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Les diagrammes suivants illustrent la mithode. 1 2 3 1 2 3 4 5 6 '-;-v?*t'-V i-^^-y: :, ^>-''^'-'-;.:"-''ir ^^f^f^^^^li^^^- :.>, :::■■■ .. ■>: ' MUCROCOTY RBOIUTION TKT CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I 13,0 "«^" M^^B Its U ia7 14.0 1 2.2 2.0 1.8 ^ /APPLIED IIVMGE Inc ^^. 1653 East Main Street Ks Rochester. New York 14609 USA ^S (715) 482 - 0300 - Phone ^S (716) 288 - 5989 - Fa« \ irjsnsESijfisss:s:^3^ A ]k[AXrAL OF LABORATORY PHYSICS. wt H. M. TORY, M.A.. Lnlu>-t>- m Mathematics, McGitl Umvos-ty. Moi-.treal: Late Demonstrator o' Physics, McDoti'iul Physics Buiidmg, McGill University. AND F. H. riTCHEU, M.S( ., A.M.I.E.E., Late Demonstrator o* Physics. McDonald Physics Building, McOitl University, Montreal. FIRST EDITION. FIRST THOUSAND. NEW YORK: JOHN WILEY & SONS. London: CHAPMAN & HALL, LiMiXEa T.'^'' '^•i^.s •'^^■^ss£^s^ir£Si?ss>F:&:^:5^ii::^f: Qvt^'^. '\''V Copyright, 1901, BT H. M. TORY. KOBHT eWniMOKtl. PRIKTKF. KET TOIIK. :.:a(*^'es^ 4 1. PREFACE. Thk present volume is iiiteinletn, and Klec- tricity, and, with additional examples and special exercises, constitutes the course in Elementary Pliy.>ies i;iven at the McDonald Physics liuildiiii;, Mc(iill University, .^^)ntreal. The method of treatment is the outyrow th of experience in teaching large classes with a limited numher of instructors, and the book is offered to the public with the h()])e tliat it nuiy be found useful toother teachers similarly situated. A separate manuscript was originally prej)ared for each experiment. The general form of treatment was approved of by Professor Cox and Professor Callendar (when holding the chair of Physics in McGill University), and afterwards by Professor Rutherford. For each experiment there is a list of references, a list of apparatus, a short statciueTit of the theory involved, practical directions, and a tabulated example. The "References'" under each experiment are to a num- ber of the best American text-books on (ieiieral Plivsic's, as well as to a number of standard English books, (lenerally speaking, any one of these will be found to meet the needs of the student. The books referred to are as follows : Elemen- tary Text-book of Physics, by Anthony and Brackett : The Elements of Physics, Xicliols and Franklin: Elementary Text-book of Physics, Knott : The Tlieory of Heat, Preston ; iii yp /a sBa taa y^gjsaiawg.g afej Wvygi IT rUEI'ACK. Klcmentary Lessons in Klectiicity and ^[ugnetisrn, Silvanus Thompson; A Text-l)<>ok of Physics, Wutson ; Physicr. for University Students, (.'iirliart; General Physies, Hastings and IJeacli; Physics, Advanced Course, Parker; Tlieory of Pliysics, Ames. I'nder " Ai>|»aratus Ileciuireir' will he found an exact statement of the apparatus necessary for the particular ex- periment. Under "Theory of Experiment" willhe found set forth the thec)ry involved in the special experiment under consideration. As most students come to the laboratory with very imiH^rfeetly formed ideas of physical theory, this portion of each experi- ment has been found especially useful, as it gives to the stu- dent a clear conception of the j»riiiciples involved i)efore ho begins the actual practice of the experiment. Under "Practical Directions" will be found just such directions as a Demonstrator would give to a student if stand- ing ' "side him. In addition, a tabulated example of the observations and results has been added to serve as a guide to the student. In cases where doubt might arise the calculations involved will also be found. The examples have been taken mostly from the work done by student;^, and will serve to give an idea of the order of ac- curacy possible. The "Blank to be tilled in by Student" has been added to enable the student to keep a permanent record of his work. The results should be first returned to the Demonstrator in tabulated form and approved of before they are entered in the bo"k. Most of the manuscripts were prepared when Mr. Pitcher and I were fellow Demonstrators in the laboratories. On Mr. Pitcher's retirement from the University and my own retire- uiS^r PREFACE. V inent as a teacher from tlie Physical Dopurtineiit, the work of publicaticju wus uiulertaken at tlie rcniot of the I'rufossur.s in charjrc. During the pa^t year I iiave revised and n.ni- ]»leted tlie separate man user ipts, rednein^' them t.. the present uniform pattern. As a result of the method (.f treatment some ap])arent repetitions occur under " Tne«>ry of Kxpiii- ment," but I have preferred to let these renuiin, so that ea» h experiment stands in a sense complete hy itself, thus j)ermit- ting the order of work to he varied. For much lielp and nuiiiy suggestions in the origimil draft- ing of the manuscripts we are indebted to J'rof. Callendar, to whom some of the manuscrii)ts, especially those on the D'Arsonval galvanometer, are due. Constant reference has been had to text-books of Practical Physics, especially to those of (ilazebrook and Shaw (which work was origimilly nsed by us as a text-book), Stewart and Gee, Nichols, and Kohlrausch (Physical :Mea^urements). As most of the proof-sheets have been read only by myself, I doubt not that some inaccuracies still remain, thoughnone I hope whieh can be considered of any conscr^uence. Especial thanks are due to Mr. II. T. Barnes, D.Sc, Lecturer in Physics, for valuable assistanee in collecting ma- terials for some of the tabulated examples. II. ^\. TOKV. McdiLi, Coi,LEOK, February 9, 1901. Trm^m y^'i^ffrre.'^ri'^ss^ CONTENTS. f I 1 ( I 1. o_ 3. 4. 5. G. ». 8. 0. 10. 11. li. 1.'). 11. !"!. (i. 1 r. 18. lU 20 21. 23. 23. 24. SOUND. PAOC 'I'lie Sonometer 1 Tlie l{esonRiice>tut)e — Velooity of Sound 4 Tlie Si rcn 8 'I'lii- Ci)iiii)avis()ii of Forks liy Heats H Lissnjoiis Figures 13 Tht! W-lociiy of Waves in a Stretched String 17 The Fircli of H Fork l>y Falling Plate 19 Laws of Vilirating Strings, Melde's Method 23 Kundt's Tube — Velocity of Sound 24 The Penduluni-chrouograph , gy LIGHT. Huiism's Pliotonieter 82 I' 11 111 ford's Photometer 34 Verification of the Law of Reflection 3fi Mtiisureuicnt of tlie Angle of a Prism, Pin Method 40 |{'f I active Index of Gla.ss, Pin Method 43 Kel racti vc Index of a Prism, Pin .Method 46 U'adius of Curvntiire of a Spherical Surface by S|dieroiiieter 51 Uiidius of Curvature of a Concave Spherical Surface by Reflection.. 54 Radius of (Jurvafiire of a Convex Spherical Surface l)y Reflection., ru The Foctil Length of n Convex Lens by Parallel Rays, Method I. . . 60 The Focal I,ength of a Convex Lens, Method II 63 The F0c.1I Length of 11 Con\-ex Lens bv Changing Position of Lens. Method III .' 65 The Focal Length of a Convex Lens by the Size of the Magnified Iniaire. Method IV. gg The Focal Length of a Conctve Lens by Divergence of Rays, Method I I _ 70 vii *!''aE5:.!r;Et!:zs'.if3KS^SE^i'3£i^.i VIU COXTEWTS. 25. The Focal Length of a Concave Lens by Meana of Convex Lens, lf"\ Method II " 72 i 26.1(1) C'onstmctjoi. of a Microscopt. (2) Construction of a Telescope. 75 vJW: The Magnifying Power of u M iscroscope '. 77 2b. The Magnifying Power of a Tt-Iescope 81 29. The Spectroscope — Mapping the Spectrum — Measuring Wave- lengths 8;j 30. The Angle of a Prism— The Refractive I dex of a Prism by Means of the Spectrometer 89 31. The Refractive Index of a Liquid by Means of a Microscope 92 HEAT. 32. The Construction and Calibration of a Spirit Thermometer. 94 33. Testing the Fixed Points of a Thermometer— Correction for Stem Ex])osure 96 34. The Coefficient of Expansion o. a Liquid by a Weight Thermometer 100 35. Coefficient ol" Linear Expansion of a Solid ]03 36. The Constant- volume Air- thermometer 106 37. The Constant-pressuie Air-thermometer Ha 38. The Specific Heat of Copper and Zinc, Method of Mixtures 117 39. The Latent Heat of Fusion of Ice 121 40. Tl e Latent Heat of Stt^am 124 MA(JNET1SM. 41. Blue-printing Lines of Force J27 42. Mapping the Magnetic Field around a Bar Magnet, Moment by Neutral Point jog 43. The Moment of a Magnet by Oscillation 5f(.tliod i;!4 44. The C(imi)arison of Moments by Oscillation . 136 45. The Moment of a Magnet by Deflection Method 139 46. Tiie Moment r)f a Magnet by the Torsion Balance 143 47. The Horizontal Intensity of the ?]artl>'s Magnetic Field i)y a Magnet- ometer ^ 146 48. Tlie E(iui valent Leiiirth of a Magnet ir,0 49. The Compass-box X'arioiiieter I'^D KLEcruicri'v. .lO. Sine and Tangent Methods of Measuring Currenta 157 51. The Absolute Measure of a Ciuiint !();! 52. The F,le<'fro.chemical Eiiuivalent of llydrotren ifi.', 5:!. The Comparison of Electro clifiiiical !:(|uiviil<-nts 170 ."i4. 'I'lif Determination of tlie lloii/nntul C..m|>oMtnt of tlie Eartli's .Magnetic Force by Tangent (iMKi.nouit'ter 17;', ^^aauiz^^'!) v'MiiiasagiaM«ciM !wa>i 5£ ;^' COMA\\TS. ix CXP. 55. The Heductiou Factor of a Galvanometer. . .. ""i^-! 56. Ohm's Law ^'" •••••••■••••a ••••••••••.,,, lT7 57. Comparis,,!. of Electrical Kesistances by Sine or 'ranp..I,t'ualva- nonifter I J „g ' 58. M«i.siirement of Hesistances, B. A. Bridge jo, 59. Measiireiufiit of l{esisiance.s. Differential (ial'vanomVt.-r" ." ! iss GO, Siifcilic Hesistance 61. Ki'Mstance of a (iaivanometer by Shunting loi 62. \VLeatstone'.s Bridge : (1 ) K.sistance of Coil ] ',2) lie.si' "anrvof (iaV- ' vanr)ineter ; (3) Kesistanro of Batteries ^ gg 63. ( 1) To Verify Joule's Law, JH = C^Ji, (g). (f,) "to Find",/ ooa 64. ( omi)arison of Kesistanc-.,.s. Ca.ey Foster iMetbod " " o,)9 65. Calibration of Slide-wire Bridge, Carey Foster Method 014 66. Variation o( Resistance with Temperaftre-Determinationof Tern- " perature Coefficient 67. Measurement of Small Resistances .joi ^ ^ 6b. .Measurement of Large Resistances ..,[ go- I I!'!' ^'°"'l'"'«"" "^ Kiectromotive For.vs. Tamr'eilt iialvanomVter 2>'^9 i 70. romparuson of Electromotive F.n es. Potentiometer Method " " " 030 71. CahbrutK..! of an Ammeter l)y Gas Voltameter.... '" 035 72. Determination of Constant of a Siemens Electro-dynnm'ometor; " ' ' ''is 7J. Calibration of an Amn.eter by Siemens Eleclro-dvninnometer " " 241 74. Determination of Resistance of a D'Ar.sonval '(ialvanometer 'by Sl'"nting •' ^^g 75. Determination of Constant of a D'Arsonval (Talvonometer !....!. " 047 76. Calibration of the Scale of a D'Arsonval (ialvanometer . .. o^i 77. Measurement of Potential Differences by D'Arsonval Galvanometer 255 78. Cahbration of a Milli-volt .Meter ' oi-n 79. Determination of the Logarithmic Decrement of a Galvanometer 265 80. The Absolute Capacity of a Conden.ser. Ballistic Galvanometer. ... 270 8L Comparison of C.mdensers, Direct-deflection xMethod " '" 275 82. Comparison of Condensers, Method of Mixtures 078 83. Comparison of Condensers. Bridge Method .'. ogQ 84. Measurement of El..ctr.miotive Forces and Besistances of Batteries' " Condenser Method ' „„„ • *0« ■r^rrn 3^ tsr** ' Tgs.'^f .' •as^a^ijTi >m-^sus::^:s3aKt:iii£Htm .61^1?' inf 'ii ^iiii Ml I II mill III I :s^r>t^':*3U«(?;i£;iaK7iAS9sr'-.:^a«^a»TrLS^{! : LABORATORY PHYSICS. SOUND. I. TO DETERMINE THE VIBRATION FREQUENCY OF A TUNING FORK BY MEANS OF A SONOMETER. References — Knott, p. 261 ; Hastings and IVacli, p. 563; Carliai't, i)t. i. ]>. 186; Tsicliols and Franklin, vol. ni. p. 160; Ames, ]>. 173; Anthony and ]>rac'kett, p. 165; Watson, p. ;r.»2: IJurker, p. 231. Apparatus Required. — A sonotneter; a tuning-fork, provided with a resonator; a rubber hammer for exciting the fork. Theory of Experiment — If a string stretched under a tension '1\ so great that the action of gravity may be neglected in comparison with it, be made to vibrate by drawing it aside at one point and then suddenly freeing it, the disturbance will be transmitted along the string as a wave motion, the velocity of the wave being given by the equation = \/l; (1) where m is the njass of the string per unit length. If I be the length of the vil»rating portion of the string, and n the vibration frecpieiu-y fi.»r the fundamental note, then T' 2///, I I II IIIHi 111111111111 'IMl(lll|flHfl liiJIlill llilHlllil illi I I il IBIWIIII IIMII l|l|||l||l lllli ll 2 LABORATORY PHYSICS. and therefore "=W. (2) In formula (2) all the laws of the transverse vibration of strings are included. If the length of the vibrating portion of t^ie string be adjusted till the emitted note is the same as that of a tuning- fork, the vibration frequency of the fork can be calculated from the formula. Practical Directions. — We shall assume that the usual form of sonometer, provided with w 'ig; ts for altering the tension, and with a movable bridge for altering the length of the vibrating portion of the string, is used. A piece of piano- wire of small diameter is generally suit- able for the purpose of the experiment. If the weight m of the unit length of the wire be not given, the wire must be weighed before attaching it to the sonometer-box, and m calculated. Fasten one end of the wire to the sonometer-box, and the other to the attachment for holding the weights. Stretching the wire over the pulley, attach 20 to 30 pounds weight. Excite the fork by a blow from the hannner. Vibrate the wire by snapping it with the fingers at the middle puiiit. rontinue the process, ad' "ting the length of the vibrat- iiiir wire bv means of the able bridge, until the strinir and fork are in unison. Care must be taken to adjust the string so that the funda- mental note is in unison with the fork. To make quite sure of this, sound the first harmonic bv vibrating the string one- quarter of its length from the end and tcmcliing it lightly at the mi'ldlo wifli the fiiigcM-. Tiiis being the first harmonic, SOUXI). 8 and an octave above the fundamental of the strinff, will enal)le tlie ear to determine at once wliether tlie fundamental is being tuned to the fork or not. If it be found that less than one-third of a meter of wire is lised in the vibrating portion the tension should be increased so that the length of the string can be increased, otherwise the string will vibrate for such a short period that it will be almost impossible to make the comparison. Measure in centimeters the length of the vibrating wire. lieud the stretching weight and reduce it to dynes. Calcuhite ?i from formula (2). Repeat the observations three times, altering the wei Mfaii value of ;? 5 lbs. 10 <( 15 ( ( 20 " Tin nynes. 2224908 4449fcil»i 6674724 8899632 128 127.8 127.7 128 4 127.9 2' = 5 X 4r)3.C X 981 Dynes, 1st observation. 1 n = ,/2224908 ,„„ , 2xl>HlV .0424- = ^28. 1st " Blank to he Jilhd In hy student, m = Observation. I WeiRlU. T in Dynes. n Mi'an value of n 2- LA n on A TOR T rilTSICS. 2. TO DETERMINE TUE VELOCITY OF SOUND IN AIR BY MEANS OF A RESONANCE-TUBE. References. — Hastings and Beach, p. 562; Ames, p. 184; Barker, p. 220 ; Watson, j). 367 ; Aiitliony and Brackett, p. 161; Knott, p. 290; Carl^art, pt. i. p. 146. Apparatus Required. — A resonance-tube; a tuning-fork; a rubber hammer; a tliermometer. Theory of Experiment. — If a tuning-fork be made to vibrate over the open end of a tubo closed at one end and of suitable length, tlie tube will act as a resonator, reinforcing the vibrations of tlie fork. The length of tube re(]uired is sucli that the time it takes the vibration to travel to tlie closed end of the tube and back must be the same as the time of a Jialf-vibratiou ot the fork. If -?? be the velocity of sound in air, I the length of tl»e tube, n the number of vibrations per second of the fork, and t the time of a semi- vibration, then _ J_ _ 2^ or V — 4tnl (1) It is evident that the fork will be reiTiforeed not only wlien the time corresponds to the first half-vibration, but will also be reinforced if the lei-jrth of the tube be such that the time it takes the vibration to travel to the closed end and back be equal to tlie time of a complete vibration and a half or any odd number of semi-vibrations of the fork. It is therefore evident that if tlie tube be such that its length can be adjusted, a series of points of maximum reso- nance can be found. Hence 2x-Pl' ^^) V = f'A.^^VML. ^LaftAnm^Jiate SOUND. 5 where a? is 0, 1, 2, 3, ct(5., c(»rresj)onding to tlie first, third, fifth, etc., semi-vihrution. This formuhv is not strictly accurate. A correction for the open end of the tubo is necessf,ry. The correction is nearly equivalent to adding to the length, I, of the tube its radiuH. TJie formula tlierefore becomes V = \n{l-\-r) Vj^ 1 ' (3) r being the radius of the tube. If now the temperature of the air in the tube be t,, the velocity v, then the velocJty at zero, ^, , is given by the equation or 4,i(l 4- r) {2x-\- 1) Vl -j- .OirSfSt ■ w Practical Directions. — A simple form of instrument suit- able for the experiment consists of two glass tubes arranged to slide up and down in a wooden frame, the tubes being connected at the lower ends by a rubber tube (Fig. 1). When the apparatus is partially filled with water, l)y adjusting the relative positions of the tubes the water may be made to rise and fall in either as desired. Adjust the larger tube until the water rises nearly to the top of the smaller one. Hold the vibrating fork horizontally over the mouth of the smaller tube, and adjust by means of the larger the height of water in the smaller, until a point of maximum resonance is obtained. n 6 LAUOltATOll Y Vll VS/C W. Ab this point is not very sharply (k'tinotl, several soj»arate adjustments should bo niiule, aiul tlie incun of the obst-rv.'- -SS7 ''^^[r Fig. 1. tions taken. The leiij^th, I, slioukl l)e measured each time to 1 mm. Take the temperature, t, of the air in resoiuuice-tube. Repeat tlie observations for third and fifth semi- vibrations if tlie tube is l(»nir enuujrh. A fork of ^TiCi J). V. is vi-ry suifMhlc for tlu- expcrimctit. * '^imvL^yy^KkJT^t if IT. f ^ 80UND. 7 A suitable hammer for vibrating can be made b^ iiisL-rting a stiflE wire into a rubber bottle-cork. Example. — Enter the observations thus: /, Ut Point. t f, -.M Point. t 15 /, 3d Point. / 31.5 33.1 31.7 31.9 15 98.4 99.0 99.1 98.3 Tub<* U(ft long enuu^'b. Mean = 31 8 = 98.7 = _ 4_x 256(31.8 + 1.5) _ . , ,, • , »« — — -:--^== — = doSOO, 1st Point. VI + .003665 X 15 _ 4 X 256(98.7 -f 1 .5) 3 4 1"+ .00366"x 15 = 33300, 2d I'oint. Mean value of Co = 33,'50 ciu. per sec. Blank to he filled in by student. I, l8t Point. t I, Sd Point. t I. 3d Point. t Mean = = v» Mean value of c„ = K'j^j-^i mji.' i/^ts.\ :»^s» -frii T7 J ■- * :jf lT. Apparatus Required. — A .-iivii with .siiitiil)l(3 Hpeed-^ov- iTiior; ail ori;:iii-[)ipi' ami timiiii;-fork of approximutcly the same fiH-tpu-ncv ; a largo vasomotor and a pair of Ih-IIows for tilliiijrit; an experinieiital oriran-ltellows for fnriii.ihiiig the Mast for tiie orpiii-pipe ; a |>rc'ssiire ::;aiii;e; nihlit-r connecting tubinij;; a sii})plv t>f weights for loading bellows; a stoj)- watch. Theory of Experiment. --If the air in an organ-pipe be excited bv a blast of con.-tant prosure, and a >iren, having a 6j)eed t>f /I revolutions pur second while receiving its impulse through y> hole-s per revolution, lie brought either into uni.suii with the note of the [>ipe or to ditl'er from it by a known number of beats, ', per second, the fre«piency Foi the organ- j)ipe can be deteniiinetl. For, if iti unison with the siren, /•'=y*«, or if licatiiig, /'= j,u _[- /,, If S(_>nie means be employed by which tlio revolutions of the siren can be kept cou-tant so that tin- beats can be counted, for a sutficient time, the above tlieory can be realized in practice. Practical Directions. — Select an organ-pipe and connect it to the bellows. Adjust the pressure of the blast by weights till the fiindament,a! note is obtairied. -:s:uLf«isL .Tir ^ ^ i SOUND. 9 Contucf tlio fffot-lKjllows fo flie paKometer ami force it full .if nil-. (.'oniKct till! {(iisornctor to tlio sirt-ii and pressiirc-^iiij^o. JSct; that thu hi»oe(l-couiiter of the Kircii I'li^a^'t's in tlio worm carried l*y the s|iiiidle. Set the or^'aii-j»i|)e and siren Koundinij, and wei^dit the g:iHornetcr till the siren gives apitroxiniately the note <.f the organ-pipe without consuming ni(»re air than can easily he Hupplied I.J the l.cllows working contstantly. liy adjusting the speed-governor, hring tlie frequency of the Hiren up or down as re d- ing as the siren was brought up or down to l)eat with the organ-pipe. Take several observations, and average the calculated results. Check the residt ]>y comparing the ]>i])e Vv ith a standard tuning-fork of nearly the same period. This may ])e done by the method of beats, thf fork being loaded to find which note is higher. Precautions. — Do not work the bellows with jerks or thev may burst. Be careful tliat the gasometer is never hard up against the stop at the toj) of its gauge or the water will be forced out of the gasometer and gauge. See that the siren is well oiletl, and the i>ivot bearings proj)erly adjusted. Note. — h\ this cxpcriineni: the greatest diiJicuilv wa«j TiLiVT'^idflR ^:tn 10 LA JiOKA TOR Y Pll YSIVS. II f encouiiturud in ki'tping the s|K't'«l of tin- hirni Kuftlcirntly con»tunt tlurii)^ olnjcrvation. For this ii h|»ft'«l-i]j()vt'riior, siiijilar to those urtc'«(i(. 1.-5 KrtHiiieiioy. 1500 lOUO 1000 4:t.4" 80.0" 2y.3 ' - 217 -f 486 - -iio St:) ftlO 607 Meat! value of i'' MO Blank to he jf I led in hy student. Siren RavolutionH. Time. Bvatn. Mi'au viiltie . 11 4. TO COMPARE THE FREQUENCY OF TWO NEARLY IDENTICAL FORKS BY BEATS. i References.— Marker, p. US'J ; Wiitson, [). I:.'*;; Aiitlumy uiid Uriickett, p. \M\ Curliart, j)t. 1. |>. l.'.'.t (4); Kiiott, |». 2^«>; Ni(tliols uiid Kniiikliii, pp. l.'jo, I7."»; Aim-s, pp. 14»;{, l.si>; IIiLstinj^K a!nl l»t'u<-li, p. kni'l. Apparatus Required. -Two forks of nearly the same j)iteli, iiiouiite is the number of beats, or X (1) (2) where X is the number of beats heard in t seconds. Kor while the lirst fork makes //, vibrations the other makes p more, and therefore in l/p of a second the second fork executes one whole vibration more th.in the other. At the 12 LABOIUTORT PHYSICS. < end of tlmt time, therefore, the Bound will be reinforced, as well as at the end of every succeeding \/p part of a second. Midway between these points the second fork has just gained a half vibration on the other, the two forks are in opposition, and there will therefore be an interval of silence. It follows that if the number of beats or loud points be counted in a given time, the difference between the frequen- cies is completely determined. Practical Directions. — It is more convenient to have one of the forks driven electromagnetically. If such a fork is available, it can very well be used as tho standard. Load the other fork near the ends of the prongs by means of the small weights provided, until the beats are such as can be easily counted. Count the time of, say, 20 beats, if the loaded fork vibrates long enough. IVfeasure the distance of the weights from the ends of the prongs and calci'.late the difference between the forks by foniiula (2). There will be overtones immediately after the excitement of the loaded fork; these, however, soon die away, and at any jite do not much interfere with the perception of the beats. To detei-niine whether the loaded fork is flatter or sharper than the standard, raise the loads a very little. Redetermine the beats per second, and if there are fewer to the second, the loaded fork was higher; if mwe, vice versa. If ilie forks are not identical, load the higher one until no beats are heard. Measure the distance of the loads from the ends of the prongs. The gradual dying away of the note nmst not be con- founded with the very slow beats which occur as the forks a])])roach unison. i ! SOUND. Example. — Enter results thus : 13 Frequency of Standard. Distance of Weight from End. 6 cm. 5.5" 4.5" Time. Beats. Frequency of Lo.uled Fork. 512 20" 25" 50 45 10 514.5 514.0 or,\4 Blank to he filled hi hy ntudent. Frequency of Standard. Distance of Weight from End. Time. Beats. Frequency of lA>atlid K2; Ilastiiiirs aiul Beach, pp. 529 and 571 ; Nichols aiul P^ranklin, vol. in. p. 152; Ant]>'>;iy uiul Brackett, p. ISO. Apparatus Required. — A pair of identical tuniiifr.fork.s (wiMi a frequency of ahout 100 I). V.) ]>rovidod with mirrors and supports; a dark lamp with a pin-hole in the chimney; a telescope; a ruldter exciting-hammer; a stop-watch. Theory of Experiment — The theory is suhstantially iden- tical with that of tlie ])recedini; experiment (Comparison of Forks hy Beats), the only difference being in the method of observation. The beats in this case are detected with the eve instead of the ear. \ u / I iiouA ion y I'liysivs. W Practical Directions.— ( 1 ) Composition along the Same Straiy/it Line. — Clamp the forks to their supports so that tlioy may vibrate in the same plane. Bring up the lamp to about a meter from one of the niin-ors, and adjust its i)osition so that an iraage of the illuminated pin-hole is seen l)v the eye when plaeed level with the pin-hole and about one-third of a meter at one side of it. I'lace tiie other mirror to face the former at about one w.vtvv distance, and so that the image of the pin-hole as seen in the former is intercepted bj the latter. riace the teleseop • at about four meljrs from the second niii-ror, and focus it on tiie image seen in this mirror. The image as secTi in the telescoi)e may be a triHe blurred owing to defects in the mirrors. If possible, clamp the supports of the forks livmlv to the table, or if not, the supports nuist be held tightly by tlie hand when ex''iting the forks, to ])revent them mo\in<'. Excite each of the forks by a blow from the liammer. Il the forks are in unison, a luminous straight line of very gradually dimim'shing length will be seen in the telescope. This image reduces eventually, on the cessation of both forks, to the image of the pin-hole, without having undergone any elongation whatever from the beginning. Xow load one of the forks and re-excite them both. A ftraight line of periodically varying length will be seen. If the vibrations of the forks have equal ami)litudes, the length will vary from a iruTc point, the original image of the pin-hole, to a line whose length is equal to the masjniiied sum of the amplitudes. The poi?it corresponds to the interval of silence in audible beats, ai:il the long line to tlie burst of sound. :f the amplitudes i.re imt the .sune, a line, equal to the ■^ SOiM). 15 magnified difference between the amplitudes, will he observed to be the niinimum length of the fluctuating line. This accounts for the period of only comparative silence observed in audible beats. Count fifty of these variations from point to point or iiinimum length to minimum length, and calculate by the >rniula ii, - », the difl'erence between the forlcs, where «, and v^ are the frequen 'js of the forks, and A^ k the number of beats in the time t. The time between any two consecutive minimum lengths corresponds to the time of one andil)le beat. Measure the distance of the load index from th. ond of the fork-prong. Repeat the observation several ...aes, changing the position of the load in each case. (2) Composition at Rhjld vl«^A'.v.— Without altering the load, turn the forks in their supj)urts so that they may vibrate at right angles. This is mo^t easily done by turnino- thorn to vibrate at 4.>° to the table, the axes of the mirrors being in the same horizontal ])lane. Adjust, as before, until the image from the . ond mirror is seen in the telescope. If the forks have only slightiv different periods, a figure will be seen, changing from a straight line at 4.")' to the horizontal, through an ellipse, to a straight line at right angles to the former line, and then through another ellipse back to the original line, see Fig. 2. HDOOHHOOS Fig. 3. 16 LABORATORY PHTStCS. The time taken to make a complete cycle is the time of one beat. As in (1), count fifty of these complete cycles. They thould be found to correspond with the periodic changes in the previous comparison. liepeat the observations with loads in same positions as in (1). (3) Procure two forks which are not identical, and load the higher one to unison w-ith the other by observing when there is no periodic change in the figure. Kecord the |)osition of the load. Precautions. — Do not touch the mirrors. On no account is the fork to be excited by striking the prong carrying the mirror. Example — Knter results thus: Oist iiice of r^oati from Kiiil of Koik. (1) 3.5 cm. (2) 4 cm. m 5 cm. (4) (i cm. (•'■») 7 cm. Perioiiic Cliiiii;;e.s. Time. 50 50 50 50 50 80.0' 00. a" 40.4" 20.0" 10.4" Distance of IjoaA from End of Fork. Blank to he jiUed hi hij i^iuihnt. Periodic Clianges Time. ?i, - )i, .6 .H 1.35 2.5 4.8 SOUND. 17 6. TO DETERMINE THE VELOCITY OF WAVES IN A STRETCHED STRING. References — Watson, p. 358 ; Knott, p. 261 ; Hastings and Ik'acli, p. 523; Nicliols and Franklin, vol. in. p. 161; Ames, p. 171. Apparatus Required — A long steel wire; a stop-watch; a pulley; weii (1) where T ia the tCTision, and ?» the mass per unit length. If, therefore, the tension and unit mass be known, the velocity can be calculated. If the time of transmission of the wave from one end of the string to the other l»e ol^served, the velocity calculated from (1) can be veritied. Thus if ; be the length of the string, t the time of trans- miasion of a wave from one end of the string and back, then 11 V = (2) Practical Directions — Weigh a known length of the wire, and find )/i. Fasten one end of the lotig wire to the wall of the room, passing the other end over a pnllcy fixed some distance away. To the end which passes over the i)ulley fasten an attach- ment for holding weights, and put uii a weight, W, of abont one kilogram. I \u 18 LABORATORY PHYSICS. Strike the wire lightly near the end. A wave motion will be now transmitted along the wire and back. Place the finger on the wire about one inch from the pulley. The return of the wave can be distinctly felt by the finger. The return of the wave can also be observed by the eye Start the stop-watch just as the first pulsation is felt, and take the time of fifty returns. Measure the length of the wire in centimeters. If the length be measured in feet, reduce to inches and multiply by 2.U for centimeters. Expresg the tension, 7", in dynes. If the veight be in pounds, multiply by 456.3 x 981 for dynes. Calculate v from the formula V = a/~. y m Calculate v from the observation of fifty returns. Repeat the observation three times with diflerent weights. Example — Enter the results thus: Obs. m I Time of Fifty Returns. T vfrom Oboerva. tions. vfrom m' 9462 7089 1st cba. 1 2(1 obs. I .02275 .0'.'275 1938 1938 20.5" 27.2" 2032622 1136471 9452 7171 Blank to be filed in hy student Obs. 1 »i I Time of Fifty Returns. T vfrom Observa- tions. 1 tifrom III' ~~ souyD. 19 I •3 7. TO DETERMINE THE PITCH OF A FORK BY THE TRACE OF ITS VIBRATION ON A SMOKED FALLING PLATE. References. — Darnes'B l*ractical Acoustics, p. 75. Apparatus Required. — A tuning-fork of fairly high fre- quency rigidly fixed to a buitaMu !3Ui)i)()rt ; a suitable '••lass l)late; a pair of dividers; a centimeter scale; a hog's l)ristlu; a plucker for vibrat- ing the fork. Theory of Experiment — If a tinukcd glass i)late be let fall freely, so as to re- ceive the trace of a vibrating tuning-fork, the trace on the j)late will be a sinuous line. The vibrations will be very close at the bottom of the plate, lengthening out toward the top, jirovided the plate at start- ing is in contact with the tracer on the fork, due to the slow motion of the plate at first. Suppose at starting the tracer of the fork be at A, and that the vibrations can be counted between the p.jints B and C. Denote the length AB by ^S", and AC If t be the time it would take the point B to fall to th« tracer, then 'S' = h/t' (1) Similarly, ^S = h^r\ (2) ^. being the ti«ie it takes the point (' to reach the tracer. Fig. y. ^1 hi 20 Hence LAJiOUATORY PHTSIC8. , <_ /'-iS, /Is where t, ^ t k tlie time it takes the tracer to pass from B to C If V be the number of vibrations between B and ^, then tlje vibration frequency of the fork is given bj the equation and and therefore n = V t, - f • (5) Since v can be counted, S and S, measured, g is known, n can be calculated. Practical Directions Clamp the fork -stand to the table. Fasten a oristle to tlie fork at an angle down- ward of about 45°. Smoke the glass plate by passin*,' it rapidly back and forth through a smoky paraffine-lamp flame. The glais plate sliould be quite thick, so as to make it strong and compara. tively heavv. Hang the plate, by means of a loop of cotton thread, to the supports provided for the purpose. Adjust it carefully so that it just touches the bristle when hanging vertically with its .u.ok .d surface in the plane of Fio. 4. 80 um). tl m vibration of the fork. Fig. 4 shows apparatus when com- plete. Set the fork vibrating by gently pulling off the plucker. If the plate dance about, its plane is not parallel to the plane of vibration, and must be adjusted. When properly adjusted, sever thecvspension by touching it midway between the supports with a lighted taper. A clear continuous trace will now be on the plate if the adjustments have been made with sufficient care. Select two points corresponding to B and C, between which the vibrations can be counted. Measure the distances S and 5, between the first point of contact and the points B and C. Count the vibrations between B and C. Calculate n from the observations. Repeat the observations three times. Example. — Enter results thus : g = 981. Observations. S Si V n 1st 2d Sd 1 1 1 10 95 10.3 106 103 108 1075 1080 1074 Mean vi line of n 1076 Blank to he filled in hy student. Observation. S s. V n l8t 2d 3d Meaa vt ilusof >i 93 LABORATORY PIIT8ICS. 8. LAWS OF VIBRATING STRINGS. -MELDE'S METHOD. pp. 173-1 7;>; Nichols and Franklin, p. IGo- Haatin... and Reach, p. 5rt3; Carhart, pt. i. p ls8 ^ with cord attaclunent; a snmll pulley fixed to an upright stand 80 that a cord can he stretched over it ; son.e snJl weights ; a piece of hnen thread or small silk cord to ^^17 of E-Periment._If a string of length I be nmde to vibrate under a tension T, we have seen that the laws of vibration are expressed by the e.pmtion n (1) Where n is the number of nbrations per second, / the half wave,e„gth of the vibration in the string, 7' the t^.sion, and m the mass per nint length. .tJL^n -«««l'ed"to the prong of a tuning-fork be vibrating, the cord between the pulley and the fork will be thrown into vibrating segments, as shown in Fig. 5, when Its length is properly a/ .' (2) 1 IT By varying the weiglii-s therefore, the law n = ^^\/ — can be experimentally verified. Practical Directions. — Weigh a known length of the string and thus find m, the mass per centimeter. Attach the cord to the prong of the fork, and stretch it over the pulley. Attach 30 or 40 grams weight to the end of the cord. fe. . the fork vibrating. Measure the length of the string between several nodes, and obtain the average length, I. Observe the weight on the string, and reduce to dynes. Calculate n from the formula 11 _l /T Now vary the weights three different times, and repeat the observations for I. Then Example.— Enter results thus : Obi. 1st r I n 512 T W 760 767 768 2d '•••WW 1 j'.:.vu 8d 88290 10.75 I'Jilled in Blank to h hy student. Ob«, T I n T . i! 9 TO DETERMIHE THE VELOCITY OF soiiMn r» VARIOUS MEDIA BY MEANS OF koNDT'S TUBE.' and !• a„ki,„ vol. ,„ ,,. i,,o; Crlrnrt, ,,t. ,. ,,. 210; Ames, p. 85; iraatmgs and Head,, p. 5til ; Anthony and Braekett Apparatus Required. -Kundt's tube with 8o,»e fine light powder, such ae cork-filings; a wet silk cloth; a centinieL scale, a thermometer; a drying-tube ; a meter or so of gas- tubmg; a pair of bellows. ^ K„Ji^''T 1*^ ^^P«"°^«'^t-If the apparatus, arranged as a Knndt s tube, be supported horizontally and some light powder evenly distributed over the bottom of the tube the powder wdl arrange itself into heaps when the rod is ruLbed Buthciently to emit a note. 80 VXD. 25 Tho rubbing produces loiigitiuliiml vibratJorw in thu r<)«l, which are cuminuiiicated to the air in the tijl>e m coiiipn-^- Bious and rurefuctiona. The iM>wder i.s forced away from the places of motion, tiio loopH, to the poiiitn of re^t, the nodes. If the rod be rigidly fixed at its centre by a clamp, its ondrt will be at tho middle of consecutive loops, the clamp bein;; at tho intcrveiung node. The length of tho rod is therefore ecpial to one-half of the wave-length of tho note emitted. Denote the length of the rod by /. The distance from heap to heap, r/, is e^ual to one-half of the wave-length of the same note in the gas. These lengths are described in e«pial times, since the gas in the tnbe vibrates in muson with the rod. The velocity of sound in any medium is equal to the wave-length multiplied by the number of vibrations per sec- ond. Therefore I 5' (1) V, V. V, and V, being the velocities in the rod and gas, respectively. Knowing the temperature, ^„ of the air in tiie tube, the velocity in it may be obtained from the formula r, = 33250 ^1 -f .Ou3»i057, .... (2) 33250 being the velocity at 0" C, and therefore v, can be calculated. Practical Directions.— See that the tube is clean and dry. Clamp the rod in the middle. Pull out the adjustable plunger, and shake into the tube either dry cork-filings or amorphous silica. Replace the plunger, and support the whole horizontally. The powder should lie in a thin coating along the bottom of the free part of tho tu!)e. 26 LABOR ATOIiT PHYSICS. Open both stop-cocks and connect one of them to the bellows through a drying-tube. Force dry air in for some time before closing the cocks. The rod, if glass, may be excited by stroking its free half with wet silk ; but in the case of brass or other metals resined chamois will be found better. If after the first rubbing the nodes in the tube are not well defined, adjust the length of the column of air by the plunger and repeat the rubbing. Continue the adjustment u: til the nodes arc sharply defined. When the nodes ha>e become sharj), measure tlie distance to each from one end of the tube. Subtract the distance of the middle one from the first, the distance of the next one beyond the middle from the second, and so on to the last one. Take the mean of these results and divide by the number of loops contained. Th;3 should give a good niean value for a Lalf wave-length of the vibrating air in the tube. Calculate the velocity in the material of the rod by for- nuila (1), having substituted the velocity in air corrected by formula (2) for the temperature of tlie room. The velocity in dry aiv at 0° C. may be taken as 33250 cm. per second. The temperature of the air may be obtained witli suffi cient accuracy from a thermometer on the table near the tube. Take ob.orvations for both the glass and brass rods. Example — Enter results thus : Temperature of air 16.4° V Hence v^ = 33250 /l. 060024. = 34230 cm. per sec. SOU^D. 27 No. of Node. Brass Rod, I = 106 cm. Glass Rod. I = 108 cm. Distance from fisioii. Length of Four Loops. Between N. ■■ Distance troin Piston. Lenptli of Hve Loops. Bft«een Nos. 1 2 3 I 1 6 1 8 9 10 10.5 21.0 82.0 4a. 5 52.6 63.0 73.0 83.0 7... 15 2i:.5 ■JOO .... 42.1 42 41.0 40.5 5aud 1 6 " 2 7 " 3 8 " 4 37.5 45 53.0 60.5 68.0 75.5 37.5 38.0 38.0 38.0 38.0 1 and (! 2 " 7 3 " 8 9 " 4 10 " 5 Mean \ length of ( 41-1, 37.7 7.09 1 loop = ^ io,a5 ■y, (for glass) = -;r-r— /\ 34230 = 487800 cm. per sec. 1', (for brass) = 108 I03y - X *' = 35620(» '• Blank to be Ji lied in hy student. Temperature of air No. of Node. i Distance from Piston. Lenitth of Betwten : Nos. Loops. : Distance from Piston. Length of Loops. Between No.-*. Mean length of 1 loop = S8 LABOliATORT PHYSICa. ^i 10. TO DETERMINE THE VIBRATION FREQUENCY OF A TUNING-FORK BY MEANS OF A PENDULUM-CHRON- OGRAPH. Apparatus Required — A Buitable pendulum; a tuning- fork; a stop-watch; a centimeter scale; a set square; a rubber hammer; a suitable clamp and stand for mounting the fork. Theory of Experiment — If a pendulum be made to swing past a fork vibrating vertically, the pendulum and the fork being so arranged that the vibration of the fork can be traced by means of an attached bristle on a smoked glass surface attached to the pendulum, then the path of the point attached to the vibrating fork wi.l be a sinuous line as ABC, A and marking the beginning and end of the swing respectively See Fig. 6. o r /• N. u D : G / ^ H / / Fig. 6. If the arc through which the pendulum swings be short Its motion may be regarded as a simple harmonic motion along the line ^4 C. I'^AHH*"^- '■ :^rj,. ■^/^. ''-'-■ '!r f--. -^ITK^,. fi'iS^^ SOUND. 29 If the time of motion from /' to G, that i.--, from IJ to J5i', can be found, u d the number of vibrationa and E^ two points on the line AC, on the same side of the centre. Erect perpendiculars DFII and EGK. Join JI auI A' to the centre of the circle. O. Denote the angle I/O A by • V . 360 <. -< "(0. - - 0)P OD _('^- -y) ^>// a . . (2) i and COS 0. - ^^ - ^ • 80 LABOR ArORT PlITSICS. If «, y, y. be measured, and 0. can l,e found fro.a the matlienmtical tables. Hence, n can be calculated from equation (2). Practical Directions-Smoke the surface of the glase plate by pas.ing.t rapidly back aiidforth through the flame of an oil-lamp 1 eplace the plate in the damp provided on the pendulum tor tJie purpose. Adjust the stop-catches on either side of the pendulum BO that when it is released from the one it swings aeross and just catches on the other. CJamp the fork whose rate is to be determined, so that it vibrates in a vertical plane. Adjust the fork and plate so that the bristle of the former just touches the latter throughout its entire swin.. When the pendulum is held in one catch, the bristle should touch tlie glass i>late near one end. Eelease the pendulum from the stop so that it swings past the fork. The bristle will describe the arc of a circle _ Bring the pendulum back to its original position and ex. cite the fork by a blow from a rubber hammer (if it be not driven magnetically.) Kelease the pen.lulum from the stop again, and over the arc already described a sinuous curve will be traced. To JimJ P.-IIaving obtained a record of the 'vibrations of the fork, without altering the adjustments of the pendulum set It swinging, and take carefully to the fifth of a second the time of 100 swings; that is, 50 complete oscillations. F-om this observation calculate P. To fvd and 0,-Take out the plate of glass. Care- fully join the extreme points of the arc by a straight line At rwo points (as D and E in Fig. (5) in fhis line bv means of a sot s.)uare, erect perpendiculars. ' ^ Measure carefully, hy means of a pair of divider'^ and mm^^mi^.m HOUND. 31 luilliineter scale, the lengths corresponding to y, y„ and 2tf. Since the values of and 0, depend only on y, y„ aud r-, they can at once be calculated. To find V. — Count carefully to the tenth of a vibration the number of vibrations l)et\veen the two perpendiculars. Precautions. — (1) Be careful not to break the glass plate when smoking it ; it must be moved rapidly back a id forth to prevent uneven heating. (2) Be careful tu adjust the stops of the pendulum so that the whole arc will be on the plate, otherwibe the length, a, will not represent the amplitude of vibration. Example. — Enter results thus: Time of oO oscillations, 07.00" Therefore r .'/ = //. = '2a = cos = C(J3 0, = l.!>4 7.;} 14.0 32.4 20.4 8.9 2.2 1(^2 128.7. 0. — .5t)° 0' ■- 82° 48' Hence, n = Blank to he filled in hy diident. Time of 50 oscillations, P y = 2<( = cos = = cos 0, 0. = /; -.i-v-- LIGHT. II. TO COMPARE THE INTEWSITIES OF TWO SOIlprpc OF UGHT. BlraSEN-S PHOTOMEraR ^ Bea!!''r nr rdT' ■'• '"• Kn°".l>.2«; I.a«,i„,. „„,, "■• !'■ 117, Antliony an.l Bn«ikeM, p. 447; Barker ,> 3S, be illuMiinatcl fro,,, l,ol,i,„l ,1, i' . ""'or I,a,„l, it n ii, iiiLitrore, the two sources of Uo-l.* +^ v. pare, be placed „„e „„ eaeh side of tbo V^L 1 , ' li^ •"'"" ^. tbe direetio., o[.„e pa;::r l^r Zr^ "^"" ga.a.-,.t „„„ „„ p,,„ „f „„„ „,„„,;, «.»;:, ^:^- "- 33 f I: t i 4 ^i^^msMM. LK.UT. 33 A substitute for the gi'eH>e-.sj)<)t may l)e made as follows: Take two rectaiitri|) of tin-foil, adjusting so tliiit two other faces are in the same plane. Place the comljinatiun between tlie sources of light so that the lights fall perpendicular to the surfaces parallel to the foil. Adjust until the two faces in tlie same plane are the same shade. liecord the observations of di>tauce> /■ and /•'. Iwcpeat the observations for thi'ce positions of tlie lamj), filament side on, filament vil^iv on, filament end on. Uei)eat the observations again with the lamj) and candle 75 cm. apart, and again 100 cm. apart. Example. — Enter results thus: Distance Position of Lump between Lnriip and Candle. I-. (Lamp.) )•,. (Candle.) /, /, - .' . ,'. Filuineiit side on 00 89.7 10.3 14.9 (1) " edfie " ;^,8.o 12. 10.1 (2) end " 34.9 15.1 5.3 {3) side " 75 r.9.r, 15.5 14.7 U) edge'- 57.0 18.0 9.9 (2) end " 52.2 22. S 5.2 (3) side " lUO 79.2 20.8 14.5 (1) edjie " 76.1 23.9 10.2 (2) end " 69.9 30 1 5.5 (3) Blank to he Jillal in h>j atiuJent. Position of Lamp. DistHnoe bet\ve:'ij Lamp and Candle. )•. (Ijimp.) , (Candle.) ///; = c'/r,'. I f f : 34 LA nouA ruit y riii\sjv\ 12. TO COMPARE THE INTENSITIES OF TWO SOURCES OF LIGHT. RUMFORD'S PHOTOMETER. References.— Tlie siime references as in previous case. Apparatus Required.— A Uiiniford i)hotoniete.' ; a wax candle; an electric lamp. Theory of Experiment.— The intensity of illuminavion on a given surface produced by a source of light is inversely as tlie square of the distance from the source of light, and .lirectlv as the cosine of the angle which tiie huninous rays make witli tl»e normal to the illuminated surface. If the two sources of light be placed in front of an upright rod behind whicli is a screen, each nill project on the screen a shadow of the rod. By altering the relative position of the two sources of I'ght the intensities of the two shadows may be made the same. Then, since the shadow of each is illuminated by the oth-?r, the illumination of the screen due to each light is the same. Suppose / to be the intensity of the one source of light, ?• its distance from the screen, a the angle which the directioyi of the l)eam makes with the normal to the screen ; then the illumination due to this source is equal to /cos a V If /,, a,, /•, be corresponding values for the second source, then this illumination is efpial to /, cos ff, i iHiK:^c^^Sd:^i»^^fiiiAi^£'^^ LIGHT. 35 iiiid fiiice tlioc are equal, we liave / cos a /, cos a <»r r' '".' I i\ cu.s n-, /, ~ /•,' CO.S rt (I (^) \l a — . 225; Carhart, pt. i. p. 211; Jones, p. 137; Hast- ings and Beach, p. 611; An.o.s p. 405; Anthony and Brackett. p. 405; ^^^atson, p. 44f!: Barker, p. 406. ^ Apparatus Required. -A di-awinnr-board; a piece of sil- vered glass about 10 cm. long and 1 cm. wide; a clip for hold mg the glass in a vertical plane; half a dozen pins III ■! I I mil III III II II IIMI IIIIMi I "III SlikliA JMI^Miii^^^illiiii^ •.>• 1.^- X* i Lium. 87 Theory of Experiment.— If u plutic minor l)e lieM in a vertical plane and a liiiuitious point plawtl in from of it, an imago will be ^een formed heliind tlie mirror, no matter from what point of the mirror it may U; reflected. Fio. 7. Let A he a luminous point. Suppose it to he reflected successively from the points a, />, E^ F, on the mirror. If the lines Zr, MJ), XI:, OF, he drawn markinjr the directions in which the image is seen from the successive points, it will be found that they all ])ass throuj;!. a point be- hind the mirror, the point where the image is seen. Denote this point by B. If A B ho joined, then by measurement it will be found that AJfis equal to MB, and that A B is perpendicular to FM. From this it follows, obviously, that the angle of incidence is equal to the angle of reHcction ; e.g., the angle PFA is equal to the angle PFO, where PF is "perpendicular to FM. 38 LA/iOUA ion Y I'll YSK S. Practical Directions.— (1) iMistun u >ln..it cf i-uU.I foolsmp pajwr \x\x}\\ a drii\viii^'-lH.Hrtl. Stick ii iiniiil.fr of pins vciti- cally into the hoard aloni; tjjio ol" the liruH of the paptr. Let these l)e represented by the points /•', h\ />, t\ in the preceding diagram. Place the mirror in tlie winie vertical |»Iane, with its sil- vered face tonching the pins, and adjust it so that i^s edges are parallel with the paper, the lower edge being about one centinu'ter above it. Stick another pin, also vertically, at a point corresjMnid- ing to .1 in the diagram. lierieet this pin successively from the points (\ />, h\ F. Thi> can be done by getting the image of the pin at A in a line with the pin at each of the points, and marking the direc- tion in eacli case by means of pins at /., J/, .\'. ^ame j.in will do for marking the \)o\\\U Z, M\ N, (). If the obse-vntions are carefully taken, the lines Z6\ J//-», X K, and (>Fw\\\ meet in a ))oint. To show tlie results, draw the complete diairmm. (2) It follows geometrically that if the angle of incidence be ecpial to the angle of reflection, the position of the ima«re is liehind the mirror at a distance e(]ual to the distance the object is in front, and that the line joining the object and imai:-e is perpendicular to the mirror. Hence the law of reflection can be verified exi)erinieiitally by n)easuring these distances. Place the mirror as I)efore in a vertical j.lane so that the lower edge is about a centinjeter above the pa])er. Stick a pin vertically at a distance of ](» to 15 cm. in front of the mirror. Xow M-hile observing the image of the jnn behind the mirror, stick another pin so as to coincide with this insa-'e. LIGUT. ;j!> In order to deteriiune wliether the two rcully coiut'i..e, uiove the eye at riglit uiiglca, hack and forth, to the direction of the two pirirt. If the second pin coinciden with the image, the two will appear to move together, otherwise they will appear to move away rom each other. Having adjusted tlie pin to a proper position, measure tlif distances of the two pins from tlie silvered side of the mirrtr, and verify with a set-scjuare the j)eri)endicularity in each case. The small differences may l)e due to tiie unevenness of the glass, or to faulty observations. Take at least six readings. Example. — Enter results thus : (I) Show complete tliugrum. {'!) Show diagram an'bitid. 10.2 112 15.2 17 nifferfncf. .2 .1 .2 .2 Blank to hf jiUed In hij utmh nt. DiHt. of Pin from Mirror. Hint, of ImaK*- b«'liind. |iiff, it is evi• i : f i I 16. (I) TO VERIFY THE LAW THAT WHEN A RAY OP LIGHT IS REFRACTED THROUGH A PrYsM THE ANGLE OF INCIDENCE PLUS THE ANGLE OF EMERGENCE IS EQUAL TO THE DEVIATION PlSs THE ANGLE OF THE PRISM. ^'^^^"'^ ^^^^ (II) TO FIND THE REFRACTIVE INDEX OF THE PRisM. "■'^arl,, J., hh : k,u)tt, ,,. 26;^; Ames, p 42{» Apparatus Required.- A prism; a pair of dividers- a cr.mmeUM- sc-ale: throe pins: a set-square p n.Mu ABC Hg. 12) from a himinous point />, at the point C>. and bo bent through the prisn. alon. a <1 root n Z eniergincr ah.ntr /^S POD w fl.o i r '^^*^"*" v^*^' /'/?s"thr .nurl f ^ ^ '''"^''^ '^^ i-.eidenco. and Vt/i-.S the an.irle of emerc^ence, where DQ and /f7? are perpen- dicular respe<.tivelv t.. J /,> ;,nd 16^ * ^ Denote PQU I.v 0. /,V>V I,,- ,;, j^^.^f. ,^^. ^ ^^v.. ^-c/>^and^Xn.etin/:..^,,^:;:;l,^^^ and Fk;. 12. QFS = 1 80 _ rf QGR= ISO- /, FQ(; = 0, Hence 1 N(,° __ / + i s,, . _ rf + + ,/. =, g^jo", ami therefore ^ ,^. ^ ^^ ^ Qji^^ ,,j. ^^ ^ ^^, N ow since 0, + ,/-, + is,) _ ; ^ j,s„o^ ^j^^^.^^ ore 20, = /, or (A. = / 48 LAliOllATOHY PUY8IC8. Hence sin /* = 2 mx- (2) It may be sl.own geometrically that when = ^., the de- viation, d, is a niinimuiii. Practical Directions.-(I) Describe a circle with a radius of 10 cm., Fig. i;{. Phu-e the prism with it. edge at .4, the centre of the circ e. Stick a pin vertically at a point 1\ such that the angle which /'./ makes with the face AB is less than a ri.rht angle. Observe the direction of the refracted image alo'nir the line AR. ^ Stick a pin at R, in such a position that the image of the pm at P is in a line with the c^h^a of the prism and Ji. Draw JJA pi ri)endicular to the face AB, and EA per pendic-nlnr to the face A C. Join PA and liA, and produce I*A till It cuts the circle in F. Then PAD = 0, AAP = y,, FAIi = 6. Draw PO perpendicular to J) A, FiV and FMto Ali Then, hN sm if) = — , t^iii '/' - pin <^ FM where /• is the radill^ .:,f t-he cirele. LIGHr. 49 Measure PO, EX, FM, and calculate the values of and 0, ^, and 6 ttoin the sines. Fig. 13. periment ll/' '^'" '"^^' '^ ''" P"''"' ^^ *^'^ "^^^^'^^ ^^ E- Substitute the values in formula (1). this^IuL^.r' ''^■'""'* ^"' "'""'""•" ^^^•^^^•^"- To aecon^plish axis and observe whether the deviation increases or decreases by obsernn. whether the direction, AI,, of the refracted ra" make, a larger or smaller angle with the direction, JF of wher I v" ,'■"'"" ^ '' ""^' reverse the process, tion, the angle will decrease. /^/i.!rn^'"'''''-^' ""'"'""'' '^"''^ ^'« found that angle r^Vli reaches a minimnin viln,. .... ' *i • ^^ which U-.V fl ".""":'"'" ^'>l>'^* '"H. then mcreases no matter ^Uiich \\A^ the ^rism is turned. 50 ?: LAIiORATORT PHYSIVS. Adjust for the exact position of „a«i,n„,„ deviation and measure 6 as before. Calculate /i from formula (2). Example — Enter results thus: Show complete diagram in each case. I. ^'Q =7.r Hii 0= .77^ h\V = 9.85 An tf} = .j)>io. JfF = \)A2 m\S ~. .042, = 50° 24' tf) = 80° 00' iii 1^' = J//' = sin 6 = i^/aw^- "•) . \ . »I 1 .. > ^<". III. ].. .,2, A.:tli(>nv and I'.rackftf. u s- '"i'-l<'''S !•• 41!>; (Wlmrt, |.t. ,, j, >>J., ' ' Apparatus Required.- A .pLercueter ; u sp|.ori<.al M„face • Theory of Experiment. -Tl,. .|,la.,-„,„.t,.r ,.,„«i..„ „f „ of tho colh,- ,., «l,i,.l, ,|„ ,,,„ „„ a,„u.l,e,l L tin.. ,s," „ «.rO,ns „ g™|„„,e,l ,|i,k, «l,icl, moves ,,„i,e near „ ,-, . ■ a.o,I n,„.^-,,t ...lo „,t„el,e.l ,„ „„e of „,o',e«». ',•::;; ...ent ,« hrst so. „„ a plane gl„» „„.f»ee and «,e een.re " ew turned dl the ,K,int jn.t ,„nehe» tl,e surface of „,e ,L It .. then ,mnsferre,l to the spherieai snrfaee, a„.i L c ntre «.•".»• turned nntil it ,«ain tonehes the snrfaJe. If , ',"2 .l.m.™,ee „f the two readinf-s. and / (he .listance hetween the Icff. ot the s|,l,eron,eter, th,., the radins of the spherieal s,,r. jaee is given by the equation • This may ho sliowii thus; I.et AIi/)C he the- sph.Mical surface (Fi-. U), a„d D the po.nt „,u.,, the sereu- of rhe sphero.uete.- touches the surface ul.eu the three h>jrs are aI>o touchin.^ it Then .1// is tlH- .iian.eter of the circle passin. ti.rouHi three points wJiere the legs rest on tlie surface. i4 H J.A uoiiA roH Y j'li rsics. If these tliree poiiitH bo joined on the ]>lune of tuu circle, an eciuilftteral triangle wonld be formed. • Denoting the distance between the legs by /, we have geometrically where a is the radium of the Rniall circle. Now (2/' - 6)6 = a\ (2) Bii:ce D/i(yh a semicircle, where 6 is tlie distance from flie point U on the snrface to the plane of the feet of the i 1 ^^pherometer, that in, the second po»itiun. k^lJL UtiBT. 68 Hence, combining (1) and (2) and solving for /•, we get (3) Practical Directions. — Tlio ecivw of the Hplieroinetor hat UHually a pitch of ^ mm., and the upright scale is similarly divided. The graduated disk is also divided so as to give exact fractions of a turn. I'lace the spherometer on the plane glass surface provided for the purpose, and turn the iscrtw until it just toJichcs the surface of the glass. Read the u})right scale and also tht disk. Place the spherometer upon the spherical surface and turn the screw until it again just touches the surface. Read the upright scale and the disk. If the graduated disk he divided into lOu ]>arts, divide its reading by 2, aisd add to the reading, expressed in milli- meters, of the upright scale. If, however, the graduated disk be a(liii|; on Hpherical Surface. 1 i (mm.) / (cm ) 1 '■ (em.) Menu val ue " ' ■ ! I I i8. TO DETERMINE THE RADIUS OF CURVATURE OF A CONCAVE MIRROR BY REFLECTION. References.-K'.mtt, pt. ■,. ,,. 2:,0; Ni<.l„.I.s and Frank- lin, vol. in. p. .•?!>: Ames, p. 413: IIa..tinirs and iJeael, p. 613: Antlumv an.l Tirackett, p. 40S : AVatson, p. 459 • Barker, p. 419; Carhart, pt. i. p. 249, uonr. Apparatus Required.— A concave mirror; a cli|>-staiKl ; a piu ; a centiincter scale ; a sphL-rometer. Theory of Experiment.— If an object be held in front of a concave mirror beyond its geometrical centre, an inverted Fi<>. 15. image of tbe object will l)e seen between the object and the nnrror. Thus if the obje be held at A (Fig. 15), and C be the geometrical centre, the image will be seen at a point />, when the angle AKC = GKD. If now the object be moved up to the centre, 6', the direct and reflected rays will have the same path along (JK. The image will therefore coincide with the object. If, therefore, the object be so placed that the image is seen to coincide with it, the distance of the object from the mirror is the radius of the mirror. Since /, the focal length, is equal to one-half the radius, it can be obtained directly. Practical Directions — Place a pin vertically in a clip in front of the mirror. Adjust its position so that an inverted image of the pin can be seen between the pin and the mirror. Move the clip toward the mirror, and adjust until the point of the image appears to coincide with the point of the liin. To determine the exact position of coincidence, let the pin and the image slightly overlap and then move the eye 86 r.A nouA TOR Y I'j/rsivs. back aiul forth so that tliey can be seen from ditferent polnb^ of tlie nurror. When the i>oint of exact coincidence is found, the pin and nnage will continue to occupy the same relative l)08.t.on to each other, no matter at what point of the mirror thev may be observed. Having thus found the point, measure by means of a cenrnneter scale the distance of the pin from the mirror. liepeat the operation several times. The mean of the observations may be taken as the radius. Verify your results by a spherometer. Example — Enter results thus : Observation. r Ist 7123 8d 72.31 8d 73.25 4th 72.20 Sth 72.18 6th 72.24 t Mean value 72.23 r by spherometer 72.3.'} Mini- to hejilled In by stiulmt. Observation. Mean value r by spherouicter tlOHT. 57 19. to DETERMINE THE RADIUS OF CURVATURE OF A CONVEX MIRROR. References. — As in Experiment 18. Apparatus Required.— A convex mirror, suitably mounted; two clamp-stands holding small upright rods; a tape meat>ure; a centimeter scale; a telescope. Theory of Experiment. -If 00,0, (Fig. 16) be the axis of a convex mirror, BB, ; A and A, two objects situated so A Fig. 16. that ^^ is equal to^,^, and AA, at right angles to 00 C and C, the positions of the image of A and A, as seen in'the mirror, 0, being the centre of the spherical surface; then _1 L_ 2 AB BC - ~ OM' ••••(!) u V r ' where w, v, and r are resi)ectivelj equal to AB, BC, and 0,B. nr Hence V = (2) 2w 4- r Denote CC, by x,, AA, by x, and if.V, the intercept m^su^v^sar^^^ ."ift^.-TViS^-stf, 58 LABOUAIORY PHYSICS. 5i OH the tangent to the surface at O^ made by joining OC and Then from similar triangles we liave and or X — «4 - r a;. /• — ■ v' 3l a?. = (9^>. + GO, » a'. « + V », ?< » (3) (4) IS since, 00, being large as compared with AA,, 00, approximately equal to AB. Combining (3) and (4), substitntM.g for v the value found in (1), and solving for /•, we obtain In practice the distance 00, may be substituted forw for the reason given above. The measurement of MN^ (x,) requires the use of a telescope. Practical Directions.— Fix the mirror in the clamp pro- vided and in an upright position. Place the telescope at a distance of two or three meters from the mirror and adjust its direction and height until the axis of the telescope is in Hue with the axis of the mirror. Place the clamp-stands with the upright rods in the positions corresponding to A and A, (Fig. Ifi), the line joining the.n passing through the object-glass of the telescope and being per- pendicular to its axis. AA, should be from 40 to 70 cm. The telescope can now be focussed on the images of the npright rods seen in the mirror. To obtain the intercei)t at the snrfaco of the mirror corre- sponding to i¥iV^or .«„ fivsten u centimeter scale across the LIGHT. 59 face of tlie mirror in a position ci^rrespondin*,' to />/>, in the fiirure. The upper edge of the scale siiouid approximately hi.sect tlie mirror. By slightly altering the focus of the telescoi)e both the scale and image can [)e seen and the distance between the images as seen on the scale observed. Head this distance, x . Measure the distance, x, between A and A^, Measui-e the distance between the object-glass of tlie tele- scope and the surface of the mirror, ?/. Substitute in formula (5) and calculate /•. llepeat the observations, changing the positions of the tele- scope and upright rods each time. Verify your results hy the spheroiueter. Example. — Enter results thus : Obs(. Method «. Mean value for/. I-en.s. Method ft. /■ Mean value for/. J*^S^^' ■^^m^^r^'-s^mij^. UOIIT. 63 1 ax. TO FIND THE FiKAL LENGTH OF A CONVEX LENS BY THE DISTANCES OF THE OBJECT AND IMAGE FROM THE LENS. METHOD II. References — As in Method I. Apparatus Required — In addition to that of Method I, a lamp and tine wire grating or other suitable object for illinni- nation will be requireil. Theory of Experiment.— As before, n and v being the re- spective distances of the object and image from the lens, we have from which/ may be readilv calculated, if v and v be observed. Practical Directions — Mount on one of tlio stands the fine wire grating, with the plane at right angles to the bi-nch. Cover the grating with a large sheet of paper having u small holp near the centre. Mount the lens on the second or middle stand, so that its axis lies along the bench in a horizontal line with the centre of the hole. The thinl stand carries the ground-ghiss screen, mounted at right angles to the bench, so as to receive the image of the wire gauze. The object, lens, and ground-glass screen should occnpv he same positions in relation to the indexes carried bv them. Place the light directly behin 1 the hole in the pajwir, and us close to it as possible. Adjust the positii.ns of the lens and screen along the bench until a clearly detined image of the illuminated object is obtained If the focal length of the lens be less than one-fourth the available length ..f the bench, an image of the illuminatctl wire grating can in tills ni.uiniT be readily obtained. .-^ ^^ r'H^f^^:'^' M LABOHATOHY PUYSICS The image is best observed from behind the ground-glass Read the position of the indexes carried by the wir« screen lens, and ground-glass screen. ' Tlie adjustment of the jwsition of tlie lens should be nuide three tunes, and a mean ot the readings taken for a and v. Calculate from // and v, the distances of the ohjt«t ui, image from the lens, the value of/, using formula (1). liepeat the observations three times, and take the mean value of/". If there be too nmeh glare from the light behind the wire grating, it will be well to cover it with thin white paper. Thecxperiuient nmst be performed in a darkened room. Example — Enter results thus : Lens A. It. Mean u. V. Meant;. ' /. Mean /. 30. ) 29.8 ^ 30.1 ) I 29.96 20. ) 20.2;- 19.9^ 20.08 1 ^^ 40. 17. n j /' 40.2 40.4 40.3 1 16.9[ ' 16.7 16.9 11.9 36. ) 35.8- 36. a) 36.0 Blank t IS. 3 ) i 18.4 \ 18.0) 18.2 1-M 13 heJiUed h < hij Hudet it. u. Mean u. V. Mf. ri i>. 1 1 /• Mean/. . . 1 UUllT. 22. TO FIND THE FOCAL LENGTH OF A CONVEX LENS BY CHANGING THE POSITION OF THE LENS METHOD lU References.— Same as M.tlio*! \{a). Apparatus Required As in ]\I thud II. Theory of Experiment— If tlic distaticp })etween ol.jcct and wrt-en l>c more than four time.-< tlie focal length of th.* lens, tlie lens will have two positions wliere a rleaily defined image of the olgect will be o! *ained on tlie groiind-glafs, screen. Let tlte dihtjince between the object and screen be /, that between the two j-ositions of the lens a, and. as before, /the focal length. Then we have 111 1 ^ , . -^ -r ~ = -T., for the hrst position. and — h - = "/.» for the second ^'. «'. / Fnrther, it is clear, since I is constant, that v — r and V = n, ; that is, the lens will be at the same distance from the ground-gla:ss screen in the second case as it was fiom the ol»ject in the first. Hence we have u -\- V = I, I/, — It z= a, ?/, = i<, and tlierefore / - a u = / +" o ' Substituting these values of >i and o in equation (1), we obtain f = ^. ■i\ 66 LA nouA roH r nirsics. TIio above rulatiofi in iiide|)Cii(!ent of the (ligtAtict's l)ctween the tiurfuce of the lunn and tho ol»ject and image, which dis- tances are uuich /nore ditticnlt to nieasure accnrately than tho distance a. For accurate work it must, however, be remembered that n -{- t) in not egl.^jir:^^^v:'^r.-.-^i./^-^^ --•••'■y rf^y.: LidJir. 07 Move tlu; Ilmi!* until, on looking tlmmgli tli»j tele8co|H', the wirurt of the ilhiii' Muted hereen arc w;cii iu focun with the other. No cuiilijHiun ut' ocreeii iiiul iiiiuge can urise if the two bo inclined to eiwh other jw suggebted. It irt iniportitiit tluit the image bcreen should not he u» > ';d after i"oeUi»f*ing the telewjope. A good pliiii i^ to Uhe u imwerful nil.} ■ ,' -i liive the posi- tive ejopiece of a teleHco|K.', iintl moi i i ii -< . nd 8creen-otan«l bo !i8 to ni(»ve with it. ^! ■ | ■ m ■• ii .d .. ;e can be obtiiined in thin way. Example. — Kntur remdtb thub: 100 72.1 72.0 Me^ ,1 :2.lo 12.0 Jiliink til hf fUtd hi hij fi(>ulent. Mean ii "a^aa^ESlBeeJU^^Xr^fM.^irt ^J!S Ill 68 LABORATORY PUT81C8. 23. TO FIND THE FOCAL LENGTH OF A CONVEX LENS FROM THE SIZE OF THE MAGNIFIED IMAGES. METHOD IV. References. — As in Metliod II. Apparatus Required. — A transparent scale, finely cliviikd (an ordinary opal-glass scale answers well); a large wliite- pajier screen ; a lens of rather «liort focns; a pair of dividers; a lamp and optical bencli. Theory of Experiment. — Let / be the length of a division of the tmnsparent scale which is nsed as an object. lA't L be the length of a division of the magnified image. Let v ho the distance of the screen from the centre of the lens when a sharp ima^c occurs on it. Then we have the ordinary relation L + l = i 0) where n is the distance from the illnminated scale to the lens. We also have the relation LI \ L or Iv' Hence by substituting in (1) we obtain / f = (2) /- + / which is the relation required. Practical Directions. — As in j)revious methods, the axis of the lens must lie along the bench and in the same horizont.al as tlie centre oi the illuminated scale. •This mftliod is applicaWe t« Miii-k l»'iist'> or comhina'ions when tbe distance Ix^tween tbe priiirii-al points cannot 1)P nojripcted. 5E^32t£^ ^W^: -^:' 1.10 UT. 69 i See that the iiKle.\ carried \\y the lens is in the same plane H8 the centre oi the lcni>, and that the index of the screen lies in the plane of tlie screen. Place the lens at a little greater distance than its focal length from the scale. Move up the white screen until a sharply defined image of the scale division is obtained. Measure to ^^ mm. the length of as great a number of inagiiitied divisions m are obtained on the screen. Itead the distance between the lens and surface of the screen. (^alculate the value of a sinirle uiaj'nitied division in ternl^ of the ol)je('t .*»; Hastings and Beach, p. 619; Kicliols and Kranklin, j). 4."i; Ames, p. 440; Antliony and Brackott, p. 41 -J. Apparatus Required. — An t'lenientarv optical IkmicIi; a moderately long focns concave lens; a lamp; a gronnd-glass soreen; a black-paper screen witli two sjiiall apertures not greater than the width of the lens aj)art; a pair of dividers; a centimeter scale. Theory of Experiment.— -Let h and r he the respective dis- tances of the source of light and the virtual image from the face of the concave lens A II. Then we have the ordinary formula for /*, the focal Icno'th of concave lenses, 1 7 1 I' 1 0) % V and r being in this case iM.th on the same >idi- of the iens. Of tlu'se values u can l)e measured dircctlv. Fi.i. 17. If imw the face i.t' \. \y Ifiis III black paper with two ;!]Hi't!i!i (• coviTcd witli ;i sJuM't of ''. "",, till- liiiht ji,t>-iii<.v I.WIIT. throtigli these H|)erture8 will give two bright patches of lig'lit, 6, i„ on a acreen placed to receive them. Then V V -\- ccj aa. cc. or V ■=■ bb. — (ui. Since a a^^ b A„ c i\ can be measured, v can be calcu- lated. Substituting in formula (1), /'can be calfulated. Practical Directions Motuit tiie lens in the n)iddle stanench, so as to receive the divergent rays of light. Move the lens along the bench until a considerable divergence i.; obtained. Measure carefully by means of the dividers and scale the ositioii8 of tlif lump, lens, antl ground-gluss K'reen to their indexes should be carefully ullitwed for. The adjustment of the position ot the lens should be made three 7l* LA noli AWRY PHYSICS. timi's, hikI the mean of the oalcuhited vuhie of ,' taken. Calcuhite r from formula (2), ami Milmtitute in (1) for f. Example — Enter results thus : 77.0 hi,. 2 03 «j 6.4 2.0 6.3 26.r) 26.5 26.5 12.33 12.33 12.32 14.6 Ulonk to hcjilhil In hi/ ,sfi((/t/if. u. .1-.,. hht. (■<■,. i: /■ 25. TO DETERMINE THE FOCAL LENGTH OF A CON- CAVE LENS BY AN AUXILLARY CONVEX LENS. METHOD U. References. — As in previon.* vxjx'nmejit. Apparatus Required.— The snuw as in Method I, except tl)e black- paper screen, and, in a;nital)le convex lens of known focal leiiirth. Theory of Experiment — A more accurate method than tlie precedini; is ohtained !•>• niakin<,r a comhination witli a convex lens of sufficient power to r.iider the comhination slij;htly convex. Suppose A /i {V\ri"!ir ol»ject at (f. It is refracted so as to form a virtual imaiie at a, and we have therefore 1^ V 1 a 1 0) wliere aM= r, and (9J/= ?/, and/' is the focal length of the concave lens. Fiii. 18. The rays are again lent from the path aC, and refracted to a focus i)oiiit b l>y the convex lens. Then as far as the convex lens is concerned the source of light is at a. We have, therefore, 1+1 = -'. V (2) where is brought to a focus at b by the combination of the two lotises. It follcws, therefore, that u ^ (\ F (-0 74 LA BO HA TOR T I'll VSirS. Ilenee, coinhiiiinj; (1), (2), and (3), we obtain the relation J. - i. _ 1 or (4) /^can be calculated from formula (8), andy* from formula (4), /', being known or found separately. Practical Directions. — The adjustments and observations are the same both for the convex lens and the combination, as i'l the case of convex lenses. It is readily seen In* inspection of formula (4) that some ire is necessary in choosing the auxiliary lens. For \i F — f^ >e small, small err 's in meJisuring them, unless the errors ■ same direction, would result in a large 'tivex lens should therefore be chosen iiference /'—/', a.s large as possible, or mid be ecjuivalent to a lens with very hat /'is very nearly eipial to/',, result thus: liappen to be in ' error iii /'. Th< so as to mak the combinat slight coTivexi' , Example. Ki vex lis. • ibservations for F. F. / n. '"!■ 12 11 ;( 12.1 120 120.5 119. S 165.9 165.4 IWl.l \p'll>'(l hi hy xtiKhitt. Coin-ex I.. 42."»; Ames, i)p. 450-4r»2; Ilastinps and Ikwli, \>\^. ♦»31-r»37; Jiaiker, pp. 456-471; Knott, pt. 11. p. 2s4; Nifliols and Franklin, vol. HI. pp ■)7-7l : Watson, p]). 4.nJ»-41»3. Apparatus Required — Three short-fdcns lenses and one long-focus lens, snitaitly mounted; a centimeter sitale; a ]iiece of wire gauze \\\ a damp-stand. Theory of Experiment. — (I) The Misor})e. — If an object All he placed in front of a short-focus lens PQ so as to he just heyond its principal focus, a real inverted and slightly magidticd image of the ohject will he formed on the opposite side of the lens tVom .1 II as AJi^. If now a second lens, J/.\'. I>e placed so that the image AJi^ is just inside its princi|ial focus, a vertical and magid- fied image of AJi^ will he produced on the same side (tf MN as A.li,^ see A „/>,,, I' ig . 1 J » . Fio. 19. The lens MX with re.-pcct to the image /I,//, forms a siu)ple mis i> Ciillcil the ohjcct-glass, .)/.\' tlie eyepiece. ilB 78 LA BOrtA TOR V PII YSICS. (2) Tlte TeleHoope. — The telu»cojie is cuii«tructed on the saiue principal an the nii8croHco])c. In the case uf the tele- scope, however, the object-glass is a h>ng-focu8 lens and forms a diminished image of a dUtant object instead of a magnified image of a near object. As in the case of the miscroscope, the eyepiece \s used to magnify the image obtained by means of the object-glass. Practical Directions.— (1) Tlte Mincroscope. — A centi- meter scale, held vertically, makes a suitable object. In front of it place one of the short-focus lenses at a dis- tance a little greater than its focal length. A suitable ])06i- tioii can be found by placing the lens quite near the object and then moving it gradually away until a real inverted image is seen between the eye and the lens. To find the exact position of the image so that the eye- piece can be adjusted, a piece of wire gauze, mounted on a stand, can be used. Adjust the position of the gauze until it appears to coincide ',\ith the image. The point of exact coincidence can be obtained bv mov- ing the eye Inick and forth in a plane parallel to the gauze and atijusting until the gauze and image continue to occupy the same relative position from whatever point they be viewed. Take another of the short focus lenses and focus it upon the vkV^v of the gauze coincident with the image. licuiove the gauze, and a magniticd image of the scale will be seen. Mejisiire eat the observations three times, changing the dis- tance (/ in each case. {'!) The a^ljll^tments for the telescope a-e exactly the LIOUT. 77 same aa for tlie luiscroscopc, tlio otily difference lieiiig tliat the ohject-f^lass is a long-focus iens and its distaiico fruin tlio )hjeet much greater. Example.— Enter results thus: TeleHCope. 74.5 168.1 121. (J lilduk to he JiUed in hy tttudent. Hiscroscope. Teleucope. a b a b • 27. TO DETERMINE THE MAGNIFYING POWER OF A MICROSCOPE. References. — As in Experiment 26. Apparatus Required. — A compound microscope; two mil- limeter scales. Theory of Experiment. — The magnifying power of a micro.*icoi>e is the ratio of tlie angle subtended at the eye by tlie image tu that subtended by the object, both l)eing at the cm. If, therefore, a microscope bo focussewer. Siiiiihirly if the iiiiignifyiug powers of e.ch of the lenses he ohserved, their product will he the magnifying jjower of the inieroscojR'. Practical Directions. — (i) Focus the microscope upon u millimeter scale. Place another millimeter scale at the side of the instru- ment at a distiince of ahout 25 cm. Looking thnuigh the microscope with one eye, adjust the l)osition of the .-econd scale until the inuige of the first as seen in the microscope api»ears to coincide with the second wale as seen hy the other eye al(»ng the side of tlu- micro- seope. Count the immher of scale divisions of the second scale covered hy as many of the niagnitietl divisions of the image as can he accurately ohserved. Denoting the niimher of divisions of scale hy (t, the cor- responding divisions of the image hy b, and the mugnifving [>ower hy J/, then M a h (1) Repeat the ohservations several times and take a mean of the results. (•J) The magnifying powers of tlie eyepiece and the ohject-glass may he found separately hy a similar method, if the microscope contain in the eyepiece a micrometer scale the vahh' of the divisions of which are known. Focu> the microM'ope on the millimeter scale and note the numl)er of division> of the image, which !> magiiitied hv hoth the eye[>iete and the olijeet-glass, covered hy a numher of divisitius of the nucromcter f-eale, whic!. is magnitied \)y the evepiicc oiilv. ;:?3Ki&i^saF ■f^i.'-kiODM&X: uuur. 70 Tlio ratio of the two, expressed in the same units, gives the magnifying power of the ol)ject-gIaiw. Thus, if we denote the magnifying {K)wer of tlie ohject- glass by ;«, tlie divisions of the scale by A. , the eorreK|)ond- ing micrometer divisions by c, and tlie constant, rev a iletinito number of divisii>ns of the micrometer scale as seen by tlie other eye through the nucroscope. Since tlie micn»meter scale is imigiiitied by the eyepiece o\\\y, the ratio of these two, when expressed in the same units, gives the magnifying power of the eyepiece. If b, l>e the sade divisions, t\ the corresponding nucroni- eter divisions, and m^ the magnifying power of the eyej)iece, then h. (3) 'e.6 The product, /// . /«,, gives ^f. Iie[K.'at the observations several times for both eve]iicct' an:%2E^^')«ft -»*sJ5rs»> Ti;^¥&mm 82 LABOBATORT PHYSICS. Looking through the telescope with one eye and observing tlie unmagnified scale with the other, the image will appear projected against the scale. Adjust the position of the eyepiece until the image occupies the same position as the scale. If the eyepiece has been focussed on the cross-hairs, it will be necessary to pull it out slightly. The exact position of coincidence of image and scale can be determined as in previous experiments by adjusting the eye- l)iece until the scale and image continue to occupy the same "elative position when the eyes are moved back and forth across the field. Having found the position of coincidence, read the number of image divisions, a, covered by the distance between the two strips of white paper. Repeat the observations several times. Measure the distance «, between the strips of pajier. Measure the distance D. Calculate M. Repeat the observation three times for different distances of telescope and object. Example. — Enter results thus: h l> (meters). ". Readinfcs for o. Mean a. M 4.35 75 5.1 5.0 4.8 4.97 15.1 5.75 75 5.2 5.2 5.8 5.28 14.3 7.28 75 5.7 5.7 5.8 5.73 12.5 ■ :!• 'tmjs^s^^s^isip^^^^'^^^^m-s^ i LIGHT. Blank to he filled In hy student. •'eailiUKs for a. Mean a. 83 M 29. THE SPECTROSCOPE. (1) TO MAP THE SOLAR SI-ECTRUM AND PLOT THE CALIBRATION CURVE OF THE INSTRUMENT (2) TO MAP A BRIGHT-LINE SPECTRUM AND MAKE A TABLE OF CORRESPONDING WAVE-LENGTHS. References.— Nichols and FraiikliTi, vol. iii. p. TtJ; Car- liart, pt. I. p. 293; Anthony and lirackett, ]>]). 439-44-I-; Ames, pp. 455-467; Barker, pp. 449-462; Hastings and IJeat'h, pp. 704-710; Watson, pp. £14-518; Knott, pt. 11. pp. ;}24-32s. Apparatus Required.— A spectroscope with niicronieter •scale; I'liicker tubes containing II, O, CO, N, etc. ; a small induction-coil; a two- volt storage-battery; a map of the solar 8j)e('trutn; a clamp-staud for PHicker tubes; a striding spirit- level; some small connecting wires. Theory of Experiment.— For tlie theory of the experiment read carefully the chapters on dispersion and the solar spec- truiit in any of the above references. ^JR?^^:i«^^i?^i'j: W^'^^i^k 8:1 LABOHAWliY PHYSICS. Practical HhtcMons.—AdJuMtment of tlm Indrument. — Focus tlie telescope by the metliod of parallax on a distant object. To do this it will generally be necessary to unscrew it from the instrument. Replace the telescope, and, the prism having been re- moved, view the slit direct and focus the colliinator. This may be done by adjusting the length of t\w cullimator-tube till a sharp image of the slit is seen in the telescope. Level the collimator and telescope by means of the spirit- level and level ling-screws attached to them. If their vertical height be the same, their axes may be assumed to be in tlie same plane. The prism should have iis refracting edges at right angles to the above plane. To insure this, level the prism table by the screws provided. Before clamping down the prism, it should be set for minimum deviation, as explained under the spectrometer. (See adjustment for mininnim deviation. Ex- periment 8(,».) The instrument should be turned to the window, and, if available, direct suidight allowed to enter the collimator. Adjust the width of the slit till sharp narrow images of the dark lines are seen. If the spectrum be traversed by dark bars at right angles to the solar lines, this is probably due to dust in the slit. This may be removed by introducing the sharpened end of a match into the slit and passing it up and down a few times. Illuminate the slit in the small tube containing the scale, and clamp the tube in a position such that the whole length of the spectrum is covered by the scale. Adjust the length of the scale-tube till a well-defined image of the scale is seen in the telescope, after reflection from the near face of the prism. It may be that the s]ie('troscope is ]irovided with a grad- iVuW^ ^,^^''^fWL TS^S^^JI LIOHT. 86 I i uated circle, in which case the scale readings will be read at the index carried by the telescope. (1) Mapping the Solar Spectrum. —With the aid of the map of the solar spectrum observe the position on the scale of all the principal dark lines visible, aiid draw to scale, on section paper, a map similar to the one below, Fig. 20. If direct sunlight has not been used, there will probably be no lines visil)le in the red end before B, and none in the violet beyond G. ^a B C D E 61 F g Q h H K .) Fig. 20. Plotting the Calibration Curve of the /nsiritment.~The following table gives the wave-lengths of the principal dark lines in millionths of a millimeter. Designation. Wave-Ifngth. A 760 B 686 C (H) 656 1> (Na) 589 E (C aud Fe) 527 b (Mg) 518 F (H) 486 G (Fe) 431 H(C&) 397 K (Ca) 393 With the aid of the al)ove table plot the calibration curve of the instrument. The scale readings may be jilotted as abscisete to the scale of one scale division equal to one centimeter; and the wave- lengths from the table as ordinates to the scale of fifty equal to two centimetors. ^S?;.V:^^'F t^''m:^i^^'w<^^s[^^^'''^:?m;^'m^^mi^ii^'^W4'%^'W 86 LA DOHA TOR Y PH YSICS. The ourvo so drawn will be similar to Fijr. '21. (2) 7\> M,,tsKr,' the Witvt-lt't„ft/,.s of i/u l!,-!f ,i (mhx.~\\'\{\w\\\. clijiiiiriji^r the iidjiistrnt'iit of CALIBRATION CURVE I i i *°°6 8 10^ W U SCALE READINGS Fm. 21. the instrument, set up a Pliicker tube. If tlie side-ou type is used, have tlie capillary section vertical and close to the slit. In the case of the end-on type the capillary section should have its axis in line with the axis of the collimator. Connect the electrodes of the tube to the secondarv ter- minals of the induction-coil, and the primary of the induction- coil through a switcli to the current supply. For the current supply a portable storage-cell will be found convenient. 1 I y-M^^m-r^i:'.^:'^^. WmW^jmfmm'm J.TGIJT. 87 t i See tliat the contact-ltreaker works contimioiislv without sparking. On looking thionj^h the tek'^cope tlie brigljt lines Keadinj Oxygan lied 830 »85 Yellow 890 Greeu 985 10.50 11.80 Blue 12.85 Hydrogen Red(C) 7.55 Blue(F) 11.70 Violet (G) i4.ao WavelfUKth from Cur\'f . 617 607 572 562 523 488 470 659 480 430 Blank to he Jill e J h, hj student. Color of Line. Scale Reading. Wave-Ienffth from Curve. LJOHT. 89 30. TO DETERMINE THE ANGLE OF A PRISM AND TO FIND ITS REFRACTIVE INDEX BY MEANS OF THE SPECTROMETER. References— Watson, p. 41)5; Carliart, pt. i. p. i>(»3. Apparatus Required — A eiKjrtroineter having a vernier provided for the prism table as well as for the telescope; a prism; a bunsen burner; a spoon of platinum f;.il for contain- ing the salt for sodium Hume; gas-tubing; a spirit-level. Theory of Experiment.— The Theory of Experiment is the same as that for " The Measurement of the Angle of a Prism by Pin Method," p. 40, and ''To Find the Index of Kefrac tion of a Prism," p. 46. Practical Directions.— The general adjustmenis are the same iis for the spectroscope, p. 84. To Measure the Angle of the Prhm.—{\) By Mocimj the Telescope.— li the adjustment for the parallelism of the in- cident light has been carefully carried out, no groat care need be exercised in centering the angle of the i)rism in question on its table. Turn the prism table so that its vernier may be out of range uf the moving telescope, and clamp it down. T'M-n th. -rism on its table till the angle to be measured points tow s tlje slit, and clamp it in position. Illuininat:^ the slit ^'ither by the sodium flame or bv turn- ing the insf uent so imt the collimator points to a window. - i^'ope to view the reflection of the illuminated '' ' faces wliich bound the angle in question. ? as narrow as possible, and adjust the position by 'he tangent-screw attached till the vertical 38 with the middle of the slit. Read the ^«^ -n of the telescope on the graduated circle. Turn the tek "to w the slit from the other face of the angle, reading tt= ^itior, of the telescone as before. Turn t slit from t Make tb. of the telescoj cross -wire coin 90 LA BORA roii r rnrsTcs. llnclamp the prwm tttl»le, set it again, luid rtpout flie uhHcrvatioiiri. Tiie im-aii (iiJTert'iuH! between the reudin^s on the two sides of tlie pribHi in t* he taken an twice the angle refpiired. Ditticulty may lie exiHTieiiced at tinst in tinding tlie reflec- tion of the slit on the faces of the prism hy looking through the telescoiKJ. It may easily he found, however, with the naked eye, and the telescope then moved up till the image in intercepted. (2) lii/ Moiu'/Kj the I'rixHi. — It will generally he necessary to change the position of the prism on its tahle so that when the slit is in view on one side, tlie vernier carried hy the prism tahle is as near as iHJssible to that carried by the telescope. The observations will be taken in the same way as before, except that the i)rism table will be moved instead of the tele- scope, and the readings taken at the vernier carried by tlie prism table. The telescope should be displaced a little, and the readings repeated. To Find the Index of Refraction of the Prinin.—lt w'll be necessary in this experiment to liave the slit illuriiinaiod by the sodium flame. Remove the prism and turn the telescope to view the slit directly through the collimator. Set the telescope so that the vertical cross-liair coincides exactly with the nnddle of the slit, and read the i)08itlon of the telescope on the graduated circle. Replace the piism, and turn the telescope so as to view the refracted image of the slit. To Determine the Minimum Deriuiion, de«!rease the angle of incidence by turning the prism tal)le, and follow the refracted ray with the telescope till a point is reached where, ^f:^'j^:^jy^^: Liairr. 91 if the prism be turind fmth.r, tl,, ivfrncfcd ray turns harlc. Head tho ))(>8itinn of tlu; t«>lt'Hc.)jM-. Tin; (lillert'lice Uctwt'tii this und t!ic h ..ucr reading i,. tl.c angle required, JJ. Eeniove ihe prism, displace the culiimator, and readjust the telescope to view the slit, llead the vernier. Kei)lace the prism and take a Kect.nd ohservatio.i fur min- inium deviation. Take a mean of the two ohse. .ations. It would he well U, check the result hy reversing the prism, 8o that the face of incidence is made that of refraction, and measuring the deviation in the opposite direction. Calculate the refractive index from the known angle of the prism and its mininmm deviation hy means of the formula sin M = r sm - Example. — Enter results thus Movin); Telescope. Reading i ReadiiiK KiRlit. j Left. 150"" 56'; 31" 10' 157 (HY 37" 15' Meau Mi)viii){ Prisni. Hitclit. Left. I For Mininiiiiii Ueriution. 59°50'ii:4°10'!54''25''59°5a' 59° 52' ;17rj.T|5r 40' 5!»' 52' 5!»°5r~j ,-)»" 52' TliriiiiKii rtit'OUKb Col. I Prism. 91° 0' 90° 35' _____ 41" 45' 41° 20 ' 49" 15' 1.66 I MoviiiK Telescope. Rt-adinit | Reading I Rijtlit. , l.eft. Mean . Ma Ilk fo hi-p'JIcil In hi/ .student Movin»{ Prism. For Minimum Deviation. HiKlit. I^-ft Throiigl Col. D Through Prism. .if.X-^Tras 92 LABOSATOSY PliYSlva. ■c, c Fig. 22. 31. TO DETERMINE THE REFRACTIVE INDEX OF A LIQUID BY MEANS OF A MICROSCOPE. References.— Watson, p. 495. Apparatus Required.— A microscope; a beaker with a fine cross or other well-defined object at the be toni ; a fine milli- meter scale for detennhiing the positions of the micro- scope tube. Theory of Experiment If an object C placed in a vessel partially filled with a liquid (e.g., water) be viewed from a position perpendicu- larly above the liquid, it will appear at a point C, nearer the surface than C, due to the refraction of the liquid. If A be the point on the surface of the liquid perpendicu- larly above C, then the refractive inde.x of the liquid is given b}' ecjuation ACf ^ = Ac; In order to measure the distances AC owik AC„ a micro- scope can be used as follows. Practical Directions — Scratch on the bottom of a beaker whicli is at least two inches high a fine cross. Place the beaker under the object-glass of the microscope, and carefully focus on the cross at the bottom. Measure with a fine scale, to ^V of a milUmeter, the distance between a fixed point on the microscope and a fixed point on the stand. LIGHT. 93 Denote tin's distance by S. The focussing and measuring sliould l)e done tliree times, and the mean position of the tube taken. Pour in some liquid and sprinkle some light powder, such as Ijcopodium, on the surface. Now focus on the refracted image of the cross, and again measure carefully the distance between the two fixed points, 6 . Take a mean of three observations. Then focus on the lycopodiuni powder on the surface, taking, as before, a mean of three observations of the distance between the points, rf,. The depth AQ of the liquid is clearly the difference between the tiret distance and the last, d - rf„ and the length AC, the difference between the second distance and the last " 96 LABOliATORY PHYSICS. As tlie boiling-point of alcohol is about 79° C, the ther- mometer must not be heated to that point. Now fasten the bulb and tube to a narrow strip of section- paper. Determine the zero-point by p,,ttin7KWftK0aSIRai «■ i HEAT. t>7 ± a, a beinj? considered plus wlien the reading is above tlie zero, and minus when below. If when the boiHng-point is observed the I ironietrie read- ing differ from 700 mm. by i., then the true temperature of the steam is 1()(» ± (/>, x .<';iT), according as the barometric reading is greater or less than 7(3() mm. Suppose the reading on the thermometer to differ from this true value by a small fpiaiitity ±_ i, /> beim; + or — according as the thermometer reading is al)ove or below the true reading. Then the total error in the length of the stem for loo degrees of temperature is ± f« :i: h. Hence a true degree on the thermometei-, supposing the 10(» ±a ±h 1(»0 tube to be uniform in bore, is indicated l)y divisions of the thermometer, and therefore any temperature t would be indicated by J"- ± /'. ±J ^ t thermometer divi- sions from the true zero, or from the zero of the thermometer 100 ±a±l 100 y. t ±a. . 0) ' I (2) If when the boiling-point is observed the thermometer be wliolly immersed in the hypsometer and the reading taken, and the observation repeated with 30 or 4(» degrees of the stem exposed, it will Ijc found that the readings slightly differ, (.wing to the exposure of the stem to the air. Denoting the length of stem exposed by d\ and the difference \\\ the readings by l-, then the stem correction i)er dca-ee is — Th"s stem correction will depend not only on the stem exposed, but also on the temperature being determined; and fms^^siiS!m»iimifig. * >■:-• tft"if3IBSJ-aii^-Ti;" 13 Jt-'JC -TWfc-.C**-' •TigSSttS*'!:- U8 LAUOHATORY J'HiSJCS. will be positive or negative according as that temperature is above or below the temperature of the room. The reading of tiie thermometer eorre6])onding to any temperature t k therefore !(»(» ±a ±h Xr?, (Ther. reading :f << T-f-') 100 or I- t = (-^) (3) 100 ±a ±b ^ being the stem correction for tenjperature t, and <5, tlie length of stem exposed when the temperature t is taken. Practical Directions.— Insert the thermometer in the mix- ture of snow and water, leaving oidv sutticient of the mercury CD ti ^ column exposed to enable you to take the reading. Head by means of the telescope the indication of the thermometer to yjg^ of a degree. This reading gives y(»u the value a. I>y moans of a 8])lit cork insert the thermometer in the hypsometer, and let the steam How freely for a couple of minutes. As before, have only sutticient of the stem exposed to enable yon to take the reading. Read the indication again as above. Read the barometer, and calculate the true temperature of steam, or find it from a chart in the laboratory. The difference between this and the thermometer read- ing gives the value h. Now expose the stem 40 or 50 degrees and read the therinometei' again. Calculate the stem correction per degree of stem ex- posure. • i^wff-^' :r" ;'^'".^*^jse$'^ss^*' -SMfiS^t'^c^fe'^T HEAT. S»9 ("alculute the teinpcratnre corresponding to a reading of •io (li'grc'L's on the tliennoniuter, isni»po8ing you can uegleut tiio .stem (•onx'ction. Kind tlie temperature by tlie thermometer of the solu- tion provided, and calculate the true temperature. Example — Enter results thus: a liaroiiifter Rfiiiliiil,'. OIiMilated Teiiipf'i'aliire of Steam. 01)Sfrve(i TennxTatiirc of Sleaiii. b 76.3 100.11 4 100.70 1 f iiiptratuif of SSolution hy Tliermonietfr. + .59 Tlwr. Ki'UiliiiK, no sicm Thfi-. R<'!uliiiK. •Jll" ^telll • xposiiii'. Coi rected TeiiipHrature. lOO.TO 10()..50 .01 42.30 4'2.76 Bhdtk to hep'lhd In hij Ktu(h-7lt. a IJaroMiPter Rending. Caleidiited Teinpenitiire of Steam. Oliserved Teiiii>erature of Steam. b Tlier. ReadiuK, no stem exposed. Ther. Reading. •i(y stem exposure. k i Tempeiatiiie of Solution by Tliernionieter. Corrected Temperature. ; 1 ''^^'m-^?'ms^^\'i4^s^''iL'mms:^'X9^-f^- ^*«! ^=5^,itq?lgv, 100 LABORATORY PHYSICS. 34. TO DETERMINE THE COEFFICIENT OF EXPANSION OF A LIQUID BY A WEIGHT THERMOMETER. References. — Carhart, pt. 11. p. 30; Preston, p. 173; Knott, pt. I. p. 214; Aines, p. 207; ^Nichols and Franklin, vol. I. p. 153; Hastings and Beach, p. 169; Antliony and Brackett, p. 208; Barker, p. 291; Watson, p. 219. Apparatus Required. — A weight tliermonieter ; a hyj)soin- eter with suitable stand for use with hunsen burner ; a bun- sen burner; a beaker; athernioineter; a small flip for holding weight tlieruionieter. Theory of Experiment. — If a glass tube be filled with glycerine or other liquid at a temperature t, and then heated to another temj)erature ^,, the li(|uitl will expand and part of it will be expelled from the tube. Let Y^ denote volume of the tube at the teinj)erature /; K, that at the temperature /, ; F, the total volume of the ex2)andod glycerine at temperature t^ ; 6^ the density of glycerine at t ; tf, the density at /, ; a the coefficient of the expansion of the glass ; ft the coefficient of the expansion of the glycerine; J/, the mass of liquid in the tube at t', J/, the mass in the tube at temperature ^,. Then the following relations hold : T^,«y, = 3/"„; (1) FA = J/.; (2) T^o^^o = M, ; (3) r, = F, |i + ^r^, - t)\. ... (4) Hence, comlnning (1), (2), and (4), S. J/„ .V, *(^ -0:. (5) > ..,^^Sr-:S'^s::TE^A^'Ts^mM£^^'^SLnt^Li£Myt'^^£Li^-iUajarir^Ksv9^^^'s^ tZZfJ'M . »S1 ^. SL^Mil3L5Jc:^CSSIWV^.jS:it 1 1 iiBA r. 101 Also and therefore Hence But V. r, - \\ r.(^-/) J/, - J/. ^ J/. («) = /^, the coefficient of expansion per \init vohime per degree of temperature. Hence (7) from which ft can he calculated if oc he known and the otiicr values ohservetl. Practical Directions. — A s-ntal>le weiirht thormonietor can ho made from a piece (»f glass tuhe 1 cm. diameter, drawn out as in Fig. 23. The hulh AB should he ahout 7 cm long. Weigh it carefully to .()(»1 gm., deno- ting the weight l)y If. Fasten the thermometer in the clip for the purpose, and adjust the vessel eon- taimng glycerine till the end of the fine tuhe of the weight thermometer is im- mersed in the glycerine. Now, hy means of a hunsen hurner, slowly heat the glass hull), thus ex{)elling some of the air hy expansion. vw. 23. Let the hull) cool, and on eooling the glycerine will rise in the tuhe and partially fill the hiiib. 10'2 I.AIUUtA TOR Y ril YSK 'S. Again hlowly heat tlu; l»ull» until tliu jilycrrinu Wegins to boil and again cool, rcjHJiiting the operation until tlu* In bubble of air is expellcil. Keeping the end of the tube still under the gl\ ferim-, ftu the bulb to about 1° above the teniperuture of tlie rouui. This can be done by putting the bulb in a beaker of water slightly wanner than the room temperature. The glycerine nuist be left for tiome minutes in the water to secure uniform temperature, the water being slowly stirred with the thermometer all the time. Read the temperature of the water, t. Kow take the weight thermometer out of the water and carefully dry with a cloth, being careful not to Jieat it with the hand or the glycerine will expand and some of it lirop from the tine tube. On taking it out of the water ' •> the cooler atmosphere of the room it will slightly contr; , thus making it possible to weigh it without loss. Weigh carefully tlie now tilled bulb again to .(lol gui. Denote the weight by IT,. TF. - W = M,. Now suspend the weight thermonieter inside a liypsometer. Tliis can easily be done, if the bulb lias been properly made, by having a split cork for the top of the hypsometor. Allow the steam from the liypsotncter to flow freely around the bulb. If it be not convenient to use a hypsometer, the bulb can be suspended in boiling water, and the temperature of the water taken with a thermometer. If the hypsometer be used, read the barometer and take the temnerature f, from the chart in the room. The overflow of glycerine should be caught in ;i beaker. UICA T. l(t:5 U'jive the bull) in the hypsoiu. or or water until the glycerine ceawes to drop from tlie ojhji end of the tube. Weigh again. Denote the weight by 11',. J/. = »; - ir; a, for glass = .00002»'». Subfltitute these results ' *''*^ furnni'H a!id calculate ft. Example. — Enter resuh -: w. W,. 1 10.670 17.875 6.H06 n.18^ "'.• Afu< lilnnktvt^ itJltd i f>y ^ '>> ; Barker, p. 2S9; Anthony and Braclcett, ]». 208; \iehols and Franklin, vol. i. p. 153;' Ames, p. 204; Knott, p. 217. Apparatus Required. — Two microscopes ; two brass tubes, one considerably larger tlian the other; a hypsometer, with rubber tubing to make connections ; a l)eam-compass ; a centi- meter scale; two thermometers. •)t L A noli, t ran y rii ) sk -s. Theory of Experiment If u hra^s rod of len^'fli / and tiiiitunii tiiinicrHtiiio / Ikj licuttHl until it iittuiiiH ii unifMi-iu U'liiporuturo /,, it will bo found on nuasuiTUient to liuvo incrt'iisnl in lenj;th. Denote tin- liMiuth at ti'mperafnie /, l>y /,. The coetlii-ient of linear e.\pan>ion between / and /, is given !)}• the e(|uation whore n is the coetHcient of linear expansion. If / and /, he niea«jured, t and i, observed, a can he cal- cnlati'd. Practical Directions — I>y menus of cork.s in the ends, arrange tlie smaller tu.< UKiide the larger one as in Fig. 24. CD is the siiiall tul>e, tne eoetlieient of whieh is to be deter- M N . ^-~ A B- ks^ a — ") l, ^J Fio 'J4. nuued. A and ^ are small glass tubes; aa„ Ji,, thermom- eters. AVi' is a rubber tube eoiiuecting the iut<:ide of the inner tube C'/) with the inside of the outer tube MN. />J* i- a ruliber tube eonneeting the liypsoineter to the inner tube; /A,, a rubber tube for eun-ying otf the steam as it flows out of the enter tube. iviake two sharp knife-cuts, (' and />, at places in the outside portion of tlie inner tube, convenient for observations, yet as close as possible to the corks in the large tul>e iJ/iV. Focus one of the mierosc(';>e8 on the cut C' and adjust until the cross-hair of the microscope, being central, is over the centre of the cut. UK AT. 105 Clump tlie microscope to the tulde or ulah on which tlie appHratus U placcMl. Siinilurly adjust the other iiiicro8Coi>e to tlie cut I). Head carefully the temperatures of the thermometers inside the tube, and take the mean of the two as t. Lij^ht the burner under the hypsometer and let the steam flow freely throu<;h the inner tube, outer tube, and again to the air. Let the steam tlow freely for a few minutes till the temper- ature becomes steady. Read the barometer, and tin; temj)eniture of the steam corresponding to the barometric pressure from the chart in the laboratory. On lookini; through the niicros('o|K's. it will be found that the cuts on the tube have now moved away, one to the right and one to the left of the cross-hairs. Count the number < f niicronieter divisions, in each case, between the cross-haira and the new p<»sitiiins of the cuts. This may be done by counting the scale divisiojis in the micro6C(»pe, or by counting the number of turns of the microm- eter head, in each case, retpiired io move the cross-hairs from their origliud positions to the new positions of the cuts. The sum of the two, expressed in centimeters, gives the expansion of the rod. Now measure, by means of a tine scale, the value of each micrometer division. This can be done by focussing the microscope on the tine scale, the divisions of which are known, and ccuuting the micrometer divisions corresponding to a scale division The cxpai;sion /, — / is thrs deteri.iined in centimeters. Now measure, by means of the beam-compass and a centi- meter scale, the length / to the nearest millimeter. Calculate a from formula (1). ffi 106 LABORATORY PHYSICS. Example.— Enter re8iilt8 thus: « '. 80 li>.5 99.5 Microiiieter;Microiiieter Oivixiuus lu Divitiionsiu RiKht Left Micruocopf. j Microscope. 6.5 6.2 /, -/ I a .oooo .147 100 184 Blank to he Jill ed in hy student. t t, t,-t Micrometer Divisions in KiKiic Microacope. Micrometer Divisiuus in Lfft Mici'uscupe. 1,-1 I a J i 36. TO DETERMINE THE COEFFICIENT OF INCREASE OF PRESSURE OF AIR BY MEANS OF A CON- STANT-VOLUME AIR-THERMOMETER. References. — Xicliols and Franklin, vol. i. p. 146; Ila'^t ings and Beach, pp. 164 and 1S2; Carhart, pt. i, p. 30; Anthony and Brackett, pp. 191 and 222; Preston, ])p. 12!> andls7; Knott, p. 211; Ames, p. 212; Barker, p. 295; Watson, p. 229. Apparatus Required — A constant-volume air-thermometer ; a nietal vessel for snow and water mixture; a hypsometer; a hunsen burner; a telescope. Theory of Experiment — Lot V„ he the volume of a mass of gas, ¥, at 0°C. or T, of the al)sohite scale, and under a IIKA T. 107 pressure /*, ; F, '1\ ■\- 1, uiid 1' the corresponding values when volume, pressure, and temperature change. The law connecting the two sets of vahies for the same mass is given hy the formula P V ' y— PV If the volume be kept constant, = MK. (1) , or T,= -B p: If the pressure be kept constant, 5_ ^ or 7^--^^ If a be the coetticient of increase of pressure at constant volume, - 1' - ^» - i - ^ - ^* (^^ "- pjt ~ 7; ~ V,t' ' ' • ^^) Hence the coefficient of iiicrease of pressure at constant volume is equal to the coefficient of increase of volume at constant pressure. The fonnula for the present experin^ent is P - P. a = PJ (3) In the actual working of the exi)eriment there are two corrections which nnist be a]>plied. which introduce additional terms in the fornuda. These will be discussed under next section. Practical Directions. — We shall assume that an air-ther- mometer of the Jolly type is used. M^^- • i' im mi. I ■¥i 5! i !' 108 LABORATORY PHYSICS. Ohsermti&ns for Freest ng-jmiit.—lhe bulb of the ther- iHoineter, liuviiig been filled witii dry air, should be first care- fully packed in snow or ice saturated with water. When the temperature becomes steady, raise the adjustable tube of the manometer until the mercury in the stationary one just touches the black glass point in the outer bulb, Kead the level of the mercury in each tul)e by means of ti.e telescope referred to the graduated scale attached to the iiif trument. Denote the readings by A and S, and the differ- 1 ce of level by jt>„. Repeat the observations several times and average the re- tiUlt. Read the barometer, denoting the reading by //,. Observe the temperature of the barometer, ai also that of the air near the air-thermometer. If the readings be nearly the same, the mercury columns need not be corrected for temperature. Observations for Boil hif/.pomt.— Insert the bulb of the thermometer in the hypsometer, and boil the water by means of the bunsen flame. Adjust the manometer as before. Read again the level of the mercun i eacli tube, denot- ing the difference by^;„ the readings by ^1, and S^. Repeat the observations as before. Read the barometer, //,. The barometer reading in this case will not usually differ much from //;, in the preceiling case. The temperatuieof the steairi, t, for the pressure //, may be found from a curve in the laboratory. Corrections — In making calculations from these observa- tions, two corrections, as mentioned before, must be noted. (1) Correction for Krjmnsion of the Glass Bull. —Tha vOiUme of air is not tlie same in each ease ou account of the HEAT. 109 expansion of the glass bulb. The relation between the two volumes is given by the equation V=VSl-{-gt), when y = .000026. Since the difference of temperature is nearly 100, F= r.(1.0026) (1) (2) Correction for Stem A'xjwsxre. — The air in the small tube or stem leading from the bulb containing the air to the tube containing the mercury remains api)roxiniately at the temperature of the room. Denoting the volume of this small tube bv v, the mass of the air it contains by ///, that in the bulb by J/,, we have the relations PV Pv where T^ is the absolute temperature of the air in the room, and T, the absolute temperature of zero centigrade. Since J/, + ^'^ = ^^ = constant, we therefore have P V Pv PV Pv (2) The ratio of the volume v to F", must be determined if it be not, as in most cases, given witli the instrument. Denote this ratio by ;•. Substitute V,r for v, F,(l + 9^) for r, and divide through by V,. Equation (2) now becomes P rP P(l + fft) rP ■'a T.-fi i:^. ^ ti liO LAliOHATOItY I'liYSlCS. Multiply both sides l.y " ^^ - », take 1 + ,jt out of every term except the first, iuul \vc obtain ^(1 + '.ir)T„r { rt r{T„P-(T„+t)l\] y 1\ \ ^T^a+yt)^' JTJ,\+yt) /• Assuming: TJ* = (7; 4- 0/'. ill tlie suuill term and iH^V'lectiuir .) ] (4) « z= In the -lolly pattern air-thermometer used in thi> lab(»ratorv _ 2..3r> ' ~ 12472^') ~ •'^'^'•^*^' ^''^' \""l"">e of the stem per centhneter being .0227. In tlie Groves pattern /• = .0150. Precautions.— ( n The tube supj.ortinj; tlie bulb is delicate and easily broken: if must th<*refore be carefully handled, especially when packin: ^ « I ' 4 ■ T? 1^ i '\t i i4'l i 112 LAliOHATORY PHY8IV8. Blanks to If Jill cd in hi/ ntndmt. FUEEZING-POIXT OBSERVATIONS. Tem|). Bar. ;>■. BOILIXU-POINT OBSERVATIONS. I\ = r, = t = HEAT 118 37. TO DETERMINE THE COEFFICIENT OF INCREASE OF VOLUME OF AIR BY MEANS OF A CON- STANT-PRESSURE AIR-THERMOMETER. References. — As in j)recedin<^ experinient. Apparatus Required.— A siiital.le glass hull) ; a liypsom- eter; a bunsuii hurrier; a glass vessel of not lees than S cm. diameter and 2.') em. ^tant volume is ecpial to the coefficient of increase of volume at constant ])ressure, or rt = PJ (1) In the present exj)eriment it is proposed to keep tlie pres- sure constant, and to measure the coefficietit by means of increase of volume from the e(|uation a = ^■^) F„ and T' being the volumes at (»0. and / respcctivelv. If the volumes be taken at ten-.^.eratures /, and /,, then a = r, - ]; . (3) where a is the coefficietit of increase of volume per degree of temperature between /, an' ul)out 10 cm. in length fnun a piece of tuhe 2 cm. in diameter. The buU) shoukl i)e drawn out to a very fine point at each end. Weigh tlie hulh, denoting tlie weight by IF'. Seal the tube at one end, and by means of a split cork insert it, sealed end down, into the hypst.meter, with about 1 cm. of the open end protruding from tlie cork. Let the steam fiov freely for about ten minutes. Seal the oj^eu end by means of a blowpipe or buiisen burner. Kead the barometer, and find the corresponding tem])erature of steam, t^. Nou fill the glass vessel, mentioned under apparatus, nearly full of water at about the tem])erature of ihe room! Ib.lding the end of ihe bulb under .va^er, break off a small bit of the top of the tube, and immediately the tube will become jwrtially filled with water, due to the cooling of the air and the consecpient change of pressure in the bulb. The bulb should be kept vertical, open end down, to prevent the escape of the air. The i)ressure in the Imlb is made up of two parts, the l)ressure of the air in the bulb, and the pressure due to the presence of acpieous vapor. This pivssurc is e(|ual to the barometric pressure plus the dilference in the head of the water in the bulb and vessel, or, barometric pressure -j- pressure of water = pressure of air -f a([ueous vapor pressure. I I ! I ' r7i»^ 116 LABOliATOliT PHYSICS. i \ Hence we can correct for aqueous vapor pressure by making the preB8ure due to diliercnce of bead of water exactly equal to it, thus making the pressure due to the air in the bulb ex- actly equal to the barometric pressure, as was the case when the bulb was in the hypsometer. Calculate, therefore, the depth of water equal to the afpieous vapor pressure at the temperature of the water, and depress the bulb until a ditferenco between the surface of the water in the vessel and bulb equal to it is obtained. In order to ao this, read from the chart in the laboratory the pressure of the a(pieou8 vapor at tenqierature of water. Denoting this by /*, we have A 13.596 /', or h = P X 13.596, where A is the ditference of head retpiired, and 13.596 the spe- cific gravity of mercury, the vapor j)ressure and baron)etric pres- ure being expressed in centimotiTs of mercury. While hold- in" the bulb in the water at depth A, seal the open end with wax. A small piece of suital)l(! wax can be kept attached to the bottom of the ve.>;sel iiit^ide, and the depth of the water reg- ulated so as to give A just as the open end of the tube touches the bottom of the vessel. It will be found convenient to have a piece of stiff wire, to use as a handle, twisted round the bulb. Stir the water in the vessel, and read the temperature t,. Kemt)ve the bulb, being careful not to lose any of the water out of it. Dry and weigh. Denote the weight by ir,. Now iill tlie bulb with water. This can be done by the method employed in filling the weighs ihermometer. mm BEAT. 117 Weigh the bull) wlieii full of water, (leiiotirig the weight by UV Substitute these weights in the forinulu, and euleulute a. Example. — Enter result^ thus: »• 100.25 1% 1*'. H, « 10.50 14.463 30.268 .00370 ill Blank to he Jilled in hy student. »• 1, (. »'. "'. a 38. TO DETERMINE THE SPECIFIC HEAT OF COPPER- METHOD OF MIXTURES. References.— Preston, pp. 211 and 215; Carhart, pt. n. p. 4-t; Barker, p. 283; Anthony and Braekett, p. 193; Watson, p. 288; Knott, p. 199; Ames, p. 217; Xiehols and Frankliji, vol. i. p. Ifi-t; Hastings and Beach, p. 188. Apparatus Required.— A regulation cylindrical heater, with hypsometer attach uients and calorimeter; two thermom- eter.'!. Theory of Experiment.— By the specif c heat of a sub- stance is meant the ratio of tlie quaiitity of heat required to 118 I A lioiiA 'fun y i'ji YHica. raise tlie tem|»t'rature of u in. •» of tiie siil)htanc'e one ecifie heat of which is to be determined. A suitable mass of copi)er can be made by twisting bare copper wire around a lead-i)r-icil, making a mass about two inches in length and one inch in diameter. The hole in the centre will be a suitable place in which to insert the ther- mometer. Through a cork in the top suspend, by a thread, this mass inside the cylindrical heater. Adjust the length of the thread till the mass is about half- way down the heater. Let a thermometer, through the cork, down into the centre of the mass. Turn on the steam from the hypsometer, and let it flow steadily for about half an hoiir, or until the thermometer sliows a steady temperature between 95° and 100°. A temperature of about 98° can usually be obtained. While the steam is flowing, weigh carefully the calorimeter, which should be of copper, and stirrer, m,. Partially fill the calorimete. xith water and weigh again, W. '- ; 111 H 120 Laboratory physIvs. I i Fix the caloriir-o r to the attachments provided for tli6 purpoisc in tlie Ix .\, luiJ svx ti:<.; second tljennometer into it bj means of the clij .ir aciuiicnt. Just hefure t'-opuiui; tlie liot nia^s of coi)per into the calorimeter, stir tlie water in the calorimeter and read the thermometer, t^. liead tlie thermometer in the heater, t. Kow slide the calorimeter under the slot in the heater, and quickly lower the mass of copper into it. As soon as the co})per is under the water, cover the calo- rimeter and stir, watching the tiiermometer and reading it when it reaches the highest poi' t, f^. A suitable cover for the calorimeter can be easily made from a i)iece of felt with holes in it for stirrer and thermom- eter. Substitute these values in formula (2) and calculate c. Determine, with the same calorimeter, the specific heat of zinc, using formula (3). Example. — Enter residts thus: Copper. 111 VI, w M (IK- III,) t '. 20.7 c 95.3 45.2 175.5 ISO. 3 98.5 15.5 .094 Blanl- to he filled in hy student. Copper. Ill '"l 1 "' M t u t, c 1 HEAT. 1-21 Zinc. 75.5 45.2 4.2 180.7 135.5 lilank to he jilled in hij fttiiJent. Zinc. m '"i cm, W M t u u c 39. TO DETERMINE THE LATENT HEAT OF FUSION OF ICE. W References. — Preston, pp. 2>So-2S5; IJarker, p. 306; Carliart, pt. ii. 61; Watson, p. 246; Knott, p. 222; Xichols and Fi an, vol. i. p. 171 ; Ames, p. 229; Hast- ings and Beach, p. 191 ; Anthony and Brackett, p. 214. Apparatus Required. — A calorimeter and stirrer, similar to that used in "Method of Mixtures"'; a pair of crucible- tongs ; a thermometer. Theory of Experiment. — During fusion heat is absorbed by a substance without changing its temperature, and an equal quantity of heat is disengaged again during solidifica- tion. The latent lieat of fusion of a substance is the heat required to convert one gram of the substance from a solid to a liquid state without changing its temjierature. Suppose a quantity of ice of weight W to be droj)ped into \ \ w I '< 122 LADOltATOHY PHTSICS. a quantity of water of weiglit jr, and temperature ^, , and the whole stirred until the ice is melted and the water is of uni- form temperature t. The heat absorhed hy the ice without clianging its tem- perature is LW\ where L is the latent heat of fusion of ice. The weight W has furthermore been raised to n temper- ature t, 80 that the total heat taken up by the ice in melting and raising it from 0^ C. to t is LW-\- Wt. The heat lost by the water is Wit, - t). Hence L W+ Wt = {t, - t) ir, , and tlierefore _ W^{t. -f) (1) In this case we have neglected the loss of heat of the calorimeter. Denoting by C the specific heat of the calorimeter, and its weight by ir, , C If, is its water equivalent, so that the heat loss is really Hence LW -^ Wt = { IF. + C 1V,){t, - t), and therefore ^ — 1^ fj' ' (2) .,,^:.^-^^^;g^^»'v^g^^^ HEAT. 123 from which, if the necessary observations be niade, L can be calenlated. Practical Directions. — Weigli carefully tlic calorimeter and stirrer, 11.,. Partially till the calorimeter with water warmed until it is aboiit 7° or 8° above the temperature of the room. Weigh again, denoting the weight by m. Then, Jl',, the weight of water, is ecj^ual to in — W^. Wrap a piece of ice in a dry cloth and break it into small pieces with a mallet. Wrap pieces of cloth around the points of the crucible- tongs, and pack ice around them to cool them to 0° C Stir the water in the calorimeter and read carefully the tenjperature ^, before dropping in the ice. Drop in small pieces of ice with the tongs (carefully drying each piece on the cloth before so doing), and stir the calorimeter steadily. Continue the process until, all the ice in the calorimeter being m^^lted, the temperature of the '>vater is as nmch belo»v the temperature of the room as it was above before beginning to put in the ice. Read the temperature ^,. Weigh again the calorimeter, denoting the weight by in. Then ir, the weight of ice added, is equal to m^ — m. C, the specitic heat of the substance of which the calo- rimeter is made, is supposed known, and hence C'lV^ is known. Calculate Z from formula (2). I I i £ 124 LABORATORY PHTSICS. Example — Enter results tlius : ^y* C .095 m '. t m, W (m, - m) L 45.2 95.7 50.5 20.2 1 12 100.6 4.9 79.6 Blank to be Ji lied in hi/ student. "', c m ^^'*mmy^ ' HEAT. 125 heat of steam by Z, the amount of heat given out by the steam is and the heat gained by the water and calorimeter is (M + an,){f, - t). Hence Lm, + m,{t, - /,) = {M + cm .)(^ - 0, or • • (1) i, can be calculated from(l) if the necessary observations be made. Practical Directions.— Weigh carefully the stirrer and calo- rimeter m,. Partially till the calorimeter with water and weigh again, denoting the weiglit by W. Then The temperature of the water should be reduced as neurly to 0° C. as possible, and when heated by the steam should be raised as much above the temperature of the room as it was previously below it. If tlie temperature of the water be 6° C, the room beinjr at 17° C, the water can 'oe raised to 29°, giving a rise of 24". The water should be stirred just before the steam is allowed to How into it, and the temperature i read. A special arrangement for a boiler or hypsometer is necessary to ;atcd ceiitrallv ntider the plate and sprinkle the iron filings in a thin even coating all over the plate. in 128 LADOHATOHY PHYSICS !*»» ;■. i Hold down tlie plate witii one hand, and vibrate it gently by shai-j) taps of the lingers of the other. Lay the plate on a piece of blue-print paper in the sun, and after exposing for five or ten niiinites, depending on the sensitiveness of the paper, wash in water. The following curves should be obtained : (1) From a simple bar magnet. (2) From a horseshoe magnet. (3) From two bar magnets with like poles together. (■A) From two bar magnets with uidike p<.les together. (5) From a bar magnet with a disk of soft iron in its field. (♦!) From a horseshoe magnet with the keeper an inch from the poles. (7) From the end of a bar magnet. To be Noted and Explained in : (1) Tiie uniform distribution of the lines and concentra- tion of the tilings around the poles. (2) The concentration and straightness of the lines between the poles, atid the curvature and thinness of the lines further away. (.'{) The position of the two neutral i>oints and the weak nature of the field. (4) The position of the neutral jjoint, and the concentrated field between the poles. (5) The crowding of the lines into the soft-iron end of the field. («) The same as in (.>), and the absence of lines elsewhere. (7) The radial nature of the field around the jwle. s \ ''nc^.^^:'^\^&¥',T?^i.C.:; ' MAdM-niSM. i*jy 42. TO MAP THE MAGNETIC FIELD ABOUT A MAGNET, AND TO DETERMINE THE MOMENT OF THE MAG- NET BY FINDING THE NEUTRAL POINT IN ITS FIELD. REFERENCES.— AirR's, p. ?.:>\\ Curlmrt, p. 3ir,; S. Tliuiiii»>(iii, p. li'+: Wiitson, |>. oits; r,iirkt'r, p. 031; Niclx.Is and Franklin, pp. L'l -:.'."i; Antlionv and IJrackett, pp. -J.-i'.t-L'f.^ ; Ilastiiiiis and IJeacli, p. .'}»;i. Apparatus Required — \ liar ina^rnct; a small t'oinpass- box; a drawinj^-board ; a lar<;e slieot of paper; a st't-s(piare ; a pair of dividers; a centiiiK'ti'r scale. Theory of Experiment.— If a compass-needle be brought near to a magnet, it will be found to take up a lixed direc- tion under tlie action of the magnet and the earth's field. This direction is approximately the direction of the line of uiaguetic force passing through the centre of the comjwss. Suppose A and // to be the positions of the ends of the compass-needle. If now the compass be moved so that tlie point previously at A is at B, the new direction of the line of force can be marked by marking the new position (7 of the point previously at />. The j)roces8 being continued, the direction of the line can be followed until it goes either otT the paper or hack to the magnet at another point. Bv repeating the process a map of the magnetic field can be made. In mapping the magnetic lleld, a j)oint will be found where the action of the earth is exactly balanced by the action of the magnet. At this point, tlie neutral point, the Is Sl| /■■ /A \ /„ s • R -B''^ Fi ••^iAfc^ySiik^ sMr'ji^mi6MAmMj»sj^^ K:m . -ti 130 LAUOllATOnY rilYSlCS. iictnlle of the compass not beiiij,' uikKt tlie control of any directive force, will take any jwhitioii iiKlitli'ivntly. No line of force will therefore pass throiii,'h this i)oint. (1) appose the mairnct be placed in tlic nia-,Mictic nierid- iun with its .V pole pointin-r north, then the ncntral point, if the niairnct he a simple one, that is, having' only two poles, will lie on the perpendicular to the magnet at its middle point. Fio 27. Let NS denote the magnet, in the meridian, K the neutral point, ^> A' being perpen the iiioiiioiit of the mairiict. [2) SuppUBt! tliu iiiagnct tu lie plaecil with its ^'^ pole poiiit- iii-r iioi'tii. Then it is ovitlciit that siiifo the action ot" the inai^iut oii a iiec'tllu north of S is tu turn ^ the north pole towani .S', while (ZZZTZZ^ /i/->N the earth's lield tends to turn f it in exactly the oppor-ite l'""-. -S. iliri'ctio!!, a neutral point lies (jii'cctlv noiih of >'. Suppose it at a distance /• from tin- ciiitrc ot the maiiiict. The attraction of a on the needle at A i> , , while the (/' — /)• f • 1 . ,. . . '/' reinilsion of 7i m tlie ui)i»o>ite direction is , , _ '■ ('' + h Hence the total force {»n the needle due to the magnet is 1)) ID or ■ih'»i wlucli is equal to where 31 is the moment of the mai^net. 23fr Hence Jf = -r-r^ ^^r,, since tlie needle is in cfpnlihrium or M (•^) ■PTjaiia»a»rjr3tg«rgsai6armiei»^ii«^/semawBai5»^^ ijWLyvi'rjoiipm^tmf vs^-hf- iS&^:.m^^is:k}^yjssk,^i^%jd^ 'i'^yi9.- /.-^ «'.»■;. t I I , 1 ■1} III ] 182 LA nouA TO It r I'll rsics. (3) Supiwse tilt) inajriiet to take up a position other than the 1. eridiim, us A /{ (Fij;. 21»), I et A' l)e the iieutml point. Then, resolving aloii^' the meridian, wo have in m // ~ -, COS ^, ± ^ COS e, ^ an. I'h't care- fully the magnetic field around the niairnet. It will be fi>und that near one point the lines of fonre bead away, as in Kig. :5<). The neutral point lies within this space between the curves. Adjust the position of the neetUe as before till no directive force acts on it. Measure /' and /*,. Drop perpendiculars, as LQ and sx (Fig. 29). on the direction of the meridian line through 1\. vn\^ V. / / / /■ // / y // / '■ /// / Fio. 30. w cos d, = jj^\ tios fy = - ^_- Measure the distances corresponding to /\'(^>, LA", Kx. Substitute in formula (:'.) and calculate M. Show diairrani in each case. I !^( 111 134 LABORATORY PUYSICA Example. — Enter results thus: II = .1584. 1 >,t case 2(1 case 3d case r 'i / AV Kx LK J/ 24. T) 32.0 80.2 2JS)() 23 It) 2270 "22.6' 7.5 3.95 3.29 8.33 Afp.iTi vnliir of M 2291 Blank to he Jilled in l»j student. 11 = r »i I A'(? A'x LK M 1st case 2d case 3il case of ^ * 43. TO DETERMINE THE MOMENT OF A MAGNET BY OSCILLATION IN A UNIFORM FIELD OF KNOWN INTENSITY. References.— S. Tliomp^on, p. 1'21; AVatsoii, p. r.04: Ames, p. 352 V Xiehols and Fmiikliii, vol. 11. p. '24: Aii- tliony and Uraekett, p. SOS; Carliart. pt. 11. p. .".!!»; ll.i.^t- iii<,'s and T?oach, p. 364; Barker, p. 691. Apparatus Required. — An o.^eillation-ltox wifli siisi)ensi(.n : several macrnets of diflFerent sizes atid eorre.^pondinj; t<.rsi(iii weiirlits: a niieronieter-iraiiire : a stop-wateli ; a e()ni])ass. Theory of Experiment. — If a lllil^n(•l, of moiiiuiit J/, i»e MAGSETI8M. 135 allowed to oscillate in a unifonn magnetic field //, the law uf its vibration is expressed by the forniula where n is the number of transits per second, and K the m(»ment of inertia of the nm-net. If observation be made for A' and «, //being known, 3/ can be calculated. Practical Directions.— Lay down a meridian line with the compass. If the bottom of the oseiHatit.n-box be provided with a mirror which has a line ruled centrally on it and parallel to the sides of the box, it will be suthcicnt to set one side of the box along the meridian line. The line on the mirror is to serve as the middle point of the swing of the magnet. Attach the torsion weight, and after it has come to rest turn the suspension-head imtil the weight lies along the line on the mirror. Replace the weight by the magnet, bemg careful to have the N pole pointing north. Set the magnet swinging through 15° or 20 . Observe the time, t, of fifty transits past the median line, 50 l^Feasure the length, I, and horizontal thickness, J, of the ..lagnet to -^^ of a millimeter. Weigh the magnet to a centigram. Calculate the moment of inertia from formula II 1 1 A^=ir(-^), r \ where TF is the wt-ight *d' the Uiagnet. ;^ ' !■ 136 LABORATORY PHYSICS. Assume the value of 7/ and calculate the moment of the magnet from formula ^[ake observations for several magnets of different dimen- sions, Ezample. — Enter results thus : 11= .1489. No. of 5 I weight, K Time of Trans, per M MtiKiiet. Onis. 53 31 50 Transits. Sfcoiiil (n). 17 8.8 1.3 350 420" 0.1189 327.8 18 8.8 \:l 53.81 354 440" 0.1136 302.8 1!) 10.4 1.0 25.18 239 332" 0.1506 341.3 20 14.8 2.0 154.77 2877 500" 0.1000 190.7 Blank to he JiUed in hij shuleni. 11 = No. of Magnet. b I Weight, K Time of 5U Transits. Trans, per Second (n). M 44- TO COMPARE THE MOMENTS OF TWO MAGNETS BY OSCILLATION. References. — As in previous oxperimont. Apparatus Required. — Two bai- magnets; a stirru]) bored to lit tlie magnets and provided witli clamj^s for fi.xing tliom rigidly together; a bell-jar or box with su6})onsion ; a torsion- weight; a stop-watch; a compass. MAGNETISM. 137 Theory of Experiment. — If two magnets, wliich are rigidly connected together, so tluit tliey niiiy be suspended pandiel and in the same vertical plane, be vibrated under the control of a constant magnetic force, the ratio of their moments can be readily obtained. For, if they be vibrated (1) with their like poles together, (2) with their like poles opposite, and the nuinl)er of transits per second, /«, and //, respectively, be noted, we have J/, = vi,-^ m,, (1) M\ = m, — III, , (-0 where ill/, and M, are the resj)ective moments of the systems in the two cases, and m^ and ///, the moments of the separate magnets. We also have (3) //being the constant controlling force, which is in this case the earth's horizontal component. By combining the above we have + < «.' — V (5) This gives a very convenient method of comparison, and is practically independent of the size or shape of the magnets. Practical Directions. — Having laid down a meridian line, hook in the torsion weii;ht and lot it come to rest. Turn the suspension-head around so that when the mag- nets are susj)endcd they will lie along the meridian. Clamp the magnets in the stirrup so that they are sus- pended near the middle of their lengths and with their like poles in tlie same direction. .'n.i«B.> *H MMtK^amyi^^m «r j^-vMsm ^ ^mM\.>^m^ 138 LABORATORY PHYSICS. Lift off the torsion-weight and hook on the magnets, being careful not to have the su^^pension fly around in doing so, a"'nd that the N poles of the magnets are towards the north. Let the system come to rest, and mark the point in the bell-jar at each end of the magnets. Set them swinging l)y means of another magnet. Note the time of titty transits past the marked point. Koverse the lower magnet, being careful to clamp it in the middle as before. Observe again the time of fifty transits jwst the same point. Obtain the nnnd)er of transits, v, and n,, in each case, and calculate the ratio ?//, and m, from formula (5). Example. — Enter results tlnis: Time of 50 Transits with Like Poles toKi'lliHr. 455 Time of ."OTninsits with l.ike I'olfs opposite. 1140 0.1099 7n, _ vO.1099)' 4 (0.0438)' ^ j g^g r«, "" (0.1099r - (O.U438)» 0.0438 I'l II Blank to h' fVc0 Transits witli Like I'oles tuRetlier. Time of .50 Transits witli Like Poles opposite. 7/1,1 "i ilr MAGNETISM. 139 45. TO FIND THE MOMENT OF A MAGNET BY THE DEFLECTION METHOD. References Wiitsoi:, p. <'.0(i; Ames, p. 3r>M; Nichols and Franklin, vol. 11. p. 23; Anthony and Hrackett, p. L>r.8; S. Thompson, ]). 124 ; Carhart, pt. 11. p. 318; Hastings and Beach, p. 361 : Barker, p. 61>1. Apparatus Required. — A magnetometer ; a magnet whose moment is to be determined. Theory of Experiment. — Let a magnet of length '21 be placed so that the line of its axis is at right angles to the majrnetic meridian, and in line with the centre of a magnetic needle. Let the distance between the centre of the magnet and the needle be denoted by . '»■'{!»; Antliony and Urackett. y. 1-Jl; Carliart, pt. 11. p. 1»51. Apparatus Required. — A ('oulonil) balaiice provitled witli a eiisioii; a Imiij,' cylindrical l.rass har; a ion" cylindrical inair.iet ; aconnuis;^; a watch; a micruineter gauge; a centimeter scale. Theory of Experiment.— If a magnet of moment M be 8uspended horizontally, and detlccted through an angle e from the meridian of a magnetic field whoso horizontal com- ponent is 7/, by X turns of a suspending vire having a tor- sion couple T \>er unit angle, the condition of ecpiililmum is 27rXT= Jflf sin (1) If a non-magnetic bar of known moment of inertia be oscillated in the stn-rup carried by the suspeusioi. wire, the value of T can be found, suice T = n-'nK, (2) where n represents transits per sec, and K the moment of inertia. To compare the moments of two magnets by this method, it is onlv necessary to observe the turns of the torsion-head re(iuired to deflect them through the same angle, when the moments will be to each other as the turns of the torsi on -head. Practical Directions.— Weigh and measure the brass bar to the second decimal place. Set it in the stirrup and level the instrument so that the bar may swhig freely all round. [ 144 LMiORATOltY I'llYMirs. Set it oscillating tliroiigli 2<> or 30 ilegrccs, and observe the time of twenty transits jMist the niiddle point of its swing. Denoting the time by <, n t-'O Calculate A' from formula A ''='"(l':i+[r.) in, I, and e being rcspectivi'ly the weight, length, and diameter of the brasH bar. ('alculate 7' from fonnula (2). Having bruuglit the brass l>ar to rest, turn the torsion- head till the brass bar lies i)aral]el to the direction of the meridian as determined liy the compass. Note through which diametrically opposite graduations on the lower circle the meridian passes. Kemove the bar and replace it by the nuvgnet, being careful to have the N pole pointing north. Twist the torsion-head so that the magnet is deflected throuirh an atigle of »".n° (,i- 7u' (W). licad the whole and fracti(tnal turns of torsion-head. iJring the l)ar back to the meridian and diHect it through the same angle, ^^ on the other side. Let j> denote mean turns of torsion-iiead. Then .V of fonnula (1) is e(]ual to I J* — „,. I, since the magnet is deflected through the angle ^. The value of //is snp})osi'd to be known. Calculate the moment (»f the givou nuignet from the for- mula (1) MAOSKIIHM. 145 Precaution.— As tlie mngjict nears the east and west posi tion, l>u curtfiil to kt-ej) it from swinging widely. If allowed t<» i)a8.s the aliovc position, it will .swing conii»letely around. Example.— Enter results thus: BUA88 HOI). w 37 m 18 14 .500 MAGNET. // - .119. * Tuniii (.f T head irMion- Mean p. 1 --'-;„• M SO'.O Right 2.48 Left 2.46 ! 2.47 1 2.35 941 Blanks to be Jill ed in by fftiuhnt. BRASS ROD. w I c K n T • // = MAGNET. « Tunis of Torsiiiii- head. Mean p. M 1 1 Tap UA LABORATORY PHT81C8. 4/. TO DETERMINE THE HORIZONTAL INTENSITY OF THE EARTH'S MAGNETIC FIELD BY THE MAG- NETOMETER METHOD. References.- S. Thuin|)i«)n, pp. 121 and 124; WaioDn, p. 615; Ames, p. 355; Nicliol« and Franklin, p. 23; Anthony and Bnickett, p. 26s. Apparatus Required. — A permanent bar magnet (prefer- ably cylindrical); a delicate mirror magnetometer with wilk- tihre suspension and j)rovided M'ith a long centimeter scale ; a telesco|)e f<»r reading deflections of the magnetometer- needle. Theory of Experiment.— Let the middle uf a iKrmanent ntagnet of moment J/ be brought up, in the end-on luisition, to a distance r from the centre of a delicately suspended magnetic needle. Let the needle be deflected in conse is tlu' diNtiiiici' from suspeiulctl ihmmIIc t<» i1h- schIu of the tele- hi'opi!, and 'li till! mean «li'tU'(;ti()ii of the iit'i't I'V means of tin- elamiw provided. Tlu' (■ x\\\ ol 'u' >cale whuuld !»o under the needle approximately. Set up the telescope and m-; le it a M-air distance /> of about one meter. Adjust the •eW'scupi- to point on the iiiirn)r, and while lookiiif; aloii- the tflt',-..upc, adjust the scale up or down tintil an imi! o tf if is si^eii. Focus til' telescope on l i- image '' the scale in the mirror. Adjust the telescope and - '<■ till tin zno readiiij; is opposite the vertical cross. Turn the scale of the telt-' -pc until its • luls are equi- distant from tlie needle. Place the deflecting majrii' its -tir; . 'ii the scale provided for it and hring it up > ;» .>tan< *■ / -< that a de- flection of 1\ liead the deflection, f?,, to ,'„ mm heinir careful to have the centre of t' distance, /', as hcforc. Read deflection, <■?,. Transfer the magnet to the other m.ii- of M.- iia^itetom- eter at the same di^tance, r. and ohtai -iii i uly the read- ings. rf„ 6^. Iv' • I- I ■■ ii.agiict. 'n;,^iic! it tli<- -ame J 3 «| 148 LABORATORY PIir.SlCS. A mean of the four readings should be taken. Hence the data for formula (1). Now unhook the needle from tlie magnetometer and re- place it by the deflecting magnet (a small aluniininm wire stirrup is convenient for Bupporting the magnet). Set the magnet swinging and count the time of tifty transits. 50 If t be the time, then )i = —. Measure tao length, /, and diameter, f, of the magnet with a pair of micronieti calii)ers. Weio-h the magnet to ^\ milligram, denoting the weight by w Calculate ^from the formula for cylindrical bars: ^='olviiig for 1, we get '-^'t^:^- (3) If ;', /*,, d^ ^,, be observi'd, ^ can l»e caloulatecl. This position of the magnet with relVivnce to the needle is called the " Broadside-on I'otiition." (•2) Suppose tlie magnet to l>e placed at right angles to the meridian, and its axis in a line with the centre of the needle, as in Fig, 33. r Fig. 33. The conditions now are the same as in obtaining the moment of the magnet by deflection method. Hence 4 rim -, = IlUxn H, . . . . (4) 6*, r, and I having the same meaning as before For a position distant /■, we also have ■i^rj/ii. ^^ (5) ^ MAONETIS^. 153 Combining (4) and (5) and solving for l^ we get A being equal in this case to lr^ tan ff^ \r tan Bj ' From (6) I can be again calculated if ^, (f^ r, and r be observed. This is known as the '' End-on Position." Practical Directions.— (1) Broadside-on Position.— ?\Ace the magnetometer in the magnetic meridian, and focus the telescope on the scale, the telescope being in a line east or west of the magnetometer. Place the magnet, whose magnetic length is to be deter- mined, at right angles to the meridian, having its centre and the centre of the needle in the meridian. Adjust the distance till a deflection of nearly the whole scale is obtained. Now reverse the magnet, and read again. The mean of the observations gives the true value for the deflection. Denote the mean deflect'on by 6. Measure the distance r. Allowance should be made for the width of the magnet. Adjust the position of the magnet to another distance, /•,, so that a deflection of about half the previous one is obtained. Read deflections and take the mean as before. Measure r,. Measure the distance between the magnetometer and the telescope scale, denoting it by K. Calculate (: ^*l' or A^ Han bj * % 154 LABORATORY PHYSICS. I 1 remembering that tan 2 # = jv, since the reflected angle ia double the deflection of the mirror. Substitute in formulii (3), and calculate /. (2) End-on Position. — Now place the magnet at right angles to the magnetic meridian, its axis being in a line with the centre of the needle. Again adjust the tlistance /• till a deflection of nearly the whole scale is obtained. Read ;• and the deflection as before. Koverse the magnet, and repeat the observations. Adjust again for a deflection of about half the previous one, repeating the readings as above. p\ tan \* Calculate //', tan ft y V Ian ft J or A. Substitute in formula (6) and calculate /. Example. — Enter results thus : BROADSIDE-ON POSITION. Posiliiiii of Maguet. N. toE. N. to \V. N. to E. N. to W. r 26.3 33.1 a Mean i 1 i a: 42 A 1.546 Calfiilaieil. I>>neth ot KHr. 15.3 18.9 18.7 9.60 9.30 18.8 9 45 13.8 E ND-OX POSITION. N. to H. N. to W. X. to E. N. to W. 40 50 113 12.3 (i.O 5.65 11.8 r».8:J 41.3 1.580 12.7 15.2 w IP Hi ■> im\* ■ .r\wUiA^ MAGNETISM. Blaiih to he Jill nd tn by Htvdent. BROADSIDE OX I'OSITIOX. 155 ] Position of MaKiit^l- )■ i Mean i \ K A -' 1 Calculatfd. of Bar. 1 : X. to E. X toW. X. to E. X.toW. EXD-ox posniox. X. to E. X. to w. X. to E. X. to W. 49. TO DETERMINE THE VARIATIONS IN THE HORI- ZONTAL INTENSITY OF THE EARTH'S MAG- NETIC FIELD BY MEANS OF THE COMPASS-BOX VARIOMETER. References. — Kolilrausch'sPliysical ^[easureineiits, p. 257. Apparatus Required. — Kohlrausch's eoinpass-box vari- ometer. Theory of Experiment. — The variometer consists essentially of a permanent matijnet and compass-box, the box being upon the top of an upri<;ht which passes through tlie centre of the magnet, the centre of the magnet and the needle having the same vertical axis. The magnet can be adjusted vertically and turned round its centre. Suppose the magnet to 1)e fixed with regard to its vertical motion, and to be turned n»und until its N pole points north. The corresjM.nding pole of the needle in the compass-box will point ilirectly south. i 15C LAjiORAToitr rinsics. 1 ' If now tlie magnet he turned through an angle 6, such that tli.3 needle lies in an east and west direction, we have /''cos = B^, (1) wlu-re J^ is the force due to the magnet, and ff, the eartli's liori/oiital component. Now let the instrument be moved to another station, where //, is the earth's horizontal component. If now the magnet bo turned through the same angle, 6^, from the meridian, the needle will take up a different position. Fio. 34. making an angle with the east and west direction (see dotted line in Fig. 34j, unless //, be etiual to //„. In this case we have ZT, cos = i^cos (d ± 0), or II, = F(cos ff :f sin 6 tan 0). . . . (2) Hence, combining (1) and (2), we have iT, = JlXi. T tan ^ tan 0). ... (3) From (3) ff. can be calculated if ff. be known. MAO NET ISM. 157 If be ^iiiall and iiitiwuml in degrees, X 'T tun = T80~ ^I'P'"^''-' and formula (3) becomes ( ir = \\ T T^- tan if \ II,. (4) Practical Directions.— 1 1 ) A<(/ '(■•<( "i''»f>' "f Station of Ihf- ereiue, //,._Cai-ctiilly lev.-l the instnunent. Set the zero of the scale carried by the magnet to one of the quadrant divisions on the tixed scale immediately below it. Lower the needle in the compass-box till it swings freely on its i>ivot. Turn the whole instrument, comi)a.>s-box, and magnet to- gether, till the needle and magnet are paraHcl, the N pole of the magnet pointing north. The exact position is found by turning till the needle reads ti» tiie ° in the opposite direction. Clamp the second stop. (2) AtliuHtinents ,it Second St,itlofi, 7/,.— Take the instru tnent now to another stati(»n. Level as before. Adjust a- before until tl • needle and nmgnet are in the meridian. Without moving the stt)ps, turn the magnet successively t.. them and in each case read the dilYercnce of the dertecti.ni from J»o '. Head in each case both ends of the needle, and take the Miean of the four readings as 0. Read the angle through which the magnet is turned from the meridian, and take the mean of the two readings as ^. //, wi'i'i iK- uivator or lcs« thaii //„ acc-Tding a;- the is'-'-d!'- in 158 LA BORA ran r physk 's. tl«e second station is (l«>H«'cfo<| tlironj^li an ungle ^leiiter or less tlian 9(» . Precaution. — Whoji oneo tlic nia^rnct lias been adjusted at tlie station of rt'tfrt'iu-c, do ut alter its po.^itioii vertically <»r move the stops, otherwise the work will have t«> he repeated. Example — Kiiter results thus. 4 Htatinn. 9 ♦ iliun. S. Kiid i>r Nemlle. - 5lH;in Vnl... ..r -f 3.5.') T 4.65 - 3.65 U Mfi'iillaii. X. Kiiil..f s. Ki.il .if .M.ii .N. Kill of Keference 8<1 4tli 3i' 30' 32' W i 1 f 3 r, , 4 3 6 t 3.5 -t-3.6 .160 .156 ,ir>8 U5 .Mriin Valiif 32 40' ■f 4.7 -f 4.7 - 2.7 - 2.6 + 4.6 - 26 -1-4.6 - 2.7 liliiuk to he filled in iy st>i, the current tiv)ws through thegalvaiutnieter in one direction, and in the opposite by joining A to l\ and B to I). /wj>^ KLKCIIUCITY. 161 rieforo cloKiuiij the oiriMiit tiiko out u jilii;: i'roin tlm rc- 6iHturK-e-t)OX 8o tliiit jtt loant ')<> oIiiiih nliiill la- in •', •rcuit. Cloiso tho circuit l»y iiioaus of the rcvei-.^iiii; . irid ad- just tuo roriistaiice until a tU-JlfCtioa <>f, su\ , l'>'^ i> v/Dtuined. Ueversc tlte current un. liotli ends of tho needle should l»e read ea. \\ time to tlie ,\j of a degree. Denote ^lie angles hy ^>, . .'', , ^'j , ^, , and the mean anglo l.y fi. With tlie current still flowing, turn the galvanometer coil round its vertical axis until the needle again reads r.oxiy. If the galvanometer be i)rn' ' 'cd wit.h i >tale t\»r measuring the angle through which the coil he turned, this angle can he read off directly. If this he not the case, wlicn rhe needle rv-.uls zcio, open the circuit and read the angk- through v.hirli it ^wiiigs hack. Since in this case the iummHc conies l)ack to tiic iruTidian, this angle will he the same as that tlirougii which th coil was turned. Reverse the current, and repeat t!ie i»peratioii a- above. Denote tlie angles by 0. , 0,, 0,, 0,, and the mean angle by 0. Then by formula (4) tati ri — sin 0. It! jg2 LABOR AWRY PHYSICS. Brin- the coil back again to its original position, and adjust the resistance until thr re.uling by the tangent method is approxin.ately 15°, and take the corresponding sine read- '"^ Adjust again for 20% 25°, ;'>(>% and 35% con.paring the tangents of these angles with the sines of correspondu.g angles by sine method. Record the resistance A' u ed in each case. Example.— Enter residts thus : Jj'hid- to h,'jil/>'d In hy 8i>;ni. Mil 4. 1 DirrprciKM". I ELECTRICITY. 163 51. TO DETERMINE THE ABSOLUTE MEASURE OF AN ELECTRIC CURRENT IN AN INCANDESCENT LAMP. References. — As in Experiment oO. Apparatus Required. — A tanjjent galvununieter (the coil of wliieli cun be ineasjired) ; a pluj; for c(>nnectin\ and ^,. 4 Then H = Measure h} means of a pair of calipers the diameter of the coil. To do this at least three different diajneters for both the inside and outside of the coil should be measured, and the mean taken. This mean diameter divided by 'i gives/-, the radnis of the coil. The value of //can be found on a chart in tlie labora- tory . Substitute tlici values in the formida C = 1 (>///• tan fi '2 rr II Measure tlu- .-.irrent thr..ugh <.ne It'.-C.P. lamp, then through twn U",-('.P. lamp:; in parallel. Then mea>inv the <-urrent through two '.Vl-V . V. lamps in parallel, and als.. tlirougli one Wl-iW. lamp. Finally tlin.ugh one Z'l-V.V. lamp and one ItJ-C.l'. lamp ill parallel. Precautions, r.e.areful not to ^hort-(•ir(Mlit the hghtmg circuit. Make all the (•unuectioii> and be suw they are cor- rect l)efore connecting the ]>hig witii tlie iamp-sockel. BLEcmicirY. 165 Example. — Enter results thui s : a" ^^ a/ «4° i Oiltsldt- Diaiii. Iiisidf l)iaiu. H. Current Aiiipa. <)ii>*it;-e.i' lamp. .. «..'. 0.."i 1 lii-vcl>e(l TvVM Id (' I- lamps. . \\.:< 14.:. (!.?< fi.V t;.r .•ii.s ■■VA.f, IT.l .48 ( lllf iJ-C.l' lump ■JU ^.11 11 9 14 :i ii.r .■il.H ;«e 1.03 i;-vfrs(-il Two:;.'*' i' lilllip.s. :>ii ■ii; ■Ji 1 . ',' •M.-i ■.'•1.1 31. H Ai.C 1.4» K«*V(»fM'u , ■Ji :ir ■■'*; :, .ll.S 3.).0 ■i.M Jildiik ti> l» p'llid in hij .sfadtnL Oiif lG-('.r. lamp. . Kfvfrsetl Thii Itj-C.r. lumps. kcverseii t)iif ;!-.•( M'. lamp . KcviMseil. T\vi> .W C.l'. lamps Keversed Olllsi.l.- Ill^i.|l Ilium ' \lla\n Current Aiiip.s. i3 52. TO DETERMINE THE ELECTRO-CHEMICAL EQUIVA- LENT OF HYDROGEN. References. — Knott, pt. ii. |>n. I'dU-jixi; Ilustino's and ]>eacli. J)].. ;;!tti_4u(»; AVutMin, p).. Tsr.-TSs; S. Tliom])son, pp. •JL'l-2-is; Xicliul-; ,111(1 Frail l< liii. pp. ♦'.7-t;i»: Ames p]). :',l7-')-22: AntlK.iiyainl UiMckftt. pp. :]'2:'>~:\2U \ liarker, pp. 741 -74<); Ciirliart. pt. ii. pp. -J.").-) lMIii. Apparatus Required. .\ taii^imt ixalvaiioinet' r, rlio coil <'t wliicli can !»(■ iiH'a.-iirf.i : a i:a< voltaiiictcf ; a resisfancc- Ixj.v ; a four-Vdlt sloraue-hattcrv or other >ource of con.>taiir ourrent; a reversin ^ ^ .> - ' (.■ Snn • (1) where ^is the detiection, // the earth's horizontal component, r the mean radius of the coil, and u the number of turns of wire in the coil. If now, in a time t'\ theijuantity of hydrogen deposited by the current, supposed constant, be //*, and the electro-chem- ical e«piivalent be denoted by t, then Ct" = rii therefore e = Vt" (2) Combining (1 ) and ('i), we have e = '2 nil III J/rt" liiu t*' . (3) If now ?«, the nuvss deposited in a given time, be meas- ured //be known, and ^ (.liserved, c can be calculute\vitch and let the liydi Now close the key a<:;ain, and take aiciuutely the time < f starting. Reverse the current every two juinutes, and take rcatlings for both ends of the needle. Denote the tirst readings by H^ . ^, , and the readings when current is reversed bv ^, , H^. The mean of the dctlections observed gives tlie value of H. Let the current flow until the tube containing is nearly full. Take accurately the timt; at which the curren otr. Measure /', the radius of the galvanometer coil. liead the volume of hydrogen in the tube of the voltam- eter. Take tiie temperature, /, of the solution in the voltameter. Kead from the chart in the room the aqueous vapor j)res- sure for temperature, t. liead the barometric ])ressiire, correcting for temperature. Kead the ditfercnce of head between the hydrogen rnd the water in the open tube. If the hydrogen tube of the voltameter ]»e not graduated, the volume can readily be obtained a> follows: Let the oxygen e>ca[K' from the oxygen tube. I5y means of a |)i})ette or siphon, take the solution out of the open tubi- down to some lixeity of hydrogen, .(((XMKSIMJ. If y. be the volume of the hydrogen at standard tempera- ture, (»" (.'. or L'7-'.."> of the absolute scale, and under standard ]»ressure, TO cm., <', the ol)scrved volume at temperature t or ti7'2.r) -f t of the absolute scale, and under a pressure P, then we have the relation n X 70 i\ X /* 27'J.') i>72.5 + t' or _r^X /' X '^72.5 (*) The pressure P'xn manre diu' to tiie i)res- ence of aipu'ous vapor in the tube c<.iitaining hydrogen. If h Im' the dilfercnce in heatl in the voltameter, then this correction reduced to centimeters ol mercury is - ., .^^^., KLKCTRICtTY. 169 of mercury. If the solution be 15 jxir cent, sulphuric acid, « = 1.1 approximately. Assuming this to be the case, we have '". = /,. , hX 1.1 \ TlV-iTli./i + O (5) and therefore 7/1 = •("+TC5y« -")=<-'-■'* X- '""'" 7«K272.5 4- t) -, • («) 01 being the aqueous vapor pressure which can be found for the tt'in|)eruture t from a chart in the lulutnttory, or from a book of tables, and .O00081H5 the density of hyihogen, that is, the mass per cubic centimeter. Substituting this value for m in e(]uation (3), we obtain t\. Example — Enter results thus : //=.1558. « = 30. Time Tirrn- of I ..f Starting. FinisbiiiK.: /" B i (iMir. , reeled). I 1 1 1 2.45 I 3.25 ;• h 15.1 30.5 '•i I'l, ;.iH,a :s6 :i7 2400 t 1S.() V .(I0;!'J5!S 70.02 1.54 Itt' 104 y: 170 LAliOHA TOR Y PH YSIC'S. Blank to Ite Jilletl in hy student. •l », 91 *. 1 'rime 1 Time ■ .f 1 of SiiirtlriK- FiniHliliiK. t" n (cor- r«Ttecr voltam- eter containing a solntion of copper snlpliate; a ;^as voltain eter containinf; a ir»-}>er-cent solution ot' sulphuric acid ; the battery (or lightin^'-cireuit); the a»lju>' ''le resistance; *he contact-key. If the lighting-circuit he used, a l(5-caii a yvA/.«' 'nir (if not lexs than lOO oIdiis in thf ri/viiit {i( lO-C. J*. hinij> n,- otlii^r reshtanci) 1/ tin' rHjhtinij-c'urnlt hr kshI. See tluit the tubes of the gas vcdtamctcr are full of the solution . Close the circuit and let it How until the hydrogen tidie of the t he connected ti» the negative pole of the suurce of current. (3) Thoroughly chan an2), or (' = -:.,. . . . (2) Ct" = ^, e et' Hence, comhining (1) and (2), 2;r« cot H X M JI = erf .... (3) m MICROCOPY RESOLUTION TEST CHART (ANSI and 'SO TEST CHART No. 2) 1.0 I.I 1^ ■ 30 IS 2.2 1 4.0 1 2.0 1.8 1.6 ^ /APPLIED INA^GE Inc S^. 1653 Eost Main Street r.S Rochester, Ne» York 1*609 USA ^^S (716) 482 - 0300 - Ptione ^S (716) 288 - S989 - Fax 174 LABORATORY PHYSICS. Practical Directions.—Comiect iji series tlie tangent gal- vanometer, the l)uttery, the c'up])er voltameter, the reversing- key, and an adjustable iesistan(;e. Put tlie reversing-key in the galvanometer circuit only (Kig. 35). Close the circuit and adjust the resistance until a suitable deHection, about 45°, is obtained, the coil of the galvanom- eter being in the meridian. A meter or two of bare German-silver wire, No. 20, makes a suitable resistance and can be adjusted at one ter- minal of the battery. Now open the circuit and take out the plate upon which the deposit is to be made. Clean, dry and weigh, as in the last experiment, and restore the })late to its place again. Ee sure that the negative pole of the battery is connected to the clean plate, otiierwise copper will be taken off in- stead of being deposited upon it. Close the circuit, taking accurately the time of closing. Let the current How for 3(» minutes or moie. Take accurately the time when the current is turned off. While the current is on, reverse everv two minutes and read deflections, reading always, if possible, both ends of the needle, denoting the four readings by 6^, , ^, , 6^, , 6^. The mean of these gives the true value of d. Unless a rapidly reversing commutator is used, the time of each reversal should be taken and allowed for. Take again from the voltameter the plate upon which the copi)er deposit has been made. Wash the plate by letting pure water flow gcntky over it, or l)y rinsing in a 10 i)er cent, solution of sulphuric acid. Dry as before by holding it neat' a Bunsen flame. Weigh the })late. The difference between the two weights is the copper de- ELECTRICITY. 175 posited. Measure the radius of tlie coil as in previous experi- ment. The electro-chemical equivalent of copper, 7i', is .Uo;}28C. Example. — Enter results thus : e. ., 9, 46.5 46.0 46 7 46.2 45.8 46 ;{ 46.3 46 1 46.5 46.3 46.0 46.5 46.1 45.9 46.3 46.2 45.9 46.3 46.1 45.7 46.2 46.3 45.9 46.1 46.1 46.1 40.3 Mean value, 0. 46.3 46.2 46.3 46.3 46.2 46.2 46.3 46.3 46.1 46.2 w Time of istartiiig. n 250.700 2.35 30 "'. Time of Finisliiiig. r 250.748 30.5 15.1 J/ t" 1 // .147 .048 1200 Blank to he filhd In hj Ktudent. Mean value, ir, 1 M Time of Siariiiit;. Time of FinisliiiiK. // 176 LABORATORY PHYSICS. 55. TO DETERMINE THE REDUCTION FACTOR OF A GALVANOMETER. References. — As in Experiment 54, Apparatus Required. — A tangent galvanometer; a gas or copper voltameter ; a storage -battery or plug for the lighting circuit; an adjustable resistance capable of carrying one-fifth of an ampere ; a re versing- switch. Theory of Experiment. — The theory of this experiment is exactly the same as the last, the only difference being, that in this case, since the value G cannot be directly measured, the value-—, the "reduction factor," is obtained. Since C — r tan 5 = ^tan 8, (r K — C . cot e (1) Practical Directions. — The connections and observations are exactly as in the last experiment. If a gas voltameter be used, observations similar to thoso in finding the electro-chemical equivalent of hydrogen must be made. If the current be taken from the lighting circuit, a lamp should always be in series with from 500 to 900 ohms resist- ance. An ordinary resistance- box is not suitable, as the coils are liable to burn out. A coil made from No. 24 or 25 German-silver wire serves the purpose. In the case recorded below a gas voltameter was used. m ELECTRICITY. Example. — Enter results thus: 177 » Mfttii. 40° 18' t" 3840 B h t a V C . 76.75 35.0 17 1.44 38. 2S .0837 .080 lilanJc to le filled hi hy student. Mfcin. t" B li / a V c a: 56. TO PROVE OHM'S LAW, C E References.— Knott, pt. 11. pp. 184-187; Watson, p. 688 ; Barker, p. 699 ; S. Tlioiiipson, pp. 1 75 and 397 ; Has- tings and ]ieacli, p. 395; ^Nichols and Franklin, vol. 11. p. 54; Anthony and Brackett, p. 317; Ames, p. 333. Apparatus Required.— A tangent galvanometer (prefer- ably one sensitive to fairly small currents); a storage battery; a resistance-box ; a reversing-switch. Theory of Experiment.— If the galvanometer, the lesist- ance-box. an'»^TT.*.A»i* -^.rK-^ChT.^^-.*^* ELECriilCITT. 179 Precautions. — Before coiiiiectirii^ itj the battery, be sure to unplug a large resistance from tlie box. Never have less than 20 ohms in the circuit, unless the resistance-box is known to be suited for ( urrents used. Example. — Enter results thus: Blank to he filed in hy student. •. 9i « tan 9 1 tan • R 57. COMPARISON OF ELECTRICAL RESISTANCES BY MEANS OF A SINE OR TANGENT GALVANOMETER. References. — Knott, p. 1!)7; Watson, p. ♦>ss ; Barker, ]). 7<>(>; Hastings and Beach, pp. 425-420; Nichols and Franklin, vol. ii. p, !>1 ; S. Thompson, p. 413; Anthony and Bruckett, pp. 319 and 860; Ames. pp. 333-H;J7. hi W if, r...'k 180 LAUOIiATOHY PHYSICS. Apparatus Required.- A sine or tnnjrent frulvanometer ; a resistance-box; a storugo Lattery ; a reversing-switch, resist- ances to be measured. Theory of Experiment.— If a w«t' BLBCTRICIT7. 181 Using equation (3), E Changing R^ to ^,, we get E = K tan ^,. = K tan ^,. Hence B + G -\- n^ _ tan g, i? 4- 6^ + A*. ~ tan ^,' or, denoting B -\- G by J', r + K tan ^. 1' + li, tan 6^,' (4) from which Y can at once be calculated. Practical Directions C-onnect in series the resistance-box, the battery, the galvanometer, and a reversing-switch. Before closing the circuit unplug from the box a large re- sistance. Set the galvanometer coil accurately in the meridian. Close the circuit and adjust the resistance until the deflec- tion is about ."0°. Denote reading by S. Reverse the current and read again, d,, taking the mean as B. Adjust the resistance again until a deflection of about 00° is obtained. lieverse and read a.s Ijefore, ^,, rf, , taking the mean as 6*,. From these observations calculate B + G. Now put in the unknown resistance A", and adjust the re- sistance in the box until the deflection is again about 60°. Use this observation with the flrst (30") to calculate the value of X. Tlepeat the operation for three or four different resistances. 182 LAJiORATORY PHYSICS, If a sine givlvanonieter he u»M'd, Kuhstituto m\ 8 fur tan f) in all till' ctilculatioiis, but the detlcetions must hv tukm in uc- cordunce with tiie hiiiu method, see Experiiiieiit ;")(). Example. — Enter results tliiis: i «. « <. *. »i K 1 80. 31.8 30.7 63. 61. 62. 30 9 11.4 12.0 11.7 11.2 11.8 11.5 30 89 2«.6 26.0 26.7 27.0 27.4 27.2 30 37 n t (I 57.0 4 . I Blank to hejilled in hy stuK „ In this case /t, = ^ — ^. - 7~T7i ^ ' Kesistance ut W . . (1) the if fore •cteU ^o ,i fl ' ,.^ m. ^MJ^^iC4J. , Ib4 LA ItnUA T and C are conneete*! thron^li it, then if the lengths All and Jih' Ite nieasnred, It^ can l)e eaU euhited. Practical Directions. — Tiio U. A. inidge consists of a uni- form wire AH stretched against a centimeter wale so that the lengths of the segments of the wire can he read off at onee. It is provided with terminals tor eonneeting in the resistances to he measnred, the standard resistance, and the battery. Fig. 37. Connect tlie standard resistance and tlie unknown resist- ance in the bridge, as in Fig. 37. Connect the battery, B, through a contact-key, K, to tlie tenninals })rovided for the purpose. Connect the point between the two resistances to the galvanometer, and through the other terminal of galvan- ometer, (r, to the sliding contact, *S'. Close the battery circuit first and then press lightly the sliding contact on the wire : the galvanometer will be de- flected. Adjust the jiosition of the contact, repeating the opera- tion until no deHtM'tion is (>l>tai!i(M|, V^ 'l 'm..~a^'W- KLKCTHIVITY. Ls;. The standard rcHiHtanco should bo a one-ohm box (Uvulud in tentlis, and the rt'Histancu sliould bo udjusti'd so that tho bahince-i)oint, tV, iw near tho middle of tho wire. Having fonnd tho balunco-point, road tho iongtiis + 2^ Blarih to he Jilhd in hi/ student. R Deflections. ff. I ! ! 188 LABORATORY PHYSICS. 60. TO PROVE THAT THE RESISTANCE OF A WIRE IS DIRECTLY AS ITS LENGTH, AND INVERSELY AS THE CROSS-SECTION; AND TO FIND THE SPECIFIC RESISTANCE OF A WIRE. References. — Anthony and Brackett, p. 319; Carhart, pt. II. p. 275: Knott, pt. 11. p. 181); S. Thompson, p. 402; Barker, p. 700; Ames, p. 333; Nichols and Franklin, vol. II. p. 49: Watson, p. 689. Apparatus Required.-- -A B. A. Bridge; a sensitive gal- vanometer; a standard resistr nee-box; a battery; a contact- key. Theory of Experiment. — If I and I, be two lengths of wire of the same material but of different diameters, then the resistance of the lirst is given by the equation /i' = 4pZ I.' that of the second by 7?, = assuming that the resistance is directly as the length and in- versely as the cross-section, p being the specific I'esistance, d and dj the diameters. Hence d^ dX . . (1) If now the ratio R/Ii^ be measur-ed directly by means of the B. A. bridge, equation (1) can be verified. ELECTRICITY. Having verified tlie relation, since It — -T,J na 189 we have = li il' I^Feasiu-ing li directly by means of the standard resistance end B. A. bridge, we calculate p. Practical Directions. — Take a meter or so of German- silver wire about Xo. IM and, with a draw-plate, draw part of it down to about So. 30. Coil the two parts together and anneal them thorouglily in a gas-flame, to bring them to the same specific resistance. Solder the ends of the wires to short thick copper con- nectors. The wire with the smaller diameter should be made shorter than the other, so as to make their resistances nearly equal. Measure carefully by means of a meter scale the lengths of the wires, and the diameters by means of a screw-gauge. Calculate the ratio, Ii/B,, by means of tMiuatioii (1). Tsow connect the two wires in the arms of the I>. A. bridge, and adjust until no deflection is obtained on making contact with the sliding c«.>ntact of the liridge. The ratio of i?to A', is obtained directly from the ratio of the two lengths, a and a,, of the bridge wire, or /«'//«', — ot/n!,- liemuve one of the wires from the l)n'l i fi a/ a. I 1 * i fl ELECTRICITY. 191 6i. TO MEASXIRE THE RESISTANCE OF A GALVAN- OMETER BY SHUNTING WITH A KNOWN RESIS- TANCE. References.— Ames, p. 335 ; Watson, p. 693 ; Hastings and Beacli, p. 429; S. Thompsoni, p. 409; Barker, p. 705; Nicliols and Franklin, vol. in. p. 56 ; Antliony and IJrackett, p. 361; Carhart, pt. ii. p. 276; Knott, pt. ii. p. 190. Apparatus Required. — A galvanometer ; a coil for shunt- ing; a resistance-box; a battery of constant E.M.F. ; a re- versing-key Theory of Experiment. — If a resistance R, a galvanometer of resistance 6', and a battery with an E.M.F. if and negligible resistance, be connected in series, then the current C is given by the equation C = E or or If be the deflection of the galvanometer, then C = K tan e, = K sin e, = Kd, according a* the galvanometer is a tangent, sine, or reflecting instnnnent, \\\ tlie latter ca^e ^ being the scale deflection. Hence, taking the second case, h ir^ra-^^^- (1) If now the rnet( r he sinnitod by means of a coil S", the other conditions remaining the same, by the tlieory of 192 LABORATOBT PHYSICS. Bhunts the total current in the circuit is given by the equation a = E and the part of the current through the galvanometer by the equation ^ _ ^ Hence C — F s R + or . . (2) ^» '- Ii{G -\- ^) + GS' (3) But C\ is also ecjual to K sin 0„ 6, being the deflection of the galvanometer in this case. Dividing (1) by (4), we have ^(r; + j^^) + OS _ sin ^ '7?(/r+ ay - ^huT^ ■ Denoting the ratio V -^- l)y r, and solving for G, we obtain . . (i) . (5) r/ 7^% - 1) (<0 from which G can be calculated. If the galvanometer be a tangent instrument, substitute for /• tan tan fl. ELECTRICITY. 103 If tlie galvanometer be a sensitive reflecting galvanometer, equation (1) becomen A' (7) Ks = and (2) becomes KS, = Ji + 6" S Ji (JS X (/+ ^' • • • (^) ■^ (T-i-^ In the case of a retlectiiig galvanometer, however, li is generally so large as compared with G that s+o + .<='''+''' to a close approximation. Ill this case, therefore, dividing (7) by 8 we obtain 6_G-i-S 6. ~ or G = (») It is usually more convenient to shunt the galvanometer for both observations. In this case equation (7) becomes K6 = equation (8) become s B.+ C/ -t- S ^ 'S + G ' GS' (10) E X s. GS^ G ^ S,' (11) 104 LABORATORY PUYHlCS. mi' Assuming now that 2i + we obtain 6 OS = li-V GS, G 4- ^: S{G + j».) b\{G 4- S) Denoting v ' 7 r we obtain on solving for G (12) Practical Directions. — (1) -AW fSineor Tangent Galvanoin- eter. — Connect in series tbe buttery, the resistance-box, and the galvanometer, putting in the reversing-key. A sn)all storage- battery is most suitable, since it has a steady E.M.F. and practically no resistance. Connect the shunt coil to the tenninals of the galvanometer, putting a contact-key in the circuit (see Fig. 40). Place the galvanometer in the meridian. If a sine or tangent galvanometer witi» sus- pended needle be used, care must be taken to eliminate torsion. To do this, lay down the meridian by means of a compass-box and turn I the torsion-head of the needle until the needle lies in the meridian. Now unplug a large resistance from the bi>x R, and close the circuit by means of the reversing-key A' lea\ing4lie shunt circuit open. Adjust the resistance R until a suitable deflection is obtained, about 35°, before turning the galvanometer. Turn the giilvauonietcr until the needle again reads icero, Fig 40. ELECT1UCIT7. 115 that is, occupies tilt' same relative position to the coil as before closing the circuit. liead the aiijjle thruugh which the j^ah aiioiueter was turned. If the galvanometer he not provided with a .scale tor reading otf directly the angle through which it was turned, then, after bringing the needle to zero with the current on, open the key and read the angle through which it .swings back. This will i»L' the dericction for the sine method. If a tangent galvanometer be used, adjust the resistance H until a dericction of above t'»0° is obtained. IJeverse the cur- rent ai.d repeat the observation, denoting thi- mean reading bv t). Now close the shunt circuit simultaneously with the battery, liepeat the observations as before, denoting the mean reading Find from the tables sin H and sin «,. Substitute the value /■(' . ^ ] with the values for R and S Vsm ^i) in ccpiatioii (»'»), and calculate <}. Kepeat the observations three times. {•!) Far a Rffednuj (Jdlranonicter. — It \'ill be necessary to caref idly adjust the galvanometer in this case if this be not already done. First carefully level the instrument by means of the levelling-screws attached. Adjust carefully the height of the needle by means of the sus})ension-head until the centre of the minor is appro.xi- nuvtelv at the centre of the aperture in the C(jil through which the light is admitted. If the needle be properly susi)ended, it will now swing tVeclv. A little further adjustn.ient of the levelling-hcrews may be necessary. 196 LA noilA TOR T PIITSICS. t' x 1! ,ij|S' Place tlio lamp (uid scale in front of the mirror, at a dis- tance of about H meter, and adjust the position of the scale until the line joiniiij; its centre with centre of the coils is at right angles to the plane of the coils, and its plane parallel to the plane of the coils. By means of the control magnet adjust the pv)sition of the mirror and needle until the light is retlected from the mirror towards the scale. The position of the retlected light can he determined by liolding a sheet of white paper in front of the mirror. The height of the scale can then he adjusted until it receives the reflected image. Vary the distance between the galvanometer and scale until a clear image is obtained. If the centres of the mirror and scale be in a line at right angles to the plane of the coils, the plane of the scale will be a parallel to the plane of the coils when the ends of the scale are equidistant from the suspension- head. Adjust the control magnet until tlie spot of light is at the zero of the scale. The galvanometer is now ready to be used. Connect the Lattery, the reversing-switch and a large resistance, li, in series as before. Unplug a large resistance from the box ; half a megohm will not be too much to begin with. Close the circuit and o])serve the dellection. If the detlection be small, reduce the resistance in the circuit until about 3<»0 scale division is <)])tained. If the spot goes oflf the scale, increase the resistance until a deflection of about 30(» scale divisions is obtained. Revenue the current and take the mean readiiig as 6. Now shunt the galvanometer with a known resistance. Adjust the shunt, S, until a deflection of about 150 is obtained. Reverse and read again. KLKCIinvliY. 1U7 The mean gives rf,. Calculate (f l».v formula (1>). Shunt the galvanometer again, S^, and adjust till ii de- tlectit.n of ahout loO scale-divisions is ohtiiini'd. Reverse and read again, taking the mean reading. \\y means of this reading and d, above calculate G from formulii (12). Example.— Enter results thus: Slue oi- Tangent (iulvuiioiiieter, Mean R s DfHtH.'tioi 6.50 -.00 2M.6 650 05. 3 1027 60.3 1027 100 26.4 825 63.8 825 100 27.6 Mean G 104.8 Blanh to he filed in hy ntudent. Sine or Tangent Galvanometer. Kef ting Galvanometer. ,_ ■ \ R .s Mean Defleotion. a R 8 Mesn Deflection. a 1 Me.in J/..... . iil 108 LA noil A I (Hi Y pii rstcs 6a. TO MEASURE RESISTANCES BY MEANS OF A WHEATSTONE'S BRIDGE. References. — As in K.\i)c>riiii(>iit r>:>. Apparatus Required. — A Wluut-toiR''!* hridjjc; resistance- to l)t' !iiea«urcd; a seiiHitive ^itlvuiioini-ttr; srvcral luittt i io : two oontJict-keys. Theory of Experiment. — (1) 7't> Mt'dxnn t/i, lirstsfmn, in a Coll of Wire. — The theory of tlie WiicatKtom''rt liridj^e is exactly the same as that of the I?. A. bridge, which is oidv a siiiipU' form of AVlieatfitone's hridj^e siiitabU' for measuriiif; small resistances. In the Wheatstone's bridge the arran«;ement is as in ig. 41. In the fiiiuio /* and Q are fixed resistances, R an adjnst- able resistance, and .s' an unknown resistance. When li is adjusted .so that no deflection <»f thi' jralvanom- eter is obtained on dosinj^ A', and A', /' _ .V p or S Q n. (2) To Midxiivi' fh( !,'• sisfiiiii-i of the (JiiltuiitomeUi' : KLKVTUIVITY. lt)0 Thonip»oiCA iVf/Aorf.— Since no current flows through the gulvanoineter, when the proiwr u.ljii?tnient8 for the n»ea«»ure- ment .»f .S" have heen made, that in, when Cuiul D arc at the same potential, tlio current Howing through each arni of the hridge renmins unclianged whether K he cU)ser not. Hence, if instead of S a giUvanoineter were in the arm <:ii, its deflection due to th ^ passage of the current throujjii the hridge would remain unchanged whetiicr A' he closed «)r not. It follows, therefore, that if the galvanometer he put in the arm Cli, and H he adjusted, until on closing CD directly through A' no change of deflection in the galvanometer is nhserve*!, T and /) have the same jM-tcntiul. For if a cur- rent flowed from C to />, the current flowing thrt.ugh the galvanometer would change, causing a change of «letlecuon. Hence Q ir or P (3) To Measut'ethe Resistance of the Buttery: Mance's Method.— li a hattery he placed in the arm Cli, a'ld the gal- vanometer again hetween C and D, on dositig A' a deflec- tion of the galvanometer will he produced, due to the current from this hattery flowing through the system. It", therefore, li h'" adjusted until no change in this de- flection is ohserved on losing A', rand /> are at the same p(jtential as far as the hattery hetween A and Ji is concerned. Hence p _ n or P ^ li = ^/?. where U is the resistance of the hattery in the arm CB. 200 LA nun A TOR T VII YSICS. u I r ! Further, since no current lions through tlie gulvaiiotneter from the battery B, when the proper adjustuienis are nuule, it may be removed altogether and AB connected directly throuffh A',. R can then be adjusted until one losing h\ no change in the galvanometer detiection is observed. In practice i. is convenient ti bring the galvanometer needle back to zero by means of control magnets. Practical Directions.— (1) In the ordinary Wheatstone's bridge the airaugement is as in Fig. 42, the letters having Fig. 'C. the same meaning as in Fig. 41, the numbers inJ^.cating the resistance that caji be unplugged from the bridge at the points corresponding to the open spaces. A sensitive gal'.anometer is required if accurate measure- ments are to be made. A reflecting galvanometer with telescope and scale or lamp and scale is most suitable. Coi.iplete the connections as in Fig. 42, putting con- tact-kevs in both the galvanometer and battery circuits. Unp.ug from both P and C^ loO ohms. Shunt the galvan- ometer with a suiall resistance while tlie trial observations are being made. Unplug a resistance from the arm li, and close the battery kov and galvanometer key in the order named. ELECIltlCITY. 201 Observe the direction of the detloctioii of the galvanom- eter. Change the resistance m H until tlie deflection is in the opposite direction. The value of S lies between these two values of R. Continue to adjust Ji until by changing it 1 ohm the direction of the reflection changes from left to right. Now open the shunt of the galvanometer so as to increase its sensitiveness. Change P and Q to \Q and 100 respectively. Adjust li as before, starting with 10 times the resistance of the smallest of the two previous adjustments. This will give the resistance to the first decimal place. Make P 10 and Q looo, rei)eating the adjustments for li. This gives *V to two decimal ])lac('s. Rei)eat the observations for the (»ther resi.-tanoes. (2) Put the galvanometer in the place of the resistance S. Put a large resistance in series with the battery between the points A and />*, thus dinuidshing the current flowing throusrh the system. Adjust this resistance until on closing the battery circuit the deflection of the galvanometer is on the scale. Kepeat the adjustments for P and Q as in (1), leaving the galvanometer circuit closed. Adjust 7? until on closing CD directly through a key no chanire in the £falvanometer deflection is observed. ('alculate G. On changing the values of P and Q in this case, a change in the galvanometer deflections will also take place, and the resistance in series with the battery may have to be atljusted to briiig the spot of light again on the scale. (;'.) Now put the battery in place of -S*, and the galvanom- eter a:rain between C and I). 202 LAliORA Tony i7/) .S7CV. Put a contact-key in the circuit between .1 and B. By means of n)a^net8 bring the spot of light to the i«ro of the Bcale. Adjust li until with /' equal to 10 and Q equal to lOO no deflection is obtained on closing the key between A and B. The resistance of the battery is thus obtained to one decimal place. Repeat the observations for the othe- batteries given. Example. — Enter results thus : Resistance. Coil A " B " C Galviinoineter . . . . Leclanche buttery Dniiiell battery. . . Dry cell 10 M 100 100 10 10 10 Blank to hejilhd in hy student. V R S 1000 2575 35.75 1000 3645 36.45 1000 2«94 29H.4 1000 273 27 3 100 14 1.40 100 85 8.5 100 503 5(1.3 Rebistance. P Q R s \ ^aKJai^*? Kl.hxrniclTY. 'xi; 63. (I) TO VERIFY JOULE'S LAW, JH = CTRt. (2) TO FIND THE VALUE OF ,/. References.— S. Tliompson, p. 436; Knott, pt. tt. p. lOO; IJarker, p. 70i> ; Hastings and Jieacli, p. MO; Ames, p. 2*25); Nichols and Franklin, vol. 11. p. 4S ; AVatson, p. 702; Anthony and Urackett, p. 31!>. Apparatus Required. — Two copper voltameters or two gas voltameters; two calorimeters with resistance-coils and stir- rers ; two thermometers. Theory of Experiment. — (1) Joule's Law may be stated p follows: T^>e heat i)roduced in a given time in any part . a circuit is proportional to the square of the current and to the resistance of that particular part of the circuit. The law may also he stated thus: If a current C tiow through a resistance Ji for f seconds, the work done in driving the current through the resistance is given by the c(puvtion w= cm". (1) If now the heat deveh)ped, which meiisuresthe work done, be utilized to warm a mass of water J/ from a temperature t to a temperature /,, we obtain the relation ir JMit, - 0, (2) where ./"is the mechanical e(|uivalent of heat, that is, the work done in raising one gram of water through 1" C. Hence JM{t, -t)= C'Rt", tidi LAUOliATOUr PJITSICS. or denoting M (<, — t) by II, (2) Since or jii = cut' JU = C'Rt", J = cut' H . (3) (4) From equation (4) ^ n be calculated if the observations for L\ R, t"y and //be nsadc. Ill tlie above ecjuations all the quantities are expressed in C.G.S. units. In making the observations, liowever, (/and R are usually measured in practical units. Since 1 ampere = ^„ C.Ci.S. units and 1 ohm = 10' C.(i.S. units, we have or JH = 10' C^RWt" ~l0V/ ' C^Rt^' • • (5) the measurements being made in practical units. The current can be measured by a copper voltameter (see Experiment 52) by means of equation C = -, where 6 is the copper deposited, e the electro-chemical equivalent, and t" the time. « 1 ELECTIUCITY. 205 7i can he measured by nieuiis of a B. A. bridge. The heat can be measured by means of a water calorimeter, the coil of wire being inunersed in it while the current tlows. Practical Directions. — To Vei'!/'/ the Iaho. — A convenient method is to use two calorimeters and two voltameters con- nected iu series (see Fig. 43). M^ and J/.iV, are two cop; i . Fid 43. voltameters ; P^and P,Q, are two calorimeters with coils 6'and L\ of different resistances ; /• is a resistance shunting one calo- rimeter and one voltameter in order to obtain a different heat- ing current in each case. If the experiment be performed in this way, two observers are necessary, in which case it will be well for one to take charge of tlie shunted and the other of the unshunted part of the apparatus. Each observer can make his own observations, cheeking when possible the observations of the other. The work recpiired of such observer will then be as fol- lows : Clean, dry, and weigh the plate of t..e voltameter on wliich the copper deposit is to be made (see Experiment 53). Denote the weight by /*. Weigh carefully the cop|)er vessel of the calorimeter, denoting the weight \y W. '2()i\ LAiwji. I run y rii rsics. I*;irtiully rill the vessri w itli watiT and wciglj again, denot- ing tlie weight liy )!', ; then J/ ir, - w where J/ is the mass L>" or -24°. In order to get the same rise of temperature the coil of the shunted calorimeter should have a greater resistance than the coil of unshunted one, and the resistance of the shunt adjusted to give a suitable current. The sliunt can l)e found by calculation if the re- sistance (»f the calorimeter and voltameter lu." known apj)roxi- mately, or better still by making a few trials and adjusting its resistance until a rise of one degree is obtained in each in approximately the same tiwe. As a source of current, the lighting circuit, if direct cur- rent, can be utcd. A couple of storage cells also make a suitable current supply. Be" .re turning on the current, stir tlie water in the calo- rimeter and read the temperature t. This must be done simul- taneously l)y the two observers. Turn on the current, recording accurately the time, and watch the rise of temperature in the calorimeter, stirring every few minutes. .1^ \ KLKVTIilCITY. 207 Tlie required rise of teini)erature will usUiiil}- he ohcuiiied in from ten U) twenty minutes. Observe carefully the time of turning otf the current. Stir (juickly reading the temperature when it reaches its highe^^t point. This will not he for some time alter the crrent is turned off, due to tlic heat in the wire. Denote the temperature by t,. "Wash, dry, and weigh carefully the i)late iii the voltameter on which the copper was deposited. Denoting the weight by 1\ and the difference by rf, 6 = I\- 1\ Measure the resistance of the coil by a IJ. A. bridge. c- * -• ('■'P- { ^' V/.. 7/= (/, - t)(,M -\- .(•{♦;-) ir). Denoting the ratio of the //obtained from the shunted calorimeter to that obtained from the nnshunted by /■, and the ratio of the G R obtained from the sliunted voltameter to that obtained from the nnshunted I)y /,, then, the law Ijeing true, /' = /',. (2) By means of the observations oi one calorimeter and voltameter, calculate e/ 10'" Preci^ations — (1) If the lighting circuit be used, be sure and have a lamp in series v 'th the apparatus. The switch in the lamp will then serve for turning on and off the current. (•J) l>e sure the negative pole of the current snj>p]y is con- nected to the j)late of the voltameter on which the deposit is to be made. Ill Fig. 43, ^'anii /f, are the negative plates. 208 LA liOH. I TOIi Y ril YSICS. u t. f (.?) If tlie coil l>e woinul on ii fruiiic tliu water equivalent of the part immersed should also be obtiuned, and tor great accuraev that of the thermometer bull) as well, lu the ex- periment recorded below these connections are put in under the heading J/ -f -^"^^ ^^^- VOI/r AM KTEIl OBSERVATIONS • M 4H-,' ,V,).'.'3,5 .Vl.fi6.5 i t" 688 688 C .K)S .y,t» 4:! rr> 1 r i.irrs Sliiiiiteil voltaiiii'lt^r L'lishiiiileil TolliimcliT... .183 .•J08 CALOUIMETEU OBSERVATIO>fc . W 90.4fi 8-.'.96 »•, M+.in).'>ir t 8.50 8.38 :J6.:5 ac.13 // 4.'i70 3551 r, l.'.fS Sliiintfd calorlmetfr Unshuiitfd caloririieier.. :«J».T.5 :.Tl.t;5 aoo.05 10' = 4.-J5. Blank's to he filed in hy atmlent. VOLTAMETER OBSERVATIONS. Pt Sliiiiiled voltameter L'lishiinted voltameter.. t" c K r CALORI>f '.TER OBSERVATION'S. \r j ir, .w^.ooriW jSlnin'e ' (•ali>rinieter. . . . ' lUnshuiiteii I'.'ilorimettT.. ] t n J 10' 1 1'. t :f * it I ELiaCTlUVlTY. 2U9 64. COMPARISON OF RESISTANCES BY CAREY FOS- TER'S METHOD. References. — As in Experiment 57; S. Tiiomp.-un, p. 420. Apparatus Required. — A B. A. Inidge; u low-re.si.stiincc giilvuiKJiiieter ; the two resintaiices to be coiiipjinMl ; two un- known l»iit nearly etjual re. obtained on the bridfro-wire ; a and h the distances of C from the ends of the bridge-wire; I the lenjrth and (T the resistance per centimetre of the wire. Let )' and /•, be the resistances of the intervening copper straps. Then we have A _■''+'■-!- <^fi mi, lii I- 1 i ■ i r S' I- E' = 1:1 210 LADORA TOR Y PII YSICS On interchanging x and y as in Fig. 44 (?>), we have on obtaining a balance again, where the new position C, is dis- tant a, and 6, from the ends of the bridge. Hence, equating (1) and (2), y + r, 4- 0-* — ^ -f- /•, + 0-6, • By adding unity to eacli side of (3) we have a- 4- /• 4- o-« + y -f r, 4- ffh _ y + »• + <^". + "'4 -^. + q'^ (2) .'/ + ''. + (^^ i^ + '■. -h <^*. (3) , (4) or a' 4- >' + y + /■■ + Q-(tt 4- ^ ) _ y + ^' + -^' 4- ^'i + q-(tf.+ ^O ^ /gx y + i\ + o-i ic 4" ''i 4" o"^! Hence, snice {a + h) - (a. 4- J,), the numerators of these fractions are equal, and therefore or y 4- r, 4- ' led. Then, denoting tlie resistance of AB by I, of A,ii, by I,, of the small coil (called the "yflfJ/ye") by G, of the copper strap (called the ^^ connector'''') by C, 'V-\\ ELECTRICITY. 215 and the resistances of the connecting wires by e, e,,f,f,, as shown in Fig. 45, we have, froni the theory of the B. A. bridge, the following relation : (1) r, being the resistance i.f the length AJ\ of the wire A,B,. It C and G be now interchanjred and /* moved along the AD until a new balance-point is obtained, we obtain the wire eciuation r: . (2) where ris the resistance of the portion of the wire between A and the new position of P. E(iuating (1) and (2), adding unity to each side and in- verting, we obtain Hence (?4./=C-f/ + ^-^, or G- C=l-r; (3) that is, the resistance of the length I - r through which the slider was moved to obtain a balance is equal to the difference in resistance between the connector and gauge. If now P be left at rest and P, moved until a balance is again obtained, it will be found that the length of wire over '^ WfFWWm^i^- r^:l! 21G lAUOUATOHY rilYSICS. wliich P. is moved is ecjual to the difference between the c(jn- neotor uiul jjau-e. Hence both wires are calibrated simnl- taneuuslv, since lengths on both wires of e,,nal resistance Iiavni- a value equal to the dillerence between the gauge an.'l connector, arc obtained. • The i-esistance of the gauge niaj be measured as in the last experiment, using the connector as the negligible resistance. The value cf a for each length is obtained by dividin.^ the value of G - C by the length. * Practical Directions.-^Like connections as in Fi.^ 45 puttmg a reversing-switch in the batterv circuit. The connector, C, at.d gauge, G, should be connected in by means of niercury cuj.s, the contact-].oints being well amalgamated. With the connector and gauge as figured, set 7' close to B and balance by moving P,. Reverse the battery current and balance again. The mean reading gives the length corresponding to the resistance I, - r., the first calibrated length on A, L\ if F be at the extreme end of AB. Interchange C and G, and, keej)ing I\ fixed, move P until a balance is obtained. Reverse the batteiy current as before and balance ajrain. The mean reading gives the lengtli corresponding to Z - r, the first calibrated length on AB. _ Again interchange C and G, and move >, until a balance IS obtamed, repeating the adjustments and observation along the wire alternately until the end of one of them is reached. Determine G - C by one of the methods indicated in tlie last experiment and calculate the value of a for each of the lengths I — r. iMpm •".•«.V'Vj^"1[' .-^V.A K ftJ..J i*S_ :jwm '^mm^m-f^m •■'••■ Vyi- •'•■ ^r- - ELECTRICITY. 217 Example. — Enter results thus ; 0- (7 =.053. ReaUinK Bri. 319; Hastings atul Beach, p. 425. Apparatus Required — A Wlieatstone l>ridge, preferably one of the dial pattern ; a sensitive low-resistance galvanom- eter; a couple of cells; a hypsometer; a vessel containing ice or snow saturated with water; some mica; a metre of line- drawn wire (platinum .000 in. is suitable); a reversing-key ; a contact- key for making a permanent contact. Theory of Experiment.— For small changes of tempera- ture the increase of resistance of pure metals is found to be nearly proportional to the incTease of temperature. If Ji^ be the resistance of a coil of wire at temperature ('., and Ii its resistance at temperature t, then R, = ^.(1 + at), . . . where a is the temperature coefficient of the wire. Hence liJ (1) (2) If t be 100*, the boiling-point of water, (2) becomes a = _ ^.00 - A loo . 7?. ... (3) If B,^ and Ji^ he measured, a can be calculated. Practical Directions — 'J'ake about a metre of .000 in. platinum wire and anneal it by passing it slowly through a I i. i_i ..J&*ir7^J m!k^mi^iw^i^A^..jm r.n:. : yr w? ELECTRICITT. 219 buiisen flame. If wire other tlian platinum be used, the method of treatment will depend on tlie material. Sokhr to each end of the plafinum wire a piece e eliminated by using a ro- versing-key. llepeat the observations several times. Example. — Enter results thus: Ice .. Steam . . Ice ... Steam . Ice Steam . . V R s « t I a 10000 4226. 5665. 4.22f) 5.665 75. :« 99.75 .00341 4227. 4.227 It a.ici the nnk.mun resistance A he connected in series witli a hattery Ji, Fig. 43. Then bv Ohnrs law, the potential hetvveen the j>oints .Vand J/ is to tliat between A and B in the ratio of the resistance It to A', or V. R (1) poll r/"V^'"rr'' ^"*"'^^*' -'-^^^^"^^ ^^^--» the pumts J/and y and the points A and Zf respectively. 1^ now JAV and AB be connected snccessively to ter- "Hl. of a .aIvanon.eter, the deflections of the galvanometer III also be proportional to the potential differences between tile points. Hence, if 6 and rf. be the deflections, 6' or X=^J,. (2) 4 irifWitiiinifiiiamiw KLKCTIW'ITY. 223 It is Ufiually necessary, however, to have iin adjustable reeistajiee in the galvanometer eircnit which can l»e adjusted so as to give aii|)ro.\imatelj equal deHections. If S be the resistance in series with the galvanometer when its tenninals are connected to M and -V, and *V, when tiiey are connected to -^1 and B ; then and H ence 6. V or K __ ^,('S -f G) V or, substituting from (1) and solving for A',, -^. - ,s + G^ 6 • (3) If G be not known, it can be found by the method de- scribed in Kxperiment 61. Practical Directions.— Connect in series a storage-batter v, the standard resistance, the unknown resistance, and an adjust- able resistanci', /• (a metre or so of bare German-silver wire Xo. 20 is usually suitable). Ucniove from one of the Pohl C(»mmutators, P. the thick wires (jii the base connecting the mercury-cups. Connect (see Fig. 4 *<) tie terminals of the two resistances. It and A', to tlie two pair- "f terminals frotn which the con- nections have bee'i removed, and the remaininji nair of ter- 224 i.AiwRA Tojir pursics. n.inals, in which the rocker t tLTininals of the second coninnitat, r. iiy '-ocking the tirst switch A /i an.l J/.V ,-an l.e succes- sively conne,-te,l to the ga!van..n.eter, and hv ro,.kin.. fh. second the current can l,e reverse■.■«:-: n-^ir;.*.p.:3Mr=ii:3.1 'iS}%2l^j^^WW^^ : KLhVTh'icrrr. 68. TO MEASURE A VERY LARGE RESISTANCE. References. —As in K\|HriiiK'iif .'iti. Apparatus Required. —A sensitive liiifh-rcsistaiice ;;iilvan- oineter: u miniher of cells; a int'j.'<.lim ; a r.'sistancc-l.ox lor slmiiting the galvanometer; a reversing-switch ; resistances t.. I»e ineasnred. Theory of Experiment — As stated in the last experiment tiie t»niinary bridge methods are not suitable for the measure- ment of very large resistances. The method liere described is a very simple and direct one. similar to that of ICxperiment 50, oidy large resistances and a sensitive galvanometer are used. Let a galvanometer (r\ a large unknown resistance A', and a battery /i be connected in -eries with the galvanometer. Let the K.M.V. of the battery used be /'/, the detlection ob- tained d, and the current through the galvanometer C. Tl leii C K X + li + (^ -, - h'd. (1) Now let the resistance X be replaced by a known resi.-t- ance //, giving a detlection (J,; then Hence E ^' " ^ + //+ v; = ^'''^■• n j^ n + (; _^ (-') or, neglecting B, .r + a ~ 6, (■') If, however, X he a very large resi>tjiuce, say a number of r 7^ >ri^::'^ mA ri y,.;->:^."r^^ i« fi i 226 I.AmtRMORY viiYsns. megolmiK, uihI R «me mep^lim, it wll l^e iic<-csHary to sliunt the jralvHiioiuettM- when li if» in the ( iroiiit. If .Vbe the resihtaiice of the «himt, (2) hecomeH ^'1 - ^x '" ^' 4- /> or (/if 4- /^X^' + '*^') + ^''"^ Coinl.iiiiiii,' (I) and (4), we obtain (/;_+ .s')(/.? + It) + ^'■'''^' . = A'tiil.lt' itm tfiTicr !«• used to >\\\\\\i tlic giilvaiiKiiu'tt'r, >' can he adjusteil until (V = rf, or /' = 1,1 a I id lience etjuation (•'») ltc«'<'iiies («) al^o a siiiiplo foniiiila for calculation. Practical Directions.— A vcn Miisitivc jjalvanoinetcr is nece»arv foi- this cxpcritnciit. (1) Mcasniv the resistance of a line drawn hy a h-ad- jiencii on a ^-trip of white iiapor. [•!) Meii>ure tlie in.-nlation of a coil of eotton-covered twin- wire. (3) Measure the insulation of a coil of ruhher-covered wire. In tlie tir.-t case the -trip of paper can he «'onnected into tlie circuit h_v means of terminals screwed into a piece of hoard, the pai>er heinir stretched on the surface of the hoard. Con- !iect in a snfMcirnt nnndx-r of hntterics to ohtain a detlection of al)out 'JOO scale-divisions. The reversini;- switch should he in the circuit so that the current <-an he reversed and the mean readin•){) 69. COMPARISON OF ELECTROMOTIVE FORCES OF BATTERIES, BY TANGENT GALVANOMETER. Refereni'^s. — Authouy and Brackett, pp. 317, 334-340, and 309; Knott, pt. 11. pp. 159-166 and 185; Barker, p[). 561, 699, and 758, 759; Nichols and Franklin, vol. 11. pp. 54 and 79-85; Hastings and Beach, pp. 390-395; S. Thompson, pp. 154 and 163-174; Carhart, pt. 11. pp. 233— 253 and 273; Ames, pp. 233, 306, and 310-316; Watson, pp. 674, 688, and 815-823. Apparatus Required. — A sine or tangent galvanometer ; a resistance- box; a contact-key; batteries to be compared. Theory of Experiment. — If a current from a battery flow through a resistance Ji, a galvaiionjoter of resistance 6r, then, if a tangent galvanometer l>e used, ,= A tan ^, (' = B+ (r -{- jr li being the resistance and A' the E.M.F. of the battery, and B the deflection of tlie iriilviiiiometer. Hence E = A\B + G + 12) tan 0. 0) If now another battery be used, E.^l.F. E^ , resistance B„ and an external resistance /i*, , producing a deflection B, , then E, = K{B, + '' Practical Directions. — Connect a Daniell cell in si rit'> \> a resistance box, the galvanometer and a reversing-key. Unplug from the box a hirge resistance. Close the circuit by means of the contact-key. Adjust the resistance E till a suitable detlection is obtained say about 60°. Read the deflection , d. Reverse the current and read the defiection again, d,. e = <5 +'?. Auain adjust the resistance until tlie defiection obtained be about ;5<»°, denoting the new resistance by Ii,. Reverse the current and read as before, rf, , ,' assuming that a tangent galvanometer is used. From this eijuation calculate the resistance li -\- ('. Afake similar observations with another battery, and calcu- h.te the resistance of 7j, + f constant E. M.K. ; l»atteries for comparison. Theory of Experiment. — Sui)pose 7:' a battery of constant E.M.F. , the poles of which are Connected to a wire AB of re- Q sistance Ji, A being tlie negative pole. Let the resistance of the bat- tery uTid connection be denoted by /■; then (' = /.' + /' If the negative p<»le of any other battery of E.M.F. /T, be connected to A and tlirongli a galvanometer to a point F on AB snch tliat no current How through the galvanometer, then the E.M.F. of/.', must be equal to the difference of |)otential between A and P produced by the battery E. Hence C = Ji, if 7i, be the resistance of AP Hence Ii\ E (1) R-\-r li r be negligible as compared with R^ or of known value, the ratio /f to E, onn tlnis be determined. ^[%!^^''sSxs^KS?^y^l^!^er^^saxm■ifi£^ptn^^s.w^.. • .'iVTj?',' ■.' o*^ cai BLECTimiTY, M anotlier battery, 7^',, be similiirly connected, and a point /', be found such that no current passes tlirougli the galva- nometer, then Hence F K li^r -/?. /••; (2) a comparison of E^ and A, independent of r. Practical Directions. — Connect to the ends of a potenti- ometer-wire tlie poles of a storage l)attery E^ Fig. 49, witli negative pole at A. Connect the negative pole of a battery, /.',, M'ith which the others are to be compared, to yl, and through a three-way plug-key to a galvanometer which is co.inected to the sliding- contact on the potentiometer. Connect to A and the galvanometer another battery, E^ , through the third connection of the three-way kev. Adjust the sliding-contact so that when E^^ is connected throuirh the galvanometer no deflection is obtained. Read the distance AP on the scale attached to the potentiometer. Connect /;', with the galvanometer, and adjust again for • d:-tlection. Read the length AP^ as before. Denote these lengths by /, and /,. Now, since the wire of the potentiometer is uniform. Hence E = fy.E. ?rmLi^xiJ^s i^'^fiets&'^'-^v^'f'naiS':. . -: flT- t i •234 LABURATUllY PllYSlCi^. Xow replace E^ by another battery ii',, aiul compare as before. K = ^ X /;.. For each comparison the length l^ should be verified. Compare witli a Daniell cell {E,) as standard the cells given, A Clark cell is preferable to a Daniell if the api)ara- tus be suitable. In this case care must be taken not to short-circuit the Clark cell. Example. — Enter results thus : Batttry Clark cell... Daniell Leclancbe . , Bunsen .... Bicliroinat<>. Grove Dry battery. 1 //388.0 E 388.0 1.434 293.2 .75a 1.08 878.8 .976 1.40 513.5 1.323 1.90 554.7 1.430 2.05 514.1 1.325 1.90 351.8 .906 1.30 Blank to he filletl in hy student . Battery. I I'h E L«n kftri' ^A'^B^JTi'iaei 'AjAT-t- - KLELiiucrrr. fio 71. TO CALIBRATE AN AMMETER, BY MEANS OF A GAS- VOLTAMETER. References. — S. Thoin]>soTi, p. 209; Nichols and Franklin. vol. II. p. 89; Ilastin-fs and IJeach, p. 421. Apparatus Required. — A gas- voltameter; a couple of storage-cells or other isuitiil>le source of E.M.F. ; a rheostat; a reversing-key ; a stop-watch; the galvanometer or aiiiuieter which is to be calibrated. Theory of Experiment. — If the ammeter or galvanometer to be calibrated be connected in series with any standardizing instrument, the indications of the latter being proportional at any instant to the current passing through it, the indications of the first instrument may be reduced to their value in cur- rent, or, in other words, the instrument nuiy be calibrated. The present experiment is one of relati' ■■ cnlibration only. For this purpose a convenient standardizing instrument is a form of gas-voltameter devised by Prof. Ayrton. In this voltameter the electrolytic chamber is sealed up, and the rate at which the mixed gases, hydrogen and oxygen, are given off is observed by the rate of rise of the electrolyte in a tube whose lower end reaches to the bottom of the electrolytic chamber. The tube is graduated above the voltameter, and the time required for the liquid to rise through a given number of divisions is inversely proportional to the current passing through the voltameter. Therefore, h^^' any given current through the voltameter and ammeter in series, the reciprocal of the time taken to rise througli one e t" t Sbow cuiTC. l-§ 288 LABOtLA Ton Y PU YSICS. 72. TO DETERMINE THE CONSTANT OF A SIEMENS ELECTRO-DYNAMOMETER. References. — S. ThoiniK-ion, j). ;5'.»2 ; Hastings and Heacli, p. 4'j;{-, Mit'liols uiid Franklin, vol. 11. p. "ill ; Anthony aiid l>ni('k»'tt, |». .■>.■|^; Haikor, y. "*.♦.■». Apparatus Required. — An olectro-dynainonieter; a copper voltuim't«'r; a .stonige Imttery of two colls ; a reversing-switcli ; !i >top watch : a rheostat. Theory of Experiment. — If a current (1 is sent in neries tliion. through the reversing-switch and rheostat, to the hattery. and I»alance the current. On reversing the current the needle should return to zero. If not, turn the wliole instrument until it tloes. Coimect the dynajuometer, hattery, rheostat, ami voltam- eter in series, and adjust the current to 200 degrees a[»prox. Open the circuit. Clean, wa^h, and weigli the copper ])late of the voltam- eter on which the copper deposit is to be made, and replace it m the voltameter. Close tlie circuit, taking the exact time. Allow the current to run for at least 20 minutes, keeping the dynamometer continually halanced I>y adjusting the con- tact piece of the rheostat. Headings should he taken every two minutes to allow for small changes of the current. vV mean of the readings gives the true value of 0, Open the circuit, taking the e.xaot time. 540 LA liORA Ton Y PHYSICS. Wftsli, dry, and weijrli tlio ciitli. L'o'.t; Hiistiiijrs and Ik-acli, j). i!41 ; McIdIs aiKJ FraulJiii, \(>I. 11. j). ,si>. Apparatus Required. — A Siemt'n,s (Iviumionu'tc r; uii iim- iiictir ul' u|>|>r().\iiiiiiteiy tlio Biiiiie rim ire : a rliioatut of suitable ri'sistiiiiee; a storage battery of several eells. Theory of Experiment — Knowing the eonstant of tiie (lynanu)nieter it ean be used very conveniently as a standard- izing instrument. If the instrument to be calilirated is of approximately the baine range as the dynamometer, it mav simply l»e conneeted in series with it, and the two in^t^ument8 read simultaneously at suitable intervals throughout the raiK'c The sijuaro root of the reading of the dynamometer, multi- ]»lied by its constant, give the correct value of the current for the corresponding indication of the ammeter, which may be either a direct-current or alternating-current instrument. Practical Directions Vdjust the dynamometer as in the last experiment. Set up the ammeter and level it until the needle swini's freely ami comes to rest at zei'o. Connect the coils of the dynamometer in series with the anuneter through the rheostat an4: Carhart, pt. ii. p. 270; Knott, j)t. n. p. l!»0; Nieliolsand Franklin, vol. ii. p, 5(i; Watson, p. 6!»4; S. Thompson, j>. 401); Hastings and Beach, j). 420; An- thony and Braekett, p. 301. Apparatus Required — A D'Arsonval galvanometer, with lamp and scale; a resistance- box of 100,000 ohms; a resist- ance-box of 2000 ohms ; a storage battery or other suitable source of current ; a thermometer; a reversing-switch. Theory of Experiment — In the D'Arsonval galvanometer the detlection of the galvanometer depends on the strength of the magnetic field in which the coil hangs, the number of windings in the coil, and the current. Since, for small deflections, the njagnetic field in which the coil swings may be considered uniform, the current may be taken as proportional to the deflection, or 6'=A'rf., where C is the current in the coil, and '?, the scale n. Suppose a galvanometer (i, a laryc lesisiiuice /.', , a iiat- tery of E.]\I.F. A' to be connected in series, and tlie galvanometer shunted by a resistance .V : then the total -^B { — -JG IS, current in the circuit is given by the eS', and ^,, and the de- flection to to .mIjOoo uhuis. ■* I «■ I 246 LAUOIiATOIiY PHTSICS. Shunt the galvanometer w itli a shunt S^. The uouuectiuus are shown in Fiiriire 51. Adjust the shunt so as to obtain a detlection of about 300 Fig. 51. readings gives rf,. X -=: scale divisions. Reverse the current and read again. The mean of the Now, change the resistance in the box /?, to --' and adjust the shunt S, until a deflection as nearly eijual to d, as possible is obtained. Reverse the current and read again. The mean reading gives rf,. a = tf. - ', and g must be determined beforehand, if not ulreadv kiiuwii. '%- .xiif -i^.^E^^'^^ssf^;^ •<*ity» -jMTHeC'if^ =i-JIW5i'^r^*^MS3HM BLBCTRWITT. 249 Practical Directions.— Set up the galvanometer as de- scribed in last experiment, and make connec- tions as shown in J'ig. 53, r being the standard •" Y/) one-ohm coil, and B a storage- battery. O is ^ \ the instrument used for measuring the main ^ current. y\/\/\/\/\A/v If a tangent galvanometer be employed for this purpose, instructions for its use will be found in the experiment on "Absolute Meaa- ^ urement of a Current by Tangent Galvan- ometer." If a copper voltameter be used, proceed as in previous exi>eriment with copper voltameter. A deflecting instrument for meas- uring the current is, however, more convenient for this experiment. In either case the method of procedure is as follows : Adjust the galvanometer current by the resistance-box H till a conveniently large deflection, of about 300 scale-divisions, is obtained. Three galvanometer readings should be taken, the current being reversed each time. Should a deflecting instrument be used in measuring C, it must be read simultaneously with the D' Arson val galvan- ometer. The whole set of readings should be taken twice. If a copper voltameter is being used, the current should be left running for twenty minutes, and readings of the galvanometer on reversal taken every two minutes, to allow for continual small changes in the current. Also the reversing-switch must be placed in the galvan- ometer circuit, and, unless an instantaneous reversing-switch be used, time must be allowed in the calculation of C for the reversals. ^KT.. \^'3v ;- w^' 2g»H«rx5aaEiSKB?'iJi»«aHWE®?; ..ii'= .;ti':».--*-^GS*.Vif f 1^ 250 LABORATORT PHYSICS. In either case, a mean of all the galvanometer readings should be taken for rf, and a mean of the main current read- ings for C. The temperature of the shunt r, galvanometer g, and resistance li should be noted at the time of observation, and corrections made for them in the calculations if necessary. The scale distance should be carefully measured and ru corded. Example — Enter results thus : DAR80NVAL GALVANOMETER, NALDER No. 8688. Data given by w*aA«r*.— Resistauce of galvanometer is 261.95 ohms at 24°.7 C. Reslstuuce r, one ohm box No. »««0, platinum-silver, correct at 18. Reslstuuce R, platinum-silver box No. 8750, correct at 17'.0 C. R (of R (of r t tot D'Arg. 0. Tangent OalTanoinet«r. n= 10. t Radius. 11,000 11,000 19.00 19.» 18.4 18.4 340.6 L 333.0 R 338.6 L 837 5 L 328.0 R 383.8 L 17- 47.8 47.4 47.8 46.7 46.8 46.7 18.2 Mean results, Ist set 836.3 47.88 Mean results. 2d set 881.8 48 73 1 1 „ 10^ (Radius) X tan Ist set, 2d set. = .466, ^^ ^71 _ _£ (11,000 + •>6.') 336.3 ~ 8041000 "^"P" = 1 volt through 8.041/2, Ist Mt. 466^ 1 (11,000 + 86-.i) bSlTS msium """p* = 1 volt through 8.028A. /^-.y-s'i! 'ly = .•■s»\^'wyt' cen£*4, S beujg connected in series with a galvanometer and a large re^igtance R^. Sup])06e S so small as compared with /?, that any small variation of S will not materially alter the current, so long aa 7?+ *5 Then the difference of potential on the gal- vanometer terminals will be proportional to the resistance 8. The deflections of the galvanometer will therefore also be proportional to S, jwsuming that the deflection is proportional to the current. If the deflections for ditTereiit values of S be observed, their ditferences from propctrtionality can be calculated and a correction curve plottetl. Practical Directions. — C'onnect the galvanometer, battery, and resistances as in Fig. .5.'), putting the reversing-switch in the galviin(»meter circuit only. If the source of current used be not as constant as re- (juired, it can be kept con.xtant by i)laciiig in the battery circuit a rheostat and tangent galvanometer, and adjusting continuously the rheostat so as to keep the deflection of the tangent galvanometer constant. A better method still would be to connect the terminals of the battery to a high-resistance potentiometer and balance it continuously against a Clark cell. This can be done by having the resistance in the Clark-cell circuit constant and adjusting the rheostat. The connections in this case would be as in Fig. 55, BLKCTHICITY. 253 If 7?, 1)0 10,000 fdiiiiH and the rehihtuiicu *S' varies from 1 to 10 oliiiiH, Ji -{■ .V Ijeing kept coustiiiit, the iimiri eircuit re- Hwtiinco will vary loss than .01 ohm '. Unplug from the btjx /.' a resistance until a suitable de- flection of say 3.'»o scale divisions is obtained. If the constant A' luis already been found, as in previous experiment, then the resistance I! may be adjusted until the same d<'f'"ction i> obtained as that for which A' was ca' culated. and tin- dilb-rences from proj>ortionality ciilenl.itfl with rej'ai d to it. Having iibtaiiuMi ,i suitable dcHirtion, reverse the current and mean the ii idings, to elinnnate errors due t<> torsiiru. Xow pliii;- in one ohm in >' and tinplug one in I', and at the rheostat mn Utv a balance against the (lark cell, Kead again and reverse. Contimie the process right down the seale. Calculate what the detiection should i»e in each case, and ^1 ri :i;.4 LA hoiu rony riirnirs. |»K»t a curve with »cale-rt'iulin;;« a^ ahHciHriOii atwi dilTei-cnccH iiri untinuteo. Tliu caKMilatotl (letlectioiis will l>o ol»tuiiie<| in iwli oawi hv taking iiiii,..tt'iitli«, iMght-teritliH, Hjveii-teiiths, etc., of the H"»*t ili'tii'ctidii. Example. — Knter rebult« thim: D'Arnoiival (ialvaiioiiiHcr, No. ;{<]'>8. I 'i 4 Mraii 10 DfHrctiori. 848.25 «... 818.2 8 278.8 7 848.0 6 808.2 5 178.3 4 188.6 a 104.1 2 1. 1. 2. 8. 4. T) 6. 8. 9. 10. 69.5 84.9 85 69.5 104.1 188.5 173.7 206.8 240.8 275.1 808.5 343.7 I'ali-iilattMt UrfltHJtion. 845.5 811.0 276.4 241.9 •.'06.8 17l.\8 138. •■ 108.6 69.1 34.5 84.5 69.1 108.6 188.2 172.8 207.8 241.9 276.4 811 845.5 DiffcriMic*^ 1 8 1.4 .9 A .3 .5 .4 4 .5 .4 .5 .3 - .1 - .5 1.1 1.3 2.5 2.8 Ki.Kt'Tiw irr. blank fo be tilled in hy student. 25.'> I 'ot curve RH directed. 77. TO MEASURE POTENTIAL DIFFERENCES BY A D»AR SONVAL GALVANOMETER. References. As in P^x|M'riiiii'iirs 74 ami T.";. Apparatus Required. — A iiMlvaiiDmctrr: a KMt.OiiO-olmi resi...tHiice-'K>\; two lo.OU(t-Mliiii Im.v..s; a revorsiii«r,kev • a iimnlRT of Itatt'i-ies. Theory of Experiment. -T^e scale of a D" Arsutival ^mha- noiretor havi?\g been oalibrited, the values AG a:ul K detei- iniiied, it may be used for the measurement of potentiie determined. I. The measurements may be made hy connecting a large resistance in series with the galvanon)eter and the source of current, in which case 1:= K6{P-\- G), (1) I -^ i-^ the terms having tlie same meaning as previous experi- ments, where A*, /i*, G are all known quantities and 6 is observed. If the volts on the lighting circuit be determined by this method, li would reiiuir-^ to be a resistance of several megohms. In the case of batteries Ji will be so large that the battery resistance can be neglected. II. Let the source of current, B, be connected to a large resistance, Ji, and the galvanometer terminal to two potential jx)ints, A, C, of tliis resistance, with a resistance r between them (Fig. 56). Fui. 50. Then the current through the galvamuneter is given by the e(|uatio'i A' C :^ /?-/• + r ^f or ELJUvnuciTr. 257 (ii) . t Ii{r-\-0) In practice r is very small in cumparigon with — — ^ — and may therefore be neglected. (3) III, A variation of this metliod would be to put a resist- ance a, in series witb tlie galvanometer. This would neces- sitate making A* smaller and r larger. In this case we would liave the equation E .. r C = 7? - /• + KA'.+ G) ^ li,^ U-^rr = Kii for the cun-ent through the galvanometer. Solving for E, we obtain or, neglecting r as compared with , ,i-=«_«^±''il'->A-d.. . (4) (5) Equation (5) may be used in calculating the volts on the lighting circuit, equation (4) in the case oi bfittcrics. Practical Directions.— 1 . If surticicutiy lar^'o resistances are available to make it possiltje t<> olitain readings directly, connect in series the source of E.M.F., the galvanometer, and the rcsiBtances. 'J.>^ LABOBATORT PHTStCP. If: Ii. case of batteries 40,000 to 50,000 ohm« will l)e neces- sary; in case of the lighting circuit a resistance from 2 to 8 megohms will be required. The reversing-key should be in the galvanometer circuit. Do not close the key until you are absolutely certain that the connections are correct and tlie resistances are all unplugged, otherwise damage may be done the resistance- boxes or the galvanometer. Read the deflection. Reverse the current and read again. Correct the readings from the calibration curve in each case, and take the mean for 6. Measure the E.M.F. of each of the batteries given. If the lighting circuit l)e direct-current, measure its voltage. If. Connect the source of E.M.F. to 100,000 ohms resist- ance, through a key, which must be left open. Unplug the 100,000 ohms from the box if the lighting circuit is to be determined. Coimect the galvanometer terminals to the potential-points hy means of a travelling plug on the box. If the box does not contain a travelling plug, it will be neces.siiry to i)ut in a small resistance- box in series with the K (0,000 ohms and use it for adjusting r. In this case Ii will l.t cjual to 100,000 4 ;•. Adjust /• until a suitable deflection is obtained. For a storage-battery Ii will be about 5000 ohms and r iiiM»ut *J0 olinis. Repeat the observations as in I. in. Xow put 10,000 ohms. 7?,, in series with (?, and reduce /*' to 10,000 and adjust as l)cfnre. Make a diagrani of the connections, and be sure you under- stan0()U(> j .. I KMKMi; iniMlO l-eclanclu' buttery \ 40«MM» lOOUU liHK)0 ;uo.5 98.5 10 295.5 97.9 no 365.4 98.2 354 7 2.22 20 262.0 2.25 2500 369 2.23 25».4 1.30 30 21«0 1.29 2500 215.2 130 Jiliiiik to hi vUnJ in h>j fitudcnt. Met ho. I 1. 11. III. I. H. 111. I. 11. 111. Siiiiii'f of K.M I". li ^^ r Corm-tcl .V K.M.K. fl1 m 260 LABORATORT PUYSICS. 78. TO CALIBRATE A MILLI-VOLT METER. References. — S. Tliompson-, p. 208; Barker, p. 720; Hastings and Beach, p. 423. Apparatus Required. — A inilli-volt meter, two single-cell storage- batteries; two resistance- boxes, one M'ith an olini divided to tenths; a potentiometer; a sensitive galvanometer. Theory of Experiment. — The calibration of instnnnents for measuring currents or potential dilTerences can be etTected by means of tlie calibrated D'Arsonval galvanometer used in the previous experunents by shunting the galvanometer. The following method, however, is simpler and the results are more easily calculated. r H • a. Z:> Bv Fig. 57. Suppose P and P, the terminals of milli-volt meter, acro.'^s which a current is flowing from the battery /?,, to be con- nected through a galvanometer to a ])Otentiometer (Fig. .57), upon the terminals of which is » constant E.M.F. A' ; then if the sliding contact Q be adjusted until no detiection of the galvanometer is obtained, we have the relation or r V Resistance AQ Ilesistance ^1 />' Resistance .1 Q Resistauce AD (1) BtECTRlClTY. 261 where F is the potential difference between /* and P,, and E that of the constant hatteiy. If, therefore, the indications of the instrument correspond- ini' to different \iiUm» of I' \>e observed, and tiiese indica- tions be compared with »#► tjitW'ulatetl vahies, an absohite calil)ration cnrve for tht* ItmKvnuttfttt can be drawn. The object of tlie present *-x{.*erinient is to find a correc- tion curve for an instnnuent wliieii has already been cali- brated. Practical Directions.— In practice it is necessary to have a standard Clark or We-xton cfll m the .system us well us tlie constant battery through the [>uientioineter. For connec- tions see Yig. 58. Fio. 58. The total resistance AD coiisists of a stretched wire AB, with sliding contact at (^, and ii resistance-box BD, with the small resistances towani the end />. //, is a standard (!ell connectod tlirough the key A' to a li.xed point C l»y means of a travellinjr plug on the box. P and Z-*, are the terniinals of the niilli-volt meter, //, the battery producing its deflections. A' a resistunce in the circuit for varying the detiections, ivnd C, the coil of the instrument. A' and A', are kept continnou.Nly balanced again.st each other, so that the milli-volt meter is culibrated against the standard cell. Hence the resistance AC must be substituted for A /J in (1). to (■ i 2t?2 LABOUA Ton Y PHYSICS. The resistancea in the various parts of the svstom will dc- l)enil on the instrument to l»e c'alil)rute(i. It is convenient to adjust the resistance l>et\veen Ji and T so that a niilli-volt corresponds to a definite leni;tli of tlie wire .1 //. Vov exanjple, if the instrument to he nilihrated lu^ a Weston niiUi-volt meter with a ran<;e of 10 milli-volts, tlu' wire Ali may conveniently he a 1*. A. hrid^e wire ol approximately one ohm resistance, and /> 6' adjusted so that a milli-volt corresponds to ten centimetres of the hrid<;e wire. The value of the resistance to he unplnjijjed hetween It and C in this case is at once determined from the relation ■ ; - "-J I? ' -i .001 _ .1 X r where 1.434 is the E.M.F. of the standard cell, /• the resist- ance of the whole wire ABy assumed to he a metre in lentaiU'C of .1 />. Calculate the approximate value of ,/■. Tiipluj^ resistances l.etweeu (' and /^ until on closing.' A' ri<> deflecti'iii f»f tin iralvaiioiiu'ter is ohtaiiied. „ 1... ..,...: r» 1 n .: ij asm li ciiii; ....1 !! Ijii-Kh- MJevrHICJTY. 2(5:5 Adjust H until a dedection of one millivolt is obtained, denoting the deflection by tf. /*• can usually be adjusted to give exact niilli-volt read- ings. Adjust the sliding contact, Q, until no deflection of tin* galvanometer is obtained. Test the balance of A\ and Ji l>efore and after the obfetr- vation, adjusting always between C'and IJ. liecord the position of Q, and the reading on the iuotru- mcni. Kepeat the observations for a nuniluT uf points up the scale. If a Clark cell Ik; used, take its temperature and correct itB E.M.F. from the eiii equation ,, i 1.434 - .0(»i2(r - \r,):A(^ / ,■ Precautions.— Do not short-circuit the staiirlard fell. Before connecting R to the battery and niilli volt im rr. unplug at least 100 ohms. Connect the negative poles of the batte^it■^ tu the >an)e end of the p5 79. TO DETERMINE THE LOGARITHMIC DECREMENT OF A BALLISTIC GALVANOMETER. References.— Hastings and T^each, p. 420; Barker, p. 780 ; S. Thompson, p. 207. Apparatus Required.— A ballistic galvanometer ; a damp- ing-coil; a battery; a contact-key. Theory of Experiment The ballistic galvanometer is an instrument for measuring currents of very short duration. The needle is long and heavy, so that its time of vibration is very large, the time of the passage of the transient current being assumed so short that the needle remains at rest during its passage. In making measurements depending on such currents the swing of the needle and not the permanent deflection is observed, and iience it is necessary to consider how much the amplitude of the vibration of the needle is affected by the damping due to resistance of the air and other causes. In a ballistic gal- vanometer, the needle being heavy, the damping is usually very small. It may Ik* demonstrated mathematically or shown experi- mentaily that the effect of damping is to diminish the ampli- tudes of the successive vibrations in a fixed proportion. Thus if a = (n - 1) log, r, or log. a, - log, a^=:{n- 1)X, where ^ = log, r. Hence ^ = 7T~_n ^'^'K* **' - !<*&• «»)• • • • (2) The value A is culled the logarithDiic decrement. We will now show that the effect of dumping on the anipli- tnde of any swing u to diniitjish it by 7.. Suppose the galvanometer needle to he set swinging and the amplitude of the first swing to be /. This amplitude is shorter than the true amplitude, since the needle has been diuujwd through a half swing. Denoting by /, the true swing, that is, the nwing that would liave been observed had no damping been present, then, from (2), A = -(log, /. - log, l\ and hence ^\ = loge /, — log, l^ or lo- /. = iA I lug, L Kl.KiTlULTlY. 267 lleuce /=t'^ + '»«.' = e X e^J = e *'. I — M 1 _j_ - j, if the damping be small. Hence if the obstTvt'd first swing of a galvanometer be I, the true swing is given bv tlie eciuation /. -= /(l 4- I)- (3) Practical Directions.— Set the galvanometer so that the needle swings freely, and adjust the lamp and scale until the spot of light is in focus on the scale. ('onnect the damiting-coil and battery through the contact- kev, and place the coil close to the coil <»f the giilvanonutcr. I?v tapping the key the action of the current in the damping- coil will set the galviinometer-needlc swinging. A little prac- tice with this coil will enable the student to bring the swing- ing needle quickly to rest. Set the needle swinging through about 300 8cale-divi>ions, and observe the turning-point of the spot of light on the >eale, following it as it swings, and again reading its turning-point on the opposite side of the scale. Count from oO to oO complete \ il»ratioiis, takuig again the turning- [loint at the beginning and end ot tlie last swing. MICROCOPY RESOIUTION TBT CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I 1.25 1^1 Hi I US I u »«• « |Z8 IIA III §23 ■■■ 2.2 2.0 1.8 ^ /IPPLIED IN/MGE Inc 5^ 1653 Easl Moin Street r-S Pochejler. Ne« York 14609 USA j:a (716) 482 - 0300 - Phone ^B (716) 288 - 5989 - Fa« f'v»'Sf.'!6:a«-'.' . ELECTRICITT. 269 80. TO DETERMINE THE ABSOLUTE CAPACITY OF A CONDENSER BY A BALLISTIC GALVANOMETER. References.— S. Thompson, p. 425; Uarker, p. 662; Ames, pp. 294-303; Carhart, pt. 11. pp. 201-21(1; Anthony and Brackett, pp. 291-295; Nichols and Franklin, pp. 65- 67 ; Hastings and Beach, p. 339 ; Watson, p. 643 ; Knott, pt. u, p. 136. Apparatus Required. — A ballistic galvanometer ; a conden- ser the capacity of which is to be determined ; a resistance- bux for shunting the galvanometer; a large resistance; several batteries; one tapping contact-key; three contact-keys that can be permanently closed. Theory of Experiment. — The capacity of a condenser is the ratio of the charge recpiired to produce a certain difference of potential betv/een its plates to the potential. If C be the capacity, Q the charge, and V the difference of potential between the plates, V — y. Suppose the condenser to be charged with a potential V through a ballistic galvanometer, in which case all the charge may be considered as having passed through the coils before the needle began to move, Then if G he the galvanometer constant, 3f the magnetic moment of the magnet, the total impulse on the needle is MGQ. If Gj be the angular velocity with wliieh the needle begins 1 1 fp:»3Ki«mrr^^«r£ S.«?!yv»J>Jk»ft .♦ !■ 270 LABORATORY PHYSICS. to move and / be its inoiiient of inertia, then Ico, the moment of momentum, is equal to the impulse communicated by the charge. Hence /co = MGQ (1) Now suppose the original position of the needle to be ABf and CJJ the pot. ion at the end of a swing, a being Pio. 59. the angle through which the needle swings. Then the total displacement of the north pole is AP, and of the south polo BR, and the work done against the earth's magnetic field to produce this displacement is given by the equation W = mn{AP + PB\ where J^is the earth's horizontal component and m the strength of one pole. Ilo^ice W = 2Ifml{l — cos it) = //J/(l - cos«) a = 2/O/sin'-. . (2) But the work done is also equal to the kinetic energy of the needle. Hence a ^ 231/1 mi' ~ 2 (^) '^;*^ '^jms^.-M9.rwk f^^iiS^ff -wtc' r.^iu.'iifiiH':? ^^r.' ELECTRICITT. 271 Equating the values of a> found from (1) and (3) and soh ing for Q, we obtain a 2 sin TT Q = 2 j 7// G X ^ M (^) If T be the time of a complete oscillation of the needle, and tlierefore M fi.r 4t' (5) Substituting in (4), n Til . a ^ = 1^«^"2' H or, since ^ = 7f, the reduction factor of the galvanometer, Q = n (6) a Hence V — -^ — ^j. — \ nV (7) If now the same potential difference be connected to the galvanometer terminals through a resistance jR, the galva- 'B^r^EV * riffs^asviRi.^j^'v i I I! .' U ■ iS,' V. ' ;il i 272 LAUOliATOItY PHYSICS. nometer being shunted with a resistance S, the current through the galvanometer is given by the equation V s Y = Ii + GS G+ 8 VS X G + S -^ = K tan dj or and hence ^0 + S) + GS ,-„= Ktmd, ^ pl^T^ST+G-Sf i tan d' Substituting in (7), TS sin i « ;rKG!-h ^')iif + G^A^i tan ^ G = (8) (9) In the above we have supposed that no damping was present when the needle was displaced by the charge, and hence for sin ^a we must write and (9) becomes = (l + 2) sin ia, TS (1 + ^] sin i« n\{G + S'jIiT'(^ Ha^^' (; All the quantities on the right-hand side of (10) can be observed and hence C determined. In this and other experiments on condensers the observa- tions are taken when the coiiden.ser is charged through the gal- vanometer, tlins obtaininir the hitstantaneonH capaniy. The value obtained will usually differ from that obtained on dis- charge, the difference being due to absorptio i. Ill "-W i •^^vrzr^sssffMi' «''Bt)LV-'£t ■ia5iis»E-.':j?> ELSCTBIUITT. 273 Practical Directions. — A simple and convenient way of connecting the apparatus so as to enable the observer to take the two sets of observations in rapid succession is shown in Fig. 60. Fio. 60. AB is the condenser, B, the source of E.^f.F., K a tap- ping eontact-key, q, r, and p plug contact-keys, S the shunt, and li a large resistance. If the condenser be provided with a discharging-plug, as is usual, q will not be necessary. If y, r, and p be left open and K closed with a quick tap, the condenser will be charged through the galvanometer. Closing q discharges the condenser, closing p shunts the galvanometer, closing r brings in the large resistance I^, and the observations for the steady current can be made. A few preliminary trials will first be necessary to deter- mine the number of batteries to be used to give a suitable throw of the needle. B and S should also be adjusted in a preliminary trial to obtain a suitable deflection. All the connecting wires should be carefully insulated to prevent leakage. Brint' the needle to rest by means of the damping-coil. Close /rwith a sudden tap, freeing it as quickly as pos- sible and observe the throw of the needle. Kepeat the observations several times, taking the mean throw. fjS&jTr«c>->-' /Mg~ y:s^i^!>-2::ssB3m^ "ss' msmxa^at: ^ I il 1 'I V I 'I ill ;ji 1 1 it 274 LABORATORY PHTSIC8. Close the keys^, j^, r, and obaeive the deflection. Read R, S^ and tf. throw Calculate sin for, knowing that tan 2a = Calculate tan 6*, knowing that tan 2^ = scale distance' scale distance* If the throw and deflection be both small and the scale di-stance of the galvanometer large, it will usually be suffi- cient to substitute for sin ^a one-half the throw of the needle, and for tan 6 the deflection. Repeat the observations. Take the time of 50 swings of the needle, and calculate jT, the time of a complete oscillation. A can be obtained from the curve for the logarithmic decrement by means of T if the galvanometer be the one nsed in the last experiment, otlierwise \ must be obtained directly. In the example given below 6 storage cells were used. Example, — Enter results thus : N ALDER i MICRO-FAB A.D No. 347f. Throw. R S i T A 2 C 104 106 1000 (i ■ 184.7 185 8".0 .006 .333 Bla nk to he filled in hy stude nt. Throw R s i T K 2 C J ELECrmCITT. 275 8i . TO COMPARE THE CAPACITIES OF TWO CONDENSERS. DIRECT-DEFLECTION METHOD. References. — As in last exj>eriinent. Apparatus Required. — A cttiulentjer whoso capacity lias been determined ; CDndeiisers for coinparison ; a ballistic galvanometer ; several batteries ; a Fold commutator ; a con- tact-key. Theory of Experiment. — If a condenser be charged to a potential v through a ballistic galvanometer, we Lave from equation (7) of tlie last experiment the relation C = KT nv a 0) the terms having the same meaning as in that case. Similarly if a second condenser be charged with the same potential, Hence KT a t\ nv sin sm 2 c\ 2 c sin • a 1 {^ . . (3) If observations for a and a, be made, C, can be calculated if C be known. __ sxr^'^iar^ Vh^ 7- csStasu'x^ y„ijah sir£ ..'^'^ts^tfTB.: .Biia'Zi^?7.^Hbrta!^'.£::«<.?:i;^iiBa&MLau .02:.. Ill a 1 .'1 % I 276 LABOHATOJir PIIT81CS. Practical Dlrectiona.— A convenient method of making tl»e connections is shown in Fig. CI. AB and CD are the two condensers, abcdef a 1 ohl commutator with the connectors on the base removed, B, the source of E.M.F., A' a contact-key. Tlie battery and 2. Ali and CI) are the two condensers, li and Ji^ two resistance-boxes connected tothe terminals of a battery -/>,, (f, h, <*, flr,, J,, e,, tlie terminals M 3ZIJ Hllll'illlllF B, Fio. 62. of a Pohl commutator from which the base connectors have been removed. By rocking the switch so as to connect h, to r,, and h to c, the two condensers will bo charged with potentials propor- tional to R and R,^ so that ELECTRICITY. 279 A* _ r Ji\- \\' By rocking the switch 8c» as to connect a, to ft,, uiul a to A, tlie battery is thrown out of the circuit ami the chur},a'» on the two condenisers neutralize each other, the nepitive phites of tlie one beinj< connected to the jwsitive plates t»f the other. If the charges are equal, a complete neutralization tukis place. If not, the two make one coiulenser syKteni char^td with the ditTerence between the two charges, and on closing K a discharge will take place through the galvanometer. If an approximate relation between C and C\ be known, H and I(, can be roughly adjusted. Otlierwise their values can only be determined by trial. Repeat the adjustment until no deflection is obtained. Between the trials the condensers should be thoroughly discharged. This can be done by keeping A' closed for a few seconds after each discharge. Record the values of H and i?,. Compare the condensers given with the standard, and calculate their values in each case. Example. — Enter results thus : Cot.'euser. R Ri C ^' Standard JM.F .2M.F .6BLF. 2000 3400 1295 .832 .lft5 M. F. .490 1 Blank to he filed in hy at x dent. CondenBer. Bi C, I 280 LABORATORY VtiYSlCa. ;1 H: * ^ .t 83. TO COMPARE THE CAPACITIES OF CONDENSERS. BRIDGE METHOD. References. — As in Experiment 79. Apparatus Required. — As in the last experiment. Theory of Experiment. — In the last experiment the charges were equal and the potentials unequal ; in this experiment the potentials are equal and the charges unequal. Suppose the Fig. 68. two condensers and the two resistances connected in the arms of a "Wheatstone bridge, Fig 63, C and C, being the conden- sers, R and iJ^Jlhe two resistances. In order that no current flow through the galvanometer on charging the condensers, that is, on closing A", L and M must be at the same potential. Denote tlie common potential of Z and Mhy Fand the potential of A by F,. The total quantity of electricity which flows into C is therefore give by the relation (V, —V\ Q =zyt = \ -^-g jt, .... (1) !-•>.«■•>- -iSJ^-W 't ■ ELECTRICITY. 2«1 where y is the current and t the short tune required to charge the condenser. Similarly the relation for C, is Hence, from (1) and (2), (2) (3) But Q Q, C=y, and C;=y, the potentials being the same on the plates. Hence £ ~ ^- ^ lience C,~ Q,~ H' or (4) If, therefore, ^and R^ be adjusted so that m charging the condensers no deflection of the galvanometer is obtained, C, can be calculated from (4), C being known. Practical Directions. — The connections can be made exactly as in Fig. 63. Be careful to insulate all the parts of the apparatus. Adjust R and E^ until no deflection is obtained on clos- ing JT. Between the trials the condensers must be discharged com- pletely. 282 LABORATORY PHYSICS. Ji and Ji^ sliould bo as large us possible. A ballistic galvanunictcr iei nut necessary ; any sensitive galvanometer will serve the purjwse. Conipure the coudensei*s as in previous experiments. Example. — Enter results thus : • Condenser. R Ki c c, Standard iM. F .2M. F .5M. F 2000 3400 1^96 .882 .195 .490 Blank to hefilUd in hy stttdent. Condenser. R R, C c, a ; I 84. MEASUREMENT OF E.M F. AND BATTERY RESIST- ANCE BY CONDENSER METHOD. References. — S. Thompson, p. 422. Apparatus Required. — A condenser; a ballistic galva- nometer; a resistance-box; a contact-key; batteries for measnrement. ELECTRICITY. 283 Theory of Experiment. — (1) If a coiideiiKcr of capacity C be cliari^ed, by means of a battery, with E.M.K. 7i', we Jiave the relation (see (7) page 27 Ij CE= K.mxU (I^ If the same condenser be charged with an E.M.F. h\, CE, = K, Bin Ja.. Hence E _ sin ^a _ <5 E^ ~ sin ia, ~ ^^ ' (2) (3) approximately, where 6 and (J, are the galvanometer thrown in the two cases, "With a standard condentier the iiJ(.tho6 Constant Pressure lUJ Ammeter, Calibration of, by Gas Volumeter 235 by Siemens Electro-dynamometer 241 B. A. Bridge 1«2 Ballistic Galvanometer, Log. Dec. of 265 Capacity of Condenser by 270 Batteries, Resistance of, by WLeatt-tone's Bridge IVIJ by Condenser Meiho*(i E.M.F. of Batteries by '■i>^^^ C-oDcave Lens, F^ >c« 1 Len^rtL of 70. 7:j Convex I^ens, Focal Leii>rtL of 60, tii), Go 6H Coulomb Balance H:^. Current. Absolute Measure of 168 Curvature nf Spberica! Surface . . Jil by Spiieroiiieter 51 by Kellec: tou . . 54, 57 385 286 INDEX. PAOI D'Arsonval Qalvanometer, Resistance of 243 Constant of 247 CalibratioQ of Scale of 251 Measurement of Potential by 25, 51 Earth's Magnetic Field, Intensity of, by Magnetometer Method 146 by Tangent (ialvanometer 173 Electromotive Force, Comparison of 229, 232 Electro-chemical Equivalent of Hydrogen 166 of Copper , 171 Equivalent Length of a Magnet. 150 Focal Length of a Convex Lens 60, 63, 65, 68 of a Concave Lens 70, 73 Galvanometer, Ballistic 265 D'Arsonval, Ke.sistance of 243 ConsUnt of 247 Calibration of Scale of 251 Potential Differences by 255 Differential 185 Reduction Factor of 176 Resistance by Shunting 191 Sine and Tangent 159 Glass, Refractive Index of 43 Heat, Specific, of Copper and Zinc 117 Latent, of Fusiouof Ice 121 of Steam 124 Horizontal Component of Earth's Magnetic Field by Magnometer Method 146 by Tangent (ialvanometer 173 Variation of 155 Index of Refraction of Glass 43 of Liquid 9'3 Joule's Law 203 Kundt's Tube 24 Intent Heat of Fusion of Ire 121 of Steam 124 Light, Comparison of Intensities by Bunsen's Photometer 33 by Rum ford's Photometer. . 34 Lines of Force, Blue-printing 128 Lissnjous Figures 13 Logarithmic Decrement , 265 'i* _' .''''..4a1».':97w% INDEX. 287 PACK Magnet, Finding Moment of 128, 134, 189, 148 Equivalent Length of 150 Magnetic Field, Mapping 129 Intensity of 14«. HS Magnifying Power of Miscroncope 77 of a Telescope 81 Melde's Method, Laws of Stretclied Strings 22 Microscope, Construction of 76 Magnifying Power of .... 77 Milli-volt Meter, Calibration of 260 Neutral Point 129 Organ-pipe, Frequency of 8 Pendulum chronograph 28 Photometer, Bunsen's 33 Ruiiiford's 84 Prism, Angle of 40, 89 Refractive Index of 46, 89 Reduction Factor of a (Jalvanometer 176 Reflection, Law of 36 Refraction, Law of ^3 Refractive Index of Glass 43 of Prism 46, 89 of Liquid. .. . 93 Resistance, Measurement of, liy Tangent Qalvanometer 179 by B. A. Bridge 182 by Differential Galvanometer 185 by Wheatstone's Bridge 199 of Qalvanometer by Shunting 191 by Wheatstone's Bridge 199 Comparison of, Carey Foster Method 209 Variation of, with Temperature 218 Measurement of Small "'21 of liarge '■•*2<'> Sixicific 1^8 l{esonance-tui)e * Siemens Electro dynamometer 238 Constant of 238 (."a'ibration by 241 Siren "^ Sonometer ' if J :ii:^l 288 INDEX. PAOI Sound, Velocity of, in Air by Resonwjce-tube ^ by Kundt'B Tube ^^ 27 in Brass *' .„ „ , 117 Specific Heat of Copper, Method of Mixture **' of Zinc j*^^ Kesistance „ 08 Spectroscope . Spectrometer ....... 'bVm 67 Spherical Surface. Curvature of oi. »«. «• Spberoineter, Curvature by Strings, Velocity of Waves in 75 Telescope, Construction of Magnifyng Power of Thermometer, Construction of Spirit Testing Fixed Points of ^ Air. Constant Volume |^ Constant Pressure J^^ „ . _ , 143 Torsion Balance Tuning-fork, Frequency of, by Sonometer ^ by Melde's Method ^^ by Falling Plate ^^ by Pendulum-chronograph 28 Tuning-forks, Comparison by Beats 2 23 Vibrating Strings, Laws of Variometer Compass-box 85 Wave-length of Light Vibrations ^" Waves, Velocity of Weight-thermometer Wheatstone's Bridge SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF .JO?lN WILEY & SONS, New York. Loxnox: CHAPMAN & HALL, Limited. 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Eisster's Modern High Explosives Svo, 8 I as a as a 00 I as 3 00 I 50 50 so SO 00 00 00 00 00 25 4 00 m ii :l KrAoutMi'i liiUo4ucUon to ^^•'^^*^J/*'^,lZ, am.,1iii with tlw Blowplp.. iimo, » 00 Vawlar'i Sowai* Worta Ai»ly»«« •,■■'.■ ' •.li " /w«it« > . •»<>• 5 *•" J'ri'.ll^^u.lo.O-.UUti^,^^ ''S:Xir.. (W.....) lUnMl ol <)«•»«*»'»• ChomUal AnalyW- »'•" g^„ j oo Snura o. In.tructlon In Q««.UU«.. Ch.mlc. An.lT.U. (Cohn.) a Tob. (Sfcoftfi/.) umo, i 5«> FuartM't Wat«r and PubUe Holth. g^„^ 3 00 Purnuw'i IUnu*l of Practical ^ylnt ,,„o. 1 »S Om'a Oaa aad F««l An»ly«ta for Engin««r« . . . . ■--■ ' „„o. a 00 SSMnclpl.. of lUth.«atl«. Ch.ml.tr,. (Morgan.)...... ^^^^ ^ ^ Hlndt*. Inorganic Ch.mi.try lamo, 75 • Laboratory Manual for Stud.ntt . . ... irJ^^r )" ' »»°' » 5° HoU.^'. T..t-boo. of I-7;t, 7w '>l^.r nrMoU- ) ■ l 8vo. a 50 T.xt-book of Organic Ch.ml.try. iwamer . gvo, 3 00 Hopkins'. Oll-ch.ml.t.' Handbook g,o_ , 50 Kaao'. Ca.t Iron , ' , . ,_.l. lamo- 1 00 Lw'I Manual of QuantlUtlv. Ch.mlcal Analyl. ^^^ ^ „„ Undau«r'. Spectrum Analy.U. (Tlngl..) .■_. ,amo. 1 00 \-^S:\Zr rx^S^K-po^ rsU. -r.nc. to Stat. ....Ki.sr;.:i-^^^---^^^^^ ; r^ Mand.V. Handbook for B o-ch.mlc«^ La^ratory . s,.„,p,i„t. , BlaK>n'. Water-.upply. {Con.lder«l Principally iron. ^^^ ^ ^^ ,d Edition. Rewritten ■ • ; ' . p.„„iotoirlcal ) "t""' ' *' Examlnatlonof WaterJChemlc..^^^^^^^^^^^ , eo Meyer'. Determination of Radicle, in taroo.. v k" ^^^^ ^ „„ MiUer'. Manual of Awaylng . .^. ■ —- — lamo. i 5o Milter-. Elemenury Text-book of Chemietry^ _. -.^ , „„ 5Si.n'.0utUne of Theory of Solution and it. Re.ulU ^^^^ ^ ^„ Element, of P^yelcal Cheml.try^._. _ _ ^^^ ^ chemical and Sanlury IflchoU'. Water-.upply. (Con.ldered mainly trom a ^^^ ^ ^^ SUndpolnt, 1883.) ; ■, . .,„i. 8to. a 00 O'Brlne'. Laboratory Guide In Che""«» An.l'^U • ; ^ g,^. , 00 s;nr;:or::.:vr.::or'^^^^^^^^^^^ e PenfleldtiC rPrurmlnatWe Mineralogy and Record of Mln.a. Te... ^^ Plctef. The Alkaloid, and their Ch.mlcal Con.Ututlon. (Blddle.) Un Plnn.r'.S:^;::::: to organic Cheml.try. (Au.ten.) ■■•••••'-:; ^ Poole*. Calorific Power of Fuels g,o^ ,5 00 » ReUlg'. Guide »» "•"'i'J^'.j^ ,„d Food froma Sanitary Sundpolnt.STO. 2 00 HichMdsandWoodmansAlr.Water.anoruu ...lamo. 1 00 SS'. cost of LWng as Modified by Sanlury Science • ^^^^ ^ ^^ Cost of Food, a Study In Dietaries.^ ■_ g^^ „ .Richards and WlllUn^TheI>Ut«yC^^^^^^^^^ ^p^ ,_ Ricketto and RusseU's Skeleton notes upo > gvo. morocco, 75 non-metallic Elements.) g,^^ 3 00 r."S:^rJ:rsrS..«»v,s..«.:.:.;:::.::.:...". 3 ,. -I'^i^f'M.'S RuMk un't lacAmpatiblUtlM kn PrtteripUoiu *♦<»• Schimpf't Ttit-kook of VohiHMtric AnaJyili « »"»»• Sptnctr't Handbook lor CiMmitU of BMt-«u|*r UouMt i6mo. mofocco. Handbook for 8«if ar Maattfaeturtn and th«lr CbamitU i6mo, morocco. Sloekbrtdft'i Rocks and Solto *"'• • TlUman't BtooMtttary Lawena In Heat »*»• • DMcriptlTt Oanaiml CiMmUtry ■*'' Traadwairt OttaUUtWa AnalytU. (Haa) »*»• TurnMurt and JtuMaU't PubUe WaUr-tuppllat 8»°. Van Dtvantw't Phytlcal Chamtatry lor Baflnnan. (Boltwood.) i Jmo. • Walkt't LMturtt on Bapk>*lvM •*''• W«lla'i Uboratory Ould« In OualiUtiv^ Ch«mle«l AnalyiU. 8vo, Sltort Court* In Inorfanlc OuaUuUv* Cbamical AnalyaU for Entln««rUif StudMtt ""°' VVhippto'i Mlcroicopy of Drlnkln«-waUr „ „ V WiMhmann'i Sugar Analy.!. SmaU 8vo. Wlhon'i Cyanide PToe«tM» '*™°' ChJorlnatlon Proc«M :„;.,' V^f""' WuUlnt'i EUm«nUry CourM In Inorganic Pharmac«utteal and Medical Chem litry 0« 50 00 oo »o 50 00 00 00 50 00 50 50 50 50 50 so umo, a 00 CIVIL ElfGIlfEERUfO. BRIDGES AHD ROOFS. HYDRAULICS. MATERIALS OF E50INEERIH0. RAILWAY ERGINBBRIHO. Bakcr'i Englnwri' Surreylng InttrumenU ■ ""»«>• 3 Blxby'i Graphical Computing Table P«P«r. i9» X a4i inchee. •♦ Burr't Ancient and Modern Engineering and the Iithmlan CanaL (Pottage. 17 eenu additional.) Svo.net.a Comrtock'i FieW Astronomy for Engineen "»»• Davis's EleTStlon and PjidU Tables "*<>• EUiott's Engineering fjr Und Drainage ""n"- Practical Farm Drainage ""<'• FolweU's Sewerage. (Designing and Maintenance.) »'<>. FreiUg's Architectural Engineering, ad Edition. Rewritten 8vo. French end Ives's Stereotomy "'"' Goodhue's Municipal Improvements "f*"' Goodrich's Economic DUposal of Towns' Refuse o»o> Gore's Elements of Geodesy *'*•' Hayford's Text-book of Geodetic Astronomy »'°> Howe's Retaining Walls for Earth ^ • ""»»• Johnson's Theory and Practice of Surveying !>n»«» »»<>• SUtics by Algebraic and Graphic Methods «'<>• Klented's Sewage Dteposal • • • """'' LapUce's Philosophical Essay on Probabilitief (Truscott and Emory.) lamo, Mahan's Treatise on Civil Engineering. (18 ) (Wood.) 8vo • Descriptive Geometry °^°' Merriman's Elements of Precise Surveyln? and Geodesy ovo. ElemenUofSaniUry Engineering ■ ■ • ■^''°' Merriman and Brooks'* Handbook for Surveyors i6mo. morocco. 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Iron, and Stone g^^ ^ ^^ Howe's Treatise on Arches „, ' \. j c. .1 8vo. 2 00 Design of Simple Roof-trusses m Wood and Steely .^ • ■ • _^ .^ _ Tohnsonl^ryan. and Turneaure's Theory and Practice in the De^^^mng^of ^^ ^ Modem Framed Structures -■■ Merriman and Jacoby's Text-book on Roofs and Bridges: ^^^^ ^ ^^ Parti.— Stresses in Simple Trusses g^^^ ^ ^^ Part 11. — Graphic Statics ; <,„„ , rn Jaruk-Bridge Design. 4th Edition. Rewritten 8vo. ^^ 5° Part IV.— Higher Structures ^^^^ ^^ ^ Wright's Designing of Draw-spans: g^^^ ^ ^^ Part I — Plate-girder Draws _ - pSlL-Riveted-truss and Pin-connected Long-span Draws. .... Svo. 2 50 Tt/o parts in one volume (**■ M m .dfi HYDRAULICS. Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from^an Orifice. (Trautv-ne.) g^^^^ Bovey's Treatise on Hydra^.ics g^^'_ Church's Mechanics of Engineering ,_ ' r'y,.„„^,. nappr, Diagrams of Mean Velocity of Water in Open Channels . . _ ^. .^^pap r. 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Whelpley's Practical Instruction in the Art of Letter Engraving i«no, Wilson's Topographic Surveying '"' Free-band Perspective '**' Free-hand Lettering. [In preparation.) ■ Woolf's Elementary Course in Descriptive Geometry Large avo. 3 oo 3 00 3 oo 2 50 I oo t 35 I 50 I oo I 35 75 3 50 3 00 7 50 3 50 5 00 3 00 3 50 3 50 3 00 ELECTRICITY AND PHYSICS. Anthony and Brackett'r Text-book of Physics. (Magie.) SmaU 8vo, Anthony's Lecture-notes on the Theory of Electrical Measurements ismo, Benjamin's History of Electricity 8vo, Voltaic CeU 8vo. Classen's Quantitative Chemical Analysis by Electirolysis. (Boltwood.). .8vo, Crehore and Squier's Polarizing Photo-chronograph »vo, Dawson's "Eneineering" and Electric Traction Pocket-book. . lomo, morocco, Flather's Dvnamometers, and the Measurement of Power iimo, ■Gudc • s D- Magnete. (Mottelay.) 8vo, H' r. a's Precision of Measurements °^°> 1 lescopic Mirror-scale Method, Adjustments, and TesU Large 8vo Landauer's Spectrum Analysis. 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Small 8vo, 8vo, 8vo, 00 00 00 50 50 50 00 50 Tm ^^■>- !?& ^ L-<» S'^-'p^;^^""""^:; ; Svo. 5 oo Button's Mechanical Engineering of Power Plants. ... ^^^^ _. ^^ Heat and Heat-engine. gvo. 4 00 Kent's Steam-bo'ler Economy ■■■■ gvo. 150 Kneass's Practice and Theory of the Injector 8vo. a 00 MacCord's SUde-valves 4to, 10 00 Meyer's Modern Locomotive Construction . . . . - • -^ ^^^^^ , ^^ Peabody's Manual of '^'J'"''^-'''^,^^s^^,ni •otheV Vapors 8vo. i 00 Tables of the Pro. ^Ztf^Sr^l^ OXi.tr Be.i-.nt^ne. 8vo. 5 00 Thermodynamics of the Steam-engine »i.u ^^^^ ^ ^^ Valve-gears for Steam-engines g^^^ ^ 00 Peabody and Miller's Steam-boiler. j^^^ g^^^ , 50 Pray's Twenty Years with »»>;^°^;"*°'„„,„- !„ Gases and Saturated Vapors. Pupln's Thermodynamics of Reversible Cycles m oases ^^^^^ ^ ^^ (Osterberg.) • ' ' ' ' " * Wi-lt '}, i amo. a 50 Reagan's Locomotives: Slmple. Compound, and Elwtric ^^^^ ^ ^^ Ro^gen's Principles of Thermodynam^s- (^u Bois ) . . . . • „„,. , 00 Sinclair'sLocomotiveEngmeRunningandH^n^^^^^^^^ ^^^^^ , 3„ Smart's Handbook of Engineering Laboratory Practice ^^^^ ^ ^^ Snow's Steam-boiler Practice • • ■ Spingler'* Valve-gear* ""'• ' S* Notes on Thermodynamics »»""•• ' "** Spangler, Greene, and MarahaU'i Elementa o! Steam-engineering 8vo. 3 oo Thurston's Handy Table. ; ■ -»'"• * *" Manual of the Steam-engine »*<>>»• 8'°' '° °° Part I.— History, Structuce. and Theory »»<>• » '^ Part n.— Design, Construction, and Operation o'o. * <»• Handbook of Engine and Boiler TrUls, and the Use of the Indicator and the Prony Brake S'"' ' "^ Stotlonary Steam-engines *'*'• ' ' Steam-boiler Explosions In Theory and in Practice lamo, i 50 Manual of £..eam-bollers, Their Designs, Construction, and Operation. 8vo, 5 00 WeUbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo. s 00 Whitham's Steam-engine Design •°'°' ' °** Wilson's Treatise on Steam-boilers. (FUther.) . . . i6mo. a 50 Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .8vo. 4 00 MECHANICS AND MACHINERY. Barr'8 Kinematics of Machinery |*°' Bovey's Strength of BlaterUls and Theory of Structures 8vo, Chase's The Art of Pattern-making "°>°' Chordal.— Extracts from Letters """• Church's Mechanics of Engineering 8vo. Botes and Examples in Mechanics ^vo, Compton's First Lessons in MeUl-working umo, Compton and De Groodt's The Speed Lathe "mo, Cromwell's Treatise on Toothed Gearing i jmo, Treatise on Belts and Pulleys iimo. Dana's Text-book of Elemenury Mechanics for the Use of Colleges and Schools "'no- Dingey's Machinery Pattern Making "m". 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"«». ^5^ Keep's Cast Iron _■ - gvo'. i 50 v..nh>r• ' »• TunVt Popular Trt«tta« on tho Wlndi '"'• * "® HAiuM's American RaUway Management :.••„•;:,■.;•:■, 1'^^°' , „ MotfsCompotltion.Dltettibmty. and nutritive Value of Foo4. Mounted chart, i as FaUaey of the Pretent Theory of Sound " •. ' " „ I, . ' I !! Rlckettt'aHlttory of ReniMlaer Polytechnic Inetitute. i8a4-i8«4. SmaUSro. 3 oo Rotberham-i UmpnaiUed Hew Tetument "^ «^' » »» Steel's Treatiae on the DUeaaee of the Dog •»»• 3 ^ Tottan't Important Question In Metrology "™' ' 5° The WorWs Columbian Eipositlon of 1893 *"' * "^ Worcester and AtWnson. Small HospiUls. EsUbUshment and Maintenance, and SufgesUons for HospiUl Architecture, with Plans for a Smau HospiUl """»• »•» HEBREW AHD CHALDEE TEXT-BOOKS. Green's Grammar of the Hebrew Language •'<>• ^ »« ElemenUry Hebrew Grammar »*°^' ' ' Hebrew Chrestomathy ■ ■ • : V. ' Gesmlut's Hebrew and Chaldee Lexicon to the Old TesUment Scriptures. "* (TregeUes.) Small 4to. half morocco. 500 LetterU's Hebrew Bible "'"• *' 16 ^^3^in^Mr£i