel each other, and (h) that on moving a CURRENT INDUCTION. 215 current towards a conducting circuit an inducted current is produced in the secondary in the opposite direction to that in the primary. Hence in all cases of electro-magnetic induction, the direction of the induced current is always such that it produces a magnetic field opposing the motion or change which induces the current. This is known as Lenz's Law. 6. Experiments Illustrative of the Laws of Induction. Perform the following experiments, noting in each case : — (a) The cause of the induced current produced. (/)) The conditions on which (a) a direct current, (/>) an inverse current, is produced. (c) Whether your observations conform to Lenz's Law. 1. Repeat Experiment 2 above, connecting the battery with the outer coil and the galvanometer with the inner coil. 2. Place the two large coils on the vertical rods showTi in Fig. 161, and connect them as shown in Fig. 164, thus forming ice rse It a bhe kue lat Ian |ne 2). lite a m ^'M 0^ 1 I '1^;; im 2ir, PHYSICAL SCIKNCK. a lar«?o elcctro-nm^^iK^t 'vitli opposite jm)1<\s at tho uppor ends of tho rods. Cofuicct with the battery as shown in the figure. Place tlie iron i'«»d within tlie small coil and connect the terminals with the galvanometer. Hold this coil over the poles of the electro-magnet, and keeping its axis in line with the poles of the magnet, move it backward and forward and turn it (^nd for end. Flu. 165. 3. Place the small coil within the large one, insert the iron rod, and connect the small coil with the galvanometer and the large one with a battery, placing a key in the latter circuit, as shown in Fig. 165. Quickly make and break the circuit two or three times with the key. 4. Repeat the last Experiment, connecting the outer coil with the galvanometer and the inner one with the battery. 5. Repeat Experiments 3 and 4, placing in the circuit a rheostat instead of the key. Alternately lessen and increase the curi-ent given by the battery by increasing and decreasing with the rheostat the resistance in t^ e circuit. 6. Repeat Experiments 3, 4, and 5, using the two large coils instead of the large one and small one, and (1) placing them CURRENT INDUCTION. 217 iron ll the xuit, ircuit il CO luit a tlie It the coils Ithem end to end, as shown in Fig. 166, with an iron rod throu 2. Is a shock felt ? Dampen your fingers and repeat the experi- ment, grasping the bare wires. The effects observed are due to what is known as self-induction. The magnetic lines of force surrounding a current in circulating around the wire pass, especially when the wire is coiled, across contiguous parts of the same circuit, and any variation in the strength of the current causes the current to act inductively on itself. On completing the circuit, this current is inverse ; and on breaking it, direct. The direct induced current in the primary wire itself, which tends to strengthen the current when the circuit is broken, is called the extra current. This self "induced current is of high E.M.F., and there- fore flows for an instant across the air space when the wires are a short distance apart ; hence the spark. 1. Why will an iron core placed within a coil of wire in a circuit increase the intensity of the extra current when the circuit is broken ? 2. If a large electro-magnet is placed in a circuit with a galvano- meter and a secondary battery, on closing the circuit the current CURRENT INDUCTION. 219 will be seen to rise gradunlly and take it8 full strength only after several seconds. Explain. 3. If when you place across the terminals of a large electro-niagnut an incandeHcent lamp of such resistance that a 1)attery current will bring it only to dull redness, you break the connection with the battery, you will observe that the lamp will become vividly incandescent for an instant Explain. Try the experiment. as 5elf, luit rcuifc Kt IS lano- Irent QUESTIONS. 1. You have a metal hoop. Describe (and give a figure of) some arrangement by which, without touching the hoop, you could make electric currents pass around it, first one way and then the other. 2. A bar of perfectly soft iron is thrust into the interior of a coil of wire whose terminals are connected through a galvanometer. An induced current is observed. Could the coil and bar be placed in such a position that the above action might nearly or entirely disappear ? Explain fully. 3. A piece of covered wire is passed a few times round a wooden hoop ; its ends are joined up to a galvanometer. The ends of another piece of covered wire which is wrapped around a similar hoop are joined up to a battery. What will happen (1) if the two hoops are brought quickly near to each other, and (2) if they are quickly separated ? 4. How could you temporarily stop or weaken a current in a wire without disconnecting it from the battery, by means of the motion of another wire through which a current is passing ? 5. The poles of a voltaic battery are connected with two mercury- cups. These cups are connected successively by : — (1) A long straight wire ; (2) The same wire arranged in a close spiral, the wire Ijeinj; covered with some insulating material ; (3) The same wire coiled round a soft iron core. Describe and discuss what happens in each case when the circuit is broken. t. 220 PHYSICAL SCIENCE. 6. Around the outside of a deep cylindrical jar are coiled two separate ])iece8 of fine silk-covered wire, each consisting of many turns. The ends of one coil are fastened to a battery, those of the other to a sensitive galvanometer. When an iron bar is thrust into the jar a momentary current is observed in the galvanometer coils, and when it is drawn out another momentary current (btft in an opposite direction) is observed. Explain these observations. 7. A small battery was joined in circuit with a coil of fine wire and a galvanometer, in whicli the current was found to produce a 8tea8. Oonstruction. Fig. 168 shows the essential parts of the instrument. A primary coil, consisting of a few turns of stout insulated copper wire, is wound around a core D made up of a bundle of soft iron wires. One end of this coil is attached directly to one of the poles of a battery ; and the other end is connected to the other pole of the battery by means of a current breaker, which consists of a hammer H sup- ported in front of the iron core by a spring A in contact with a screw B, the wires being connected as shown in the figure. The spring and screw are also connected w'th a condenser C, C^ made of alternate layers of tinfoil and paraffined paper, in such a manner that one is joined to the even sheets of foil and the other to the odd ones. A secondary coil, consisting of a great number of turns of very lino insulated wire, is wound on the outside of the primary coil. The terminals of this coil are attached to binding posts placed above the coil. Action. When the primary circuit is completed and the battery current passes through the coil, the core is magnetized, the hammer is drawn in, and the circuit broken between f li I im « 1*1 'Hi 222 PHYSICAL SCIENCE. the Spring A and the screw B. The hammer then falls back, the circuit is completed, and the action goes on as before. An interrupted current is thus sent through the primary coil, which induces currents of high electro- motive-force in the secondary coil. The function of the condenser is to prevent the extra current induced in the primary coil, when the circuit is broken, from passing across the break in the form of a spark, and prolonging the time of fall to zero of the primary current, in consequence of which the rate of variation of the flow of the magnetic lines of force across the secondary coil would be diminished and the electromotive-force of the induced current lowered. The extra current flows by the shunt circuit into the condenser, and causes a difference in potential between the layers of foil connected with the two wires. This immediately gives rise to a current in the opposite direction which flows back through the primary coil and instantaneously demagnetizes the soft iron core, thus causing the direct current induced in the secondary coil, when the primary circuit is broken, to become shorter and more intense. The potential-difference between the terminals or the secondary coil can in this way be made sufficiently great to cause a spark to pass between them when they are placed a short distance apart. This potencial-difference is increased by increasing the number of turns of wire, by increasing the current in the primary coil, and by decreasing the time required for it to fall to zero each time the circuit is broken. The iron core, on account of its magnetic permeability, increases the number of lines of force passing through the coils. > . \. V CURREINT INDUCTION. 223 e A bundle of iron wire is used instead of a solid bar of iron to produce a stronger magnetization, and to prevent the circulation of induced currents in the iron itself. 2.— Applications of the Induction Coil.* 8. Electrical Discharges in Partial Vacua. Experiment 1. Connect the terminals of an induction coil with nietjil electrodes inserted into a glass vessel of the form shown in Fig. 169. Adjust the sliding ele< trode so that an electrical dischai'ge will pass between the knobs, and exhaust the air from the vessel. Observe the changes in the character of the dis- charge as exhaustion proceeds. The effects of the electrical discharge in partial vacua are exhibited best in Geissler Tubes. These tubes are made in a great variety of forms (Fig. 170), and contain .various rarefied gases usually at a pressure of about 2 mm. of mercury. The wires from the terminals of the induction Fio. 169. coil are connected with platinum electrodes fused into the ends of the tubes. The colour effects of the tube de- pend mainly on tlie nature of the residual gas. Every gas glows with a more or less brilliant colour of its own. Fluorescent substances, such as uranium, glass or a solution of quinine, become beautifully luminous when placed within an excited tube. ^If an induction coil of sutficient power is not available, a Toepler-Holtz or Wims* hurst electric machine may be used in performiiiir the experiments in this section. o- 170. board screen coated with one or the other of the above salts. The screen when 'm ' ^i 'I ' i 228 PHYSICAL SCIENCE. exposed to the action of the rays becomes luminous, and any object opaque to the rays interposed between it and tlie tube casts a shadow upon it. Fig. 179 shows the shadowgraph of a hand. Since tlie ring, the needle, tlie bones and the flesh are of diflerent densities they cast shadows of varying degrees of depth. (3) Tlie Roentgen rays affect sensitive photographic plates. Permanent images of shadowgraphs can, there- fore, bo made by substituting a photographic plate, enclosed in its holder, for the fluorescent screen described above. To make a shadowgraph sharp in outline the object should be placed as neai' as possible to the screen or plate. V 12. Electric Waves. Hert« discovered that the oscillating spark discharged between the terminals of an induction coil gives rise to electro-magnetic waves in the ether. These waves are probably similar to light, but of much greater wave- length and lower vibration frequency. Hertz used as\a detector, to show the presence of these waves, a copper wire of the form shown in Fig. 180. He found that when the wire was supported on an insulating stand in a darkened room, small sparks were seen to pass be- tween the metal knobs at the ends of the wire whenever electric waves were set up by his oscillator. The distances at which waves can be detected by the Hertz method is limited to a few feet. Branly discovei^d that metal filings, when thrown together loosely and made part of an electric circuit, ,■ 1 Fio. 180. CURRENT INDUCTION. 229 WT^ mi have normally a high resistance, but become under the influence of electric waves good conductors. This principle is applied in the construction of the coherers, now commonly employed as the detectors of electric waves. Fig. 181 shows a coherer consisting of a glass tube containing two metallic plugs separated by metallic filings. The coherer is made a part ^"*- ^^** of the circuit by connecting the plugs with the wires. The discoveries of Hertz and Branly, demonstrating the possibility of signalling at a distance by electric waves, have lead to the development of the modern system of wireless telegraj)hy. 13. Wireless Telegraphy. The following experiments show how electric waves may be set up and detected, and illustrate the principle of wireless telegraphy. Experiment 3.— To Construct an Oscillator, or Transmitter. Arrange apparatus as shown in Fig. 182. A, A are brass balls about 4.5 cm. in diameter attached to rods made to slide ■ i M Fio, 182. through metallic holders C, C, supported on insulating posts B, B. W, W are wings to act as condensers. They may be made of sheet copper and should be at least 50 cm. long and 2 cm. wide. •• ■ 230 PHYSICAL SCIENCE. Adjust the balls A, A so that tlioy will bo ono or two millimotros apart, and connect C, C with Uk? terminals of an induction coil, j^iving a spark of at least a quarter of an inch in length. The oscillatory discharge? between the balls will set up electric waves in the ether. Experiment 4. —To Construct a Receiver. Arrange apparatus as shown in Fig. 183. A is a coherer which may l)e made as follows : — Take a heavy glass tube Fio. 183. about 2 or 3 mm. in diameter and 5 cm. long, and shut up loosely within it, between two bright metallic plugs, fairly coarse filings from a U.S. nickel five cent piece. The plugs should be 2 or 3 mm. apart and be connected with wires as shown in the figure. B is an electric bell mounted beneath the coherer, on a vertical board, in such a position that when the bell rings the hammer will strike the coherer lightly. CURRENT INDUCTION. 231 two an nch up }rer ubc |up ly gs as a le C is a standard relay (Fig. 151, page 197), D and E aro batteries, D consivstiug of one dry cell, and E of three or four similar cells. Fig. 184 shows the way in which the coiuiections A Flo. 184. are to be made. The coherer is connected in a circuit with the battery D and the coil of the relay ; and the bell is connected with the battery E, in a circuit which may be closed or opened at F, by the relay. W, W are wings, similar to those of the transmitter, con- nected with wires leading from the coherer. Adjust the relay and the plugs of the coherer so that a current will be just on the point of moving the armature of the relay. Place the transmitter a short distance from the receiver, and, by closing the primary circuit of the transmitter, send a spark across the spark-gap between the balls. Note the effect on the receiver. The electric wavx's set up by the transmitter cause the filings in the coherer to become a conductor. The current thus allowed to pass operates the relay, which closes the circuit containing the bell. i 232 PHYSICAL SCIENCE. When tho tllinjrs in the coherer once become a con- ductor, they retain tliis property until shaken up, tliere- fore the bell would continue to rin liii I! (Fig. 205) and witli but .sufficient opening at tlie top to give tlie upper carbon freedom. Since tlie oxygen in the globe soon becomes exhausted, and the absence of draft prevents its renewal, the carbons of the enclosed arc burn away very slowly. As a usual thing they last about ten times as long as when burning in the open air. • Grouping, Regulation, Etc. Arc lamps are usually connected in series, that is, the negative carbon of one lamp is connected with the positive carbon of the next, as shown in Fig. 192, and a constant current flows from one pole of the dynamo through each of the lamps to the other pole. Regulators for maintaining a constant distance between the carbon points as they burn away, are of a great variety of patterns. In inost of them the regulation is accomplished by the action of two electro-magnets or solenoids. Fig. 205 shows an enclosed arc lamp with its regulator. M is a solenoid^ wound with coarse wire, con- nected in series with the carbons. N is an electro-magnet with two windings, one of coarse wire in series with the solenoid and the carbons, and the other of many turns of fine wire in a shunt between the carbons. Fig. 205c shows the way in which the connections are made. Since the current in the shunt passes around the core of N in a direction opposite to that in the coarse wire series coil, it tends to neutralize its magnetic effects. When the carbons are together and the circuit closed, the current passes through the coarse wire winding of the magnet N, the solenoid M, and across the carbon C HEATINC. AND LlOIlTINr, ICFFKCTS OF THE CUIIUENT. 257 11 the Durns 205c )ince in a )il, it osed, lug of on C Fig. 205a Fig. 2056. Pro. 205c. and C to the conductor. The solenoid M draws up the iron phmger supporting the magnet N, while at the same time N grips the cii'cular armature B, and, in being lifted, turns it on its axis. The small pinion attached to B is turned, and the rack A bearing the carbon holder is raised. The carbons are thus separated and the arc formed. As the carbons burn away and the potential - difference between them increases, sufficient current is shunted throuo-h the fine wire hiu .i.iKxpmqam 258 PIIYRirAL SCIENCE. The oloctroinotive-l'orce rccjninMl for an ojxmi arc li<;f]it is about 50 volts, and for an enclosed arc fj-oni 75 to 80 volts. The current used in the open arc is connnonly from 6 to 10 aniperes, and from 3J to G amperes in the enclosed arc. If a current of 10 }imi)eres passes through each lamp (Fig. 192), where there are four lamps in series, what current passes from the one brusli of tlie dynamo to the other i ii ii o80 only the 102), 111 the CIIAPTEU XVII. ELECTRICAL MEASUREMENTS. I.— Ohm's La./. We liave learned that the Strength of a current, or the quantity of electricity which flows past a point in a circuit in one second, is dependent on the E.M.F. of the current and the resistance of the circuit. Tlie exact relation among these quantities was tirst enunciated by Ohm. It may be thus stated : — 1. Ohm's Law. The current varies directly as the electromotive- force and inversely as the resistance of the circuit. Practical Unit. The unit resistance is the ohm, which may be de- fined as the resistance of a uniform column of mercury 106.3 cm. long and 1 square millimetre in section, at O^C. The unit current is the ampere, which may be de- fined as a current which deposits silver M iJift rate of 0.001118 grams per second. The unit electromotive-force is the volt, which is that E.M.F. that will cause a current of one ampere to flow in a circuit whose resistance is one ohm. If is the measure of a current in amperes, R, the resistance of the circuit in ohms, and £, the electro- motive-force, Ohm's Law may be expressed as follows: — = 1 259 T'StSS 260 PHYfllCAI. RCIKNCB. I:P QUESTIONS. 1. Tho c'loctromotivo-forou of ,1 h.'ifctory is 10 volts, Iho rosistanco uf tliu otills 10 ohms, >iiiil tliu i'(.!sist.iiiou of tliu extonuil circuit 20 oliins. What is thu cinrunt '( 2. Thu «liiruit3iicu ill potuntial hutwcun a trolley wire ami thu rail is 500 volts. What ciirroiit will flow through u c«»niluctor which joins tht'ui if the total resistance is I,0e the E.M.F. of a battery to ring an electric bell which rent parts of any circuit in which a current is ilowing, and compare them with one another. QUESTIONS. 1. The end, A, of the wire ABC is coiniected with the earth, and tlie ditferonce in potential between the otheV end, C, and the earth is 100 volts. If the resistance of the portion AB is 9.<5 ohms and that of BC 2.4, what current will How along the wire, and what will be tlie potential-difference between the point B and tlie ear til ? 2. The poles of a battery are coiniected by a wire 8 metres long, having a resistance of onedialf an ohm per metre. If the E.M.F. of the battery is 7 volts and the internal resistance '0 ohms, find tlie distance between two points on the wire such that the potential- difference between them is 1 volt. What is the curr jnt in . iie wire ? 3. The potential difference between the brushes of a dynamo supplying current to an incandescent lamp is 104 volts. If the resistance in the wires on the street leading frcnn the dynamo to the house is 2 ohms, that of the wires in the house 2 ohms, and that of the lamp 204 ohms, wdiat is the fall in potential in (1) the wires on the street, (2) the wires in the house, and what is the potential-difference between the terminals of the lamp ? 4. The potential-difference between the brushes t)f a dynamo supplying a current of 10 amj)eres to 38 arc lam[)s comiected in series is 2000 volts. If the fall ii.' potential in the coimecting wires in the circuit is equal 'to the fall in two lamps, what is the fall in potential in a single lamp, and what is the resistance in the connecting wires ? 5. A cell has an internal resistance of 0.3 ohms, and its E.M.F. (m open circuit is 1.8 volts. If the poles are connected hy a conductor i'li- ELECTRICAL MEASUREMENTS. 263 vuvmo f the Lino to and (1) the is the J nanio !totl in lecting is the in the whose resistanci is 1.2 ohms, what is the current produced, and what is the potential-difference hetween the poles «)f the cell ? 6. The E.M . of a battery on open circuit is 15 volts. When the poles are connected by a copper wire a current of 1.5 amperes is produced, and the potential-difference between the battery poles falls to 9 volts. Find the resistance of the wire and the internal resistance of the battery. II.— Measurement of Resistance. 3. Wheatstone Bridge. The resistance of a conductor is usually measured by an instrument called a Wheatstone Bridge. It consists of a series of resistance coils made of German silver wire connected by conductors arranged in three sets A, B, and C, with connections for a battery, a galvanometer, and the resistance to be measu/ed, as shown in Fig. 206. w Fia. 206. The coils are mounted in a box, and the changes in the resistance are made by inserting or withdrawing conducting plugs, as shown in Fig. 207. 264 PHYSICAL SCIENCE. Tlio >)ranchcs A and C usually liave three roils each, the resistances of which are respectively 10, 100 and 1000 ohms, and the branch B lia^J a combination of coils which will oive any number of units of resistance from 1 to 11,110 ohms. The conductor whose resistance (X) Fia. 207. I:?: li 8 I is to be measured is inserted in the fourth branch of the bridge (Fi<4\ 200), and the resistances A, B, and C adjusted until the oalvanometer connecting M and N stands at zero when the keys are closed. Then the current in the battery '.s flowing froiu P, partly through X and C and partly through B and A, to Q, and since no current flows from ^\ to N, the potential of M nuist be tlu^ same as that of N, therefore the fall in potential from V to M in the circuit PMQ must ecpial the fall ii. potential from P to N in the circuit I'NQ; but the fall in potential in a part of a circuit is proportional to the resistance of that j^ortion of the circuit (Art. 2, page 201). ELKCTUICAL MKASUKEMENTS. 265 acli, coils 'roiii ,(X) Hence of the ukI C ,iid N Iroiu P, |(1 A, to iteutial fall in A, e(i[ual Q ; but )rtional (Art. 2, or X B C ~ A The resistances A, 1> luul C are read from tlie coils, and the calculations made. Experiment 1. Measure witli a wheatstoiie bridge the resistance of your galvauoscope, thi; coils used in Experiment 2, pai^'o '2\'2, an , incandescent lamp, etc. Experiment 2. Place two copper electrodes a distance apart in a solution of copper suli)liate, and measuie with the wheatstone bridge the I'esistanct^ hetwcen tiiem. Would llie result of thu ex[»oriment Ihj the same if" platinum cloetrodos of the same size were used ^ If not, why i 4. Laws of Resistance. Experiment 3. Measure with thc^ wheatstone bridg(^ tlu^ r«'sistances of jiieces of the same win; •.•.•!'«)S(> lengths are propoi'tional to 1, 2, 3, etc. 1. In what proportions are the resistances? 2. What is the relation between the length of a wire and its resistance ? Experiment 4. Kepeat Experiment 2, keeping the areas of the pai't of the elcctro»les innnersed constant, and varying the distance between them. How does an incrciiso in the tlistance hetwe^rv'iCr-r^'r-r-!nj-- -^ K^A/vwvwvvv Fio. 209. ELECTRICAL MEASURKMKNTS. 271 ce of ■j the imber )f the wire in the to be urrent- o£ the. ot* two ig. 209. Tlu! conductor U in parallel with tlie <;alvaii()inet»'r (J i.s called a shunt. If G is the resistance of the galvanometer, R the resistance of the shunt, and C the total cn/rent, the amount of current through the galvanometer For the sake of facility in calculation, it is usual to make R \^, ^V> ^^ win of CJ, when, by the above fornuila, the current through the galvanometer will be ^^, j^^, or ttjVtf of the total current to be measured. QUESTIONS. 1 . The poles of a voltaic battery are connected by two wires in parallel. If the resistance of the one is 10 ohms and that of the other 20 ohms, find (1) the resistance of a single wire equivalent to the two in ])arallel ; C2) the proportion of the total current passing through each wire. 2. Find the total resistance when the following resistances are joined in series : — ^h ohms, 2\ ohms, 2| ohms. What would be the joint resistance if the resistances were joined in parallel ? 3. What must be the resistance of a wire joined in parallel with a wire whose resistance is 12 ohms, if their joint resistance is 3 ohms ? 4. The joint resistance of ten similar incandescent lamps con- nected in multiple is 10 ohms. What is the resistance of a single lamp ? 5. Four incandescent lamps are joined in parallel on a 100-volt circuit. If the resistances of the lamps are respectively 100 ohms, 200 ohms, 300 ohms and 400 ohms, find (1) the total current passing through the group of lamps; (2) the i)roportion of the total current passing through the first lamp; (3) the resistance of a single lamp which would take the same current as the grouj). if I !!!r I ii; f i'i 1 'I! 272 PHYSICAL SCIKNCK. (}. A •^'jilvfinoinctcr avIiosc rosistMnci! is 1,000 oluns is used witli a shunt. If j'l of tilt! lotul curivnt passes through thu galvuiioiuoter, what is the rosistanco of the shunt 'if 7. If tlio shiuit of a •'alvanoiuutor lias a resistance of — of the ^ n galvanouKiter, what fraction of the total current i)a8se8 through the galvanometer i 8. The internal resistance of a Daniell's cell is 1 ohm ; its termi- nals are connected (a) by a wire whose resistance is 4 ohms, (b) by two wires in parallel, one of the wires having a resistance of 4 ohms, the resistanci; of the <»tlu'r wire being 1 ohm. Compare the currents throu~r''~>r-\ ^«?' ^aS ^4^ Fio. 210, — ^|~«r'^->~> — j|- 13. The Current Given by Series Arrangement. By Ohm's Law but E ^ ')i e, and 11 = ?a ?• + H, where 11 is the niimbor oi cells, e th(3 E.M.F. and r the internal resistance of each, and Rj the e.\t(nnal resistance in the ciicuit. Hence no. C = 11 r + llj 2. Multiple Arrangement. 14- Multiple Arrangement Defined. Generators are connected in mnltiple, or parallel, when all the positive poles are connected to one con- ductor, and all the negative poles to another, as shown in Fio-. 211. 15. Effect of Multiple Arrangement on the Internal Resistance. If n cells are arranged in multiple, and r is the internal resistance of a sino-le cell, V the internal resistance of the group -- because the current in passing through the liipiid fi-om one set of plates to the other has n paths opcnc'd up lo IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I^Kfiia ^^ Hi Hi 12.2 1.1 l.-^l^ ^ M K25 |J4 ||_L6 |<4 — V r. '> <5k ».y '/ /<^ Photographic Sciences Corporation ^V^. ^ ^!^^ 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716) 872-4503 274 PHYSICAL SCIENCE. it, and therefore the sectional area of tlie cohinin of liquid traversed is n times that of one cell, hence tlie re- sistance is only — of that of one cell. (Law 2, page 266). n 1...1.1...1..LJ. FlO. 211. 16. Effect of Multiple Arrangement on EM.F. When all the positive plates are connected they are of the same potential ; for a similar reason all tlie negative plates are the same potential, hence the E.M.F. of n cells in multiple is the same as that of one cell. This method of grouping has the effect of transform- ing a number of single cells into one large cell, the Z plates being united to form one large Z plate, and the C plates to form one large C plate. It must be remembered that the potential-difference between the plates of a cell is independent of the size of the plates. Upon what is this poteiitial-diflfereiice dependent ? 17. The Current Given by Multiple Arrangement. V but E = c and R - — h Ri, n where n is the number of cells, e the E.M.F. and r the internal resistance of each, and Rj the external resistance. Hence ■■ C = -1- n + Ri ill iiiiin of the re- ge 266). ELECTRICAL MEASUREMENTS. 275 ley are of i negative of n cells :ransform- :eU, the Z vnd the C inembered .lates of a and r the resistance. 3. Multiple-Series ArraDgrement. Sometimes both methods of arrangement are simul- FlO. 212. taneously employed, as shown in Figs. 212, 213. Fiu. 213. 18. Current Given by Multiple-Series Arrangement. To determine the current given by a number of cells grouped in multiple-series, consider each group in nml- tiple as a single cell, and determine the current given by tliese groups when connected in series. Thus, if n is the total number of cells, r is the internal resistance and e the E.M.F. of each cell, and m the number grouped in multiple, the E.M.F. of each group in multiple = e and the internal resistance r m n but there are — such groups connected in series. m I ':> '. 276 Hence PHYSICAL SCIENCE. C = n VI 71 — I m m X n in, ne 4- R, ^(>- m' + Ri nr VI + >hR| Whore 11, is the external resistanc(^ in tlie cireuit. The internal resistance of all the cells when grouped in this way is iir 19. Best Arrangement of Cells. It is manifest that when tlie external resistance is veiy great as compared witli tlie internal resistance, to overcome the resistance, the electromotive-force nuist be increased, even at the expense of increasing the internal resistance, and the series arranjjfement of cells is the best. When the external resistance is very low as compared with the internal resistance, the object of the grouping is to lower as far as possible the internal resistance, and the multiple arrangement is the best. Between these extremes of high and low external resistance some form of multiple-series grouping gives the strongest current. A gent'-al rule for determining the best method of grouping in any case may be found as follows: — Let 11 denote the number of cells, r, the internal resistance of each cell, e, the E.M.F. of each cell, Rj, the external resistance, ' m, the number of cells in a multiple group when the current is a maxiuium. !lj ' / lit. The is way is stance is stance, to 5 must be > internal the best, onipared o-nniping mce, and en these me fonn urrent. lethod of s: — when the ELKCTRICAL MEASUREMENTS. 277 Then C ')i. e n r m + m P (Art. 15.) n e C is a maximum when the denominator / n r is a minimum : but this quantity is a minimum wlien r H r m ~\ — ]/ m Rj ^ , n, is a minimum because 2 ■/ >• ^ \{,^ is constant, since r and Rj remain always the same. Now \\— ~ ]/ w Rj is a minimum wlien it e<[uals zero, because a square cannot be less than zero. Therefoie the current is at a maximum when n r ~\ or or or — y' m Rj = ]/ m Rj = n r m n r m = m Rj 2 = ^1 ' n r but - ', is the internal resistance of the cells. Hence For a given external resistance the maximum current is obtained when the internal resistance is equal to the external resistance- i > 1' i II ''•'I ! '1 ; i i|! I ii .1 nil hi :; \ i' 278 PHYSICAL SCIENCE. When n r - Ri, m = nr \r; Or The current is a maximum when the cells are so arranged that the number in each group in multiple -V _ / internal resistance of one cell X total number of cells external resistance 20. Example. Wh.at is the best way of arranging a battery of 18 cells, each having a resistance of 1.8 ohms, so as to send the strongest current through an external resistance of 1 ohm ; and what is the current ? " The number in each j^roup in multiple Vn r / 18 X 1 .8 ► ,.„ Since 6 is tlie factor of 18 nearest 5.69, the cells are to be arranged in .3 groups, in each of which 6 cells are joined in multiple, the groups being joined in series. The E.M.F. of each group = 1 volt 1.8 * . and the internal resistance = -^ = .3 TT ^ 1 C = 1, = ,. --,r-r^ = 1.57 amperes. Iv .«> X o + 1 ^ QUESTIONS. 1. 50 Grove's cells (E.M.F. of a Grove cell = 1.8 volts) are tmited in series, and the circuit is completed by a wire whose resistance is 15 ohms. Supposing the internal resist^mce of each eel' to be 0.3 ohms calculate the strength of the curre-it. ELECTRICAL MEASUREMENTS. 279 ixranged f cells lells, each st current it is the \ are to be oined in are United jsistanco is 11 to be 0.3 2. Eight cells, each witli half an ohui internal resistance, and 1.1 volts E.M.F., are connected (a) all in series, (6) all in parallel, (<•) in two parallel sets of four cells each. Calculate the current sent in each case through a wire of resistance 0.8 ohm. 3. Ten voltaic cells, each of internal resistance 2 ohms and electro- motive-force 1.5 volts, are connected (a) in a single series, (b) in two series of five each, the like ends of the two series being joined together. If the terminals are in each case connected by a wire whose resistance is 10 ohms, show what is the strength of the current in the wire in each case. 4. You have 20 large Leclanchd cells (E.M.F. = 1.5 volts, r = 0.5 ohms Ccich) in a circuit in which the external resistance is 10 ohms. Find the strength of the current which flows (a) when the cells are joined in single series ; (6) all the zincs are united and all the car- bons united, in parallel arc ; (c) when the cells are arranged in groups of 2 in multiple ; (d) when the cells are arranged in groups of 4 in multiple. 5. The current from a battery of 4 equal cells is sent through a tangent galvanometer, the resistance of which, together with the attached wires, is exactly equal to that of a single cell. Show that the galvanometer deflection will be the same whether the cells are arranged all in multiple or all in series. 6. You are required to send a current of 2 amperes through an electro-magnet of 3 5 ohms resistance, and are supplied with a num- ber of Grove cells, each of 1.9 volts E.M.F. and 0.25 ohms internal resistance. How many cells are required ? 7. Calculate the number of cells required to produce a current of 50 milli-amperes (one one-thousandth of an ampere), through a line 114 miles long, whose resistance is 12^ ohms per mile, the available cells of the battery having each an internal resistance of 1.5 ohms, and an E.M.F. of 1.5 volts. 8. A current of not less than 0.016 amperes is to be sent through an external resistance of 360 ohms. What is the smallest number of Leclanch^ cells, each with E.M.F. 1.4 volts and resistance 15 ohms, hy which this can be efiected ? What would be the maximum strength of current obtainable if double this number of cells were used? 280 PHYSICAL SCIENCE. hi 9. The wire used on Tiulian telograjili lines is iron wire of No. 2 B.W.(j., liaving fi resistance of 4.0 ohms per mile. The batteries consist of cells of 1.04 volts E.M.F. and 30 ohms resistance per cell. Assuming that the resistance of the instruments is 80 ohms, and that a current of 8 milli-amperes is re(piired to work them, find how many cells should be employed on a line 200 miles in length. 10 How would you arrange a battery of 12 cells, each oi ohms internal resistance, so as to send the strongest current through an electro-magnet of resistance 0.7 ohms ? 11. Find the best arrangements of 24 cells having an external resistance of 3 ohms, each cell having an internal resistance of 2 oliULS. 12. You have a battery of 48 Daniell cells, each of 6 ohms internal resistance, and are reciuired to send the strongest jxKssible current through an external resistance of 15 ohms ; how would you group the cells? Find also the current produced and the difference of potential between the poles of the battery, assuming that the E.M.F. of a Daniell cell is 1.07 volts. 13. You are supplied with 12 exactly similar cells, the internal resistance of each of which is one-fourth of the external resistance of the circuit : how would you group the cells so as to obtain the maximum current ? 14. If you wish to heat a platinum wire, at a distance from the battery, to as high a temperature as possible, what sort of connect- ing wires will you use, and why? And what arrangement of battery-cells will you adopt ? If in the last case the insulation of the conducting wires was very imperfect, show whether it would be better to increase the number of cells arranged in series, or the number arranged in parallel ; supposing that you have seme additional cells at your disposal. 16. A circuit is formed of six similar cells in series and a wire of 10 ohms resistance. The E.M.F. of each cell is 1 volt and its resistance 5 ohms. Determine the difference of potential between the positive and negative poles of any one of the cells. KLKCTRICAf. MEASUREMKNT8. 281 )f No. 2 Mvttories per cell. Ills, and eiu, tind 1 length. ) ohms rough an external stance of .3 internal ie current yrou group ferenco of that the e internal resistance obtain the 16. Six Daniel! cells, for each of which £=^1.0.") volts, r- 0.5 ohms, are joined in series. Three wires X, Y, and Z, whoso resi.st- ances are severally J3, 30, and .'JOO oliu.s, can be inserted between the poles of the battery. Determine the ciuTent which flows when each wire is inserted separately ; also determine that whieh flows when they are all inserted at once in parallel. 17. The poles of a battery consisting of 40 Daniell cells in series are connected by a resistance of 280 ohms, and the current i>ro- duced is 0.535 amperes ; when the external resistance is increased to 1080 ohms the current is reduced to one half : Hnd the average resistance and E.M.F. of each cell of the battery, and determine the difference of potential existing between the poles of the battery when the external resistance is 280 ohms. 18. A Daniell cell> the internal resistance of whieh is 0.3 ohms, works through an external resistance of 1 ohm. What must bo the resistance of another Daniell cell so that when it is joined up in series with the first and working through the same external resist- ance the current shall be the same as l)efore ? If the cells are joined up in parallel how will the current be modified ? B from the : connect- rement of wires was crease the 'ranged in Is at your d a wire of It and its il between ANSWERS TO QUESTIONS. Page 16. 2. .952 sec. 4. (l)(«) 1103.843 ft. per sec. ; (6) 1109.72J) ft. per sec. ; (c) 1129.24 ft. per sec. (2) 893.522 ft. per sec. (3) 4149.63 ft. i)er sec. (4) 4.703 sec. 5. 819°. 6. 419.9. m. per sec. 7. 15.004 sec. 8. 1118.04 ft. per sec. 9. 4700 ft. per sec. 10. 671658ft. 14. UOyj^ft. per sec. 15. 30.34. in. Page 25. 1. 4. 123 sec. 2. 2801.3 ft. 3. 112.924 ft. Page 32. 3. 52 in. ; 1109^ ft. per sec. 4. 33,792 cm. per sec. Page 43. 1. 1, h h h etc. 3. 1. I. h I. etc. 5. W, U W, f ^ W, etc. 6- 1, h h h etc. 7. Equal. 8. 80 pds. 9. Divided by 2. ' , 10. From C to G. 11. G of third octave above. 12. Vibration - number will halved. 13. 3/10.5:^7.8. be 1. 7^ in. 2. 1126.4 ft. per sec. 3. 8 59 in. ; 34.37 in. 6. 3:2. Page 57. 6. 41.55 cm. ; 124.65 cm. ; 207.75 cm. ; 83.1 cm. ; 166.2 cm. ; 249.3 cm. 283 284 ANSWiSKS TO QUK8TI0N8. V\iiK 74. 1. 9:4. 2. 72:5. 3. 121:400. 2. 12 cm. 3. 20.93 in. (}. 2 ft. from candle. Paor 94. 4. 12 in. ; 3r» in. in front of mirror ; 18 in. in funxi of mirror ; 24 in. behind the mirror. Paqr 2f)0. 1. ^ ampere. 2. ^ ampere. 3. 208 ohms. 4. .19 ohms. 5. 22 volts. 1. 8i amperes ; 80 volts. 2. 4 metres ; ^ ampere, 3. 1 volt ; 1 volt ; 102 volts. 6. 13.5 volts. 7. 10 amperes. S. 3 ohms. 9. 15 ohms; 15 ohms. Paor 262. 4. 50 volts ; 10 ohms, 5. 1.2 amperes ; 1 .44 volts, 6. 6 ohms ; 4 ohms. 1. 72 ohms. 2. 52,008 ohms. 3. 3.13 ohms. 4. 0.9434 ohms. 5. 20.31 ohms. 6. 14.337 ohms. 7. 22.5 m. 8. 135.9 yds. 9. 181 Jm. 1. 16S ohms ; § ; i. 2. 8^ ohms ; l^ ohms. 3. 4 ohms. 4. 100 ohms. 5. 2i amperes ; ^^ amperes ; 48 ohms. Page 267. 10. 0.6 mm. 11. 2.653 mm. 12. 4:1. •• 1.3. 2 ohms. 14. 1 : 100. 15. 1080 yds. 16. 3.04. 17. (1)20.9 ohms; (2) 78.8 ohms Page 271 6. 10 ohms. 7. 1 w+1 8. 9:25, AN8WEKS TO QUESTIONS. 285 of mirror r if mirror ; mirror. I 'AUK 278. 1. 3 amperoH. 1*2. 2. \i ainpcreH ; l,\i; amperes; J ampiriiH. 3. ^ ampt 'u in eacli case. 13. 4. (a) l.i) amperes, {!>) 0.14% ampere, (<•) 1.2 amperes, ir>. ((/) 0.702 ampere. lO. 0. fl cells. 7. riOe.'lls. 8. 5 cells in series ; 0.027 ampere. 9. 10. 10. 3 cells in each group in multiple. 17. 11. 6 cells in each group in mui II [)le. 18. 4 c«;lls in each group in mul- tipie ; 0.3*J ampere ; 5.b5 volts. 3 cells in each group in nuil- tiple. 0.7') volts. Through X, l.or) amperes ; through Y, 0. I5K«) ainperu ; through Z, 0.0207 amjitre ; through all three ..105 amperes. 1.07 volts; 13ohms; 14.08 volts. 1.3 ohms. volts. 78.8 ohms. ; ' ' 11 ill I I ! 1 ' ll'l INDEX. The references are to payes. Aberration, spherical, of mirrors, 102 ; of lenses, 121 Action, local, 155 Air columns, vibration of, in stopped pipes, 48 ; in open pipes, 49 Alternating current, uses of, 245 Alternator, 244 Ampere, unit of current, 180, 259. Angle of refraction, 98 ; critical, 104 Arc lamp, 254 Arrangement, multiple, of cells, 273; multiple- series, of cells, 275 ; series of cells, 272 ; best arrange- ment of cells, 276 Armature, forms of, 241 Attraction, laws of magnetic, 1?4 Axis, principal, and secondary, of spherical mirrors, 83 ; of lenses, 110 Beats, 31 Bells, electric, 201 Bichromate cell, 161 Bridge, Wheatstone, 263 Bunsen's grease^spot photometer, 70 ; cell, 163 Cell, voltaic, 153; Smee's, 160; Grenet, or bichromate, 161 ; Grove's, 162; Bunsen's, 163; Leclanch^'s, 163 ; dry, 164 ; gravity, 165 ; Daniell's, 167 ; storage, or secondary, 176 Centre of curvature, 83 ; of figure, 83 Chord, major, 37 Colour, due to refraction, 124 ; to absorption, 126 ; to interference, 128 Colours, mixing of, 128 ; com- plementary, 130 Consonance, 227 Critical angle, 104 Crookc's Tubes, 224 Currents, laws of, 192; measure- ment of strength of, 180, 202 ; induction, 210 ; primary and secondary, 214 ; direct and in- verse, 214 ; extra, 218 ; unit of, 180, 259 ; alternating, 245. Curvature, centre of, "83 ; radius of, 83 Daniell's cell, 167 Diatonic scale, 37 ; intervals of, 38 Dispersion of light, 124 Discharges, electrical in vacua, 224 Dynamo, principle of, 233 ; de- scription of, 238 ; series-wound, 238 ; shunt-wound, 238 ; alter- nating current, 244 Electric waves, 228 Electrical discharges in vacua, 223 Electrified bodies, positively and negatively, 152 287 288 INDEX. in ! I. 1 I I Electromotive series, 154 Electromotive-force, 155 ; unit of, 259 Electrodes, polarization of, 176 Electrolysis, 1G9 ; of water, 169 ; of hydrochloric acid, 109 ; of salts, 170 ; theory of, 172 ; laws of, 180 Electro-magnets, " 1 89 Electrons, 226 Electroplating, 174 Electrotyping, 175 Equivalents, electro-chemical, 180 Fields (magnetic), 141 ; superposi- tion of, 144 ; due to electric current, 185 Fiehl-magnets, forms of, 24.3 Fluoroscope, 227 Focus, principal, 84, 111; real, and virtual, HI ; conjugate foci, 86, 114 Fundamental note, 37 Galvanometers, 202 ; the astatic, 203 ; the D'Arsonval, 204 ; the tangent, 204 Geissler tubes, 223 Gravity cell, 165 Grenet cell, 161 Grove's cell, 162 Grouping of cells, 272 ; of in- candescent lamps, 253 ; of arc lamps, 254 Harmonic motion, 1 Harmonic scale, 36 ; harmonics, >./ ; harmonic triad, .37 Heating eifect of electric current, 251 Illumination, intensity of, 66 Illuminating power, 66 ; measure of, 67 ; comparison of, 70 Images, by means of small aper- tures, 64 ; from plane mirrors, 76 ; virtual and real, 77 ; mul- tiple, in inclined mirrors, 78 ; multiple, in parallel mirrors, 88 ; formed by concave and con- vex mirrors, 88 ; formed by concave and convex lenses, 117 Incandescent lamp, 253 Induction, magnetic, 139; explana- tion of, 139; of currents, 201 ; laws of current, 214 ; self, 218 ; coil, RuhmkorfiF, 220 Intensity of sound, 19 ; of illumi- nation, 66 Interference of sound-waves, 28 ; of light, 128 Key, telegraph, 195 Lamp, arc, 254 ; incandescent, 253 ; grouping of, 254, 256 Leclanche's cell, 163 Lens, 109 ; converging, or convex, 109 ; diverging, or concave, 109 ; axis of a, optical centre of a, and focus of a, 110 Lenz's law, 214 Light, nature of, 59 ; rectilinear propagation of, 64 ; laws of re- flection of, 75 ; laws of refrac- tion of, 96 ; index of refraction of, 99 ; total reflection of, 102 ; phenomena of total reflection of, 103 ; dispersion of, 124 ; undu- latory theory of, 131. Loops, in pipes, 51 ; in organ pipes, 52 INDEX. 289 Magnet, electro-, 189 ; laws of, 191 Magnetic induction, 139 ; Held, 141 ; lines of force, 1.42 ; fields, superposition of, 144 Magnetization, methods of, 140 Manoinetric flames, 55 Measurements, electrical, 259 ; of resistance, 263 Medium, velocity of sound de- pendent on the elasticity and density of, 12 ; intensity of sound dependent on density of, 19 ; reflection of sound by change of density, 24 Mirrors, concave and convex spher- ical, 82 Morse code of signals, 200 Motion, harmonic, 1 Motor, electric, 247 Multiple arrangement of cells, 273 Multiple - series arrangement of cells, 275 Musical interval, 37 Musical scales, 30 ; harmonic, 36 ; diatonic, or natural, 37 ; of equal temperament, 40 Nodes in pipes, 51 ; in organ pipes, 52 ; in closed pipes, 53 ; in open pipes, 54 Octave, 37 ; designation of, 39 Ohm's Law, 259 Ohm, unit of resistance, 259 Optical bench, 72 Organ pipes, 51 Overtones of pipes, 52 Period of vibration, 2 Permeability, magnetic, 145 Phase of vibration, 3 Photometer, Rumford's shadow, 68 ; Bunsen's grease-spot, 70 Pigments, mixing uf, 130 Pitch, 33 ; of any note, determina- tion of, 33 ; standard of, 39 Polarization of a cell, 157; methods of preventing, 159 Poles, of a magnet, 134 ; two poles of a magnet insepara1)le, 134 ; consequent, 136 Potential, 150 ; defined, 151 ; fall of, in a circuit, 261 Potential series, 153 Prisms, refraction of light by, 107 Pulse of rarefaction and of con- densation, Quality of sound, 53 Reduction of ores, electrical, 176 Reflection of light ; laws of, • 75 ; total, 102 ; phenomena of total, 103 Reflection of sound, 21 ; from con- cave surfe ••:'s, 23 ; by change of density, 24 Refraction of light, laws of, 9G ; angle of, 97 ; index of, 99 ; in prisms, 107 ; through lenses, 109 Refraction of sound, 25 Relay, telegraph, 197 Resistance, unit of, 259 ; nteasure- ment of, 263 ; laws of, 2<>5 ; specific, 266 ; and temperature, 267 ; in divided circuits, 269 Resonance, 45 Resonators, 47 Ruhmkorff's induction coil, 220 ; application of, 223 Rumford's shadow photometer, 08 290 INDEX. Scale, harmonic, 36 ; diatonic, 37 ; of equal temperament, 40 Semi-tone, major, 3S Series arrangement of cells, 272 Shadows, 65 Shunts, 270 Siren, 33 Smee's cell, 160 Solenoid, 190 Sound, 1 ; origin and transmission of, 1 ; theory of transmission of, 7 ; velocity of, dependent on elasticity and density of medium, 12 ; velocity of, in air, 14 ; intensity of, dependent on amplitude of vibration, 19 ; in- tensity of, dependent on density of^ medium, 19 ; intensity «f, de- pendent on distance, 20; rein- forcement of, 26 ; reflection of, 21 ; reflection of, from concave surfaces, 23 ; reflection of, by change of density, 24 ; refrac- tion of, 25 ; waves, interference of, 28 ; beats, 31 Sounder, telegraph, 196. Spectrum, 124 Storage or secondary cell, 176 Telegraph, the electric, 195 ; action of, 198 ; wireless, 229 Telephone, construction and action of, 248 Tones, major-, and minor-, 38 ; major semi-, 38 Transformer, 232 Transmission of sound, theory of, 7 Unit current, 180, 259 Velocity of the transmission of sound, 12 ; of soun