Physical Laboratory Manual for Secondary Schools

PHYSICAL

LABORATORY M ANUAL

FOR SECONDARY SCH OOL S :

R EVISE D E DI TI ON

F D A . L . M C HAR E A A M . S S ,

H E A D OF TH E D E P A R T M E NT OF P H Y SICS D E TR OI T C E NTR A L H IG H SC H OOL

NEW YORK CINCINNATI CH ICAGO A M E R I C A N B O O K C O M P A N Y COPYR IGH T , 1909 , B Y

CH ARLES F . ADAMS.

’ ENTE R E AT STAT IONE R S H AL L LO NDON . D ,

AD AH P H Y B I A N S S LA . . PREFACE

S INCE the ﬁrst edition of this book was published the physical laboratory has become the rule rather than the I i n w exception in the schools . t s o possible to b uy well m ade apparatus suitable f or the l aboratory of the second ar s at r as na r s so a at a s ab u y chool e o ble p ice , th t co t of o t one hun dred dollars an equipmen t can be procured by which a good complete laboratory course can be estab h T r a r m r or s m ar lis ed . eache s lso a e o e le s fa ili with the m d r r r F gene ral etho s of labo ato y p ocedure . or thes e reasons much of the matter in the former edition in re ard s rm and m a n a ara us ha g to the ize , fo , the ki g of pp t s

b n m r m s . In a d man u n ee o itted f o thi f ct, the e ds po the time an d energy of the scie nce teacher a re so heavy that it is believed he can spend his time to bette r advantage in r d n an in m a n r Th othe irectio s th ki g appa atus . e school a utho rities should furnish the apparatus an d a suitable place f or storing it ; the teacher should see th at it is well

a n ar an and ut awa in d rd r a t ke c e of, kept cle , p y goo o e s h d u n soon as he as ﬁ nishe si g it . Although laboratory work in our schools has been

r a x n d in as f ew ars r su s a v in g e tly e te de the l t ye , the e lt h e n m any cases been disappoi ting . It has been said that w r is n r n r s n nor ns ru v and the o k eithe i te e ti g i t cti e, it is thought that the m ain cause of this is the se verely m quan titative character of the exe rcises . It ay be that the quan titati ve aspect of the wo rk has received too m uch

and ua a v v r uan emphasis the q lit ti e too little . E e y q tita 3 6 7 3 1 5 7 4 PREFACE

v x r s h w v r has its ua a v a u r w ti e e e ci e , o e e , q lit ti e fe t e hich

s ud n s u d be br u a r a and und rs an the t e t ho l o ght to pp eci te e t d, not th rough the quan titati ve work but as a prelimi nary to The au r is n n a t r ub has it . tho of the opi io th t the o le ar s n not aus x r s s are uan a v i e chiefly bec e the e e ci e q tit ti e, b ut because of the nature of som e of the e xperimen ts m nd ara r r the selves a the ch cte of the appa atus employed . Of w a ss n r s f or xam av ra h t po ible i te e t, e ple, to the e ge r or f or a m a r is an x r m n in r a n gi l , boy th t tte , e pe i e t b e ki g wire ? Or how is it possible to inspire respect f or the ub and n r s in w n a ara us and th s ject i te e t it, he the pp t e methods used are such that the teacher m ust apologize f or the results After twen ty years of e xperience in the physical labora r w ar ass s au r r s n s s x r s to y ith l ge cl e the tho p e e t the e e e ci es, which have been thoroughly tested in his own classes and in r s s w a firm a a ur can othe chool , ith belief th t co se be selected from them which will be both instructive an d T i nterestin g to the pupil . he methods and apparatus s r b d W v d r su s in ands u de c i e ill gi e goo e lt the h of p pils . The n umber of exercises is sufficiently large to allow n r u The m h co side able latit de of choice . s all school wit a limited equipment or the l arge school with ab undance of m eans can fi n d suitable m aterial f or a laboratory course of r A f e x rc ar n r u one yea . w e e ises e give which a e s ited f or a little more advanced work which some may wish to

Th n um r x rc rm r give . e be of e e ises also pe its some va ia tion of the work from year to year and gi ves room f or development in the sm all school as its eq uipmen t in

r c eases . If a r d s r s n um r uan a v oh the te che e i e , the be of q tit ti e servations in m any e xperime nts m ay be reduced to a m i nimum and the q ualitati ve feature of the work em A u n n r u phasized . ltho gh the book co tai s seve al q ali PR EFACE 5

’ ta tive x r s s is au r s ﬁrm n n at e e ci e , it the tho co victio th the place f or the purely illustrati ve experimen t is in the ur r m ra r an in h lect e oo the th t e laboratory . ’ This m anual is inten ded as a companion book f or Adams s P s s f or ndar s and numb r in ar n hy ic Seco y School , the e s p e theses in the various exe rcises refer to paragraphs in that

bo . It m a w v r be us d s ara or w an ok y, ho e e , e ep tely, ith y other text .

CONTENTS

CHAPTE R I

SIM PL E M E A SU R E M E NTS E XER CISE P AGE Th r 1 . e M ete Stick

2 . The Diagon al Scale Th 3 . e Vern ier Th m 4 . e M icro eter Screw Th 5 . e Beam Balance T 6 . he Jolly Balance r n 7 . Graphic Rep esentatio of Results r r 8 . Density of a Rectangula P ism Sign iﬁcant an d Doubtful Figures D t f n r C Den si y o a Cyli de f r 10. Density o a Sphe e

CHAPTER II

M E C H A NI C S OF SOL I D S

c l r te M oti n 11 . Uniformly A ce e a d o m t n f ncurr n F r 12 . C o pos i io o Co i g o ces e orce 13 . Parall l F s l 14 . The Pendu um

. T e n m Len t of Are 15 h Pe dulu . g h en f F r e 16. M om t o a o c I n 17 . The n clined Pla e E t t 18. las ici y

CHAPTER III

M E C H A N ICS OF FL U I DS

D wnw r ressure in L u s 19 . o a d P iq id t r re s ure i n L u s 20. La e al P s iq id CONTENTS

E XERCISE r ressure in u s 2 1. Upwa d P Liq id The B rometer 22 . a ’ 3 Bo e s Law 2 . yl 2 Dens t of ter 4. i y Wa

B uo nt Force. The r nc e of Arc me es 25. ya P i ipl hi d v of So s D nser t n \V ter 26. Specific Gra ity lid e ha a t l e t n t r 27 . Specific Gravi y of So ids Les s D nse ha Wa e c c t o u e n So in em 28. Spe ifi Gravi y f Liq id s by w ighi g a lid Th

29 . Speciﬁc Gravity Bottle

30. Speciﬁc G ravity of Liquids by BalancedCol umns

CHAPTER IV

SOUND

Vibration Rate of a Tuning Fork e oc t un V l i y of So d . ’ e ocit of un I V l y So d n Solids. Kundt s M ethod Scale Ratios V r t ons of Str n s . L n Vib a i i g aw of Le gth . Frequency of a Fork The Tension Balance f or the Sonometer r t on of Stri n f Vib a i gs . Law o Diamete r ibr t on V a i of Strings . The Law of Tension

CH APTER V

L IGH T

Photometry Inte nsity of a Lamp The Plane Mirror Index of Refraction of Water Tangen t and Sine of an Angle R efraction Angle of a Prism R efraction by a Prism The Con cave M irror ' T he Focal Length of a Len s . The Focal Length of a Conve x CONTENTS

E X8 8 01 83

. n Im e 49 Focal Length of a Le s . ag s v en of t 50 . Wa e L gth Ligh

CHAPTER V I

H E A T

Testing a Thermomete r Coefﬁcient of L inear Expansion Expansion of Ai r r v l n Speciﬁc Heat. Wate Equi a e t Heat Changes during Freezi ng Heat of Fusion of Ice Heat of Vaporiz ation of Water Vapor Ten sion The Dew-point 1 9 i t? » : I M“ CHAPTE R V II

M A GNE TI SM A ND E L E CT R I C I T Y

The First Law of Magnets Eﬁ ect of Breaking a M agnet M apping a Magnetic Field by a Com pa ss Mapping a M agnetic Field by Iron Fili ngs The Voltaic Cell Polarization of Cells Deﬂection An Electromotive Series Electromagnets The Tangent Galvan ometer Reduction Factor of a Tangen t Galvanom eter Electrom otive Force and Joining Cell s ’ Ohm s Law

. . of e E . M F C lls Resi stance of Wires R esistance of Wires Resis tance of Cells l . of e Resistance and E . M . F a C l Current Induction Current Induction 10 CONTE NTS

APPENDIX

NOTE S A N D SUGGE STIONS

TA B L E S M tr E v 1 . e ic qui alents m 2 . Useful Nu bers and Formulas 3 Den s t es . i i n 4 . De sity of Water at Different Temperatures t n n L n t f e n 5 . Accelera io a d e g h o S conds Pe d ulum rr ti n of B r meter f or e r t r i M 6 . Co ec O a o T mpe a u e n illimeters A r e e of B e r D ren E 7 . ve ag H ight arom te at iff e t levations rr t on of B r me r r t re 8. Co ec i a o te f o Te mpera u in Inches 9 Correction of Baromete r f or Elevation above Sea Level f 10. Velocity o Sound f n re 1 1 . Size o Pia o Wi Re r 12 . Indices of f action n n n 13 . Si es a d Ta gents efﬁc e nt of L ne r Ex n 14. Co i i a pansio

15. Speciﬁc Heats

16 . Tension of Water Vapor I h r I n 17 . Veig t of Wate Vapor Saturated AiI t 18 . Boili ng Point of Wate r a Diff erent Pressures r r n f e to e e- r B 19 . P opo tio al Parts or Wh ats n Slid wi e ridge

S ze etc . of Co er re i , , pp Wi PHYSICAL LABORATORY MANUAL

HA E 1 “ " C PT R 3 f i t

SIMPLE ME ASUEEIIENTS

EXER C ISE 1

THE METER STICK

ths b a ter tic t . o measur e len me s k o estimat Purpose T g y , e

t t s o ll meter s a n d to learn how to r ecord the esults . en k f mi i , r — m r . Apparatus . A ete s tick A sheet of paper an d

other objects which m ay be measu red .

1 M ur n h Procedure. ( ) eas e the le gt of a s heet of paper a n d several other objects less than a m eter long to the n ar s m r x r ss n r su s in n m r e e t milli ete , e p e i g the e lt ce ti ete s an d ten ths of cen timeters .

FIG . 1 .

P a m r s c on b c as in F ur 1 n ot as l ce the ete ti k the o je t ig e ,

in F u r 2 . D o not b n at end m r s ig e egi the of the ete tick ,

nd ma b rn r m r because the e y e wo o i pe fect . 12 SIM PL E M EASUR EM ENTS

Do n t c u c n im rs f I om A B but n o o nt the e t ete to , ote the positiori Of A an d: the position of B on the measure and r ob gbbs by subtracting A f om B . r results In a w ay sim ilar to this

’ l osSibly your record resembles the follo wi ng in some particulars

The as r r a s rs m n a r rd l t eco d l ck the ﬁ t ele e t of good eco ,

a is n a n ss . It is m r v r n c rr in s v ra re th t , e t e , o eo e , i o ect e e l

s ects . III s c n d c um n ﬁ ur s are ar p the e o ol , the g e too l ge ; n m n n m n d r r ac i d a c . is n ot v an a s s the e o i tio gi e , p ope p e n ot f or un s are n ot ac d und r un s nor ns left it ; it pl e e it , te

d n In rd u n m i w r n n c m . t u e r te s . the thi ol the c s it e too

- m an m s The a u s as c um n a re s v d n . y ti e . f lt of the l t ol elf e i e t The n umbers 22 and 84 should be writte n and “ " “ B ut ou sa am out xa 22 and 84 . , y y, it c e e ctly Uniformity an d neatne ss w ould suggest the additio n of the decimal poin t and the cipher ; but the re is a better r as n f or i 22 m r use . n ou w r ca e o the Whe y ite it , the i pli tion is that you are a ttempti ng to read only to the nearest cen timeter an d that you a re n ot payi ng any a ttention

a v r m m m s ha ou a re wh te e to the illi eters . i plie t t y r ad n to the n ea r m m et r w ch is ac in the e i g est illi e , hi the f t THE DIAGONAL SCALE 1 3

r s n as . The r r r has a s n ﬁcan c p e e t c e ciphe , the efo e , ig i e , “ and 22 d s n ot m an as ou u did “ t a oe e , y tho ght it , h t it came out exactly it mean s th at 22 was the nearest

n m r ce ti ete . 2 M asur the sam b s a a n s m ( ) e e e o ject g i , thi ti e to the r m nea est te nth of a illimeter . It will b e necessary to m a ra n m m r b D n esti te the f ctio s of illi ete s y the eye . o ot

it in a v s or uar rs b ut in n s . Of urs ou do h l e q te , te th co e, y cannot do it very accurately at ﬁrst and there will be

n d r b un rta n ab u s n co si e a le ce i ty o t the e te ths . n a m m r i on e undr n A te th of illi ete s h edth of a ce timete r. Express your results in centimeters an d hundredths of n m rs and see ou can a v d all aul s ur ce ti ete , if y oi the f t of yo last record . III some of your future experiments it will be possible a nd d s rab r a n s m m rs in rs e i le to e d to te th of illi ete , othe n n s n m rs and ss b in s m n o ly to te th of ce ti ete , po i ly o e o ly m ur r to centi eters . See that yo reco d always indi cates w a ou are a m n do h t y tte pti g to .

EXER C ISE 2

THE D IAGONAL SCALE

t s the dia o c Purpose. To learn o u e g na l s ale. d d A r v rs w r n . A Apparatus . pai of i i e ith sha p poi ts n i A s r ra tw m diago al scale (F g . t ip of b ss with o s all r c rosses uled upon it .

D rm n un t Procedure. (1) ete i e the i of the scale . (2) Count the n umber of spaces into which the unit of the scale is divided by the diagonal lin es at one en d of the un numb r s a s rm d b scale . Also co t the e of p ce fo e y the c lines runni ng lengthwise on the s ale . (3) Note that the diagon al lin es and the horizontal lin es r form a large n umber of small pa allelograms . 14 SIM PLE MEASUR EMENTS

What is the length of the top and bottom of each of ’ these parallelogram s ? 4 N a rs a na li n w c s a r ( ) ote th t the ﬁ t di go l e , hi h t ts at r sca rms w r r m the ze o of the le, fo ith the ve tical f o that n point a triangle . H ow lo g is the base of this triangle

' (5) By geometry dete rmine the length of all the lin es r in that triangle pa allel to its base .

6 H ow f ar is it f or xam on r n ( ) , e ple , the ﬁfth ho izo tal li ne from its intersection with the ve rtical from zero to its

FIG. 3 . i ntersection with the second diagonal ? on the third hori z on tal n ur ? ﬁ ? e c li e fo th fth t . H ow f ar is it from the vertical on the ﬁfth horizon tal to . the fourth diagonal ? to the sixth diagonal ? eighth ? ninth ? (7) What do the diagonal lines rep resen t or express ? What the horizontal lines ?

8 B aid s a s r ad the n s ( ) y the of the c le, p e poi t of the di viders s o that they shall be units apart ; units a r Let n r pa t the i st uctor ve rify in each case . (9) By the dividers and the diagonal scale measure the distance between the poi n ts of intersection of the two L crosses on the strip of brass . et the i nstructo r ve rify the m eas urem ent .

— B t n f h N. B . o h poi ts o t e dividers m ust always be on the sam e horizon tal line . TH E VE RNIER 15

EXER CI SE 3

THE V E R NIER

. t t c a a uxi Purpose To lea rn o use he vernier, whi h is n l

4 r ab on e to ia ry sca le (Fig . ) attached to a la ger sca le to en le r ea d accur ately very sma ll p a rts of the divisions of the la rger

FIG . 4 .

s cale. For xam a s a is r e ple, if c le g aduated in ten ths of n s is ss b aid i che , it po i le by the of a vern ier to read to hundr d s an n e th of i ch by that scale . — A aratus . A verniered ca r F pp lipe ( ig . 5) or othe r i ns rum n a v n a s a w a r r t e t h i g c le ith ve nie .

— B r on e can u e rn m Procedure. efo e s a ve ier he ust

dete rm ine its least count . It is found as follows 1 D rm n the un s al w r is an ( ) ete i e it of the c e , hethe it

in n m r r or r un . ch , ce ti ete , deg ee, othe it (2) Count the numbe r of divisions into which this unit

is divided and calculate the val ue of the smalles t di vi sion . (3) Measure the length of the vern ier by the la rge

scale . 1 6 SIMPLE M EASUREMENTS

(4) Count the number of divisions in to which the vernie r is divided and calculate the value of its smallest

divi sion . (5) Find the diff eren ce between the values obtained

n O ra n 2 and 4 . T s diﬁ erence is as n i pe tio s hi the le t cou t . It i s the s m allest value that can be m easured by this

vernie r and scale . Record your results as follows

rm n as un v rn r H aving dete i ed the le t co t of the e ie , let

us learn how to use it . n v rn r is its r n and The ﬁ rst li e of the e ie ze o li e, the

mb r 1 2 3 . others are nu e ed , , , etc First set the ze ro of the vern ie r on the zero of the scale ;

v rn r a n the s a sa 5 u n s and then move the e ie lo g c le, y it un s n so a its r n 3 divi sions of the it, etti g it th t ze o li e n on exactly coincides with the li e the scale . The zero of the vernie r is now exactly 5 un its and 3

divisions from the ze ro of the scale . M ove the ver nie r a tiny am ount farther un til its line 1 n n on coin cides with the next li e beyo d it the scale . H ow f a r did you move it ? What is the distance now betwee n the zero of the scale and the zero of the ve rnier

18 SIMPLE M EASUR EM ENTS

am un a n n ar sca on D . n B and ar o t lo g the li e le , Whe K e in n d E s u xa n r co tact, the e ge of ho ld be e ctly o the ze o of the linear scale and the zero of the circular scale should e xactly coincide with the line r unning lengthwise on the nd r n cyli e D near the ﬁgures . Whe the screw is turned ba s an e w n B and If is en x ua t ck , the di t ce b t ee th e actly eq l o n n ar s a x s d v The ur the le gth of the li e c le e po e to iew . p pose of the ci rcular scale is to enable one to read accurately ra n n n x the f ctio of the last divisio of the li ear s cale e posed .

— t Caution . Nevcr use more han a very slight f orce in

turnin the screw. H old 0 li htl so tha t the n ers will g g y , ﬁ g sli the scr ew turns hard or ther e is a ratchet R p if if , ,

a t t cr b t a lw ys urn he s ew up y hat.

Procedure. 1 D rm n un and a s va u ( ) ete i e the it, l o the l e m a d v n If nn of the s llest i isio of the line ar scale . this ca ot be d n ns n urn s r w ba un t a con o e by i pectio , t the c e ck il siderabl rti n he Sca is v s b and n a a r e po o of t le i i le, the by p i of d v rs m ar w n t or m r d s ns w i ide co p e t e y , o e , ivi io of it ith b En s and m tr s andard ru s oth gli h e ic t le . 2 D rm n 1 9 r i ( ) ete i e the pitch 1 ) of the sc ew . This s done by observing how f ar the edge of E moves along the

n a r sca n r w i r d x n li e le whe the sc e s turned a oun e actly o ce . (3) Ascertain the number of di visions in the ci rcular scale and calculate the least count of the ins trume nt ; this is the distance measured on the linear scale when the scr w urns one rcu r F x a n . or am e t ci l divisio e ple, if the s r is m pitch of the c ew m . and there a re 50 divisions on r u ar sca n r n w s the ci c l le , the the sc ew moves le gth i e

mm . w n urn d all wa ar und but n he t e the y o , o ly {a of

mm . r m m o . w n urn d u r d n . , , he t e one circ la i visio

F v rcu ar d v s ns 1 r i e ci l i i io then m ean mm . ; 0 ci cular v s ns mm di i io , . etc . (4) Set the sc rew at diff erent positions and read the TH E BEAM B ALANCE 19 d s an s n a as n ns ru r v r ur i t ce i dic ted, ki g the i t cto to e ify yo d Th n b n an i n r e a ings . e dista ce etwee B d K s obtai ed by a dding the fraction of a di vision in dicated by the circ ular r x d s cale to the numbe of whole divisions e pose to view . A n object is measured by placing it between B and K a nd urn n the scr w u un n a urs or un t i g e p til co t ct occ , til c is us d b r w the caution iven the obje t j t hel y the sc e , g

v n a bo e bei g observed . Record da ta as follo ws

EXER CI SE 5

TH E BE A M B AL ANCE

o wei h a n ob ect b a bea m balan ce. Purpose. T g j y — F Apparatus A beam balance ( ig . 7) and a box of F m ca ba anc s are nc s d in ass w eights . ine che i l l e i lo e gl cases to exclude the dust and to protect the balance from i n not in use b am is ra s r m r r . cu rents of a Whe , the e i ed f o the knife edges ; and the re are rests unde r the pans to

Th b am is w r d f or use urn n a s teady them . e e lo e e by t i g

d r v r in r n n s rum nt he m ille head o a le e f o t of the i t e , and t 20 SIM PLE M EASUR EM ENTS

rests un derneath the pans are lowered by pushing in a sma s or in A n s nd r n r is a a d to ll top p . lo g, le e poi te tt che b am and s n the e , wi gs to and f ro over a scale as am v ra the be ib tes .

Procedure. (1) Before the balan ce is us d a da e e ch y, it should be le veled ; s is d n a thi o e by , spirit level or a sm all pl umb bob a ttached FIG . 7 .

to the bal ance . (2) The position of rest f or the pointe r after it ceases n n rm T s ; s not n s wi gi g should be dete ined . hi doe ofte cc n d xa w t m dd n sca an d i i ci e e ctly i h the i le poi t of the le , it s not w tr ad us so t a w is n ar ell to y to j t it h t it ill, if it e it . It requi res too m uch time to w ait f or the beam to cease swinging in order to dete r mine the position at which the poi nter would come to rest ; and hence the position of rest is fo und by observing the t urning poin ts of the

n r w is v bra n HII “H poi te , hile it i ti g, and taki ng the mean of these

n s . The s n r st poi t po itio of e ,

w v r is not m dw a b ho e e , i y e

w n an two ns c u v urn n n r t ee y co e ti e t i g poi ts, sin ce f iction and the resistance of the ai r reduce the am plitude of vibration at each swing ; but it is found by taki ng an odd numb r urn n n s sa 3 e and 2 e of t i g poi t , y to the l ft to the T w right . his ill throw the greatest and the least on the THE BEAM BALANCE 21

sam s . For xam su s n er to m v e ide e ple, ppo e the poi t o e v r a s a av n w n v s ns nd ma in s o e c le h i g t e ty di i io , a i g e the e um F r m 0 divis ions to be n bered ( ig . 8) f o on the left to r n r i 20 on the ight ( ot f om the cen ter n both directions) . S uppose the following observations are taken

TU R NING POINTS

os t on of p i i rest.

M ean

In w in w s are a te eigh g a body, the eight dj us d until the pointer has the same position of rest as at ﬁrst ; this posi r tion is foun d as befo re, not by waiting f o the beam to

c n . In s r n n r O r eas e swi ging ob e vi g the poi te , the perato s hould be directly in fron t of the cen ter of the scale so rm h that the line of sight is no al to t escale . No person is ﬁtted to use a sensitive balance unless he is able and willing to conform to the following r ules :

r . See that the ba lance is lev Rules f o Weighing el, ' - a nd that the p ans are f ree f rom dust. Use a camel s ha ir t brushf or removing the dus . (2) Sometimes the beam of the balance will not start to

rate o itse . To set it swin in wa t a little a ir u on it vib f lf g g , f p b a uick movement o the hand or touch it ver li htl b y q f , y g y y ’ o the c mel s -ha ir brush the tip f a . (3) See that all of the weights are present in the box inn ei h n lace the ox convenientl bef ore beg ing to w g , a d p b y i - n near the r ght hand pa . 22 SIMPLE M EASUREM ENTS

4 Never lace ob ects or wei hts on the ans nor remove ( ) p j g p , them f rom the p a ns except when the bea m is raised f r om the knif e edges a n d the balance i s at r est.

5 In a rresti n the beam a lwa s wait un til the ointer ( ) g , y p c t r o the l he m shoul a lwa s be is over the en e f sca e . T bea d y raised slowly an d caref ully to a void injuring the knif e edges .

6 Never touch the wei hts with the n ers but l t them ( ) g ﬁ g , if wi th f orcep s p rovided f or the p urp ose. (7) The weights should never be anywhere but on the pan or in their places in the box . (8) Place the object to be weighed in the lef t-hand pan

- and the weights in the right hand pan of the bal ance. (9) Do not select weights to place upon the pan in a hap h zard wa but tak e ﬁ rst the lar est one ou can use and a y , g y then add others in their order f rom the largest to the small

t hould ou f ail to f ollow this rule ou ma lace es . S y , y y p a large number of small weights upon the pan only to ﬁ nd that you must remove them all and substitute a larger weight f or them which y ou f ailed to try . (1 0) Check the ﬁnal result that has been f ound by add in he wei hts on the an b notin the acant laces in g t g p , y g v p

in h i h n in . the box , and add g t e we g ts belo ging there

11 The ob ect to be wei hed should be cool an d nothin ( ) j g , g tha t is wet or that would injure the p an must be p laced

directly up on it. (1 2) Fin a l observa tions must be taken with the balance

c o t case l sed o avoid currents of a ir .

The rules prin ted in hea vy type apply as well to larger r d r and coarse balances an should always be obse ved . TH E JOLLY B ALANCE 23

EXE R CI SE 6

TH E JOL L Y BAL ANCE

To stud the a ction o the Joll balance and Purpose. y f y to learn to weigh objects by it. — A a an Fi . A t Apparatus . Jolly b l ce ( g se of

m r w s . The n s n r ra s r n the et ic eight lo g, le de spi l p i g of b alance has n ear its lowe r end a bead or pointe r which is used as an index in meas urin g the change r n If o i n length of the Sp i g . y u s ight past this index at the scale b a ou w n c a ck of it, y ill oti e th t the position of the index on the s cale changes when the eye is

Th ar n r aised or lowe red . is app e t displacement of the in de x due to diff eren t positions of the eye is c alled parallax . In observi ng the position of the i ndex on the

a ara ax m us be a v d d . s c le, p ll t oi e It is done by using a mirror scale and always placing the eye so that the index covers its own

r image in the mi ror .

r Procedure . Read and e co rd the position of the i ndex of the sprin g with no load in the pan . 2 P 2 in ( ) lace a g . weight the pan and take the position of the

Fro . 9. F nd index again . i the elonga tion of the spring by taki ng the diff e re nce betwee n the a ra r ad n w u ad an d the r a n ve ge e i g itho t lo e di g w ith load . 24 SIMPLE M EASUR EM ENTS

3 R ea w 4 6 8 10 . . a wa s a n the ( ) ep t ith , , , g , etc , l y t ki g position of the in dex both before and after using each

ur ru r w ou ar s w t weight . Yo inst cto ill tell y the l ge t eigh you may use . Record your results as follows

H av n b a n a a we sh u now Discussion . i g o t i ed the d t , o ld h x s tudy the table to see what t e results teach . E ami n e r d umn H the results in the fou th an ﬁfth col s . ow do diff erent loads affect the elongation ? Is the elongation doubled when the load is doubled ? Is the elongation

‘ r n a is mu 3 If so r a t ipled whe the lo d ltiplied by , p ob bly r d T the elongations are propo tional to the loa s . o test h s ou m ak an two ads and h r cor t i , y ight t e y of the lo t ei r n n n a ns and rm a r r n w m espo di g elo g tio fo p opo tio ith the , and then p rove the propo rtion to see if it is true b ut if

u a us d 10 d ff r n ads in ur x r m n r yo h ve e i e e t lo yo e pe i e t, the e

26 SIM PLE M E ASUREM ENTS

m r or in n s and n s n es meters and milli ete s, i che te th of i ch ,

every ﬁfth and tenth line being heavier than the others .

n a r usua w r - an Some point o the p pe , lly the lo e left h d

rn r i a d ori in and is a wa s mar 0 . The co e , s c lle the g l y ked

3 6 9 12 15 18 21 24 27 30 33 36 39 - n l 1 cma s cm. Elonga ti o s Sca e ,

FIG . 10.

r n a n r u the r n is axis of abscissa ho izo t l li e th o gh o igi the s ,

m a x s 2 b in a wa s m ar d X a nd the or Si ply the i of 1, e g l y ke ; ti a n r u is i f r a s or a xi ve r c l li e th o gh 0 the ax s o o din te , the s GR APHIC REPRESENTATION or RESULTS 27

f n m r d o Y a wa s a Y at u r x r m . , bei g l y ke the ppe e t e ity

uan s r r s n on X are a an d Q titie ep e e ted c lled abscissas, those

on Y ordinates . Let us illustrate the method of procedure by the da ta of x r T r r r the last e e cise . his w o k should be ega ded as a raw n ra r an as a wr n x r an d S u d be d i g the th itte e e cise, ho l ex u ll n and x ec ted with a the neat ess e actness possible .

n f or r d m r Procedure. (1) Choose a poi t the o igi n an a k

0 an d m ar ax s X and Y b rs X and it , k the e of y the lette

Y (Fig . (2) Decide which quantity you will represen t on the

a x s X ads r n a ns ou m a r . i of , lo o elo g tio ; y y choose eithe u s u n P r n in S ppo e yo let elongatio s be the abscissas . i t n r r r n ns n r eat cha acte s the wo d elo gatio ea that axis . 3) Choose a suitable scale by which the diff erent val ues d ﬂ x P r n s a re be a o on a s . a s n an d to l i the i i t the c le cho e , m ar how m uc a a v n r r s n s as s wn in k h e ch he y li e ep e e t , ho

ur the ﬁg e .

In doing this you will need to use your own judgment as to what i s cale is best and most convenient. Do not make t so s mall that on ly a. sm ort on of the s eet is occu e the com ete wor nor so all p i h pi d by pl d k, large that the paper will not b e large enough f or the work . By divid i n the r est num er to b e re resente the num er of s u res g la g b p d by b q a ,

w e can see w t sc e ma be us e . 15 ence 1 cm . ha al y d H , m ay be used to represent or any larger number of centimeters of

h let . re re m e on t on . We s ou not 1 cm sent s er num er f or l ga i ld p a all b , the sheet would n ot be large enough f or the curve ; neither should w e let it re resent muc r er n um er f or we the curve wou p a h la g b , if did, ld e occupy too little space on the paper. W might choose b ut 3 r t r w ill be easie o w o k out.

4 n c n a ns are absc ssas ads w be ( ) Si e the elo g tio i , the lo ill “ P r n the w rd ad a n ax the ordinates . i t o lo s lo g the is of s u c r r n ad n Y an d choo e a s itable s ale to ep ese t the lo s . I 2 u r nd 20 i r d this case there are 0 Sq a es a g . s the la gest loa . 28 SIMPLE M EASUREMENTS

i 1 u 1 . It s easy to see that cm . sho ld represent g M ark a av n w t n umb r ram r r n e ch he y li e i h the e of g s it ep ese ts . (5) Find a single poin t on the paper that will represen t ﬁr nd i rr nd n both the st load a ts co espo i g elongation . The ad nd it n a n are lo a s elo g tio the coordinates of this point . r Any poin t on the ho izontal line 2 cm . from 0X will

r r s n a 2 . n 1 cm . 3 cm n a ep e e t the lo d of g Si ce . of elo g

n cm . 3 w r r nt cm . tio , ill ep ese

n a n . H n an n on a v r a n cm . of elo g tio e ce , y poi t e tic l li e w r n d from OY ill rep ese t the elongation . The esired i a n r n poin t s t the i te sectio of these two lines . Use a sharp-poi nted pen and m ark this point with a dot r h m r and sma r o w a s a u ss x. ll ci cle , 0 , it ll obliq e c o , In like man ner locate and m ark points f or all other ord na co i tes . (6) Draw a ﬁne smooth line that will hit as m any as T s n i d r possible of these points . hi li e s calle a c u ve ur d r ra whether it is c ve o st ight . Do not draw a broken or wavy line from poin t to point .

Cur dra n in Discussion. ves w this way are ex tremely n T n at n r useful in scie ce . hey ofte tell a gla ce the elation w n two uan s v n w n xa m a h m bet ee q titie , e e he the e ct t e atical relation is unknown . n urv is a s ra n as in s as Whe the c e t ight li e , thi c e, it shows that the two quan tities are directly proportional ; a a e had r us l arn d in a ff r n f ct w p evio ly e e di e e t way . If a n a s w u urv i r ba poi t f ll itho t the c e , it s p o ble that an error or m istak e was m ade in obtaining the data f or that

u curv m a s r r poin t . Th s the e y e ve to detect erro s in the

r and m s a s in a u a n u r wo k i t ke the c lc l tio s . S ch a cu ve is often useful f or determining intermediate values f or one of the quantitie s co rrespon ding to gi ven values of the

r uan i . For xam we c n othe q t ty e ple, a see that a body DENSITY OF A R ECTANGUL A R PR ISM 29

n n a n 30 cm . w s ab u . which causes a elo g tio of eigh o t g , a nd the weight of a body causing an elo ngation of 1 8 cm . a w u d w a b d weighs g . Wh t o l be the eight of o y m D rm n causing an elon gation of c . ete i e it by the v n in as x r s and c urve ; also by the method gi e the l t e e ci e , compare the two results .

EXER CISE 8

D ENSITY OF A RECTANGULAR PRISM

To determine the densit o Purpose. y f

wood rom a rectan ular r ism o that substance. f g p f ,

A ba nc or a b am nc . Apparatus . Jolly la e e bala e Steel

r u s vern iered ca rs or d v d rs an d a na sca . le , lipe , i i e di go l le

m r u r rism w A s all ectang la p of ood .

M ur P r . 1 as n b r a an d rocedu e ( ) e e the le gth , e dth , n ss b s v ra m s ac m in a d ff r thick e of the lock e e l ti e , e h ti e i e n e t place . 2) Weigh the block by the Jolly b alan ce or by a beam

e urv ou av rawn . balance . (Us the c e y h e d ) (3) From the average of the m easureme nts taken: ﬁn d

nd ca u a m . v um a ass 1 c c . the ol e of the block, lc l te the of u n m rs su s an m sin c (c bic ce ti ete ) of the b t ce co po g the blo k . a ub ~ i This will be the density of th t s stance . What s density ?

4 R a a v us n n s ns t ad m r ( ) epe t the bo e, i g E gli h i e of et ic u n ts and nd n m ass x r ss d in un s 1 i , ﬁ i g the (e p e e o ce ) of

c u . in . If means are not at hand f or ﬁndi ng the weight in

un s r u w t in ram s un s . Table o ce , ed ce the eigh g to o ce (See

1 A nd x . , ppe i ) a s a urac ur w r r duc As te t of the cc y of yo o k , e e the vol ume in cubic centimeters obtai ned by meas uremen t to c ubic

s a nd v um in c ub n c s cub n r i nche , the ol e ic i he to ic ce timete s . 30 SIMPLE M EASUR EMENTS

Tabulate the data as follows

OBJE CT

METR IC UNITS ENGLIsu U NITS

Le ngth Thick ness Bread th Thick ness

Vol um e

Reduced volume

We ight

Density of

t te the k nd of wood or th n m of he u n S a i e a e t s b sta ce.

SIGN IFICA N T A N D D OU B TF UL FI GU R E S

The numbe r of ﬁgu res to be kept in a res ult often n u u troubles a stude t . H e s ally retains altogether too n m n and f e d n m a y in ultiplyi g too w when ividi g . H ow " m an d ma a s s a I ? as s w n in y eci l pl ce h ll keep he k , he fact

is not a u s t n d m a a s at all and s it q e io of eci l pl ce , he hould “ n r ask a u s n . H e s u ask H ow m e ve th t q e tio ho ld , an y " signiﬁcant ﬁgures sh all I keep ? In some cases he m ay r in rs n two ss in rs ur keep th ee, othe o ly , po ibly othe fo it depends upon the acc uracy with which the measurements n r n n r b m can k If e te i g i to the p o le be ta en . he should

r fi ur s m a n ot av an d m a ac s keep th ee g e , he y h e y eci l pl e , or he m a av six or m r or ss as cas ma y h e , o e le , the e y be . The ru s ar m c w w a ar le of ith eti , if follo ed, ill t ke c e of the DENSITY OF A R ECTANGULAR PR ISM d ecim al point ; othe r conside rations will decide the n um n r The ud n b e r of significa t figu es to be kept . st e t should r emember that n o m easurem ent can be m ade which is E k n ow n to be exactly right . rrors always occur in e ve ry m n m easure e t . Th b a i r a n one d u u e es t us ge s to et i o btf l figure only . H w v r in av ra a n umb r s rva ns o e e , the e ge of e of ob e tio , on e mo re figure m ay be retain ed th an in the indi vidual b s rva n s s a d ff r n w n o e tio , e peci lly if the i e e ce bet ee the F ur n d u s e ve ral observations is s mall . ig es followi g a o bt f ul n r not m r d u u av no n fi n o e a e e ely o btf l, they h e sig i ca ce

r whateve . H ow shall one decide what ﬁgures are sure and what a re doubtful ? In results obtained directly from observa ti on the student m ust use his j udgmen t in deciding how

m an fi ur s are sur . If f or xam as fi ur is y g e e , e ple , the l t g e b a n d b s m a n ra n a d v s n is o t i e y e ti ti g the f ctio of i i io , it of course doubtful ; and if in measuring the same thing sev ra m s r su s var fi ur s a d ff r are in e l ti e the e lt y, the g e th t i e u do bt . In results obtained by calculations b ased upon the results a n r m x r m n s ud n can see wha fi ur s obt i ed f o e pe i e t, the t e t t g e a re doubtful by underlin ing or w riting in red ink all u u fi ur r u u r ss b ut ru s III do btf l g es th o gho t the p oce , le r u n r a n d IV render this p ocess n ecessa y . The following rules should be observed in recording r e sults

e ec e rst doub ul ure. I . R j t all figur es af t r the fi tf fig If necessa r substitute ci hers or the r e ected ur es to locate y, p f j fig the decima l p oint. t ined b 1 the re ec II . In crea se the last ure re a ted fig y , if j

figur e f ollowing it is 5 or g reater than 5 . tain in roducts n o more ur es than ther e are in th III. R e p fig e f a ctor ha ving the lea st n umber of sure figures . This r ule is 32 SIMPLE M EASUR EMENTS

not in va ri able . It is better to r eta in two doubtf ul ﬁg ur es throu hout the ca lcula tions until the end when the rule ma g , y be a pp lied .

IV . R etain in quotients as many figures as ther e ar e in t e a cto n t b r a h f r havi g the f ewes n um e of sure figures . C rry the division to on e more figure than you intend to keep s o tha t ou ca bs y n o er ve R ule II .

i r V . C p hers a dded o p refixed merely f or the p urp ose of locating the decimal p oint do n ot count as significant figures

others do count.

L et us ill ustrate these rules and principles by the follow ’ ing data taken from a studen t s notebook

OBJEC T t p le block

M ETR IC UNITS lJNGL Isu U NITS

Trials Le ng th B read th Thick nes s Leng th Bread th Thick nes s

cm .

Average

m c . c . o u e 5 3 6 l . V l 2 cu in .

2 6 me 1 7 5 3 9 8 4 4 c . 0 5 3 6 uce v u 5 8 i . Red d ol c 1 7 4 1 1 3 6 c u. n

oz .

M . . e r . in . Den si ty of aple 7 g per c . c . oz . p cu

Observe how i nconsis te n t this pupil was in retaini ng r m s v n w v ﬁ ur s x r ss the v um s f o e e to t el e g e to e p e ol e , us d n n in n r while he e o ly o e the ﬁ al esult .

34 SIM PLE M EASUREM ENTS und r v n n ns n i un ru u nd e the gi e co ditio ; he ce, it s t thf l a m ll r r isleading . A ﬁgu es afte the ﬁ rst doubtful one a re n d w orthless a mean ingless .

If ab v ru s are a d a cu a ns the o e le pplie to the c l l tio , the results will be expressed in th ree ﬁgures as follows

V m e . r u . n . o u c c . o c i l ,

R e u . . or n in . ce vo ume c c o . d d l ,

e t . or oz . W igh , g

Dens t of M e . er c . c . or oz . er cu. in . i y apl , g p p

Let u r v s his r rds in E x r s s 6 and 8 the p pil e i e eco e ci e , unde rlin ing or writing in red ink all doubtf ul ﬁgures in obser vation s an d calc ulations an d apply the rules to the r wo k . E XER C ISE 9

D ENSITY OF A CYLIND ER

o determin e the den sit o Purpose. T y f

r om a c linder o tha t meta l 14 f y f , m A m nd r r r r . Apparatus . s all cyli e of b ass o othe etal T C a ers s ru s or d v d rs and d a na sca . w o lip , teel le , i i e i go l le

- u r u Fi . 1 m r s q a e c t blocks ( g 1) and a ete stick .

FIG . 11 .

n Procedure . Fi d the average dimensions of the nder b n car u to m asur its d am r at s v ra cyli , ei g ef l e e i ete e e l

iﬁ er nt nd ff r n d e places a i n di e e t di rectio ns . The diam ete r m ay be m easured either by calipe rs or by placing the cyli nde r between tw o squa re-cut blocks whos e Sides a re placed agai nst a rule r a nd then m easuring the d s an b w n the b c s D o n ot b n at end i t ce et ee lo k . egi the of DENSITY OF A SPHERE 35

u m asur but m asur b w n two mar on a r le to e e , e e et ee ks the

s ma n n s a m m r b . The s cale, e ti ti g te th of illi ete y the eye distance betwee n the blocks can also be measured by the d use of the di vide rs and the iagonal scale . (2) Weigh the cylinde r and determine its density as in

r d n x r is . Tab 2 A nd x f or the p ece i g e e c e (See le , ppe i ,

form ula f or calc ulating the vol ume of the cylinder . ) se a abu ar rm s m ar a on a 30 m a n U t l fo i il to th t p ge , ki g m f two instead of three col u ns or the dimensions .

EXER CISE 1 0

DE NSITY OF A SPHER E

o ete in e the densit o Purpose. T d rm y f f r om a sphere of tha t substance . — E . m s or x r A r Apparatus Sa e a f e cise 9 . small sphe e

Th v rni r r o f wood or m etal . e e e ed calipe or the microm

r r m u d f or m n r m ete sc ew ay be se aki g the measu e ents .

M u Procedure. (1) eas re the diamete r of the sphere in

r d ff r t d r i . 1 se ve al i e e n i ect ons If the blocks (Fig . 1) are d m u s s a b n s a m im r . e , e ti te y the eye the te th of ill ete ' (2) Weigh the sphe re an d dete rmin e its density as

b r . Ta 2 A n d x f or rm u a f or calcu efo e (See ble , ppe i , fo l

latin g the volume of a Sphere . ) Use a ab u ar rm s m ar a v n f or E x r s 8 t l fo i il to th t gi e e ci e , n r d havi ng only o e colum n f o the imensions . CHAPTER II

MECH ANICS OF SOLIDS

EXE R C ISE 1 1

UNIFOR M LY ACCELER ATED MOTION

To determine the r esulta nt o un orm Purpose . f if

n orml a cceler ated motion the two motions bein a t an d u if y , g right a ngles to ea ch other (2) F rom a study of the cur ve thus generated to derive the la ws of unif ormly a ccelera ted motion — Fi T Apparatus A P ackard M achine ( g . hi s m achi ne co nsis ts of an i nclined plane made of a glass

n n in d an s s a . A aux ar A v a a pl te ili y i cl e pl e gi e teel b ll, on e nc in d am t r un rm m t n acr ss the ate i h i e e , ifo o io o pl while it rolls dow n the plan e with u niformly accelerated m The otion . ball is m ade to t race its path on coordinate 36 UNIFORMLY ACCELER A'I‘ ED M OTION 37

r r n u n rb n r pape by olli g po ca o pape . Soft carbon trans f e r paper and coordinate paper m arked with time intervals ac r ss and s a n r va s at r o the top p ce i te l the left a e used . The plane Should be inclined until the ball will not roll

O R a r at r r «r a s the p pe the ight befo e it e che the bottom .

Procedure See that the upper edge of the plane I r a -han r r u d u is le vel . ( n e lity the left d co ne sho l be j st a trifle higher than the right or the m oti on across the p lane will not be quite uniform b ut slightly retarded by r n u m a n m n rva s war as f ictio , th s ki g the ti e i te l to d the l t h lo nger t an at ﬁ rst . ) (2) Turn the clip aside and place a Sheet of coordinate r i r 12 B u r p ape on the plane as shown n Figu e . e s e that it is in contact with the guide at the bottom and that the vertical zero lin e is exactly at the en d of the ledge T rn a n a r in a B . u the clip back gai to hold the p pe pl ce . (3) Loosen the scre w and adj ust the aux iliary plan e s o that a mark on it is exactly on the horizon tal zero n a r or so a d is xac one li e of the p pe , th t the le ge e tly If ux ar an is half inch below this ze ro lin e . the a ili y pl e

r r ac d ba on r n off w s r p ope ly pl e , the ll olli g of it ill t ike the n p ape r exactly on the ze ro li e . 4 P a a s arb n a r s ns v s d w n ( ) l ce heet of c o p pe , e iti e i e do , ove r the cobrdinate paper and test the adj ustme nt of the

ux ar an a w n ba r as f ar as a ili y pl e , by llo i g the ll to oll the L arb n a r see en d of the ledge only . ift the c o p pe to if it

r x on r n . If not r ad us aux s t ikes e actly the ze o li e , e j t the r iliary plane and replace the carbon pape . 5 h n all is r ad ac ba at - an d end ( ) W e e y , pl e the ll the left h of the auxiliary plane and allow it to roll down the plane .

— m the a r r m m ac n an d Discussion . Re ove p pe f o the hi e n c ba m v s ward m ake a careful study of it . Si e the ll o e to

n rm m n av v r ca n s the right with u ifo otio , the he y e ti l li e 38 M ECHANICS OF SOLIDS

The n rs ns m ark off equal inter vals of ti me t. i te ectio of the line m ade by the ball with these ve rtical lines tell whe re m the ball was at the en d of each equal i nte rval of ti e . Co unt the number of s mall squares from the top lin e to

a n r c ns s ma n the n s . T s e ch of these i te se tio , e ti ti g te th hi will give you the spaces trave rsed with uniformly accel

1 n r a m . c ra d m i n in 2 3 . v s te ot o , , , etc , i te l of ti e Record the results as follows

F n a v ra v c t 21 f or 1 un 2 un s i d the e ge elo i y ) it, it ,

. d d m b v n s b t. etc , of ti e y i i i g y Fin d the ﬁnal velocity or velocity at the en d of each in terval of tim e by m ultiplyi ng the ave rage velocity by 2 b caus w n a b d has un rm acc ra d m n it e e he o y ifo ly ele te otio , s 0 v av ra v or V C ar n rac ns w e e ge elocity , le i g of f tio , 2

av 2 V = v h e a Find the acceleration by di vidi ng the ﬁnal velocity v f o r the end of any given un it of time by the time t 28 and

Fin d the average of the results obtained f or a and with

' this average compute s f or the diﬁ erent time in te rvals by 2 the form ula 8 g- a t an d pl ace the results in the last m r s r h colum n . Co pa e the e esults with those of t e second c um n ol . EXER CISE 1 2

COMPOSITION OF CONCU R R ING FORCES

Purpose. To study the comp osition of two con curring or ces a nd to n d thei r r esultan t a n d e uilibra n t 50 f ﬁ q , COM POSITION OF CONC UR R ING FORCES 39

— T r r n balan c . Two f Apparatus . h ee sp i g e s pieces o d u n ﬁ s h line . A block of woo abo t a foot long h avi g a n m r h r n r m near ne e d . n ail o ook p ojecti g f o it o A cla p .

nn s Fi . 1 3 tw Procedure. Co ect the hook ( g ) of o

f ba anc b a rd 0 60 cm . n av n ﬁ rs o the l es y co 5 to lo g, h i g t passed it thro ugh a loop in the

en d of another cord 20 to 30 cm . i long . Attach th s sho rter stri ng d to the hook of the thi r bal ance . (2) Place the bala nces thus conn ected b acks dow n on the ta ass n r n s ble, p i g the i g of the ﬁ rs t two over n ails dri ven in

he ab 30 50 m r . t t le to c . apa t If the in dexes of the balances a re not at ze ro whe n in this s n a wan m us be po itio , llo ce t m ade f or their displacemen t in

all future readings . (3) Now pull the thi rd b al a n ce toward the opposite side FI G. 13 . of the table until each balance

r rs s ra un s but se a n n m is egiste eve l it , e th t o e of the x n F in s tretched to its full e te t . asten this third b al ance place by attaching it to the hook in the block of wood nd am n s d ab a cl pi g thi block to the e ge of the t le . (4) Place the n otebook or a sheet of paper under the 1 1 u n n rds and ac two d s 0 or 5 cm . j ctio of the co , pl e ot

d r u d dr a part exactly under each cor . Th o gh these ots a w

n If r n d lines to the poin t of i ntersectio . the th ee li es o n ot m at a c m m n n r a x r m n Suc eet o o poi t, epe t the e pe i e t . cess in this experiment depen ds largely upon the accuracy r c r r w r an d ca e with whi h these lines a e d a n . Sec u e the 40 M ECHANICS OF SOLIDS n b b w s or a r b ns and u e a n ote ook y eight the p pe y pi , s pe cil

- w a ﬁn e n and a n d ru r . ith poi t, thi e ged le

5 R a a a an w r a ar an d r r th ( ) e d e ch b l ce ith g e t c e , eco d e fo rce den oted by it upon the li ne running toward the n r m w r di n i n bala ce f o hich the ea g s take .

In wr n r m a nd r x r s u n iti g the e i e of the e e ci e, the st de t sho uld obser ve strictly the orde r indicated in the follow ing notes and questions (6) Designate the j un ction of the lines by A and the direction of the fo rces by arrowheads . (7) Lay off from A distances to represen t the m agnitudes r r r on n s n a n m b B of the fo ces eco ded the li e , i dic ti g the y ,

and D . (8) E xtend any one of the lines from A an equal dis

an in s r c n and s na E . t ce the oppo ite di e tio , de ig te it by Conn ect the poi nt B with the extremities of the distan ces n laid 0 5 on the two adj acent li es . ’ (9) What is the force opposite to AE called with refer en ce to the other two forces ? Why ? ’ (10) What is the force AE called with reference to its two adj acen t forces ? Why ? 1 1 a ﬁ ur has b n rm d and w a ar ( ) Wh t g e ee fo e , h t p t of that ﬁgure is AR EXER CI SE 1 3

P AR ALLEL F OR CES

o stud the com osi tion o two ara llel Purpose. T y p f p f orces .

— T 250- r n ba an s ra ua in . w S Apparatus o g . p i g l ce g d ted

- A n b ar a m r n radu 1 . . d 0 g spaces light woo e ete lo g, g ated in millimete rs and having wire loops at each end f or A r n the inse rtio n of the hooks of the balances . ho izo ta l rod upon which the balances m ay be s uppo rted (Fig .

A set of weights .

42 M ECH ANICS OF SOLIDS

EXE RCISE 1 4

THE PEND ULUM

To show the rela tion between the len th o Purpose. g f a p endulum and its time 76 — . m ﬁne r a . A ar u Apparatus So e th e d l ge b llet . A r a - n Th stop watch o clock with a s weep second ha d . e clock sho uld have an electric attachment and be connected with a telegraph sounde r so as

n v r Ca r . A c to sou d e e y second . lipe s lamp

Fi 15 w s ua r a ws . A rod Fi . 16 ( g . ) ith q e j ( g ) r n n ndu m f or meas u i g le gths of pe l u s .

— D n o a w r Caution . o t llo the a c of swing be r a r t an a b u 1 to g e te h o t 1 6 of the length of

the pendul um .

Procedure. (1) M asur am r 1 e e the di ete of

the bullet . 2 Tie a r a b u 2 ( ) piece of th e d a o t m . lo ng

Em ' 15 ° to the bullet and suspend the b ullet from the

m a wn in F ur 15 m a n n u um r cla p s sho ig e , ki g the pe d l f om

200 m . n 150 cm . to c lo g . 3 M ur th n d ( ) eas e e le gth of the pen ul um . To do this hold the end of the rod A against the lowe r edge of the

am n s d bar B u un us t u s wer cl p, the li e the p til it j t o che the lo

rf l Fas n bar set r w . su ace of the b u let . te the by the sc e Place the rod on a table and m easure by two meter sticks

r n r d ar u ra the distances f om the e d of the o to the b . S bt ct T h from this le ngth the radius of the bullet . his gives t e length of the pe ndulum becaus e the ce nter of the bullet ma be ca led ce n r of sc at on the ndu um y l the te o ill i of pe l . TH E PE NDULUM 43

4 D rm n m ndu um a i ( ) ete i e the ti e of the pe l , th t s, the m r u r ma ti e eq i ed to ke one s wing . This is done by ﬁnd in g the time required f or a large nu mber of s wings or v ra n s and v d n s m b n umb r ib tio di i i g thi ti e y the e of swings .

M ethod o Takin the m — F r f g Ti e. i s t learn to express

m r r . For xam ns a r r ti e p ope ly e ple , i te d of eco ding a time 15 m 1 ’ as in . and 2 . 10 sec c w r 9 hr . 44 of o lock , ite it min . 4 8 s c L t e . e the whole class practi ce until all can record c or rectly the time at which the i nstructor taps the table w ith a pencil . The re should be a heavy ve rtical line just back of the

n u um at r s . n is s w n n pe d l e t Whe it i gi g, the passage of the pendulum thread past this mark is called a coinci A n dence. coi ciden ce between this pen d ulum and the c c ndu um a s urs w n a r lo k pe l l o occ , he the tick of the l tte o urs at th sam m rm r cc e e ti e as the fo e passe s the li ne . Let one person (A) count the swings of the pendul um w hile another (B ) records the times of beginning and B r n r ending the count . efo e starti g let them ag ee on a b u how m an v b ra ns w be un d sa ab u 50 o t y i tio ill co te , y o t r Th un u d b n nd end o about 100. e co t sho l egi a with a cc

n n n ndu um an d nd m i cide ce betwee this pe l the clock pe ulu . Let A watch the pe ndulum and when a coi nciden ce o urs a s na B b a n r w a ru er cc , gi ve ig l to y t ppi g the ﬂoo ith l , at the sam e time begi n ni ng the count with the word “ r and un n 1 2 3 . at a suc d n as ze o co ti g , , , etc , e ch cee i g p sage of the pendulum by the m ark . Let B a and w n ars s na w tch the clock, he he he the ig l r m A n t xa s n and m nu a nd r rd f o , o e the e ct eco d i te eco the m b n n n ti e of egi i g . n r a s 5 or 100 v bra ns A When the cou t app o che 0 i tio , let give a w arning signal to B so that the latter shall be n is r ad end his un wa tching the clock . Whe A e y to co t,

h m do at n d n w n u um let i it a coi ci e ce ith the clock pe d l , 44 M ECHANICS OF SOLIDS tappin g the ﬂoor at the time so that B can note and re can s un at an cord the time of ending . A clo e the co t y

n xa at 50th or 1 00th coin cidence he pleases ( ot e ctly the ) , n m provided B is ready to hear his signal and ote the ti e . r At the n ext trial A and B should exchange wo k . It is probable that your ﬁrst res ults will not be at all n n w r un ou at as r accu rate . Co ti ue the o k til y get le t th ee results that agree fai rly well ; the n take a shorte r pendu

r r . If m rm s a an r lum and epeat the wo k ti e pe it , t ke othe n le gth .

If a s wa is us w r is m u s m r . ar top tch ed , the o k ch i ple St t

a at a n n at the sam m s ar n the w tch coi cide ce, e ti e t ti g the " count with the word zero . After countin g about 50 or 100 br ns s wa at a n n r m m vi atio top the tch coi cide ce, e e ber ing the count at which you stop . Reco rd the results as follows

R A D I U S O F B UL L E T

L as oTu TIM E t S ARE R OOT , , Q U W IIO L N O R o . P or O NE O P LE NG TH T IME V IB R AT IO NS PE ND UL U M V I B R AT IO N Vt

n Discussion . I the six th column draw a li ne under the results Obtained f or any given length and place the a ver a e Of r su s b w g the e lt elo it . If the res ults in the last column are cons tant (as f ar as sur ﬁ ur s f or all n s n ou a v d r the e g e ) le gth , the y h e e i ved a

r r n a r r . p opo tio . St te this p opo tion in words Ca s ns an in a um n The m ll thi co t t the l st col K. ti e of a pendul um of a ny length divided by the s q uare root of its

’ n s u d ua K in ur a or J K ‘ le gth ho l eq l yo loc lity , If \/l E THE PENDULUM . L NGTH OF ARC 45

ou n w t and ou can ﬁn d l . Fr m ur va u y k o K, y o yo l e f or K ca u a l w n t : 1 nd u ﬁn d n lc l te he , a th s the le gth ’ n m of a seco d s pen dulu f or your locality . ’ F rom the value Of l f or a secon d s pendulum just Oh tained and the form ula calculate the value of g f or ur a yo loc lity .

EXE RCI SE 1 5

THE ENDULUM LENG H OF A R P . T C

' Purpose . To show the ej ect of amp litude on the time of vibr ation of a p endulum

. am a f or Ex r s 14 Apparatus S e s e ci e .

x Procedure. This e perimen t should be completed at one session unless it is certain that the pend ulum will not r d be distu be . 1 ndu n m r n Its x ( ) M ake a pe lum about o e ete lo g . e act n is n ot m r an b ut sam n m us be re le gth i po t t, the e le gth t p r r u h s e ved th ougho t t e experimen t . 2 D rm n t m r u r f or one v ra n as ( ) ete i e the i e eq i ed ib tio , i n r n x r m n arc r u w the p ecedi g e pe i e t, the th o gh hich the pe ndulum swi ngs being less than (3) Start the pe ndulum s winging through an arc of u an d rm n m f or one v bra n as a bo t dete i e the ti e i tio , befo re . 4 D rm ne r d are b n ab u ( ) ete i the pe io , the ei g o t It is not sufﬁ cien t in any case to ﬁ nd the time of one ra n a n m f or 100 v b ra ns us n vib tio by t ki g the ti e i tio j t o ce , b ut the average of at least three determinations sho uld be taken . The number of degrees in the arc can be determined approximately by comparing the chord of the arc with 46 M ECHANICS OF SOLIDS

n n u um r m m r n a w n the the le gth of the pe d l , e e be i g th t he chord of the arc equals the le ngth of the pendulum the arc is Exact measu rements of the arcs are n ot

required . Tabulate the data as follows

TIM E or ON" V I BRATION

Fin d the a verage time f or all arcs less than f or all arcs about f or all arcs about and compare the

times of these three averages .

EXER CISE 1 6

MOMENT OF A FORCE

. To test the rinci le o m om ents the la w o the Purpose p p f , f

lever a nd to stud the r ela tion o the wei ht o a bod to its , y f g f y

center of gravity W .

— r m v n a n n Apparatus . A leve cla p ha i g k ife edge a d stan d upo n which the kn ife edge rests and t urns freely

A m r h . m . A mete r stick . set of et ic weig ts A A r or r r m platform balance . b ass clip ide with the ete r

stick .

1 r Procedure. ( ) Weigh the meter stick with the b ass

clip . (2) Slip the meter stick th rough the clamp and ﬁ x the

x 50 m ar . If m k nife edge e actly at the cm . k the eter stick will n ot e xactly b alance horizontally on the knife d a b rass u n so a w and e ge , pl ce the clip po it th t it ill , keep in sam s n r u u x r men the clip the e po itio th o gho t the e pe i t . M OMENT OF A FORCE 47

m r s w ba an w u the n If the ete tick ill l ce itho t clip, the the la tter should be dispensed with and should not be weighed

w ith the mete r sti ck . The cen te r of gravity of the meter stick is j ust below the kn ife edge . Call it 0 .

3 us n a r a a 100 . w ( ) S pe d by loop of th e d g eight W, bar at a d an d r m an us nd on the right of the ist ce l f o 0 d s pe

' a 200 . w on at a n t w g eight Wl the left poi t a hich it will a n ex ctly bala ce the weight on the right . Record its stan r m un r d F nd m m n di ce f o 0 de r i the o e t of each r fo ce .

4 R a a v a n ﬁrs w at an h r ( ) epe t the bo e, pl ci g the t eight ot e o r poi n t n the ba .

5 nd a 50 . 1 w ( ) Suspe g weight and a 00 g . eight at

ff r n n s on r bar r c rd n di e e t poi t the ight of the , e o i g the r s v w s and d s an s und r IV d a nd W d e pecti e eight i t ce e I, l , 2, z, nd ﬁn h n on w r h 200 w a d t e poi t the left he e t e g . eight m m m n r will e xactly balance the . Find o e t of the fo ce on um m n r the left and the s of the oments o the ight . 48 MECHANICS OF SOLIDS

n 1 . 6 R a a v us a 00 w and a 50 . ( ) epe t the bo e, i g g eight g t r n n on th r and 20 weight a diff e e t poi ts e ight a 0 g . weight

nd a 20 . w on a g eight the left. (7) M ove the knife edge toward the left end of the

bar sa 20 or 25 cm . and as n . T n ﬁnd a n on , y , f te it he poi t

w r 200 . w or a 1 00 the left he e a g eight g . weight will r r exactly b alance the uler . Reco d the weight of the ruler and the distance from 0 to the kn ife edge respec tivel as W and d on r . R a s a n y 1 1 the ight epe t thi , pl ci g the rd r k nife edge at another point . Reco the esults as follows :

WEIGH T OF M ETE R STIC K_

Th om nt o a o ce is ts m o t Discussion . e m e f f r i i p r an ce in roducin rotation a bout an axis a nd its am un or p g , o t meas ure is the p roduct of the f orce by the lever arm on which it acts What relation do you discover between the momen ts of the forces on the right and those on the left ? Those on the right which produce rotation i c wis d r n are a d iti e m m n s and n a clo k e i ectio c lle pos v o e t , those on the lef t which cause rotation in a coun ter-clockwi se di rection are called negative momen ts . Wh at is the al geb raic su m of all the m om e nts on the bar ? To what class does this leve r belong ? Show that the data taken illustrate the law of the le ve r .

50 MECHANICS OF SOLIDS

rwwv essary to pull the car up the plane at unif orm sp eed af ter the -ear a us t o s ar b ut it is star ted. Give little p h t t it, keep the hands of the string and p an in making the

test. 3) Likewise ﬁnd what weight in the pan will allow the I5 roll down the plan e at a unif orm sp eed it is

started. 7 , 1 l

n d tan 80 cm . pla e a is ce of , Fr m n the plane by B . o

B m ans ru m asur v r a , by e of le, e e the e tic l B distance to the is line by B 0 . 0

v r a r s Of car or s u will be the e tic l i e the , goe p

an 80 c m . w at sam m s the pl e , hile the e ti e the

w s or P a v r a 80 cm . eight , , f ll e tic lly (5) D ra w in yo ur notebook a diagram in which the dis s B C and A0 an d an at A are rre tance AB , , the gle co ctly r r s n d and r r on AB and B C s an s he ep e e te , eco d the di t ce t y represent . Record the results as follows THE INCLINED PLANE 51

Di cus io n car i n u in s n. s w s Whe the goi g p, the eight the pan is g reater than it should be by the amo unt of fric t on v r m w n car is n d wn is ss an i o e co e ; he the goi g o , it le th

it s u am un r c n v r m . H n ho ld be by the o t of f i tio o e co e e ce, ta king one half of the sum of the two averages eliminates the friction and gives the true fo rce necessary to m o ve u n ff r n w the car p the plan e . O e half the di e e ce of the t o

m r averages gives the a o unt of the f iction . ’ A r n N w n s ﬁ rs law m t n w n car cco di g to e to t of o io , he the has un rm s d two rc s an and w s and ifo pee , the fo e , the p eight w car ac n wn an xa bal the eight of the ti g do the pl e , e ctly n a r a ce e ch othe . W l

C m ar two ra s . If are ua o p e the tio , 13 h they eq l a s f ar as he sur ﬁ ur ou can rm a r r n t e g es go , y fo p opo tio r m i m u r f o them . State n wo rds the eaning of s ch a p o r po tion . n n or Whe the car mo ves up the plane 80 cm . the pa o w r P a 0 m H n the w r P d 80 or p e f lls 8 c . e ce po e oes P x

P x l un s w r . At sa m m car is d , it of o k the e ti e the lifte v r a a s an B 0 or h an d w r d n u n e tic lly di t ce of , , the o k o e po - it is eq ual to W x h 86 H ow do these two qua ntities of work compare ? Wh at law is illustrated ? Compute the eﬁiciency $4 04) Of the plan e considered

as a m a h n . T s m a d n d v d n h c i e hi y be o e by i i i g W x ,

w is us u w r n b P F x l . F re re hich the ef l o k do e , y ( ) p s e nts the friction and hence (P + F ) x l i ncl udes the us eful work done by the pan a nd weights as well as the n w ork wasted i overcoming friction . D raw a ve rtical lin e on your diagram downward from the line AB of the right length to represent W: Resolve n n two m n n s one r nd cu ar AB this li e i to co po e t , pe pe i l to and one on AB . Measure the com ponen t on AB an d

rm n r r r s n s . C m ar i dete i e the fo ce it ep e e t o p e t with P . 52 M ECHA NICS OF SOLIDS

EXER CISE 1 8

ELASTICITY

o t e re ation b t the bendin a Purpose. T show h l e ween g of ruler an d the f orce app lied to bend it 141

A r Apparatus . ule r or m ete r stick clamped ﬁrmly to h a ﬁrm support (Fig . T e ruler has a pin inse rted

FIG. 19 .

in its end as an n x and a h n ar its r end r m i de , ook e f ee f o which a scale pan is s uspended . A meter stick is s up r v r ca n ar end ru r or m rr r po ted e ti lly e the of the le , the i o m a b A scale of the Jolly balance y e used in its stead . set of weights .

1 n r Procedure. ( ) Read the position of the pi o in dex on s a av d n ara ax and s m a n n s of the c le, oi i g p ll , e ti ti g te th r millimete s . 2 P l 0 w in an nd n r ( ) lace a 0 g . eight the p a agai ea d r n T n r m v and reco d the position of the i dex . he e o e the n n n i n nd x If weight a d agai ote the posit o of the i e . it d s not r urn it r na s n Obs rv w oe et to s o igi l po itio , e e hethe r f m it does so after w aitin g a ew oments .

u 2 . 30 . u 1 R a s n 00 0 tc . 0 3 e 0 0 . ( ) epe t, i g g , g , , p to g , al ways readi ng the position of the index after each load is d remo ve . ELASTICITY 53

Record the results as follows

P O ITION or INus x AV ERAGE DE PL BO’I‘ ION LOAD S , , e u No LOAD W ITHOUT LOAD OR 1)

— r n um rs as umn con Di scussion . A e the be of the l t col s a n ? If so wha s s n ? t t , t doe it ig ify n ad and ns u n r na Usi g the lo s deﬂectio , plot po coo di te r m pa per a curve showing the elation between the . Si nce the load and the elastic force of the ruler are in

e u r um are ua . a r a n x s s b w n q ilib i , they eq l Wh t el tio e i t et ee ’ ela s tic force of the ruler and the load ? Is R ooke s law ve r iﬁed by this experiment CH APTER III

MECH ANICS OF FLUIDS

EXE RCISE 1 9

DOWNWAR D PRESSURE IN LIQUIDS

o show the rela tion o own ar r Purpose . T f d w d p essure in a liquid to dep th

. A n r a ass ar a u in Apparatus cyli d ic l gl j bo t 8 cm .

am r and 40 m . ha vi n —3 di ete c deep, g 1 W

section paper ruled in mi llim eter s or in twentieths

an h. A a u ab u 5 m n an d of inc gl ss t be o t 7 c . lo g

4 m m . ns d am e r n as s wn in F ure 20 i i e di et , be t ho ig , the tube being ﬁlled with merc ury at the bend to

a d Of b u cm A m f r n h epth a o t 3 . cla p o holdi g t e ub ns s n two s Of w a t e, co i ti g of piece ood e ch piec e ha vi ng a sh allow groove across the middle Of one

side . These pieces are held together by a rubbe r band ub n a d in r , the t e bei g pl ce the g oove between

them .

Procedure. (1) The jar bei ng nearly full O f wa r a ub in c m n u r te , pl ce the t e the la p a d s ppo t it in the jar by resting the clamp across the top

of the jar . The tube can now be moved easily up and d wn and w be ld at an d s r d s n o ill he y e i e po itio .

2 t m u b ab u 15 m ) Wi h the o th of the t u e o t c . b w s ur ac wa r n n elo the f e of the te , ote the positio

s ur a wa r on s a . To on e FIG . 20 . of the f ce of the te the c le DOWNWAR D PRESSURE IN LIQ UIDS 55

o n u u w ard Fi . 20 at s sur a l oki g obliq ely p ( g ) thi f ce , it a ars a r an m rr r R a s the ppe like b illi t i o . i e eye gradually

u n n s h us ra s m rr r- sur a til the li e of ig t j t g ze the i o like f ce , an d n n its s n on the ote po itio the scale . (3) Note the height of the m ercury surface in the sho rt

a rm u ha is n h r of the t be ; t t , the poi t w e e the m ercury and

w a r m in u All air m u r te eet the t be . the st be em o ved from s r arm u the ho t of the t be . This measuremen t can be taken best by wrappi ng a band of paper with a straight edge about the jar an d sliding it d own un til its upper edge is on

r u r a level with the me c y . Sight th rough the wate r to the edge n of the paper o the opposite side . The paper m ay be held in place r r nd by a ubbe ba . (4) In the sam e m anner oh

FIG . 21 . s e r ve the height Of the m e rcu ry in n arm ub estimatin ten ths d the lo g of the t e , g of a i vision n l h r m r m n n in this a d a l t e othe eas u e e ts take . (5) M ove the tube down a f ew centim ete rs a nd repeat ab v m asur m n s not m n ﬁrs on e the the o e e e e t , o itti g the t ,

r r s urface of the wate in the ja . R ecord the data as follows

SU RF A CE or MER CU RY IN M E RCUR Y IN D E PTH or E L EV ATION EL E V ATIO N P E R W A TE R SIIORT ARM LONG AR M WA TE R or M E R CU R Y UN IT or DE PTH

The q uantity in the fourth column is the depth of water x r n r ssu r on m rcur and is u nd b a n e e ti g p e e the e y, fo y t ki g the diff eren ce between the quantities in the ﬁrst tw o colum ns . 56 M ECHANICS OF FLUIDS

E XER CISE 20

L ATERAL PR ESSUR E IN L IQUIDS

l a n Purpose . To show the relation of a ter l p ressure i a li ui to q d dep th.

— am f r Ex r s 19 x Apparatus . S e as o e ci e e cept a th ub i n n a t ra a s th t e t e s be t so as to ope l e lly , i shown n Figure 22 .

Procedur . l The r dur is in nera e ( ) p oce e , ge l,

sam as in r d n x r In the e the p ece i g e e cise . this

as w v r w a r an d m r ur m us c e , ho e e , the te the e c y t Th r u not come togethe r in the tube . e p ess re of the w ater will be transmitted to the mercury by n d ir the i close a . One meas urem en t more than was taken in that x r s w be n ssar — of e e ci e ill ece y , the depth

n r r n n To do the ce te of the late al ope i g . t s m a ur u r d arm hi , e s e to the ppe e ge of this

an d n add to r us u the this the adi of the t be, its diameter having been pre viously foun d b a rs y c lipe . The table f or this exercise requires one

F‘G 22 ° additional col um n f or the depth of the a ra O n n l te l pe i g .

na C ISB 2 1

UPWARD PR ESSUR E IN L IQUIDS

Purpose. To show the r ela tion of up wa r d p res r i su e in a l quid to depth.

Apparatus . S ame as f or the preceding exercise xc a u O ns d wn ward as s wn in e ept th t the t be pe o , ho i F g ure 23 .

Procedure . 1 P r c d as in ast x r s ; p m ( , 23 ) o ee the l e e ci e ,

M EC ANICS OF F UIDS 58 . H L

i the ivory poi nter h. Why is th s adj us tment necessa ry 1 7s) ? (4) Adjust the vernier to the top of the mercu ry by urn n m ad D Fi It w r t i g the illed he ( g . s lo e edge s u be an n m r ur so ho ld t ge t to the top of the e c y, that a white background can be seen on either side

ut n t n r m r r b ot a the ce te of the e cu y su rfa ce .

R a in o n s and n m t rs e d the height b th i che ce ti e e . (5) Take the temperature by the ou tside

thermometer .

6 In Ta 8 A nd x ﬁnd r ( ) ble , ppe i , the co r n f or m era ur us n a und ectio te p t e , i g th t fo by r n h n r m n the thermom ete o t e i st u e t . If the ° ° m ra ur is a v 32 F . or 0 C . su ra te pe t e bo e , bt ct

this correction ; othe rwise add it . Why ? (What eff ect does temperature have on the density of mercu ry ?) 7 In Tab 9 A nd x ﬁn d r ( ) le , ppe i , the co r n f or va n a v sea v us n h ectio ele tio bo e le el, i g t e temperature given by the outside therm om

Add s . ? As r a n eter . thi Why ( ce t i the ele

va tion from the instructor . ) (8) M ake Observations f or s everal consecu

v a s at sam ur da a n ti e d y the e ho of the y, d record the results as follows :

FIG . 25 .

E R E O S O N R P R P N I E U O T N T N I T E O A O T I R I A H M T T G I C E C V I T P E E E E N R M R L H E R E R E C O T O C C BOYLE’S LAW 59

(9) Obtain the United States Signal Service report f or h m da a n ar st sta n and a m in the t e sa e ys t the e e tio , pl ce the l m a ur r su s w em and ex l ast column . o p re yo e lt ith th , p lain any dis crepancy if you can .

EXER CISE 2 3

BOYLE ’ S LAW

' o d the e ect chan e o ressure on Purpose. T stu y j of g f p ’ h olu o as or to ver B o le s L aw t e v me f a g , if y y ’ M elde s M ethod . 1 r . A r m n a ou 1 0 cm Appa atus piece of ba o eter tubi g b t . n s a d at one end Fi T s ube n a ns near lo g, e le ( g . hi t co t i its center a th read O f mercury M about l n 45 cm . o g which i ncloses som e air BF between it and the c losed end of the t A rr ube . n a ow strip of paper graduated in c entimeters and milli m eters is attached by paste Or glue to the tube exten ding from its sealed end up b n m r ur eyo d the e c y . FIG. 26. This paper scale en ables us to read the length of the air column inclosed by u i the mercury . Since the cross section of the t be s u ni

rm s n h is a n as um air . The fo , thi le gt t ke the vol e of the tube is held at its cente r by a clamp L which turns on a horizon tal axis s o that the tube can be turned through 60 M ECHANICS OF FLUIDS

n bar m r The a u n h an a gle of A o ete . t ble po w ich n d xa the wo rk is do e shoul be e ctly level .

n the u is v r a G b n u r s r Whe t be e tic l, ei g p, the p es u e on the air B F is measured by the barometer reading the , length Of the mercury th read AB . When the tube is r a n wn r ssur on BF is m a r ve tic l, G bei g do , the p e e e su ed by the baromete r AB . n u is n in d an d A is r an th Whe the t be i cl e highe th B , e pressure is the barometer readi ng t he diff erence be w n AD and B E or A O but w n A is w r an B t ee , he lo e th , the pressure is the barom eter readi ng the diff erence T between AD and B F . his follows because pressure of an u n s on its d and the y liq id depe d epth, depth of the r r i n It m me c u y s the dista ce A 0 . ( ight be better to call the diff erence between AD and B E negative when A is w r an B and n a wa s add a ra a h lo e th , the l y it, lgeb ic lly , to t e m baro eter reading . )

Procedure. 1 R ad ar m r in n m r ( ) e the b o ete ce ti ete s, n ot m a n an rr ns f or m ra ur Or va n ki g y co ectio te pe t e ele tio , because the temperature of the me rcury of the barom eter i sum sam a a in s as ed to be the e s th t the tube . (2) Place the tube in a ve rtical position with the open end u and m asur m r s G p, e e by the ete tick the heights n A r of A a d B above the table . lso ead the length or m i a r vol u e of the a r B F by the p pe scale . (3) Turn the tube carefully by the clamp L a f ew

r s and a a n m as ur AD B E and B F . deg ee g i e e , , Co ntin ue this p rocess un til the tube is agai n vertical Y u 1 with G down . ou should have abo t 0 diff eren t rea d F m ings . or one Of the let the tube be in such a pos ition

a B F is us w w a was at rs f or an r th t j t t ice h t it fi t ; othe , r m s w a w as at rst and f or an r th ee ti e h t it fi ; othe , four times what it was at fi rst . Record the results as follows DE NSITY OF WATE R 61

B A R OM E T E R R E A D ING

V OL UME or AIR A D - B E B F OR V

io It is a law m a m a s a w n Discuss n. of the tic th t he the r du two ar a s is ns an two uan s p o ct of v i ble co t t, the q titie r u P con a re i nversely proportional . Is the p od ct x V s an at as as f ar as sur ur s ? t t, le t the e ﬁg e An other way to consider this is to notice whether the p ressure is 4 as great as at ﬁ rst when the volume is 2 tim es as great ; 4 as great when the press ure is 3 times as g re at ; etc . E XER CISE 2 4

DENSITY OF WATER

o determine the densit o water . Purpose. T y f — r A a an . A bur . sma b a . Apparatus . ette A ll e ke b l ce r A thermom ete .

1 a a r is an and dr Procedure. ( ) See th t the be ke cle y, a nd then weigh it . 20 40 (2) Measure out in the beake r from to cc . of

distilled water by means of a burette . ur w wa r ar u w n To do this, ﬁll the b ette ith te , c ef lly ipi g T n a w off any on the outside of the instrumen t . he llo s ome water to run out of the burette by the stopcock into a waste dish until the surface of the water is below the ze ro at the top and all the air bubbles a re driven out of the N r a ar s lower end of the burette . ote with g e t c e the po i r on s a and n tion of the su rfaceof the wate the c le , the

h b a r . a llow the water to be m easured to ﬂow into t e e ke 62 M ECHANICS OF FLUIDS

Read again the amount of water in the b urette ; and by subtracting the ﬁrst reading from the last obtain the vol ume wat r in the a r of e be ke . (3) Weigh the beaker and water and then take its temperature (see n ote in Exercise 51 in regard to read in th rm m r g e the o ete ) . Stir the wa ter carefully with the the rmometer until the mercury is stationary before read n m r u i g the te pe at re . (4) Fin d the weight of the water and calculate its den it in Ex r s y as e cise 8. Record the data as follows

Weight of empty beaker Weight of beaker and water Weight of water taken Temperature of the water Fir st reading of the burette Second reading of the burette Volume of water taken Density of water found Dens t of w ter at ven tem er ture see e 4 A en x i y a gi p a ( Tabl , pp di ) Error Percentage of error

If m rm s the av ra Of s v ra d rm na n ti e pe it , e ge e e l ete i tio s shoul d be foun d and then the e rror and the percen tage

r of error dete mined .

E XER CISE 2 5

B AN H E IN I LE F AR CHIME D E UOY T FORCE . T PR C P O S

— d h lation betw en the loss o wei ht Purpose. To ﬁn t e r e e f g i of a body immersed in a liquid and the liquid it d sp la ces .

— d a r . w Apparatus A beaker ﬁlled with distille te . A h ﬁn ax d r ad . T m Jolly balance . A piece of e w e th e e e

o nd r wh d ns w as d rm n d in E x r s 9 talli cyli e ose e ity ete i e e ci e .

T n r Procedure. aki g the cyli nde whos e weight an d v um w r un i n E x r s 9 ﬁ nd it w w i ol e e e fo d e ci e , s eight h le SPECIFIC GRAVITY OF SOLIDS 63 i t is mm d rs in d s l d wa r . T i e e i ti le te o do this, either sus p e nd the cylinder from the under side of the balan ce pan b a r ad or a an has a an ass a y th e ; if the b l ce p of gl , pl ce i t in that . In the la tter case the index reading with no

Record the data as follows

Weight of the cylinder in air Weight of the cylinder in water Loss Of weight in w ater Volume of the cylin der

Di — r scussion . What volume of wate was di splaced by the cylinder ? What weight of water was displaced by the cylin der ?

W hy See Exe rcises 9 and 24 . H ow does the loss of weight in water compare with the w eight of the water displaced ? H ow many times denser is the cylinder than water ? The answer to the last question will be the speciﬁc Of u an m s n n r gravity the s bst ce co po i g the cyli de . What i s speciﬁc gravity ? H ow can the volume of the cylinder be determined from the data of this exe rcise and the preceding exe rcis e ? Compare the vol ume so obtained with that obtained in E x r s 9 an d rm n rr r and er n a e ci e , dete i e the e o the p ce t ge of m n rr e rror assu i g this to be co ect .

E XER CISE 2 6

SPECIFIC GRAV ITY OF SOLIDS DENSE R ‘ THAN WATER

— o d t rmi e the c v Purpose. T e e n sp eciﬁ gra ity and the n sit o bra ss or other meta l 1 84 1 88 de y f ,

— a an or m Apparatus . A Jolly b l ce a bea balance . A f d d r . A c o ax d r gl ass of istille wate pie e w e th ead . A piece M ECHANICS OF FLUIDS

rass or r subs an w s s ra i of b , othe t ce , ho e peciﬁc g vity s to r n be dete mi ed .

r . d in r Procedu e Weigh the soli ai . (2) Weigh the solid while it is im mersed in dis tilled

wa r . To do s r sus n b a r d r m te thi , eithe pe d it y th ea f o und r s d the ba an an or ba an ha the e i e of l ce p , if the l ce s two ans one a v r a s d in r p , bo e the othe , pl ce the oli the lowe

t e a t s t pan to weigh it in wate r . I n h l t er ca e he lower p a n should be immersed in water to a bout the same dep th through out the entire exp eriment. From its weight in air and in water compute the den s ity of the solid and compare with that of water in accord r ance with the p inciples of the last exe rcise .

— To rr f or rr r du R emark s . co ect the e o e to the fact that °

wa r us d is n ot at 4 C . m u n un the te e , ltiply the de sity fo d by the density of water at the te mperat ure at which it w as in 4 T be un Tab A nd x . us . s m a To ed hi y fo d le , ppe i ﬁnd m un rr r ur r su s m ar h m the a o t of the e o of yo e lt , co p e t e 3 with those given in Table . n ba an is us n a ns the Whe a Jolly l ce ed, the elo g tio of

r n n m a us d m du us S r n n ot sp i g alo e y be e , the o l of the p i g

n d r d T us in ab v x r is a re re being co si e e . h the o e e e c e, if p n n d x r d n w no ad b n d x r ad n se ts the i e ea i g ith lo , the i e e i g

d in air and c a w ad in wa r with the loa , th t ith the lo te , — — then (b a ) di vided by (b c) will equal the Speciﬁc gravity of the substan ce .

T m a be x a n d as ws m r r s n n his y e pl i e follo , ep e e ti g the modulus of the sp ring i m(b a ) weight in a r . n m (c a ) weight i water .

c a m b c ss w in w a m(b a ) m ( ) ( ) lo of eight ter .

H m b a m b c b a b c s e nce , ( ) ( ) ( ) ( ) peciﬁc gravity .

66 M ECHANICS OF FLUIDS

n r in wat r and mm rs r u u the cyli de e , keep it i e ed th o gho t

entire e xe rcis e . 3 If a b am an i us un r s n r ( ) e bal ce s ed, co te poi e the cyli de

h . If a ba an is us a n x r a wit shot Jolly l ce ed, t ke the i de e d r ing with the cylinder in wate . (4) Place the wax in the scale pan above the cylinder

nd w or a n x r ad n . a eigh it, t ke the i de e i g (5) Fas ten the wax to the cylinde r by thrusting the n n d r n and mm rs wax and n r poi t of the cyli e i to it, i e e cyli de r in wate . 6 If a b am ba an is us d a su ﬁ n w s ( ) e l ce e , pl ce f cie t eight in the pan to which the cylinder is attached to exactly T restore the equilibrium . hese weights will equal the

weight of the water displaced by the wax . If a Jolly

a an is us d ta nd x r a n a a n . b l ce e , ke the i e e di g g i The rem arks Of the last exe rcise in regard to correction f or tempe rature and method of calculation will apply to

s x r s . In a t w t J ba an r thi e e ci e f c , i h the olly l ce the ope a tion s and calc ulations are exactly the same as in the las t

x r e e cise . n a b am ba an is us w in air d Whe e l ce ed, the eight divi ed by the weights added to restore the eq uilibri um will give h h t e speciﬁc gra vity . W y Use sam a u ar rm a f or as x r the e t b l fo s the l t e e cise .

EXE R C ISE 2 8

SPECIFIC GRAV ITY OF L IQUIDS BY W EIGHING A SOL ID IN TH EM

t i t Purpose. To de er m ne he sp eciﬁc g ra vity an d density of alcohol or other liqu ids A . ba anc or m Apparatus Jolly l e a bea balance . A

c a ass rod or a ass s r f or a s n pie e of gl gl toppe i ke r . A u d w s s c ra v is to be d rm n d liq i ho e pe iﬁc g ity ete i e , s uch SPECIFIC G RAVITY OF L IQ UIDS 67 a r b n n r s n a s n or su ur a . glyce i e , e zi e, lcohol, ke o e e, lph ic cid A r the mometer .

WI TH A BE AM B A . AL ANCE

Procedure. 1 F nd w s n r n r ( ) i the eight of the i ke i ai . 2 F nd w s n r in wa r u n n ( ) i the eight of the i ke te , s spe di g a r ad or the u d is an a d b a a n um it by th e , if liq i ci , y pl ti w r r m nd r d f n u s O a n . i e , f o the e i e the b la ce pa 3 D r s n r and ﬁnd its w in u ( ) y the i ke eight the liq id . 4 Ta th m ra ur r ( ) ke e te pe t e of the wate .

B . WI TH A JOL L Y BAL AN CE

1 Ta nd x r ad n w n i i s r n a r a . ( ) ke the i e e i g ith the i ke , 2 Ta nd x r a n w s n r in wa r b ( ) ke the i e e di g ith the i ke te , . (3) Take the index reading with the sinker in the

u d c . liq i ,

(4) Take the temperature of the water . If the liq uid an d the wate r have been standing f or some t m in the sa m r m m ra ur ma be i e e oo , the te pe t e of both y um d e sa m u r u rr r a ss e to b the e witho t s e io s e o .

B r rans rr n s n r r m one u an r efo e t fe i g the i ke f o liq id to othe , nd dr r al ways wash a y it ca efully . Record the results as follows

D E NSIT Y IN D ENSIT Y IN SUBSTANCE GR AMS P ER OUNC ES P ER CUBIC CE NTIMETER C UB IC INC H

Di cu ion . If m r r s n s m du us Of s r n s ss ep e e t the o l the p i g, then m(a c) loss of weight Of sinker in water and m (a b) loss Of its weight in the othe r liquid . By the p rin ciple of Archimedes these losses are the Weights of 68 M ECH ANICS OF FLUIDS

H n a c u ds . m equal volumes of the two liq i e ce , ( ) m(a b) or (a c) (a b) the Speciﬁc gra vity of the liq uid . EXER C ISE 2 9

SPECIFIC GR AV ITY B OTT LE

o determine the s eci c ra vit o li uids b Purpose . T p fi g y f q y mea ns of a specific gra vity bottle Al A a an . A c rav b . Apparatus . b l ce spe ific g ity ottle a b i a a d a . B ws to w a ss u s cohol ello , hich gl t e tt che by

A rm m r . A s a w a n n a n rubber tube . the o ete h llo p co t i r A u d w s rav is be ing tepid wate . liq i hose peciﬁc g ity to determined .

1 i r u l an Procedure. ( ) See that the bottle s tho o ghly c e i and dr . In an n b r n s ﬁ na w t d s y cle i g the ottle , i e it lly i h d wa r and n w a a r w h dr b tille te the ith lcohol, fte hic y it y passing a stream of air th rough it by m ea ns Of the bello ws u If air i w arm d s m w a b and the glass t be . the s e o e h t y d n a ub in am a Bun s n b urn r hol i g the gl ss t e the ﬂ e of e e ,

r the bottle w ill be dried m ore quickly and tho o ughly . 2 m b or a n d x r a n ( ) Weigh the e pty ottle , t ke the i e e di g m in n with the e pty bottle the pa .

F t d d r a n o (3) ill the bottle w i h istille w ate . See th t air bub s r m a n in b an d a is u to the ble e i the ottle , th t it f ll

r top of the stoppe . (4) H ave the shallow pan ready with some water in it 30° A at about C . llow the bottle to stan d in this f or a f ew m nu s un w a r in ha m s m d l i te , til the te it s co e to o e e i n m ra ur w c w be n d a a rm m r ite te pe t e , hi h ill i ic ted by the o ete

i r a placed n the pan . Reco d this temper ture at the time

i n r T s m ra u the bottle s take f om the water . hi te pe t re ° ° u d 5 o 3 s be ab v a the r m sa 2 t 0 C . ho l o e th t of oo , y 5 b t d r on u s d an d w ( ) Wipe the o tle y the o t i e eigh it, or a the nd x r ad n w in ba an an t ke i e e i g ith it the Jolly l ce p . SPECIFIC GR AVITY OF LIQUIDS

6 Em a nd dr the b and h l w u . ( ) pty y ' ottle ﬁll it it the iq id T re at this in the same way the bottle full of w ater was r a br n n sam m ra ur b ad n t e ted, i gi g it to the e te pe t e y di g w arm or w a r wa r in an as as cold te to the te the p , the c e

m a r u r and s rr n r u . y eq i e , ti i g it tho o ghly 7 u u or a ( ) Weigh the bottle f ll of the liq id, t ke the n r d n i dex ea i g with it in the pan . (8) Return the liquid to the bottle from which it was ta n and r u ans s rav b ke , tho o ghly cle e the peciﬁc g ity ottle r n b efo e p utti g it away .

If a is the nd x r a n f or m b f or i e e di g the e pty bottle, the u wa r and c f or the u u d b ottle f ll of te , bottle f ll of the liq i , then (c a ) divided by (b a ) will be the speciﬁc gravity

Of the liquid .

rr f r m r n x Co ect o te peratu e as in the precedi g e ercise . Record the results in a form similar to that used in the r last exe cise .

T Th t t t ttl e n r m n ul ter e n NO E . e fac ha the bo e do s ot e ai f l af b i g

It is due to c ntr ct n . take n f rom the water is Of no conseq ue nce . o a io f ter in h Equal volum es are taken at the temperature O the wa t e pan .

EXER CI SE 30

SPECIFIC GRAV ITY OF L IQUIDS BY H AR E ’ S ME THOD OF BALANCED COLUM NS

o determi the s eci c r avit o a li uid Purpose. T ne p ﬁ g y f q by comp a ring the height of a column of it with tha t of a lumn o wa ter when both ar e su orted b the same co f , pp y p ressure .

Y- la ub ab u . A u w h two ss s Apparatus t be, to hic g t e o t

d am r re n d b s r m n and 8 mm . in a 50 c . lo g i ete joi e y ho t

s Of rubb r ub n A rubb r u a u 30 cm . piece e t i g . e t be bo t and s d a n c is a ac rd long, clo e by pi chco k , tt hed to the thi

h - u Two umb rs one n a n n dis bran c of the Y t be . t le , co t i i g 70 MECHANICS OF FLUIDS

tilled w ater and the other the liquid to be

rm m t r . tested (see Fig . A the o e e u Procedure. (1) S upport the t bes

n a s n w two ass i a vertic l po itio , ith the gl

tubes standi ng one in each tumble r . . (2) Raise the liquids in the tubes r to a height of 30 or 40 cm . by a pa tial exh austion of the air through the rub ber u and n s u a ir t be, the clo e the t be t b m tigh y the cla p . Watch the liquids in the tubes f or a f ew mom ents to see whether the liqu ids I a or not . f s ws a f ll t hey do, it ho th t the tube is not closed air- tight by the

clamp . (3) Measure the ve rtical height of the two columns above the surfaces of d n the liqui s i the tumblers . (4) M ake th ree diff erent sets of m asur m n s an n s of e e e t , ch gi g the height umns m the col each ti e . Record results as follows

DE SITv IN D l NBITY I N gRA M éUNOES L ’Q‘m ’ S PER CUBIC P ER CUB IC CENTIM ETE R INCH

— Discussion . Since each colum n of liq uid is supported sam r ssur and s nc r sur a x r by the e p e e, i e the p es e e ch e e ts is proportional to its height and dens ity we can compare the density of the liquid with that Of w ate r by dividing the height of the w ate r col umn by that Of the other liquid . CH APTER IV

SOUND

EXER CISE 3 1

V IBRATION R ATE OF A TUNING FORK

o n v o Purpose . T determi e the ibra ti n ra te of a tuning f ork

— A un Apparatus . t ing fork m aking from 100 to 300 A vi b rations per secon d . pen d ulum of a k n own rate Of

r n and arran m a and r a an r v ib atio , ged to ke b e k elect ic c ircuit a t eve ry s wing by a mer A c ury con tact . n n u r elay . A i d c Two tion coil . A b a tte r i e s . n ara us s wn a pp t , ho i n F ur 29 in ig e , which A is a m e

F" 29 : ta o rum ab u lli d , o t 1 2 cm in am . r and 15 cm . n s u r d on a a di ete lo g, ppo te sh ft t a has a ra n at one en d A r a is cut on one en d h t c k . th e d

Of t s s a so a w n drum i r v d m hi h ft, th t he the s e olve it o ves longitudinally . A s mall ﬂex ible poin t c is cemented to the end one Of r n s r H F a Of an old of the p o g of the fo k , piece

r r m n A - hairsp i ng f o a watch bei g used f or it . bass V iol

A rd r . b ow . ca ndle or an o ina y gas jet

1 um n n r n Procedure. ( ) G o e e d of a st ip of pape r lo g n u r a ar und drum and as w d as e o gh to e ch o the , i e the

m i n nd ast n ar und the drum dr u s a . lo g, f e it tightly o 71 72 SOUND

(2) Smoke the paper e venly and thinly by holdi n g a cand am or a as r m a ﬁsh- a urn r a a n s le ﬂ e , g jet f o t il b e , g i t

and r v v n rum ra . it, e ol i g the d pidly (3) Fix the fo rk in pos ition so that the poin t c j ust tou che s a r The s r w B aff r s a ﬁ ne ad us m n f or s the p pe . c e o d j t e t thi d r m n u ma r c e . purpose . This adj ust e t sho ld be e with g eat a (4) Co nnect one te rminal of the secondary of the in

uc n w r and r w dr u m . d tio coil ith the fo k , the othe ith the Connect the p rimary Of the coil with the batte ry an d with

n ac ma r r a and r a w the co t t ke of the el y , the el y coil ith the r n Th n u t n c a nd other batte y a d the pendulum . e i d c io oil the battery used with it m ust be large e nough to produce a spark at c to pen etrate the pape r at each swi ng of the r pen dulum . T urn the sc rew up against the vib ato r of the

r induction coil so that it can vibrate only a ve y little . 5 r in v bra n bow and urn ( ) Set the fo k i tio by the , t the d rum with a steady motio n in the direction shown by the

rr Turn r at t a o w . the d um so that the re will be leas t wo a r s at r r u sp k e ve y evol tion . (6) Rem o ve the pape r from the drum by cutting it

a r ss n ar la n ar u a sm d sur a c o e the p, bei g c ef l th t the oke f ce not u n P a r r u s a does to ch a ythi ng . ass the p pe th o gh hell c

varn s and w n is dr un n um r Of v ra ns i h , he it y co t the be ib tio r m one in a r n x but one a is f o hole the p pe to the e t th t , the n um ber m ade d uring one complete vibration of the n u um It is a m m a us n u um pe d l . l ost i possible to dj t the pe d l so that the times taken f or the swing of the pen dulum on each side of the merc ury co ntact will be eq ual to each r n n s f or un n vib ra ns f or othe , he ce the eces ity co ti g the tio I l n two half periods . t wi l assist the cou ting to m ark

every ten th vibration . Dividing the n umbe r of vibrations counted by the time of one com plete vib ration of the pe nd ul um will gi ve the

num r v b ra n s r e r s c n d be of i tio of the fo k p e o .

74 SOUND

1 Le n r n d r t the Procedure . ( ) t o e pe so hol the fo k a m u ub a n n ow and n w o th of the t e , t ppi g it lightly the ith m a in v bra n w an r rs n the llet to keep it i tio , hile othe pe o changes the level of the wate r in the tube by raising a nd F n in wa r s lowe ri ng the bottle . i d this y the sho te t depth Of air um n s r s nanc a n the col th at give the best e o e, t ki g the

av ra o ra r e ge f se ve l t i als . 2 If ub is n n u r s nan w ur ( ) the t e lo g e o gh , e o ce ill occ

With an air colu m n about th ree times as long as the ﬁ rst . In the same man ner as befo re locate the position of the

water f or this secon d resonan ce .

(3) Measure the diameter of the t ube . (4) From a thermometer sus pe n ded near the tube de rm n m ra u r Of the a ir a nd ca cu a te i e the te pe t e , l l te the = velocity of sound . v . 6 x t . Record the results as follows

L ENGTH OF A IR COL M N L E NGTH o r A IR CO L MN U , U , l ST R ESONA NCE 2D R ESON ANC E

Wave length

Diameter of tube Correction

Freque ncy of fork Temperature Of air

Velocity of sound (by experim en t)

un t Velocity of so d . 6 )

E rror VELOCITY OF SOUND IN SOLIDS 75

Discussion . This experi men t enables us to determine the n d Th r le gth of the soun waves . e ai column f or the fi rs r s nan or one r a r n r t e o ce, thi d of th t f o the seco d eso n a nc v s n arl uar r wa n e, gi e e y the q te ve le gth ; this should b c rr c a t e o e ted by the dditio n of . 7 of he di ameter of the 21 8 nd mu a then ltiplied by 4 . K n owing w a v n and r u nc r v the e le gth the f eq e y of the fo k , the elocity ca n be a u a ed or n w n wa n and c lc l t , k o i g the ve le gth the ve r u n of r can a u a s n locity, the f eq e cy the fo k be c lc l ted, i ce

n x l or n

EXER C ISE 3 3

K NDT ’ M E H D V E LOCITY OF SOUND IN SOL ID S. U S T O

ermin e the velocit o sound in brass or Purpose . To det y f

la ss 203 205 207 21 1 212 2 18 g , , , , , ,

— u T Fi . 31 ab u 1 m . n Apparatus . A glass t be ( g ) o t lo g T u is c d a r i r . s b s and 4 cm . n diamete hi t e lo e by co k

FIG . 31 .

n P is m v in and out b the rod R . The pis to , which o ed y othe r end Of the t ube is closed w ith thi n sheet rubbe r s tretched o ver it and held in place by a rubber band . Some ﬁne dry co rk d ust m ade by rubbing a baked cork on sandpaper is distri buted along e ve nly withi n the tube . A in d am r av n 1 m . b rass rod D abo ut 1 m . long and c i ete h i g 76 SOUND

rdb rd u d n nd r a disk of ca oa gl e to o e e . This od is clam ped between two strips of wood at its cen te r and fas tened ﬁrm ly

to the table by a n iron clamp . A piece Of cloth or soft

r r d w wd r d r n . leathe co ve e ith po e e osi A thermometer .

1 u r i Procedure. ( ) S ppo t the glass tube as shown n Figure 31 so that the cardboard disk on the end Of the rod

res ts lightly against the sheet rubber . Place the thermom

eter near the tube . (2) Stroke the rod from the cen te r towards its free

e nd w cl . It w v a ar n and ith the oth ill gi e high , cle ote ; w n air um n in u is Of r r n t he the col the t be the p ope le g h , it

r d will set the co k ust in to viole nt agitation . (3) V ary the le ngth Of the ai r colum n by changi ng the position of the co rk pis ton until the agitation Of the dust is It w a r n r u ara r d w greatest . ill g the i to g o ps of p llel i ges ith

unoccupied space s between the gro ups . When the air c umn i r r ad us d in n r w an ol s p ope ly j te le gth, the e ill be x n um f u ac w b r Of s r u s all O a n . e t hole e the e g o p , eq l le gth If ad us m n is not xa two end r u s m a the j t e t e ct, the g o p y

not be pe rfect . (4) M eas ure the le ngth of the air column and count the

n umb r Of r u s . The n m as ur d d v d b e g o p le gth e e , i ide y the n um b r r u s m as ur d w v n Of one e of g o p e e , ill gi e the le gth d r u . If the en d r u s are m r o not m as ur g o p g o p i pe fect, e e

or co unt them . 5 M asur n rass rod and a ( ) e e the le gth of the b , t ke the u ir temperat re of the a near the tube . 6 To ﬁ nd v l t s und in ass su s u e a ( ) the e oci y of o gl , b tit t

- 1 l d 1 m n nd m . thick w al e glass tube abo ut . lo g a c in

d am r f or b rass rod and r a ab v O ra i ete the , epe t the o e pe

ns us n a dam w n c t to s r ass . Th tio , i g p oole lo h t oke the gl e v c s und in w d r n or r subs an s can elo ity of o oo , i o , othe t ce be nd fo u by the same method . VELOCITY OF SOUND IN SOLIDS 77

The average Of several determ inations should be

ta ken . Record the res ul ts as follows

Di u si n . n rod is set in v b ra n sam sc s o Whe the i tio , the e

ra t vibra n is mmun a d air the ub and e of tio co ic te to the of t e,

r T r the s ound is reé nf o ced by the air column . he e are as m any vibrating air columns as there are group s of cork Th n d d dus t ridges . e poi ts mi way between the iff ere n t r u r a no v bra n r n d A i s a e s o s . s n g o p pl ce of i tio , o e the

r v us x r s s an r m the w a r or a p e io e e ci e the di t ce f o te , pl ce of

n o v ra n m u ub or ac Of r a ib tio , to the o th of the t e , pl e g e test vibra n is one ur Of a wav n so in s the tio , fo th e le gth thi , dis tan ce from a node to the middle Of a group is one fo urth

a wav n or s an r m one n d of e le gth , the di t ce f o o e to the i a n h r n e x t s one h lf of a wave le gt in ai . Like wise the dis tan ce from the center of the b rass rod to its en d is one ur a wav n in brass or w l rod i fo th of e le gth , the ho e s n H n c wav n h i one half a wave le gth long . e e the e le gt n brass f or a given rate of vibration w ill be as m any tim es as long as a wave length in air f or the sam e rate of vib ra tio n a s the le ngth of one gro up is con tained in the length 78 SOUND

T r n Of the rod . his atio of wave le gths will also be the ra Of v Of s un in rass a in air or tio elocity o d b to th t , the velocity of sound will be as many times greate r in b ras s than in air as the wave length in brass is greater than th a t in air . Calc ulate the velocity Of so und in air f or the tem erature a n and n r m da a x r i p t ke , the f o the t of this e e c se u calc late the velocity of so un d in b rass .

EXER C ISE 3 4

SCAL E RATIOS

o illu tra te the r ation b t e n itc a Purpose . T s el e w e p h n d vibr a tion f r equency an d to determin e r a tios or in ter va ls be tween the notes o the di a tonic scale an d the ke n ote 231 f y ,

233,

A r n n O Apparatus . si e co sisting f a disk of b rass or

a rdb ard w nc n r rc s s m un c o ith eight co e t ic ci le of hole , o ted

on an r c m r or on a w r a . A b w s elect i oto O hi ln t ble ello ﬁ d w a rubb r ub n end w a tte ith e t e , i to the of hich glass tube is i nserted .

un m r in Procedure . Co t the nu be of holes each

rc b n n n w the nn r r . ci le, egi i g ith i e ci cle (2) E xpress the number of vibrations that each circle will produce w hen the disk is rotating an d a jet of air is

d r d at a r in s u ss n . To s n i ecte e ch ci cle cce io do thi , let den ote the n umbe r of rotations per second m ade by the uff air ass s r u m a disk . E ach p of as it p e th o gh a hole y be n r d a v bra n and r r r w a co side e i tio ; , the efo e, the e ill be s m any vibrations per secon d f or any circle as there are holes in r m u d b n f or xam r are 24 the ci cle ltiplie y , e ple, if the e in ﬁ rs r 24 n w x r ss n um r holes the t ci cle, ill e p e the be of

n er n f or r vibratio s p seco d that ci cle . (3) E xpress the ratio of the n umbe r of vibration s per SCAL E R A TIOS 79 s ec ond produced by each circle to the n umbe r produced by the in n e r ci rcle in com mon fractions red uced to their r n i c mm n ac r in a lowest te m s . Si ce n s a o o f to e ch of

w an out and nc n or ra r a these, it ill c cel he e , the te of ot

n d s not n be n wn . tio , oe eed to k o (4) Set the disk in rotation and when it has attain ed

un rm s d r a air a a n s ac c rc a ifo peed, i ect jet of g i t e h i le of

s in ra d s uc ss n b in n n w nn r rc . hole pi ce io , eg i g ith the i e ci le D i B e careful that the tube does n ot touch the disk . es g

F IG . 32 .

n n r du d b us m r m In a te the to es p o ce y the c to a y n a es . ( s ad Of us n a b w s r duc air ac te i g ello to p o e the jet of , pl e the r ubber tube in the mouth and blow ai r from the lungs r u th o gh the hole s Of the disk . ) (5) Set the disk in rotation and direct a jet of air at a

n r r r i n r n si gle ci cle of holes while the ate of otation s i c easi g . Wha t relation between vibration rate and pitch does this ill ustra te ? Reco rd the results as follow s 80 SO UND

— m n h x Discussion . These ratios deter i ed by t is e peri m n c rc s a v c rr c n um b r s a re e t, if the i le h e the o e t e of hole , the sca le r a tios or the In ter vals between the keynote a n d d N n um b r the other n otes of the iatonic scale . ote the e of d r n n t r va in sca m a r n s iff e e t i e ls the le the jo to e ,

m n r n s an d m a r s m n s . the i o to e , the jo e ito e

EXE R C ISE 3 5

V IBR A IONS OF S R INGS L A W OF L ENG H T T . T

o eter mine the ela tion between the len th o Purpose . T d r g f

t b t r e a str ing a n d i s vi ra ion f quency . — A s n m r F i ﬁ w a s n Apparatus . o o ete ( g 88) tted ith i gle r d A ui ar or r stri ng an d h aving three b i ges . g t othe

rum n m a b u d stringed inst e t y e se .

FIG . 33 .

1 Plac tw o b r d s un r w r Procedure . ( ) e the i ge de the i e

m k no w n d s ta nc a ar as 80 or 1 00 cm . P u at so e i e p t, l ck the wi re w ith the ﬁnger and use the ton e produced as the

n or D o in ol w n ra n s . key ote , , the f lo i g ope tio (2) Place the thi rd or m ovable b ridge under the wire

82 SOUND

— Th r a n w n n s Discussion . e el tio bet ee the le gth of a string and its freq uencies is shown by compa ring the ratios

s w i h ra i ir of the le ngth t the t os of the frequencies . r s ra s and s a in w rd Compa e the e tio t te o s what they m ean. n o n Illustrate by usi g tw otes as D o and M .

Corollary to the First Law . The lengths of two strings in unison are directly p r op ortional to the f r equ encies of the two str ings when their lengths a re

C D ma de equa l. E — F Proo . Let CD and E i 34 f F (F g . ) be two s tr n s e u in e n th and let E G a i g q al l g , , " r f E 1 be in t o un son w t CD . pa , i i h

Freq uency of E C Le ngth of E F 1 the rs t law of str n ( ) by ﬁ i gs. Freque ncy of E 1" L e ngth of E G

2 Fre uenc of D Fre uen c of E G ( ) q y C q y by hypothesis.

n (3) Le gth of CD Length of E F by hypoth esis .

Su stitut n t ese v ues in the ro ort on we ve b i g h al p p i , ha Freq uency Of C D L en gth of C D . Q . E . D . Freq uency Of E F L e ngth Of K G

This pri nciple is of great use in proving the other laws of str ings u n th po e sonometer . E XE R CISE 3 6

FRE QUENCY OF A FOR K

r t vibra tion re uen c o a or Purpose. To dete min e he f q y f f k by comp a ring it with a sta nda rd f ork by mea ns of a vibr a ting

r st ing . — A n m r ﬁ d w a S n w r . pparatus . A so o ete tte ith i gle i e

A un n rk 1 a n wn ra v bra n a nd t i g fo NO . of k o te of i tio

an r r N 2 s r uen c is b e d rm n d . othe fo k o . who e f eq y to ete i e

r ﬁn h w r w c Procedure. Fi s t d t e le ngth of the i e hi h is in un i son with the sta ndard fo rk by changin g the le ngth of the w i re u n til th e re a re n o b ea ts when the two are

sounded h r . Ca h en t L . toget e ll t is l g h I FR EQUENCY OF A FORK 83

2 u an n n s n w r ﬁnd in ( ) Witho t ch gi g the te io of the i e, the same w ay a length of the wi re in u nison with the fo rk

w s r u n is un n wn . Ca h s n L . ho e f eq e cy k o ll t i le gth 2 Record the res ults as follows

Fre uenc Of St n r Fork NO. 1 V q y a da d , I

TR I ALS AvE RAGE

Fre uenc ound f or Fork No. 2 V q y f , ,

i un The frequen cy Of fo rk NO . 2 s fo d by proportio n a cc rd n la w of E x r s 35 as l ws : V : V o i g to the e ci e , fo lo I 2 L L . 2 I

TH E TEN SION B A L A N CE F OR TH E S ON OM ETER i The tensio n b ala nce (F g . 35) is a s mall steel le ve r a ac d at on end Of a s n m r Fi The w r tt he e o o ete ( g . i es o f the sonomete r are attached to the k nife-edges A an d B by rings groo ved on the i nn e r ci rcum fere nce and the

a an r a n n r n - d r u cr m b l ce ests ag i st a othe k ife e ge o f l u F .

W n u rum is a t n c N . 1 w is xac m id he the f lc ot h o , hich e tly w a b w n A a nd B the tw o w r s are und r ua ten y et ee , i e e eq l s n w n u crum F is at s m r n c as at 4 io ; he the f l o e othe ot h , the te nsion on the w ire at A is to the tensio n on wi re a t B as the length B to 4 is to the length A to 4 according o Ex r s 1 3 55 t e ci e ,

E XER C ISE 3 7

V N LA W O D IAM E ER IB RATION OF STR I GS. F T

b t e n ia ete s o Purpose . To deter min e the r elation e w e d m r f wir es and their vibra tion f requ en ci es 84 SOUND

— A aratus . A s n m r e w h two s r n s of pp o o ete ﬁtt d it t i g , an w r Of d ff r n d am r T pi o i e i e e t i ete s . hese wires are at tached to the sonometer by means of a tension balance

Fi u rum F b n at n 1 o a t ( g . the f lc ei g otch s th t the wo

w r s are un r ua ns n . A m r m r s r i e de eq l te io ic o ete c ew . T h ree bridges .

r h r Procedure. Measu e the diameters of t e wi es m r r by the ic omete screw . Take several diff eren t m eas urem ents a w r at d ff r n a s r c r n of e ch i e i e e t pl ce , e o di g the diameter Of the smaller wire under d and of the ' ar r F n h a ra di ff re l ger unde d . i d t e ve ge of the e n t m a u e s rements .

2 Ta e s m m asur d n sm a r w r ( ) k o e e e le gth of the lle i e , 0 d n d in an d ﬁn as 1 0 cm . ( esig ate by l the table) d a ' n l ar r w r w is in un s n w t le gth of the l ge i e hich i o i h it, h d v . . h n a n i e as the same pitch . T e student ca use to a a in n r nan and a 21 6 t ge doi g this both eso ce be ts , As the correct length is approached the beats becom e w r and w r b s r n s are s un n or if on e fe e fe e , if oth t i g o di g ; i un nd nd n n c d r s so ded a f ew seco s a the s ile e , the othe w l be und ra n r s nan n s r n r the il fo vib ti g, the e o ce bei g t o ge ' n r r ea e the correct len gth is attained .

R a d ff r n n f or l an d ﬁ nd the epe t this with i e e t le gths , ' n ratio i each case of l to l. Record the results as follow s A F E N N VIBRATION OF STR INGS. L W O T SIO 85

— A rd n c r ar a Discussion . cco i g to the o oll y p ge ’ 82 rat of l l ua s ra the r ue nc s , the io to eq l the tio of f eq ie lI I _ Z5 ’ O f two s r n s w n r n s are ua . l the t i g he thei le gth eq l , , I n ’ ’ n and d b n r s v n r u nc and , ei g e pecti ely the le gth , f eq e y , d m t r r r w r an d l n an d d s ma r ia e e of the la ge i e , , of the lle

r w i e . r m r r 4 a nd r m m r n a an Co pa e the two atios 7 , e e be i g th t 7 3 e quality of. ratios is a proportion an d that what is r r E 2 in rds wha ur true of is also true of . State wo t yo l n r u r es lts p o ve .

NOT E — S nce the vo umes of the two w res the en t s e n i l i , l g h b i g e u l are to e c ot er as the s u res Of t e r m ete rs t e r q a , a h h q a h i dia , h i 1 39 ’ w e ts must be so. ence w and w e n the igh al H , , b i g w7 t is the respective weights of equal lengths Of the two wires. Wha re lation between the vibration rates of the two wires and their weights E XE R CISE 3 8

V B A I F RIN T HE L F EN I N I R T ON O ST GS. AW O T S O

o r in t t t v b tio Purpose. T dete m e he rela tion be ween he i r a n f : equency a nd the tension qf a vibra ting str ing

A n Apparatus . so omete r ﬁtted w ith a Ritchie tension b a an Fi 35 and l ce ( g . ) two strings of pia no w ire of the sam e diam

r r d . e te r . Th ee b i ges erniered a r or A v c lipe , d ivide rs and diagonal

FIG . 35 . scale .

M r r car u d s anc s Procedure. (1) easu e ve y ef lly the i t e

d to th n ot h o Fi . 35 r m B an A e c t b e us d as B 4 ( g ) f o e , f 4 a n a v ra O ﬁ ve m as ure m n s . and A , t ki g the e ge e e t 86 SOUND

2 A ac the ba an an d w r s s n m r ( ) tt h l ce i e to the o o ete , r P ac two placing the f ul crum F at the p oper n otch . l e bridges un de r both wi res at some meas

r n a r u ed dista ce ap t . (3) With some

m asur d n t e e le g h , of

w r A w r w i e , the i e ith

the r at r t ns on g e e e i , m d as 1 00 b . ( esig in h n ated by L A t e

FI G . 36 . ta b e ﬁn d a n l ) , le gth

r B in un m d lB of wi e ison with wi re A . Us e the etho d s r b d in as x r e c i e the l t e e cise .

t w h d ff r r d ﬁ nd r Re pea it i e e nt lengths f o L A an the atio

L in ac ca r r u ws lg to A e h se . Reco d the es lts as follo

AR M A A RM B

Discussion . B the cor ar a 82 ra y oll y, p ge the tio

Of l to L the r t r u n o r n s B A a io of the f eq e cies of the tw st i g

B — w h n r r u n s a e a i . e . e thei le gth eq l , é A W

Arm A ten s ion on B By the law Of parallel fo rces 55) A rm B tension on A

Can you fo rm a p roporti on show i ng the rela ti on bet wee n the r uen c es the w ires an d the r ten s n s ? If SO f eq i of i io ,

a i n w rd m n n f h r r s t te o s the ea i g O t e p opo tion . CHAPTER V

L IGH T

EXE R CI SE 3 9

PHOTOM ETRY

Purpose. To study the rela tion of can dle p ower a n d of n it u i n te s y of ill mina tion to distance . — A aratus . A B uns n h t m r w n t pp e p o o ete , hich co sis s of

d s of un s z d a. i k i e paper with a g rease spot at its ce nter

Fi . Two m rr rs are us ua a d on on ac ( g i o lly pl ce , e e h

d s so a s d s can s n s m u s i e of the di k , th t both i e of it be ee i l

n ousl . T o ck s ac ca ab of d n ur ta e y w blo , e h p le hol i g fo

S z “ A n m n d s ca d x . c an dles . So e ca le of the i e lle si es

ca b n c c n s s n tw o m r s c s as n ed en d Op ti l e h, o i ti g of ete ti k f te to en d on a board ; or the e xercis e m ay be condu cted by Th pl acin g the photomete r and can dles 0 11 a lon g table . e photom eter suppo rt and c an dle blo ck s Should be n otched

r n d r m . so as to slide along the m ete r s ticks . A da ke e oo 87 88 LIGHT

P an s u n b n w Procedure. lace the c dle po the e ch ith m t r b w n m a v n an un ua n um ber the photo e e et ee the , h i g eq l

nd s on the two s d s as 3 and 2 or 4 and 3 . of lighted ca le i e , , (2) Place the two sets of candles some exact distanc e

a ar sa 150 cm . r rd n s an un r S in p t, y , eco i g the di t ce de the table . 3 B m v n m r and f ro ﬁnd su a ( ) y o i g the photo ete to , ch position f or it that its disk is illuminated eq ually on both T b w n r th sides . his will e the case he the cen te of e dis k has sa m or n ar sam a aran as w l the e , e ly the e, ppe ce the ho e d s or w en its two s d s a ar a n o m rr rs i k h i e ppe like i the tw i o . (4) When the correct position f or the photomete r is

und r c rd d s a n s r m s an le fo , e o the i t ce f o the di k to the c d

ﬂa mes on each side .

R rd m asur m n s f or ten d ff r n r a s av n eco the e e e t i e e t t i l , h i g the larger n umbe r of candle s on the right duri ng h alf Of r a s and on f or r m n the t i l the left the e ain i g tri als . Re cord the data as follows

T ri als Ave rage Of (1 s q uared

Ave rage of D squared

Error

Pe r ce n t o f P I ror Ave ra e g ,

90 LIGHT

EXER CI SE 40

INTENSITY OF A L AMP

Pur ose. To measure the can dle ower o a la p p f mp .

h m x r Apparatus . T e sa e as f or E e cise 39 ; a lamp n r r whose ca dle powe is to be m easu ed .

1 th m Procedure. ( ) Substitute e l a p f or on e set of candles an d light two candles on the other side of the

m r photo ete . (2) Place the lamp and the can dles som e distan ce

a ar as 100 or 1 50 cm . an d n set m r a p t, , the the photo ete s

in E x rc s 39 f or ua um na t n . e i e , eq l ill i io (3) Repeat the m eas ureme n ts se veral tim es either with the same distan ce from la mp to candles or with other

distances . (4) Calculate the candle powe r Of the lamp by the ﬁ rs law d r v d in E x rc s 39 in a as and t e i e e i e e ch c e ,

ﬁnd the ave rage Of the se veral results .

No or CA N D L ES D ISTAN E TO CA ND LE S DISTA N To L AMP C A ND L W . C CE E PO E R OF LA MP

E XER CISE 4 1

THE PL ANE M IRROR

o t o tion o Purpose . T ﬁn d he p si f an image f or med by a p la n e mi rror a nd to comp are the angle of in cidence with the angle of reﬂection .

—A m rr r n n r Apparatus . i o co sisti g of a st ip Of plate

ass b ac n d on one s d as n d a b c b a s r n gl l ke e i e , f te e to lo k y p i g

r rub r ban d Fi . A r u r . A r ra r o a be ( g le p ot cto . A TH E PLANE MIR ROR 91

a r d v r A in . A r p i of i ide s . p silve ed mi rror m ay be u s d and in a cas a ur a e , th t e the b ck s f ce is the reﬂectin g

s ur a . ac n d ass f ce With the bl ke e gl , the fron t s urface is the reﬂecting

r s u face .

Procedure. (1) With a well s harpened h ard pencil draw a clear ﬁ ne n N Fi 8 a r s li e M ( g . 3 ) c o s ( n ot length wise) the cente r of a s heet of paper and label it mir r or Place the mi rror (block B ) on the paper with the reﬂecti ng s urface of the mirror exactly coin cid ent w s n ith thi li e . 2 n i r m rr r ( ) Set a pi n f ont of an d to one side of the i o ,

a n 8 or 10 r as at 0 . cm . m r pl ci g it from the i ro , (3) Pla ce a straight-edged rule r on the paper so that its edge points exactly at the image of the pin seen i n the

m rr r . To s a the on a v w ab i o do thi , pl ce eye le el ith the t le n d r m n 10 n s and s a back f o the e d of the ruler 8 or i che , ight a lon g the edge of the ruler at the im age with one eye on ly .

B e careful n ot to push the mirror oﬂ the line with the ruler .

4 n ru r is r a d d ﬁ rm ( ) Whe the le ightly pl ce , hol it ly a n d draw a ﬁne lin e along its edge as close to it as pos

an d E T . s ible . In this way d raw two such lines as CD A r r m v n r u r s s n s s n fte e o i g the le , te t the e li e by ighti g a long them to see if they poin t exactly toward the m i age . (5) Remove the mirror and extend ve ry carefully these

n s un m The n in rs n is li e til they eet . poi t of te ectio the p os ition of the image of 0 . M ark it I . (6) From the point whe re 01) meets MN draw a lin e nd r n to 0 a e ect a o rm al to MN at that point . 92 LIGHT

(7) Place arrowheads on the li nes to show the direc n r m in an d mar the tio of the light f o the p to the eye , k “ " “ angle of incide nce i a n d the angle of reﬂection r . (8) Meas ure these angles by a protracto r a nd record th num r r in e be of deg ees of each angle the angle itself . 9 D r n m ) aw a li e fro 0 to I .

— a Di scussion . In a real im ge the light actually passes hr u m a in ir m I t o gh the i ge ; a v tual i age it does n ot . s this image real or vi rtual ? H ow does the li ne M N divide the line OI ? Are these ? li nes pe rpe n dicular to each other Wha t position does the image of a poi nt in a plane m irro r occ upy ? H ow do the angles of i nciden ce an d reﬂection com pare ?

EXER CI SE 4 2

INDEX OF R EFR ACTION OF W ATER

P r o e. To determin e the index o r c u p s f ef ra tion of wa ter .

A aratus . A s ua r ba t r a r one s d of c i pp q e te y j , i e whi h s co ve red w ith a pape r ha vin g upo n it a ci rcle graduated

in d r T eg ees . he pa per within the ci rcle is remo ved and its vertical and horizontal d i a m e te r s a r e m arked by lines on the ass m a gl , de by a glass cutte r or by th reads cc m ented across the

r e Fi ci cl ( g . The gra dua ti on should b egin w ith zero at the ends of the ve rtica l dia m ete r a nd e nd with 90 at the e xtre m itie s of INDEX OF REFR ACTION OF WATER 93

r n d r the horizontal diameter . A piece of ca dboard co si e ab ar r an the to a r in w c r is a s ly l ge th p of the j , hi h the e lit 1 d 0 m . A m m rr r u about 2 m m . wide an c long . s all i o s p d Th x r n r r po rted on a stan . e e pe ime t can best be pe fo med r in a room s omewhat da ken ed .

r x h Procedure. (1 ) Fill the jar with w ate e actly to t e r n d a u r a a ho izo tal iameter . See th t the s f ce of the w ter

it r coi ncides with the diamete r alo ng s e nti e length . (2) Place the cardboard over the top of the jar with s at r h an s radua d rc an d us n the lit ig t gle to the g te ci le ; , i g d r t sun or a b am ar ﬁc a s nd r u i ec light e of ti i l light, e it th o gh the slit by m eans of the m i rro r so that it will strike the

’ a n r r w ate r exactly t the ce te of the ci cle . (3) Read the angle of inciden ce and the an gle of ref rac

t n b radua d c r If s x nds v r io y the g te i cle . the lit e te o e the s ar a so a a ar r bb n ide of the j little , th t p t of the i o of light

us ra s radua d c r on u s d an j t g ze the g te i cle the o t i e , the gle d r of incidence can be rea mo e easily . Read at the center of the edge of the ribbon of light . The path of the light in the water will be more easily seen if a tiny amoun t of i s oap s added to it . Reco rd the data as follow s

TR I AL Sl NE or I SINE or It

Average value found f or the in dex

Acce te v ue e 12 A en x p d al (Tabl , pp di )

Error Perce ntage of e rror 94 LIGHT

(4) Change the angle of incidence by a new adj ustmen t s ns the ar ar b ard and m rr r and r a of the po itio of j , c d o , i o , epe t m u m n T r the eas re e ts . ake meas u ements f or se ve ral diff er nt n d n an e i ci e t gles .

Let I r r s n an s n n and R an s ep e e t the gle of i cide ce, the gle r r of ef action .

For va u s s n s an T 1 3 the l e of the i e of gles, see able Na u ra n s and Tan n s A nd x ( t l Si e ge t ) , ppe i .

TA N GEN T A N D S IN E OF A N A NGL E

T s are r n m r ca t rm s . Let B F 40 he e t igo o et i l e A C ( ig . ) be

an an . B as a c nt r and an n v n n rad us gle With e e , y co e ie t i , as B A s r an are cu t n , t ike t i g the

ro two s ides of the a ngle . F m the point whe re the a rc cuts n sid as A x nd a ne o e e, , e te li n n arc un in ta ge t to the , til it ’ ter ct n B C as at D . se s the li e , The ratio of this line AD to AD 8 rad us B A or is the i , , the B A Fro . 40 . ' f tangent of the angle AB C. O course this ra tio will be the same whatever the radius ° I is b us a an n an an 45 may be . t o vio th t the t ge t of gle of

is 1 f or n AD w u d n ua AB . For an s , the li e o l the eq l gle ° ss han 45 it is ss an 1 and f or an s b w n le t le th , gle et ee ° ° 45 an d 90 is m r a n 1 b n nﬁn f or it o e th , ei g i ity If a lin e be drawn from the point where the a rc cuts one s d as C r nd u ar h r s d as CE i e , , pe pe ic l to the ot e i e , , the Y ratio of this li ne to the radius is the sine of the angle AB

B ra h m a A C. This tio will obviously be t e sa e wh te ve r rad us m a but no an can a v a s n r r the i y be, gle h e i e g eate

than 1 . R EFR ACTION 95

Tables can be fo und in the back part of any trigonom etr v n an n s n d n n y gi i g the t ge t a si es of a y angle . (See al so

T b 1 n d x T r s r h a 3 A . s a a e ca d t e r l le , ppe i ) he e tio lle natu a an n s and n tur l s n s d s n u s m r m t ge t a a i e , to i ti g i h the f o the logarithmic sin es and tangen ts .

EXER C ISE 4 3

R EFR ACTION

t a c e a th o a o t Purpose . To r e th p f a r y f light hr ough a block of p late gla ss with p a ra llel edg es a nd to mea su re o o the in dex of ref ra cti n f the gla ss .

— Apparatus . A rec tang ula r block of thick plate glass having its op

posite edges parallel . A

protracto r . Tw o straight d d r u r e ge le s .

Procedure D ra w a lin e AL on a sheet of pape r an d place the block of glass B upo n it as

h i u r 1 s ow n n Fig e 4 . D ra w the lines de a nd f g m aki ng them coin cide ex actly with the edges of

B ; also draw ef and dg . (2) Place on e ruler at FIG . 41 . K so that its edge exactly

nc d n coi i es w ith li e AL .

P ac r at H so a as ou s l e the othe th t, y ight 96 LIGHT

n d r u ass no and st s a s m alo g its e ge n u th o gh the gl , h ll ee n n is rr l ac d to be in one straight li e . Whe it co ect y pl e , d n o hold it ﬁ rmly and raw the li e n . 4 R m v ass and x nd n o to n do ( ) e o e the gl e te the li e , cc s P D er en r n n r n 0 . D ra w a m a ki g the i te sectio , l o p p dicular to f g a t c and NJ perpendicular to do at o. (5) Place arrowheads on the path of the light from L

M ar n s n n an d to c to o to the eye . k the a gle of i cide ce refraction abou t the point c by arcs a nd the lette rs I and ’ ' R a nd ab u n o b ar s and I an d R . , o t the poi t y c F n (6) Measure these angles by a protracto r . i d the n s an s in Tab 1 3 A nd x and a a si es of the e gle le , ppe i , c lc

n d x r ract n air ass a nd ass air . late the i e of ef io , to gl gl to

rna rc s ma be draw n ab u the n ts As an alte tive , ci le y o t poi 0 and o as cen ters an d the sin es constructed and measu red

Record results as follows :

ANGLE or R E b lN E or 1 Sun or R IND E X FR A CT IO N R

l Discussion . Show what a w of refraction is illust rated at c a nd what one at o H ow does the path of the light after passi ng throu gh the ? glass com pare w ith its dire cti on bef ore e nte ri ng the gla ss H ow does the i ndex of refraction ai r to glass compare w ith th a t of glass to air ?

98 LIGHT

L S = D w s CT CBE F . But B E is a CB E ike i e , + C A h lf

d AD r or an F a CDF K is on a f . h lf , the ef e R A e h l of S CT Record the values of S CT a nd R AK in two columns

‘ and ﬁ nd a ra a u R the ve ge v l e of AK .

E XER C ISE 4 5

REFRACTION BY A PRISM

c t Purpose. To tra e he p a th of light through a p rism ; to mea sur e the angle of devia tion produ ced by a p rism ; and f rom it an d the va lue of the r ef racting angle measured in the last exercise to ca lcula te the index of ref raction of the glass of the p r ism

at s . A r sm w s r ra n an Fi Appar u p i ho e ef cti g gle A ( g .

- 43 n n . r r i w r . d r r ) s k o A p ot acto A straight edge ule .

FIG . 43 .

1 D raw a d a na n a ro Procedure. ( ) i go l li e GK c ss a shee t of paper an d set the prism on end on this lin e with i F r angle A abo ve it as show n n the igu e . ( 2) Placin g the eye on a level with the table and look in t r u the r sm in r c n L E s r r g h o gh p i the di e tio , the ob e ve eem e n 0 at will s to s e the li e G R T. (3) The p ri s m mus t n ow be set f or the angle of least de viati on This is the most difﬁ cult part of the

e xpe rim en t . R EFR ACT ION BY A PRISM 99

B urn n the r sm and f ro ab ou A as an ax s the y t i g p i to t i , poi nt T may be m ade to m o ve either a way from or toward

n m r d a n G. Whe it is oving towa d G the angle of evi tio

i d r n B r m m . s ec easi g . y t ial ake it as s all as possible

4 A r s n r s m f or as d v a n ac a ( ) fte etti g the p i le t e i tio , pl e ru r b s n a n as in Ex rc s 43 so a its le y ighti g lo g it e i e , th t

d nd i in r n e ge a the l ne 0 G seem to be one st aight li e .

T dr n hen hold the r uler ﬁ rmly an d aw the lin e L E . A other person can at the sa me tim e sight along the li n e G0

r r R m ru r n d n b a t the ule . e ove the le a test the li e y sight in n n u m n r g alo g it . L E a d 0 G sho ld see to be o e st aight li n e . A pin placed at G m ay assist you in seeing the line i r u r N rs n . th o gh the p ism . ote the colo of the p (5) D raw an outlin e around the base of the pris m ;

n r m r m d n dr E the e ove the p is an d exten L E to T a d a w O .

i r m G OEL s the path of the light f o G to the eye .

6 The an K DL r r s n d b D in ab an d ( ) gle , ep e e te y the t le in th D t o m e s uss n is the an d v a n f or r s . i c io , gle of e i i the p i

M asur r r r R a x r m n an d e e it by a p ot acto . epe t the e pe i e t

n ur m n ﬁ d the average of se ve ral m eas e e ts of the angle D . (7) D ra w the li nes P S and EH perpe ndicular respec i l A n t ve y to B a d A C. Reco rd the res ults as follows

TE IA Ls A NGLE D

Average of D 1 00 LIGHT

ar how is b n on en r Discussion . State cle ly the light e t te

n r s m and on av n r sm a s d s na i g the p i le i g the p i , l o e ig te the two angles of incidence and the two angles of ref raction . To determi ne the index of refraction we m ust k n ow the size of the i ncident angle i and of the refraction a ngle r . These can be calc ulated from the a ngles A and D which Th r l ws have been m easured . e p oof is as fo lo

r m i t f or h an as vi a n When the p is s se t e gle of le t de tio , = ' ' é i A r 4 i A r and A v A u . B m r , , y geo et y , A FH S A A because the sides of one are respectively pe rpe ndicula r to the sides of the othe r ; also A EH S ’ ' ' i A A i n i r A 2 r . T r r r r . + , Si ce , he efo e, i A ( 1)

4 = é i n v . n D v u a d u v D i v r . S ce + , 4 + ubs tut n D f or v and A f or r in s ua n we S ti i g 5 % thi eq tio , a v i i D A or h e % 4 ,

H D A) .

Since the i nde x of refraction sine of the angle of in cidence d v d d b s n a n r ra n i i e y the i e of the gle of ef ctio ,

sin % (D A) Index of refraction sin é—A

The s n s s an s can be und in Tab 13 i e of the e gle fo le ,

A ndix a nd nd x r ra n as ppe , the i e of ef ctio of the gl s of the r m u d r m m p is calc late f o the .

EXER CISE 4 6

THE CONCAV E M IR R OR

To mea sur e the oca l len th o a conca ve mi Purpose . f g f rror an d to study imag es f ormed by a conca ve mirror .

A n ca b n c c n n Apparatus . opti l e h o s is ti g of a meter

s c as n d u n a b ard . A s m m r s ti k f te e po o i ple ic o cope, such

LIGHT slowly backward until you can see a dis tinct im age of the In n lines th rough the mic roscope . doi g this keep the eye T as near the mic roscope as possible . he image of the li n es n is now in the plane of the eedle .

4 n rr s n f or 0 is und m asu r ( ) Whe the co ect po itio fo , e e

' the ol ect distan ce u or d s an r m m rr r y , the i t ce f o i o to the

b c i . e . r m M 0 . o je t, f o to 5 A n m a ma d s n v x a a a 28 c m . ( ) g i , ke the i ge i t ce e ctly the n 26 cm: etc ; an d ﬁnd a position f or 0 1n each cas e as before. Fi all em ire b 0 and m v n b N ar £6) n yr o lock , , o i g lock c e f u bac and r ﬁnd a s n f or i n w a n in lly k fo th , po itio it hich verted im age of the needle can be seen as large as the h d i n T n w b . needle itself . e ee le s o the o ject Reco rd both

n m a nc un d object distance a d i ge dista e der u an v. If ou av d fﬁ u in s n ma s y h e i c lty eei g the i ge , let the i n structor rem ove the m ic roscop e an d adjust the m irror or card by placin g the eye in line with them and abo ut 10 i nches back of the needle . Record the results as follows

“ X D‘

Discussion . The focal length f is found by the form ula 1 1 1 + wln ch can be reduced to the more convem ent 5 f u x v rm W 1 6 i a s ns 3 F . 1 81 fo , f h t po itio , g ) u v do im age and objec t occupy i n all trials b ut the las t ? In the last ? Wh at ca ses 31 6) are illus trated ? Desc ribe

l f or e a c t r the im age complete y h ial . TH E FOCAL LE NGT H OF A LENS 103

EXE R CISE 4 7

TH E FOCAL L E NGTH OF A LENS

. To measur th oca l le th Purpose e e f ng of a convex len s .

A DI R E T NL I H T . BY C SU G — n 1 . Apparatus . An optical be ch m long . A sm all

m r n rd c on vex len s . A s all sc ee of white ca board or h n g round glass . T e scree an d lens should be supported on blocks arranged to slide along the m ete r stick of the optical bench .

P rocedure. Place the lens and screen upon the o a b n av n an cr n n rm ptic l e ch , h i g the pl e of the s ee o al to

h m r s c an d a x s ns a r l t t a . e e e ti k, the i of the le p lel to it (2) Place the apparatus in a beam of sunlight so that the ra s sha be ara m r s c and y of light ll p llel to the ete ti k , ,

n hr u th n sha b r d on r ass e s e c v sc n . p i g t o gh le , ll e ei e the ee (3) Move the screen ba ck and forth un til a position is fo und f or it in w hich a small well - deﬁned im age of the s un is fo rmed upon it .

4 M as ur d s an r m ns cr n ( ) e e the i t ce f o the le to the s ee .

R a ra n s v ra m s an d a av ra epe t the ope tio e e l ti e , t ke the e ge of the several meas urements as the focal length of the ns le . This distance is the focal length of the lens because the ’ s un s rays are parallel

B . BY A D I STA NT OBJE CT

— The sam as f or r c d n x r m n Apparatus e the p e e i g e pe i e t .

r r . 1 D raw d w n w nd w s ad s av P ocedu e ( ) o the i o h e , le n a narr w n n at b m an d s u r i g o ope i g the otto , ppo t the optical bench so that it points th rough this opening at som e distant object . 1 04 LIGHT

(2) Place the lens upon the bench and back of it the rdb rd r n nd n ad us d s anc b tw n ca oa sc ee , a the j t the i t e e ee lens and screen so that a dis ti nct image of the distant n object is formed upo it . The m r is x ud r m the r m x o e the light e cl ed f o oo , e cept

a n r u ns r m a w l be. th t goi g th o gh the le , the bette the i ge il (3) Meas ure the distance from the lens to the im age r r n d r r a n h o sc ee an eco d it s the focal le gt of the lens . (4) Remove the cardboard sc reen and put in its place m r us in E x r s 46 L a m the ic oscope ed e ci e . oc te the i age formed by the le ns by means of the microscope j ust as i x r you d d in that e e cise . (5) Measure the distance from the le ns to the n eedle n and record it as the focal le gth of the le ns . Reco rd the res ults as follows

Pos 1T 10 N or LENS Pos m oN or IM AGE FOCAL L E NGTH

Discussion . Par B w n ar ar s r n is us t , he the c dbo d c ee ed,

us ra nd m r ill t tes the eye a the ca e a . The microscope and the le ns form a crude as tron omical sc ns rm n b v a nd m r tele ope , the le fo i g the o jecti e the ic o s cope the eyepiece of the telescope Theo retically in Part B the image is betwee n the

r n c a us the ns and its s c n ar us 323 p i ip l foc of le e o d y foc , a nd the distance measured is g reate r than the f ocal

n b ut i r le gth ; practically it s at the p incipal foc us . This is tr ue beca use the a ngle between rays com ing from each poin t in the di s tant object and passi ng th rough the le ns is so sm all th at they a re practically parallel he n ce they meet

in an r nc a cus and rm the m a r pl e of the p i ip l fo fo i ge the e .

106 LIG H T

EXE R CISE 4 9

CAL LEN H F A EN IMA ES FO GT O L S. G

P To determine the oca l len th o a convex lens urpose. f g f

by conjugate f oci a nd to study imag es f ormed by the lens . — n rdb rd r n . A n . a a Apparatus . optical be ch A c o sc ee

- . A r n c nd r ha v n a T A len s . A gas light sheet i o yli e i g

u d r n d m w a . cut in its side . The room sho ld be a ke e so e h t

F101. 45 .

u r Procedure. Set p the appa atus as shown in

F ur 45 a n as h w n c nd r on a ig e , pl ci g the g lig t ithi the yli e level with the T a nd the en d of the m eter stick on the n d b th T bench agai nst the cyli e r elow e .

2 M a s anc r m T s r n S sa ( ) ke the di t e f o the to the c ee , y, m s anc m u b m r n 1 00 c . (this di t e st e o e tha fou r times a n Of ns and m v ns bac and the foc l le gth the le ), o e the le k forth near the T un til a position is found f or it that gives d n T n n a large isti ct im age of the o the scree .

3 M asur u Ob c d s anc i . e r m T ( ) e e , the je t i t e, . f o the to

ns and v m a d s anc i . e . r m ns the le ; , the i ge i t e , f o the le to

r n M ur m an r d d r H the sc ee . eas e by e s of a pai of ivi e s the

T a height of the nd h the height of the im age .

4 C a c u a the ca n t Of the ns b ( ) l l te f , fo l le g h le , y the 1 1 1 - form ula See if you can form a propor n e f

n w the va u s Ob a n e d f or u v H a nd h. If so tio ith l e t i , , , , what does it m ea n ? WAVE LENGTH OF LIGHT 107

(5) Note what positions Object an d im age occupy with r es us s ndar us and n pect to the foc , the eco y foc , the le s

323 D scr b m a m . , e i e the i ge co pletely (6) M ove the lens away from the T toward S until a s m a d s n m a is rm d and r a m a ll i ti ct i ge of it fo e , epe t the e s

u rements . and , etc , of 7 P c S in new n and r a x m ( ) la e a positio epe t the e peri ent . Record the results as follow s

Average value f or f os t on of O ect in tr 1 P i i bj ial , os t on Of m e in tr 1 P i i i ag ial ,

State these positions by means Of the points of refe rence

T rial 1 illus trates how pictures are projected by the m n r agic la te n . EXER CISE 50

WAV E L ENGTH OF LIGHT

o th v n th o ium li ht Purpose. T mea sure e wa e le g f sod g .

A r Of d ff rac n ra Apparatus . photog aphic copy a i tio g t ing having a known n umber of li nes per cen timeter (abo ut A ur Of 3000 lines per inch or 1 1 81 per centimete r) . so ce s odi um light con si sti ng Of a Bun sen b urner h avi ng around its top a piece of asbestos paper which has b ee n soaked in c Of sh a saturated sol ution of sodi um n itrate . A pie e eet i ron having in it a slit nearly a m illimete r wide and 2 or

. m u be s m w a m . n m r The r m s 3 c lo g . A ete stick oo t o e h t

darkened . LIGHT

P s r n in r n the Procedure. lace the heet i o f o t of b urne r with the slit S ve rtical and on a level w ith the r T b a a m Fi . u r a m s M ﬂame ( g S ppo t ete tick, , y cl p

FIG . 46 . in a horizontal position in front of the slit and j us t below

u r n t in a n c i r n it . S pport the g ati g a G li e whi h s pe pe dicular to the m eter stick and which passes through the n m slit a d the ﬂa e . (2) Fix the distan ce from the gratin g to the m ete r stick

xa at m ﬁn a u as 300 cm . C al s e ctly so e de ite v l e , l thi distance D . (3) When the Observer looks through the gratin g at

s w see two m a s one on r the lit, he ill i ge of it, the ight n Of it a d one on the left of it . Let a s econd pers on ' m o ve the paper m arke rs r an d r u ntil their edge s m a rk the exact positions of the se images as see n by the one " r looki ng through the grating . The distance f om r to 7 d d 2 i d n m di vi e by s the ista ce fro slit to image . C all it d . Possibly two othe r im ages Of the slit m ore distant f ro m the slit m ay b e see n ; if the distan ce between h m can be m asur d one ur Of t e e e , fo th it will gi ve the distance d . (4) Let the Obser vers exchange places an d repeat the wo rk .

5 C an d s an D 350 or 400 cm and r ( ) h ge the i t ce to . epeat w r the o k .

1 10 LIGHT

from the space bi to r is exactly one whole wa ve len gth n r an a r m ao r two n s m t lo ge th th t f o to , the pe cil of light ee in sam as and n ns a r rm n ﬁ rs the e ph e i te ify e ch othe , fo i g the t

d ff ra n m a Of s . A s d s anc sr ncr as s i ctio i ge the lit the i t e i e e , the diﬁ erence between ar and br i nc reases ; a nd when it b m s xa two w wav n s s nd dif eco e e ctly hole e le gth , the eco m fraction image Of 8 is formed . In the sa e manne r im ages

Of rs rd r s nd rd r . are rm d on the ﬁ t o e , eco o e , etc , fo e the

d n r n r s s . I a t i s x r m n m a othe i e of e li y, thi e pe i e t the i ges Of the slit are fo rmed on the retina Of the eye and those ’ s n on ru r a t r and r are v r ua b n r d ee the le i t l, ei g p ojecte

r . i on the rule by the eye The slit itself s seen at 8 . Let r b e s n the rs m a s n the po itio of ﬁ t i ge of the lit, the the path br is j ust one wave length longer than the pa th b x d a r . Sin ce the space a is e cee i ngly mi nute the lin es ar nd b re r a r M o u a r a p actic lly pa allel . ake r eq al to or an d

draw a c. be is w av n s u . a b k be D the e le gth o ght , , = and sr d . The triangle acb is a right triangle and is 8 d x k 8 1m ar bsr and Q 1 or bc u s r u il to , Witho t e io s ab br br

error we m ay substitute bs or D f or br and we then have rmu a n ab f r a n the fo l give ove o the w ve le gth . CHAPTER V I

H E AT

EXE R CISE 5 1

TESTING A THE RMOMETER

e in oint nd the boilin oi nt Purpose. To test the f re z g p a g p of a thermometer

m r u r rm m Apparatus . A e c y the o eter . A F r n A cup of about 1 1. capacity . lo e ce

s ab ut 1 1. a a or b r a ﬂa k of o c p city, , ette , Copper or tin dish like that shown in “ " Figure 48 or Apparatus A of the H ar

va rd s . If a as is us d a li t ﬂ k e , the he t r is ing from the ﬂam e abou t the sides of the

r rr r Th ﬂ ask m ay give ri se to a la ge e o . e ﬂa sk should be set in a large square of A r m r . n a s bestos pape r. ba o ete A iron

r r r n Bu n r r. t ipod o eto rt s ta d . A nse b u ne

S m an or sn w . o e cle ice o Fm , 43 ,

M A A . To TE ST TH E ACCUR ACY OF TH E FR EE Z IN G P OINT R K

Pr r us nd rm m r in cu ocedu e. S pe the the o ete the p b y a clam p so that its freezi ng poi nt m ark shall be about on a v w cu le el ith the edge of the p. 2 P ac ab u bu b Of rm m r and its s m ( ) k o t the l the the o ete te , a s f ar u as r n n mar ﬁne ice c s or s n w p the f eezi g poi t k , hip o . (3) Allow it to stand se veral min utes un til assured that

r T r h the me rcu y has become stationa ry . he n ead t e posi

n f m r r m n n f d r O cu s a t s O a . tio the e y, e ti ti g the e th eg ee 1 1 1 1 1 2 HEAT

It i n ot n ssar a w Read it several times . s ece y to llo the u as as m s as i s w ater to run out of the c p as f t the ice elt , n d n If n Of is r s n b r r su s w Ofte o e . ple ty ice p e e t, ette e lt ill be Obtained by s urroundi ng the the rmomete r with wate r . ’

Pr s n s T r Of H ea . ( e to heo y t, p

r rm m ete r . n nd r x ments in w c t e o N B. I thi s a all othe e pe i hi h a h is use it is ver m ort nt in t n the re n t t the line o d, y i p a aki g adi g ha f In the o ow n sight shall be perpe ndicular to the thermometer . f ll i g experiments in Heat very m uch depends upon the accuracy with which the readi ngs Of the th ermometer are taken .

TE ST TH E BOI L I NG P OI NT M AR K B . To

1 F as or bas n ab u one r Procedure. ( ) ill the ﬂ k i o t thi d

u wa r and a v r am so a wa r f ll of te , pl ce it o e the ﬂ e th t the te

r rm m r a s hall boil vigo ously . S us pend the the o ete so th t

n r . The its bulb shall be 2 or 3 cm . above the boili g w ate stem should b e surrounded by the neck Of the ﬂask as f ar b n n m up as the oili g poi t ark . (2) When assured by se veral readings that the me rcury m n r f m r ur has b s a a r r si n O c . eco e t tio y , eco d the po tio the e y (3) Read the b arometer an d com pute the true boiling point Of wate r f or the gi ven press ure by allowi ng C . pe r cen timeter of va ri ation from a b aromete r reading of

m . r in . 76 c o C . er n c ra n r m , p i h of va i tio f o ° S ubtract this correction from 1 00 when the press ure is

b w 6 cm . or i d n is ab v . The elo 7 n . ; a d it whe it o e ba rometer reading sho uld b e corrected f or temperat ure

b r a n r T 14 A nd x . s u . b efo e pplyi g thi le (See a le , ppe i ) Record the re sults as follows

hermometer T NO. Graduation Of stem exte n ds from Observed freez i ng poin t Error Barometer Computed boili ng poi nt Observed boiling poi nt

1 14 H EAT the left Of on the scale and 13 squares to the right Of ° 98 on the scale and a lin e dra wn as s how n in Figure 49 .

T r us s ur v us su s a te m o illust ate the e of thi c e , let ppo e ° r B r rr n urv pe rature Of 55 was obs e ved . y efe i g to the c e the error at that tempe ratu re is seen to be positive H ence the true temperature is

EXER CIS E 5 2 COEFFIC IENT OF LINEA R EXPANSION

c e c nt o linear ex a Purpose . To mea sur e the o fﬁ ie f p nsi on of bra ss .

— F r n in a Apparatus . A b rass tube TT ( ig . esti g r v in b k is n d rm ab an g oo e loc C, fas te e ﬁ ly to the t le by

FIG . 50 .

r c am The ub r s u r r n . ss n a at B i o l p t e p e e po olle , the rolle r resting on a piece of ground gl ass fastened to the b c D w c is a . A r lo k , hi h lso clamped to the table wi e poin ter P is solde red to the end of the roller and is c un rba an d b a w in x n o te l ce y eight at one end . A p e te ds th rough the tube at A an d is held ﬁrmly agai nst the block

C b a s r Of b rass n ot s w n in th ur R ub r y t ip ho e ﬁg e . be ub s K an d L a re a a d nd ub t e tt che to the e s of the t e TT.

A m rr r s ca i i o le s placed at S.

n tub is a d b ass n s am r u Whe the e he te y p i g te th o gh it, it e xpands toward the right and turns the roller over a

w a m v n n r little y, o i g the poi te o ver the scale R R .

Procedure. ( 1) Remove the rolle r from its place and m asur its d am r b a m cr m e e i ete y i o eter sc rew. Also meas COEFFICIENT OF LINEAR EXPANSION 1 15 ure n n r r m its ti r r the le gth of the poi te f o p to the olle , d n diu r c l a d i g the ra s of the oller ; all this ength l.

2 P a r r und r ub a a n w ( ) l ce the olle e the t e g i , ith the n er in s n s wn in F ur 50 and m asur poi t the po itio ho ig e , e e n ub r m n A n B us a v the le gth of the t e f o poi t to poi t , j t bo e

r r u d be a ﬁle m ar at the middle of the rolle . The e sho l k

n r l r B to ﬁx the positio of the ol e . ‘ (3) Attach K to the water faucet and allow col d water

h r a n r u h to run through it f or a while . T e wate esc pi g th o g

n Ta L is caught in a vessel standi ng in a si k . ke the

m r ur s wat r s m a n n s Of a r . te pe at e of thi e , e ti ti g te th deg ee

r r u This will be the tempe ratu e Of the b as s t be . (4) Read the position Of the tip of the pointer on the u d d n n r a n s c ale S. This sho l be o e at o ce afte t ki g the

t m ra ur wat r . Let s be R . e pe t e of the cold e thi I 5 D s nn ub K r m au w ( ) i co ect the t e f o the f cet, blo hr u x w a r and n a a a t o gh it to e pel the te , the tt ch it to r A t r am boile so as to send stea m thro ugh it . f e the ste ssu s r m L a s r m r ad a a n s n i e f o ho t ti e , e g i the po itio of the

ti Of n r on S. Let s be R . p the poi te thi 2 (6) Take the temperature of the stea m as in Ex e rcise 51 B or m u n n r m bar m r , , co p te the boili g poi t f o the o ete T m ra ur u t reading . his will be the te pe t e of the t be wi h m n r u the stea passi g th o gh it . R ecord the results as follows

en t of o nter l D m eter Of R o er d L g h P i , ia ll ,

en t of u e L d l L g h T b ,

TE M P E R ATU R E S PO I NTE R R E A D INGS EXP ANSION COE FF ICI ENT P E R or E xPA N

C an e R R : R h g , 1 D EG REE SION 1 16 HEAT

If 6 cm . m r a ru r i o Discussion . the a k of le s plac ed n

1 n r r top Of a pencil (Fig . 5 ) a d is then olled along tow a d

r h un n l has r 1 cm . or r m A to B the ig t til the pe ci olled , f o , m r n be at n n the 5 cm . a k will the the top of the pe cil a d

FIG . 51 .

mar w ab v C or 2 cm . rom A the the 6 cm . k ill be o e , f ; r r w v r w av ra v rs an are on nc ule , ho e e , ill h e t e ed the pe il r u l d n . T s s ws a r rav s a s anc e 1 cm . lo g hi ho th t the le t e i t twice the length of the a re through which the penc il turns on its own axis . i a end Of n the If a poin ter oP s att ched to the the pe cil, are a traversed by a poi nt on the s urface of the pencil is to the arc R t rave rsed by the tip of the pointer as the radius Of the pencil r is to the length of the pointer l ;

= - - H n a R r z l. But ru r m ves e ce , the le o

= - Or 2 R r + l R d z I. twice as f ar as this, n s a ara us the ex ansion o the Applyi g thi to the pp t , p f tube the di sta nce the p ointer moves on the sca le x dia meter of roller length of the poin ter . The e xpansion di vided by the change of tempe rat ure gi ves the expans ion per degree ; this di vided by the le ngth of the tube gives the coefﬁ cient Of expan sion

11 8 HEAT

(2) Remo ve the tube and stand it in front Of a m eter s tick or a m irror scale and measure the length from A to b r d n C y ea i g the positions of A and C. °

T . s w be v um air at 0 C . t hi ill the ol e of the , o ° 3 P rm r w a r ( ) lace some water at about 50 C . (wa e te m b r a i d us n r ight e k the jar) n the eep jar . S pe d the the m ometer in the w ate r by a wi re which is ben t over the d f N u in r n ar e ge O the jar . ow place the t be the wate e rm m r A r a f w m m n s ad us b and the the o ete . fte e o e t j t the D as before an d at the same time take the temperature of wa r t the te , r Si nce the water in such a jar very soon becomes several d r s d r at b t m an at an r er eg ee col e the o to th the top, othe p son should be constantly sti rri ng the water w hile this u L t s rr r R be m v d a dj stmen t is bei ng m ade . e the ti e o e up and down at the back Of the jar so as to avoid hitting ub an d rm m r the t e the the o ete . (4) Rem ove the tube from the jar and measure the air m n colu as before . Record the results as follows E I A E E E SP C FIC HEAT . W T R Q UIVAL NT 1 19

° Discussion . u ra n v um at 0 C . or t r m S bt cti g the ol e , o, f o its v um at r t m ra ur t v s ex an ol e the highe e pe t e, n gi e the p f ir D v n s x ans n b the n i s ion O the a . i idi g thi e p io y cha ge n t m ra ur t v s x ans n f or one r e pe t e ( 1 0) gi e the e p io deg ee, b ° and dividing this result y the vol um e at 0 C . gi ves the ° fﬁ n or ra n Of its v um at 0 C . w h it coe cie t, the f ctio ol e hic

e xpands per degree . Reduce the average coefﬁcient which you Obtain to a com mon fraction having 1 f or its numerator and compare

it with 2 45 . EXER CI SE 5 4

E IF HEA WA ER E SP C IC T. T QUIV ALE

n t s ci c Purpose. To ﬁ d he p e ﬁ hea t of a lso to

mine the water e uiva len t o a ca lo i deter q f r meter .

- A rm a ba an . Apparatus . pl tfo l ce A set m r A as n A thermo ete . b i 0

- A a one e nd . c lorimete r ma de

though n ot is better to a woode n ring in w rimeter can be s uppo rted as FIG . 53 . 5 in Figure 3 .

1 d r nd h a Procedure. ( ) Weigh the cylin e a t en pl ce it r l n ook- h in a basin Of wate tha t is kept boi i g . H t e m — ‘ im a m cyli nder sv t hat the be 1 20 HEAT

r (2) Weigh the empty calorim eter (the i nn e cup) . (3) Fill the calorimeter about se ven eighths full Of r us n hearl n u a r m r w n wate , i g y e o gh to ﬁll the c lo i ete he lin r is mm rs in T s wa r s u d of de i e ed it . hi te ho l be M M — - - - - ‘? M the sam e tempe rature w he - m e f t he f ee mr pr ef

a- a r m r Ol ably a degree or two c older . Weigh the c lo i ete

and water . 4 Ta m ra ur Of n wa r v r n ( ) ke the te pe t e the boili g te , co e i g as m uch Of t he stem of the thermometer as possible with

the water ; I l l u .

r If (5) Set the calorimete r near the boilin g w ate . it is n t in an u r cu s d r m a Of am o o te p, hiel it f o the he t the ﬂ e by standin g a boa rd between it an d the ﬂame and a void

n Ta m r r w a r handli g the cup. ke the te pe atu e of the te r a ar with g e t c e . (6) Just a s soon as p ossible af ter ta king the temp era ture o the wa ter rans r c nd r r m the b n w at r f , t fe the yli e f o oili g e

- - -- - ca r m r b the wise . Rem ov e the m s r to the lo i ete T , ti the water aroun d the cylin de r thoroughly with the ther

m om eter and r ad m ra ur . R ad s v ra m e the te pe t e e it e e l ti es, rr n r sti i g the wate each time .

Caution . Unless these two tempe ratures are read with r a ar ur A rm m r r su s w be w r ss . g e t c e , yo e lt ill o thle the o ete

can n r d r i d R m m ot be ea accu ately if it s one hastily . e e r h i ll be t is n a the following e xe rcises . (a) On ly the top of the mer cury threa d s hould show above e wa t r the n t k th e when rea di g is a en . (b) The line of sight must be p erp en dicular to the ther

mom eter to a void ar a llax or ou m a ea sil ma ke an er ror p , y y y o ha l a d o f f egr ee r more.

0 You must stir the wa ter tho o ( ) r ug hly .

d E s tima te tenths o a de r c ( ) f g ee a r ef ully .

122 HEAT

The mass of the calorimeter x s the ther ma l cap a city r m n ua n or wa ter equivalent of the calo i eter. H a vi g this q ou can in all x r s s in wh s a r m t r is tity, y e e ci e ich thi c lo i e e used add it to the amo un t Of water take n and then d rop the calorimete r from further consideration in the solution of the p roblem .

E XER CI SE 5 5

o st d the hea t cha c rin durin the Purpose. T u y nges o cur g g s i ca tion or reezin a li uid 389 ol diﬁ f g of q ,

- . n f b n r A 6 n Apparatus A basi O oili g wate . i ch test “ " tube (a test tube on foot is most conven ien t) . A A n r. m thermom eter; A watch . basi of cold wate So e ha a r r um su a . sodi thio lp te , c lled hypo by the photog phe

1 F Procedure. ( ) ill the test tube about two thi rds u l w th r s a s Of and m m d n f l i c y t l hypo , elt the by hol i g the u n n wa r n r s re test t be i boili g te . Whe the c y tals a all m be sur all are m t m ra ur u elted ( e el ed) , the te pe t e sho ld ° n 0 not be m uch if a y abo ve 7 C . 2 H av n n wa and all in r a n ss su ( ) i g otebook, tch, e di e , p port the tube with the the rm ometer standing in it in a ° n f d a r t ab u 1 5 and a n basi O col w te a o t O. t o ce begin to re cord the temperature and the time f or every ﬁfth degree n Let ne u a Off m while it is cooli g . o p pil c ll the te pe ra u r n r n n d r m D t es while a othe otes a ecords the ti e . O not d ur u ur n ist b the liq id d i g the cooling . °

3 n has n ar 20 C . r in ( ) Whe it cooled e ly to , d op a crystal or two of hypo and the n record the temperatu res and m as ra as ss b un ra an s c ti e pidly po i le til pid ch ge ease . The u ma in air ns a Of wa r liq id y be cooled i te d cold te , but the process is slow and the cooling should con tinue o nly f or abo ut (4) Using the tempera tures as ordinates an d the times HEAT OF FUSION OF ICE 123

rom b nn n as a s as ur r f the egi i g b ciss plot a c ve . Sta t at the o rigin with a tempe rature of

R rd r su s as ws m a n umn eco the e lt follo , ki g the col s a page long

r Discussion . W ite an explanation of the curve in your T i x r r n n otebook . h s e pe iment illustrates unde cooli g ; that is n a u b w its r n n w t u , the cooli g of liq id elo f eezi g poi t i ho t n its freezi g . What does it teach about solidiﬁcation or freezing as to the production of heat ?

Th use f r NOT E . e o sodium thiosulphate f o this experim ent was r r sugges ted by P ofessor 0 . K . Studley of the California State No mal

School.

E XER C I SE 5 6

HEAT OF FUSION OF ICE

o deter ine the hea t o usion o ice or the Purpose. T m f f f so-ca lled la tent hea t of wa ter — m r rm m r . A a Apparatus A calori ete . A the o ete pl t

rm an m an . A h. fo bal ce . So e cle ice clot

1 a r m r Gr it-M e Procedure. ( ) Weigh the c lo i ete , w eed -4m m record its weight and water

equi valent In the tabular form . (2) P repare seve ral l umps Of clean ice varyi ng in size ’ from th at Of a wal nut to that of a hen s egg . (3) Fill the calorimeter about three fourths full of water ° n a r and a r m r . at about 40 C . and the weigh the w te c lo i ete 124 HEAT

(4) Place the calo rimete r in its outer cup and then s ti r ring thoroughly with the therm om eter take its tempera ° ur a cura . It s u d not be mu an ab v 40 t e c tely ho l ch if y o e C . 5 Imm d a a r r ad n m ra ur add ( ) e i tely fte e i g the te pe t e, i u l umps of ce to the water . Wipe each l mp dry befo r e

dr n in . Add the ar um s at ﬁrs n a r oppi g it l ge l p t, the l te ,

as the wa r c s sma l r um s . te ool , l e l p (6) Stir the w ater an d ice consta ntly with the the r

mometer m an wh wa c n m ratur u , e ile t hi g the te pe e . J st a s soon as the ice is all melted re ad the temperatu re agai n ° a ura . Th t m ra ur sh u d be b w 1 0 I cc tely e e pe t e o l elo C . f

is not add m r . it , o e ice (7) Weigh the calorimeter and the wate r it contains s o ha am un Of ice a has n add d can be Ob a n d t t the o t th t bee e t i e . Record the results as follows :

Discussion . The heat los t by the wa te r an d the m r calo ri ete is used partly in m elting the ice and partly in

126 HEAT

l h r m er in the s n s wn in F ur 54 p ace t e calo i et po itio ho ig e , b and n ac n by ﬁrst removing the lock B the repl i g it . Steam Should be issuing vigorously from T before the calorimete r is put in position . 5 a c r s m ratur in a r m r ( ) W t h the i e of te pe e the c lo i ete , ° and when it has risen to about 35 (it will take b ut a f ew

m m n u r m v a r m r. o e ts) , q ickly e o e the c lo i ete m ra ur ura Stir thoro ughly and take the te pe t e acc tely . (6) Weigh the calorim eter and water to ascertain how much steam has been added . (7) Fin d the temperature Of the s team Gather -di rectly

Record the res ults as follows

TRIA LS

M ass of calori meter M ass of calorimete r water M ass of water taken Water equivalent of calorimeter Mass of calorim eter water steam Mass of steam added Temperature of water and calorimeter at ﬁrst Temperature of the same after addition of steam Temperature of ste am

o e ees ter and No. f d gr wa calorimeter are warmed

f ee h n ense te NO. o degr s t e co d d s am is cooled Heat of vaporization of water

Accepted value E rror Pe rce nta ge Of error VAPOR TENSION 1 27

— The a r u b m n Discussion . he t p od ced y the stea i con de nsin n t wa r at sam m ra ur as s am g i o te the e te pe t e the te , a nd a v n u b s sam wa r in n are the he t gi e p y thi e te cooli g, n d r m F r both gi ven to the cold water a the calo i eter . i st ﬁ nd r m r r n d how m uch heat the w ater a c alo i ete eceive . If from this amount you subtract the amount of heat n b n n s am or wa r re give to it y the co de sed te hot te , the m ain der will be the amount of heat produced by the steam in n n r m T s r ma nd r v d cha gi g f o steam to wate r . hi e i e di ide by the n umber Of gram s Of steam added will give the a m ount Of heat produced by one gra m of steam in con in r r n a r de ns wa r o a Of va a w . g to te , the he t po iz tio of te

EXE R CI SE 5 8

V APOR TENSION

o t a t t e va or t si o Purpose. To sh w h h p en n or pr essure of a sa tura ted vap or dep en ds on its temp era ture ; a lso to obser ve the tension of a liquid a t the boiling o p in t of the liquid .

— - Apparatus . A U shaped tube — — (Eigv é é j havi ng its short arm l T c osed . his tube contains som e m ercury and a small amoun t Of a In s end m lcohol the clo ed , -Fi r “ he g ure . The e should be no ai r in the c s d end u lo e of the t be . A similar tube containing a little wa r ns ad A te i te of alcohol . ther m om eter . A tes t tube with a tw o hOle stopper contain ing a little

A n » alcohol . co e shaped ﬂask 0 11

M . " N M ew-w A ; L . 128 HE AT

1 F as n ar u wa r and Procedure. ( ) ill the ﬂ k e ly f ll of te s upport the U-shaped tube containing alcohol in the ﬂa sk so that its short arm is enti rely covered by the water . S uspend the thermometer in the water bes ide the tube or bi nd it to the tube with rubber bands .

(2) H eat the wate r slowly and watch the alcohol . As soon as it vapo rizes note carefully the movement of the n me rcury and also the temperature changes . Whe the m r r i sam in tw o a rms va r e c u y s at the e level the , the po tension Of the alcohol vapor eq uals the atmospheric

N m ra ur ns an s urs . pressure . ote the te pe t e the i t t thi occ H ow does the vapor tension change as the temperature rises ? 3 R m ub r m as u r ( ) e ove the t e f o the ﬂ k . S ppo t the thermometer in the test tube con taining the alcohol by u i p shing it th rough on e of the holes n the stopper . The u la thermometer should not q ite touch the alcohol . P ce s s ub in warm w a r at n a r un thi te t t e te , he i g the l tte til h n m r ur di the alcohol boils . W e the te pe at e rea ng has m ns an a m ra ur t beco e co t t, t ke the te pe t e a which the

h r in r alcohol boils . T e othe hole the stoppe should be large enough to allow the vapor Of the alcohol to escape r f eely . 4 wa r in as a u an n ( ) With the te the ﬂ k bo t i ch deep, support the U-sh aped tube contain ing water in the ﬂas k

us a v . B a r in j t bo e it oil the w te the ﬂask . Watch the vapo rization of the water in the tube and note at what n m r ur c m s s a n r If poi t the e c y be o e t tio a y . it does not b m s a nar is b aus air n rs eco e t tio y , it ec e e te the ﬂask and

s . TO r v n s v r as s w cool it p e e t thi , co e the ﬂ k loo ely ith a piece of pape r th rough which a hole has been m ade f or the tube . Note what happens to the vapor tension if this a r s s as so s am ann a p pe clo e the ﬂ k the te c ot esc pe freely . E x a n pl i .

H EAT

Carefully avoid breathing on the cup or placing the r i u r hands nea ts o tside su face .

4 Add ne w s m a uan s Of warm water s rr n ( ) ll q titie , ti i g thoro ughly and letting each addition produce its eff ect

N h m r tu f r befo re adding more . ote t e te pe a re O the w ate w n h m h he t e oisture on t e outs ide begins to disappear . Ca T m r r r ll it e pe atu e Of disappea ance . The ave rage of the tempe ratures Of appearance a nd

a r t dis ppea an ce will be the deu p oint. 5 T m ur i m ( ) ake the te perat e of the a r of the roo . (6) Look up in Tablegl‘ﬁ the n umber of gra ms of wate r vapor required to saturate the air at the m ra ur Of r m a s at m ra ur the te pe t e the oo , l o the te pe t e of

ew - n The a r uan i uan t o a r d poi t . l tte q tity s the q ti y f v po actua r i i f r m o ﬁ nd lly p esent n the a r O the oo . T the r a v um d ﬁnd ra the va or a ua el ti e h i ity, the tio of p ct lly p rese nt to the quantity that co uld be present at the

v n m r u r gi e te pe at e . Reco rd the results as follows

T R IA LS

Te mperature of appearan ce Te mperature of disappearan ce

Aver e of the two or dew- o nt ag , p i Temperature of room Gram s of water vapor per cubic meter at dew- point Grams of water vapor to saturate 1 the air at tem perature of room j Relative h umidity CHAPTER V II

M AGNETISM AND ELECTRICITY

EXER C ISE 60

THE FIRST L AW OF M AGNETS

t d t a ct n o on t Purpose. To s u y he io f e magnet upon ano her

440, 441 ,

- A aratus . Two arn n n s . A bar ma ne pp d i g eedle g t. m n A A c r . a w x c r w r . o k So e se li g a . sau e ﬁlled ith wate

1 M n tw n r n Procedure. ( ) ag etize the o eedles by d awi g the same pole of the bar m agn et seve ral times along the w n ac a wa s in sam r n hole le gth of e h , l y the e di ectio . (2) Note which pole of the bar m agnet is us ed and nd d i uc i which e Of the nee le s last to hed by t. (3) Float one of the n eedles on a cork in the saucer Of

r h- w a ter . M ark the no t seeking pole wi th seali ng wax or m r n n a r in so e othe co venie t way . Repe t the Ope ation with

’ r d the othe nee le . (4) B ri ng the n orth -seeki ng pole of the other needle n ar s Of a n n d and n e to the pole the ﬂo ti g ee le , ote the

- Tr u s n . T n x n res ults . y also the so th eeki g pole he e cha ge

the needles and repeat the ope rations . IS the end of the needle las t touched by the bar magnet r m am in a as bar . a net u the s e pol ity the pole of the g sed, or opposite ? H ow do like poles aff ect each other ? unlike poles ? 5 T s an u r m ass r n su c as a s v ( ) e t y p ight of i o , h to e, the n end Of a d s or a s w a m ass or a m a n i ro e k , po t, ith co p g et iz d arn n ne d s us n d d b an un w e d i g e le pe e y t isted thread, 131 132 MAGNETISM AND ELECTRICITY

rs at the n at m . Is ma n ? ﬁ t top, the the botto it g etized If so how are its s a ? , pole loc ted

EXE R CI SE 61

EFFECT OF BR EAKING A MAGNET

P . To test the ma netism o the ieces o a urpose g f p f magn et.

A . A m a n A m ass or a a n n d pparatus g et. co p ﬂo ti g ee le x such as that used in the last e ercise . A piece of watch 1 m n spring about 0 c . lo g .

1 M a n wa r n Procedure. ( ) g etize the piece of tchsp i g n m ar i and test a d k ts poles . (2) Break the spring in to tw o pieces and test the en ds Of each piece f or m agnetism by the compass or the ﬂoati ng needle . 0 (3) B reak these pieces and test the parts again as r C n nu s r s r n an d n befo e . o ti e thi p oce s of b eaki g testi g as

lon g as you can . (4) Lay the pieces dow n in thei r o riginal o rde r an d note thei r arrangeme nt as to thei r m agn etic properties r s o pole .

D O o n x Discussion . y u thi k this e periment s upports the theory that the m olecules Of a m agnetic substance are m agnets and that in a m agnet the like poles of the m ole cules point in the same di rection ?

E XER C ISE 6 2

MAPPING A M AGNETIC FIE LD B Y A COM PASS

o m the ma n etic eld o a ba r ma n b Purpose. T ap g ﬁ f g et y

ea ns o a com a ss 452 m f p , — A b r m n . A r r s a a a s a r. Appa atu . g et l ge heet of p pe A m a c m s ll o pass .

1 34 MAGNETISM AND ELECTRICITY

EXE R CISE 6 3

MAPPING A MAGNETIC F IELD BY IRON FILINGS

To ma ma netic elds o ma nets b iron Purpose. p g ﬁ f g y ﬁlings and to study p ermeability

T o bar m a n s . A rs s ma n . Apparatus . w g et ho e hoe g et A sm all piece of s oft iron a nd an arm ature f or the ho rs e

s ma m u s n ba c n a n n r n n s . shoe m agnet . A ll li g o t i i g i o ﬁli g

r A f ew pieces of thin boa ds .

Procedure.

P A R T A

(1 ) Place a bar m agnet upon the table and about it m r sam n ss as ma n an d so e boa ds of the e thick e the g et, a m s r then spread ove r these s ooth heet of pape . (2) Sift from the m usli n bag i ron filings evenly an d t in l v r s a r an d n ta n w a n h y o e thi p pe , the p it ge tly ith pe cil or jar the table with the fist . (3) M ake a drawing in your n otebook Of the figure formed .

PA R T B

(1) Place two bar m agnets parallel to each other and a u on e rd r n a ar r un s b bo t thi thei le gth p t, thei like pole e n ing adj ace t . M ap out the ﬁeld in the same m anne r as Par in t A .

2 R a the ra n a n s a a nt ( ) epe t ope tio , pl ci g like pole dj ce .

P AR T P E R M E A B I L IT C, Y

(1 ) M ap out as in the preceding exercise the mag n a rs s m a n rs w u an r etic ﬁeld of ho e hoe g et, ﬁ t itho t y a ma n w n r ur a a m ur . t e, the ith at e

2 P a sm a c s r n n ar but no i ( ) l ce the ll pie e of oft i o e , t n

n a w the s Of r s m co t ct ith , pole the ho se hoe agnet ; or place TH E VOL TAIC CELL 1 35

n s two bar m a n s but not it between the u like pole of g et ,

m and m a out ﬁ as b r . in contact with the , p the eld efo e The piece Of i ron Should be about as large as a sil ver

‘

uar r and as c as m a n s . It can be q te , thi k the g et kept from sliding towards the m agnets by sm all bits Of w ood . Permanent copies of these ﬁgures can be Obtained by

n a s Of uns a r m s n d w a s u placi g heet ized p pe , oi te e ith ol

n Of ann n a r u v r fi ur rm tio t i , c ef lly o e the g e fo ed by the P r s a r d wn n u n fi n iron fili ngs . es the p pe o ge tly po the li gs b a b r and n OE ar u a w n the y lotte the lift it c ef lly, llo i g

n s n to a r . n dr brus OE fili g to cli g the p pe Whe y, h the n nd a n o m ad in ur n b fili gs a f ste the copies s e yo ote ook . Beautiful pri nts of these fields m ay be m ade upon blue

r n a r or u n ra a r . TO s a p i t p pe po photog phic p pe do thi , pl ce the m agnets upon a dra win g board an d cover them with the

r n ﬁ n sensitive paper . Then sift the i o li gs upon the paper T m d n in a w n t as before . his ust be o e light that ill o

aEect a r n a r r x sur is m a . the p pe , the p ope e po e to light de For blue -print paper the board should be placed in direct s unlight f or 10 or 15 minutes . The ﬁlings are then r removed and the paper washed f or a half hou .

EXE R CISE 64

THE V OLTAIC CELL

P r . To stud the essen ti a ls o a voltaic cell tha t is u pose y f , , a o- called batter an d to learn a bout local a ction in a cell a y, 458

— u r - r u ul Apparatus . A t mble about two thi ds f ll of s

huric a d O 1 ar a d 15 or 20 ar s Of p ci , s 4 ( p t ci to p t

a r . A s r Of z n c and one Of C r a s s r s w te ) t ip i oppe , l o t ip of

r m a s suc as r n ad an d a um n um . A rod Of othe et l h i o , le , l i T r carbon . wo ext a tumblers to place the metal strips in 136 M AGNETISM AND ELECT RICITY

n w c am s when not in use . A sta d ﬁtted ith l p to hold the Fi A a van sc . metal s trips in the acid ( Fig . g l o ope ( g or bette r a tangen t galva i nom eter (F g . A little r mercu y .

1 Procedure. ( ) Witho ut us n am s and s an d i g the cl p t , place the zi nc st rip in the acid alone and n ote what occurs on ur D m its s face . o the sa e w ith

the copper . (2) Place both strips in the liquid and note what occ urs on

FIG . 56 . sur a a ﬁ rs w n the f ce of e ch ; t, he are not in n a s nd w n u n u n they co t ct ; eco , he to chi g de r the u r w n h u u s d liq id ; thi d, he t ey to ch o t i e the liq uid ; and ur h w n a re d in am and fo t , he they hel the cl ps a re nn b r s N ff on co ected y wi e . ote the e ect the coppe r of repeatedly m aki ng and breaki ng the co nnection between the plates . Whateve r apparent action you Observe on the zi nc is

n n a oc l a o k ow s l a cti n . n a van s is in use m us a (Whe the g l o cope , it t be pl ced so a w r its ar n r and u th t i es of coil e o th so th . ) (3) Let the metallic con n ection between the plates be m ade by the wi re of the gal vanoscope or the gal vanom eter by joinin g to

FIG . 57. its bindi ng posts the wi res attached to the clamps . Note the action Of the needle on m n nn co pleti g the co ection .

A w r a aff ts a m a n n n ar i e th t ec g etic eedle e it, as this

M AGNET ISM AND ELECTRICITY

r in Discussion . We lea n chemistry that the gas pro ' u x r m n i n If u u d ced in this e pe i e t s hydroge . yo sho uld se h s c f or a w n w u be c nsum w h t i ell hile , the zi c o ld o ed, ile

c r u d a ar n be unaff d . H n the oppe wo l pp e tly ecte e ce , altho ugh m uch of the chemical action was appare ntly on T r r was r a all on n . a a the coppe , it e lly the zi c h t p t of the chemical action on the zin c which liberated hydroge n on n ca d l l c n c n r bu s no u rr n the zi c , lle oca a tio , o t i te c e t to the in ur wi re and is useless and wasteful . State yo book

h i r n ow it s p e ve ted . W rite out fully in your book what you consider to be n the esse tials of a voltaic cell .

EXER C ISE 6 5

POL AR IZ ATION OF C ELL S

io o c . To stud ola riz a t n ells i ts cause and Purpose y p f , , its r emedy

— A v m r v Apparatus . tange nt gal a no ete ha i ng a coil of

0 m r n 25 to 5 Ohm s resistan ce . A tu ble co tai ni ng s ulph uric T m s tri c r . w r acid and w ater . So e ps of oppe o ca bon

d z r m ma n . m n r rods . A st ip Of a alga te i c So e it ic a cid . 4 Th and u in Ex rc 6 . A sm a r us e st sed e ise ll po o cup .

A glass spatula .

ur . 1 F rm a s m as in Ex r s 64 Proced e ( ) o i ple cell e ci e ,

us n a dr an r a . If has r n b n i g y, cle coppe pl te it ece tly ee us d in a s u d be a d in a B u n s n am a nd e cell , it ho l he te e ﬂ e , r c n polished with eme y cloth . Join this ell to the lo g coil A n as n d b c m of the gal vanom ete r . s soo the ee le e o es s till record the n um ber Of deg rees Of deﬂection and then w atch r c r the needle f or se veral mi nutes . Note whethe the u re nt

b c m s w a r or s r n r or r ma ns sam . The e o e e ke , t o ge , e i the e eff e ct whi ch you will probably Obs e rve is called polariza of tion the cell . POLAR IZ ATION OF CELLS 1 39

2 A r a van m r r a n b m s c ns an ( ) fte the g l o ete e di g eco e o t t, stir the acid about the copper plate with a glass spat ul a ve ry vigorously so as to remo ve the hydrogen from it . What does the needle Show about the curren t while you are sti rri ng What happens to the n eedle as soon as you s top stirri ng ? Does the result seem to show that the hydrogen is the cause of the polarization (3) Short-circuit the cell by holding a s trip of COpper i n n r nd n T co tact w ith the coppe a zi c plates . his will p roduce a greater q uantity Of hydrogen on the coppe r .

T n W u d s urb n an c nn n s a out he , itho t i t i g y of the o ectio , t ke n a and ut a an dr r s r in its the zi c pl te p cle , y, coppe t ip

a n n a n n d at sa m m . pl ce, oti g the ctio of the ee le the e ti e You will see that the hydrogen on the other copper plate

d rr n n d r n s en s a cu e t i the opposite i ectio .

This explain s why hydrogen pola rizes a cell . It tends

n rr n r h h to se d a cu e t backwa d thro ug t e cell .

4 If m r m s r a all ab v w r us n ( ) ti e pe it , epe t of the o e o k , i g

r r in r a ca bon od place of the coppe . (5) Fill a small poro us cup w ith som e Of the sol ution from the tumble r a nd place the porous c up in the tum bler

d c rb n r n P ac n c s r in an the a o od withi it . l e the zi t ip the a cid outside of the porous cup an d then con nect the cell

r a v n m r as befo e to the g l a o ete .

r d 2 A w c a z n ad or 3 cc . Of s r n llo the ell to pol i e , the t o g

- a n n it ric acid to the porous cup . W tch the eedle of the ga lvan omete r f or some time . Che mistry teaches us th at the nitric acid will use up the hydrogen by furn ishing

u n nd rm wa r D s r o xyge n to ite with it a fo te . oe it p e ven t polarization

ll m m a n re Discussion . A cells use so e che ical ge t to p ve n t polariz ation by acting upon the hydrogen or other

elemen t appearin g a t the positive plate . 140 M AGNETISM A ND ELECT RICITY

E XER CI SE 66

DEFL EC’I‘ ION

o stud the a ction o an elect ic curre t Purpose. T y f r n upon t n e e a magne ic e dl .

r m Apparatus . A dry cell o so e other form of the voltaic u a N 22 . A b u m . ns d r w r a u O . cell o t of i l te coppe i e bo t , n attached to one pole of the cell . DO ot attach both ends w r f or n w ar e nd of the i e to the cell , the the cell ill pol iz a

A m ass or ma n n . become useless . co p g etic eedle

I m mb r r Procedure. ( ) Re e e that the cu rent always ﬂows through the wi re toward the zin c plate of the cell i when the con nection s m ade . Stretch the middle portion w r ab v m ass n d and ara o of the i e o e the co p ee le p llel to it, s

urr n w ﬂo r N that the c e t ill w towa d the south . ote the

‘ eff ect On the needle on closing the ci rc uit by holdin g the r nd r in c n w r T f ee e of the wi e o tact ith the othe pole . his action is called deflection . Record the deflection (not the n umber of deg rees ) simply as east or west accordin g to r n n r n n the di ectio the o th pole of the eedle tur s . (2) Try the same with the curren t flowing from s outh to no rth abo ve the n eedle . 3) Note the eff ect when the wire is placed un de r the n eedle so that the c urren t flows from north to south below n d the ee le . 4 A a n n f w urren n ( ) g i , ote the ef ect ith the c t flowi g r m u f o so th to n orth below the needle . (5) Pl ace the compas s on the en d Of a book standing on end and s tretch a portion of the wire in a vertical posi n n ar n N r n d . ff tio e the o th pole of the ee le ote the e ect, firs t w en the cu rr n is w n u and n w n , h e t flo i g p, the he the urr n i o w n n c e t s fl i g do w . (6) Repea t the las t operations at the south pole of the r n eedle . Can you tell f om the results of the above opera

142 M AGNETISM AND ELECTRICITY

i i n n arran so as urn as n ts positio a d the coil ged to t e ily, the coil wo uld be turned so as to ass ume an angle with

the m agnet when the cu rren t is sent th rough it . Ga lva r n ometers consis t essentially of a coil of wi e and a m agn et . In some instruments the magnet is the m o vable part an d

h r i i sta na r w in rs t e v rs s ru . the coil s tio y , hile othe e e e t e It would be well f or the studen t now to m ake a st udy of galvanometers both by reading about them and by ex am in in an a n r n g y vailable i st ume ts .

EXER CISE 6 7

AN ELECTROMOTIV E SER IES

o Purpose. To determine whether on e meta l is p si ti ve or n ega tive with ref erence to another i n a cell . — A aratu . am as f or Ex r s 64 and in a n pp s S e e ci e , dditio

a s r n ad carb n and a um num . pl te of i o , le , o , l i

Procedur . 1 Ta n one s a s as r e ( ) ki g of the e pl te , coppe , rm a w ac rs in u rn and fo cell ith e h of the othe t , by the galvanoscope determine in each case which is the positive and w ch i hi s the n egative plate . (2) Con ti nue the above process u ntil as m any diff e ren t mb na ns as ss b av b n m ad w ﬁve a co i tio po i le h e ee e ith the pl tes . (3) Arrange the plates in a se ries s uch that if any two m be a n rm a rs in th s r s s of the t ke to fo cell, the ﬁ t e e ie hall s v be the po iti e plate . Record the data in a table as follows ELECT ROM AGNETS 143

EXER CISE 68

E LE CTR OM AGNETS

c Purpose . To study the constr u tion of the electromagnet a n d to learn up on what its p olarity dep ends

dr r r s ur O r r Apparatus . A y cell o othe o ce f elect ic cu

r n T r r r m r n u r r e t . h ee O fou ete s of i s lated coppe wi e

- 2 u . n a u . A 4 n s b A r rod bo t NO 6 . i ch te t t e soft i o of a

d am r a s n s ub rod a n i ete th t will lip i to the te t t e, the h vi g

ﬁ r n nd . A m n a le ma at o e e m ass r n ﬁ s . k co p . So e i o li g

1 n r n Procedure . ( ) Wi d the w i e i a n eat close spi ral aro un d the tes t tube and then connect the ends of the wire

c us s nd n an tr urr n r u to the ell , th e i g elec ic c e t th o gh it . Test the coil of wire to see if it is a m agn et by applyin g

ac end nds m ass a s b a n e h of it to the e of the co p , l o y pplyi g

nds Of r n ﬁ n s . If it a ra s ﬁ n s the e it to i o li g tt ct the li g ,

r u n break the ci c it and ote the result . (2) Re ve rse the c urre nt in the wire by chan ging the c n n ns at c and r c r an an in c o ectio the ell, e o d y ch ge the oil , m Th testi ng it with the co pass . e m ate rial of the tube has n othing to do with the eEect obse r ved . The tube may be m r x r d r br an a a c r n s uc as a w o ass . of y te i l e ept i o , h p pe , oo , (3) Place the i ro n rod within the tube an d repeat the

m r h x r . R rd u n T e pe i ents eco the eff ect of si g the ba . e

r r d i d co i on o s calle a r e. (4) Begi n at the middle of the wire an d w in d half of it on on in e test tube a nd h alf on another . Wi nd it s uch a w ay that the mouth of on e tube shall be a no rth pole and the m u r s a be a s u so a ub s o th of the othe h ll o th pole , th t the t e m placed side by s ide practically for m a horseshoe agnet . Is it the way the wi re is wou nd or the di rection aro un d the coil that dete rm in es the poles ? (5) Note the eEect on the st ren gth of the m ag net of reducing the n umbe r of tu rns Of wi re in the coil . 144 M AGNETISM AND ELECT RICITY

(6) Gras p the coil in the right hand so that the ﬁ n ge rs

en ci rcle it in the same direction as the c urre nt ﬂo ws . Note towa rd which pole the th umb points an d thus de vi s e a rule by which the poles of an electrom agnet can be d rm n d n d r c n curr n is n w n ete i e whe the i e tio of the e t k o ,

r r n h r re n wn o the di ectio of t e cur e n t when the poles a k o . Let ud n n ow xam n and s u an r b the st e t e i e t dy elect ic ell,

ra s un d r r a and r ns rum n s wh c teleg ph o e , el y , othe i t e t of i h

r m rm an elect o agnet fo s a part .

TH E TA N GEN T GAL V A N OM ETER

TH E L AW OF TH E TANGENT GALV ANOMETE R m Fi 58 i The law of the ta ngent gal van o eter ( g . ) s that the strength of the curr ent is p rop ortion a l to the ta ngen t of the a n le o de lecti on For x a m s u s a g f f e ple , ppo e th t a curren Of an am er ass r u h a an n t of p e , p ed th o g t ge t a va n m r r duc s a d n and a an g l o ete , p o e eflectio of th t othe r current of unk n own strength produces a deflection Of By the above law the strength of the secon d cu r r n an b d t rmin b m r n fir e t c e e e ed y co pa i g it with the st . L et as eq ual the st ren gth of the unknown curren t in T ampe res . hen ° x tan 31 tan

F r m a ab an n s Tab 13 A nd x i o t le of t ge t ( le , ppe i ) , it s ° fo un d that the tange n t of 31 is and the tan ge n t Of ° 61 is hen ce

x amperes .

It is e viden t from the abo ve ill ustration that it is n eces sary to k n ow what deﬂe cti on some kn own curren t will produce in a ny pa rtic ul a r gal va nom eter in order to use

a van o m e ter f or measur n s r n c ur n the g l i g t e gth of re ts . It is m ost conven ien t a nd the refo re c ustomary to take

M AC NETISM AND E LECT RICITY

ings at the two ends of the pointe r a re n ot the sam e an d do

n ot agree with those gi ve n whe n the c urrent is reve rsed .

T s rr rs w c s u d be sm a m a be aus d b he e e o , hi h ho l ll , y c e y the pointer not bei ng s t raight and at right angles to the

n d or b ax s on w c the n d e u rns not b n ee le , y the i hi h ee l t ei g

a t c n r radua d rc or b n r n ot the e te of the g te ci le , y the poi te T bei ng adj usted to ze ro at both e nds at ﬁ rst . O elimina te

s rr rs is n cessar a d ub r ad n s at the e e o , it e y to t ke o le e i g ; th

is r ad os t n ac e nd the n r an d n , to e the p i io of e h of poi te the n r d n re ve rse the c ur re t an d take the ea i gs agai n . The average of the fou r readings take n m us t be consider ed as

the tr ue deﬂection . The obse rve r m ust b e ca reful not to h ave any i ro n abo ut

r I m m n his pe son . f a o ve e t of the needle occ urs upon the a pproach or retirem e nt of the obser ver f rom the in str u m n is an nd ca on ha r is s m r n or s t e t , it i i ti t t the e o e i o eel,

s uc as n v s s or s ta s ab u n the h k i e , key , y , o t the clothi g of

Obs r r a w r nd r accura r m s e ve th t ill e e te wo k i po sible . P aralla x m ust be a voided by placi ng the eye above the n eedle so that the poin ter hides its own image in the m ir

ror bene ath .

n v r ss b is s a rran a a ra u Whe e e po i le , it be t to ge the pp t s or to selec t the coil of the gal van omete r so that the deﬂec tion shall n ot vary w idely from si nce the eEect of an

rr r i r ad n i s a a n th n n e o n e i g s le s t th t poi t a at a y othe r . ° ° An e rro r of 1 at 45 will prod uce an e rro r of abo ut per ce nt in the res ult ; while an e rror of the sam e am ou n t at or will p roduce a n e rro r in the res ult Of abo ut

10 per ce nt . To prevent the con necti ng wi res from in ﬂ ue n ci n g the

n d . the a van om e r t s u d be w s ee le of g l te , hey ho l t i ted

e r e r ac the n s r um en together wh e th y app o h i t t . For the e x pl a n ation Of the m ea nin g of tangent of an

a n le see a e 94 . g , p g RED UCTION FACTOR OF A GALV ANOM ETER 147

E XER C I SE 69

R E D UCTION FACTOR OF A TANGENT GA LV ANOM ETE R

To ea s r the cu ar en t a ssin t r o Purpose . m u e p g h ugh a ta ng en t ga lvan ometer by electr olysis a nd so to determine the

alva n ometer constan t or r edu ction a ctor 533 537 g f , ,

- A n en a van m r . A wa . A Apparatus . ta g t g l o ete tch ba r of 2 or 3 S ora c s or o e tte y t ge ell , n

r 4 D n A l Of f om to 6 a iell cells . vo tam eter ; this is a n elec trolytic cell

9 n n Of dee r u (Fig . 5 ) co sisti g a p ja f ll of w ate r con tainin g from 20 to 30 per

n su ur c ac d T wo a n um ce t of lph i i . pl ti

c r d s a re m m ers d in u d ele t o e i e the liq i , the w ires leadi ng to these elect rodes u b O r passi ng th ro gh glass tu es . ve the n at v c r d w ch ma b e s im eg i e ele t o e , hi y ply a a n um w r an n v rt b ur is pl ti i e, i e ed ette placed as Shown in Figure 59 . A ther

m m e r ba r m r . A comm u o te . A o ete

r i 60 ta to (F g . )

All of the galvanom eters in the laboratory m ay be connected i n series with the volta m eter and all st n r z e at the s me t me the a da di d a i , ru t r t i n th r It is des r i nst c o taking par e wo k . i able also to i nclude in the ci rc uit a m ilam m eter by whic h the in structor ca n check the work of

FIG . 59 . the students .

1 Th ara u nn Procedure. ( ) e app t s should be co ected as

m F L e r shown by the diagra ( ig . t the pupils t ace out rcu s ud n c mm u a r an d v am the ci it, t yi g the o t to the olt

r an d n m draw a a ram in r n t ete , the let the di g thei o e s r r s n n xac c n n c ons T e c rcu book ep e e ti g the e t o e ti . h i it 148 M AGNETISM A ND ELECTRICITY

u d be s d s n n c ns an d s sho l clo e to te t the co e tio , to te t the

f urr n r b n n n act r r n O ua w . st e gth the c e t, befo e egi i g l o k The deﬂectio ns Of the gal vanom ete r should be ° between 30 an d (2) Fill the burette by lowe ring it to the bottom of the ja r and Ope ning n d the pi chcock . Re a the position of the w a te r in

FIG. 60. bur a v n a the ette , h i g it s

b on v w wa er in th r near as possi le a le el ith the t e ja . O a n d u r v r n r The n lift it s ppo t it o e the egative elect ode .

S uspen d a the rm om e ter beside it .

3 n all are r ad a t a v n S n c s he ( ) Whe e y, gi e ig al, lo e t

rc u at c m m u a r h s ci it the o t to , t o e ha ving w atches n oti ng the exact time . (4) Observe the deﬂection of

n d at ac end a nd n the ee le e h , the re vers e the cu rre nt by the com m utator and read the deﬂection

n A w cu rr n ﬂow agai . llo the e t to f or ab u ﬁ n m n u es or un o t ftee i t , til

. f d r 30 or 40 c c . O hy oge n have bee n ge nerated . Obse rve the Voltameter ne d car u dur n s m e le ef lly i g thi ti e , a n d keep the deﬂection an d cur Battery re nt cons tant by raisi ng or lowe r ing the burette o ve r the n egati ve

FIG . 61 . r d elect o e .

5 B r a the c rcu t c mm u a r n n th ( ) e k i it a the o t to , oti g e m h n e xact ti e a t w i ch it is do e . (6) Lower the bu rette till the le vel of the water in side

150 M AGNETISM AND ELECTR ICITY am r w n f or one s n d a is on e u mb b r pe e ﬂo i g eco (th t , co lo ) li e °

dr n 0 . n ates c . c . of hy oge at C a d 76 cm . press ure . T n b law a n nt a van m t r he , y the of the t ge g l o e e ,

the reduction cu rrent tan o a vera e 0 f g tan 45 j f a ctor used I deﬂecti on

current u sed reduction f actor tangen t of a verag e def lecti on u beca se tan 45 1 .

EXER C I S E 7 0

E L ECTROMOTIV E FOR C E A ND JOINING CELL S

t o m o e o t e . F . o w or r i Purpose . T mea sure h E M f s ngle

. o me cells oined in seri s a cells a lso the E M F . the sa e n d , f j

o d a r a llel i n ba tt r j i ne p e ies .

—JM l s d r Apparatus . D anie l cell used as a stan d Of

its d r b n v s . M ~ ei g olt y ll 005 ) th r h a r b e m ur d ce e w s e as . q, g cells o e to e e 00 r r m u . A s s an c sa 50 ohms . A c m a A high e i t e, y o t to ’ n o r u If D A rso val gal van mete p rovided w ith a Sh nt . the de ect on is too a r e educe the r s s a nc Of S u n ﬂ i l g , r e i t e the h t

M . . r until the l argest E . F to be m eas u ed w ill n ot ca us e a deﬂe ction beyond the en d of the scale The s tu den t should learn to use the gal van om eter under the guid

f n tr uct r If the er Of s c is a it a nce O the i s o . z o the ale t s ce n e r a vera de e c n is bta n d b a n on e t , the ge ﬂ tio o i e y t ki g

a sum Of two o s e d c ns n o a un be h lf of the ppo it eﬂe tio , cco t

k r ing ta e n of the ze o readin g . If the z e ro of the scale i s at its e n d avera e d c n is ound b a n on , the g eﬂe tio f y t ki g e ha lf the diffe rence of two Opposite deﬂe ctions .

— o Caution . D o n t allow the D an iell cell to stan d on ’ n c rc u b ut c ose the c rc u b a w re a f ew Oh ope i it, l i it y i of ms n resista ce . otebook .

' Da n ell cell a (I obtain the a “ AL M L “ (3) Joi n the w1res to each of the other cells in tu rn and Obtain the average deﬂ (4) Form a batte ry ing the M ia-battery an d Obtai n the average deﬂec

r n d i r tion . Cells a e joi e n se ies by connecti ng the n egati ve pole Of the ﬁrst cell to the posi v s c nd n a v s c nd ti e of the e o , the eg ti e of the e o - s v Of the rd etc . i re don to the po iti e thi , g

(5) Form a batte ry Of the sa me cells by joini ng them pa rallel W nd obtai n the

av ra d c n . T o n m ara e ge eﬂe tio joi the p llel, connect all the negati ve poles togethe r and a a w r A m and all s v tt ch i e to the , the po iti e

r n r B ones togethe a d attach w i e to them .

R rd r su s as ws : m 62 , eco the e lt follo g ,

Volts per ce ntim eter of deﬂ ection

D EP LEC T IO NS

OBT A I N E D Firs t Seco nd A ve rag e 152 M AGNETISM AND ELECTRICITY

— T m m asur n is Discussion . his ethod of e i g

’ a d on O m law I E B s law urr n I b se h s , y thi the c e t R i r r na r m v rc E the resist s p opo tio l to the elect o oti e fo e , if

r r m e mu a nce R is constant. The efo e to use this ethod w st k eep the resistan ce constan t ; but sin ce the i nte rn al re

i an es diEerent c a re not ua r s s an s st c of the ells eq l, the e i t ce of the circuit R is changed by a ch ange of cells . T o o ve rcome thi s difﬁculty the high resis tance is used in the c r u so a an s in r s s a n due use i c it, th t the ch ge e i t ce to the of diEerent b atte ries will be s uch sm all fractions of the whole resistan ce that thei r eff ect on the result will be h u n . T e r s an is ra a ns an b t egligible esi t ce p ctic lly co t t, u n ot absol tely so.

F . i r r nd M . s n rr n The E . a c u a p opo tio l to the e t, the current to the deflectio n : hence the 1s propor ti T r rm n r r onal to the deflection . he efo re by fo i g p opo F n M . . Da l tions with the deflection an d the E . of the iel cell and the deflection of the other cells you can calculate Of r It is r and it the the othe cells . bette

m o m n d . . F a o unts t the sa e thi g to i vide the E M . of the

' D a n b d n the D an an d iel cell , y the eflectio of iel cell us r d n T th obtain the volts pe cen timete r of eflectio . he of the other cells will then be Obtained by m ulti n r plyi g thei deflection by this quotient . This gal vanom ete r with the high resistance is vi rtually

oltmet r ac n n r du d a v e a s a a a in . I , l ki g o ly c le g te volts t w o uld be easy f or you to make a scale f or this galvanom e t r ra d in e g duate volts . Comm erci al voltm ete rs are simply galvanometers of

r s s an c w s a s r ad n n v high e i t e ith c le e i g i olts .

. F m r . r r Co pa e the E M . of the batte y fo med by the cells in se ries with the sum of the of the separate

m n . m r h . M . o cells co posi g it Co pa e t e E . F f the batte ry

154 M AGNETISM AND ELECTRICITY

as x rc s and m as ur s the n a diEe re n ce the l t e e i e , it e e pote ti l betwee n poin ts on the wire A O j ust as it measured

. F . in x r m n E . M that e pe i e t.

1 n r Procedure. ( ) Co nect the appa atus as show n i n r a d in ur n Figu e 63 and dr w a iagram of it yo otebook . (2) Set the block D so that the poi nt P is ex actly 1 r m d as s n as a v n m r i 0 c m . f o A an oo the g l a o ete c oil s d d n a cc ur at rest rea the eﬂectio s a ately as poss ible . Without m ovi ng D re verse the current through the gal vanometer by means of the commutator and take the

deﬂection again . 3 R a ab v v n AP d ff r n va u s as ( ) epe t the o e , gi i g i e e t l e ,

20 cm . 30 cm . . , , etc Record the results as follows

D EPL ECTION

L ENGTII A P

Second Average

— T u u x r m n c urr n Discussion . hro gho t the e pe i e t the e t through the wi re A O is supposed to be constant ; if it

i n ot v r n ar so r su s w b e va u . s e y e ly , the e lt ill of little l e It can not be absol utely con stant because c urren ts of various val ues are ta ken from it at A and passed a ro un d

through the galvanomete r back to the wire AO at P .

T urr n r u a van m r w v r a re hese c e ts th o gh the g l o ete , ho e e , so e xtrem ely sm all on acco unt Of the resistance R that r the e rrors due to it w ill n ot be perceptible in your esults . av n two urr n s ns d r a n s an We h e , the , c e t to co i e , co t t c urren t through the wi re A OP and a variable curre nt r u a van m t r th o gh the g l o e e . . F F CE E M H O LLS 1 55

The la r due P . D . b w n A an d P is r r tte , to the et ee , p opo

n l P . D rr u tio a to thi s . ; b ut the cu ent thro gh the gal va n om eter is a s r r n a d n H nc l o p opo tio l to the eﬂectio . e e, ’

P D . w n A and P re r r n the . s bet ee a p opo tio al to the deﬂe ctions . H aving studied out the meaning Of the last col um n Of ur r su s r d on r n a uan s yo e lt , p ocee the p i ciple th t q titie propo rtional to the sam e qua ntities are proportional to ’

r n D . n d each othe a nd fin d the relation bet wee the P . s a the len gths AP ; then between the len gths AP and the resistances between A an d P ; an d fi nally between the ’ r m n r n r m n P . D . a d s a c a d s f o A to P the e ist es f o A P . Plot a curve using the lengths AP a nd the deflection s

Th r n ou u n as coOrdinates . e elatio which y o ght to Obtai

D . nd r n n between the P . a the esi sta ce alo g the wire when i m ’ the current is constant s O s law . , h

NOT E . S ou t n ent v n om eter b e use lace n ot er h ld a a g gal a d, p a h colum n i n the table f or the tangen ts of the angles of deﬂection and in the last colum n place the quotients of the tan gents divided by len gths A P . A voltm eter m ay be substitute d f or the galvanom eter and re sist n ce an d the n the uot ents of the re n s of the nstrum ent a , q i adi g i by l b e l ce in t e s o m the lengths A P shou d p a d h la t c lu n .

EXER C ISE 7 2

F F M . . E E . O C LL S

asur e E . . l t Purpose . To me M F of cel s by a p otentiome er .

— A n m r m f ns s n 6 . o Apparatus pote tio ete , co i ti g of

28 G r man s v r w r . A ns v a van m r No . s e il e i e e iti e g l o ete , ’

r l i . A r n x T r or ur a D A sonva s best esista ce bo . h ee fo Dan iell cells an d a cell whose electrom oti ve fo rce is to

A m a n be determ i ned . ov ble co tact key such as that 4 used in Exercise 7 . 156 M AGNETISM AND E LECTRICITY

Procedure . Connect the apparatus as shown in F ur 64 in w c E i a n D n ig e , hi h s si gle a iell cell used as a

s a n ar E . M F . T t d d of . he battery at L m ust be Of su ch strength and its in ternal res istance so p ropo rtion ed to that w r m n r a . of the i e of the pote tio ete th t the P . D from A to

FIG. 64 .

B w r a r an E M F ill be g e te th the . . . of any cell or battery la to be p ced at E . For testing cells n o st ro nge r th an a

L eclanché tw o D an s at L are f i cell , iell cell su ﬁc en t . The m sa e poles of the cell at E and of the batte ry at L m us t n n c d A . M a r s s an at 1 00 be co e te to ke the e i t ce R , or m r m s or as a r a o e, oh , l ge s the sensitiveness of the gal va n om eter w r ill pe mit .

2 As in E x r s 73 ﬁnd a s n f r ( ) e ci e , po itio o the sliding C on w r Of r rd u key , the i e the heocho , s ch that when it is

C s d r s a be n o d n Of a an lo e the e h ll eﬂectio the g lv om ete r .

n rr s n f or C is n ar a a U til the co ect po itio e ly tt ined, the key at K s u d b e s d act as a s un f or ho l kept clo e , to h t the g al an m o t r . v e e This key sho uld also be closed between all

r a s b r n a van m r r t i l , to i g the g l o ete to est . The resist ance at R should be as l arge as possible an d yet h ave the a van m g l o ete r se ns iti ve to a slight change of the pos ition of C.

158 MAGNETISM AND ELECTRICITY

EXER C ISE 7 3

RESISTANCE OF WIRES

o ea su re the resistance o a conductor b Purpose. T m f y

a a mmeter 495 m eans of a voltmeter a nd n ,

A D n or a dr . If r s s Apparatus . a iell cell y cell the e i t

i a r n r ns rum n s not v r s ns t v a nce s l ge a d the othe i t e t e y e i i e ,

’ A v m r or the a a ra us se ve ral cells may be needed . olt ete pp t A us ed in Exe rcise 69 . n

r A Of c r ammete . s pool oppe wi re Of k nown length a nd

diameter .

Procedure. (1 ) Conn ect ba r a mm r A Fi the tte y, ete ( g . and the resis ta nce D B to be measured in se ri es (if

a dr ba r is us d a ve y tte y e , le the ci rcuit b roken un til j us t ready to m ake the obse rva (5 F IG . . J n tio ns) . oi the voltm ete r

V as a s un n ds w r m as ur h t to the e of the i e to be e ed .

D r d a m the c n n t ns in ur n b a w a iagr of o ec io yo ote ook . (2) Close both the circ uit of the voltmeter an d th at Of r a ru m the am mete r and e d both i nst ents . The a m mete r gives the strength of curren t th ro ugh the wire an d the

m P . D . n i n volt eter the betwee ts e ds . Record the res ults as follows

K IND o r LFNGT H or RE8“ mm C L, R“ l STA NC‘ DIAM ETE R V OLTS Au PE RRS W IR E W R E I M E ASUR E D PROM T A B L E RESISTANCE OF WIRES 1 59

’

. B m l R T Discussion y Oh s a w E I . herefo re di viding the n umbe r of volts -obse r ved by the n umbe r of ‘

am r s v s r s s an c w r . From Tab 20 pe e , gi e the e i t e of the i e le ,

A nd x b a n r s s anc w r and c m ar ppe i , o t i the e i t e of the i e o p e

u r r s u w i . If m rm s m asur r s s yo e lt th it ti e pe it , e e the e i t an Of a ra s und r Of a r or ce teleg ph o e , n elect ic bell, of a tan n a n m r ge t g lva o ete .

EXER C I SE 7 4

RE SISTANCE OF WIR ES

To m eas ur e r esista n ce o wires b ans o the Purpose . f y me f Whea tston e slide-wire bridge

— ’ Apparatus A D A rson val galvanom eter ha vi ng a s un t is v r d r A r s s a nc h if it e y se nsitive . A y cell . e i t e ox a n c O n n m s b h vi g oils f k o wn resista ce . So e spool of

10 0 - a

FIG . 66 .

n n m r A a s n w i re of k ow n lengths a d dia ete . Whe t to e

- r d T n av brass or Slide wi re b i ge . his co sists of a he y ’ ’ r a nd S coppe r strip S S (Fig . 66) and two shorte on es S

A rm n r r B xac fasted upon a board . Ge a s ilve wi e A e tly a mete r long is st retched f rom S to S an d a meter stick is

d i m v w c c nn on placed besi e it . K s a o able key by hi h o ecti can be m ade at any desi red poin t on the wire AB as at C. 160 M AGNETISM AND EL ECTRICITY

The is n b ndi n s s 4 and 8 a va cell joi ed to the i g po t , the g l nom t r 1 a nd r s s anc be m as ur d X o 2 e e to 7, the e i t e to e e t

and 3 and r s s anc box R 5 a nd 6 . L is a , the e i t e to key to h ’ ’ joi n the gal van ometer to the strip S . T e strips S S a n d S a nd S are broad and thick so that thei r resistance s a re

ra r p c tically ze o .

Theor of he Br d e — en the o nt C is corre l n y t i g . Wh p i ct y placed o the w re AB and oth e s K an d L a re c ose n o c urrent w ﬂow i , b k y l d , ill through the galvanometer and the poi nts A a nd B are at the same potential . X is the res st nce rom A to D and R the res s n r ta ce om D to B . i a f , i f ' " Let R be the res st nce of the w re rom A to C an d R the res i a i f , ist n n urrent w r u ance from C to B . Whe o c ﬂo s th o gh the ga lva nometer and

A a nd B a re at the some oten tia l these our res is ta nces a re ro ortiona l p , f p p , ’ " R : X R R .

Proo . S nce A and B are at the s me otent the of oten f i a p ial, fall p t rom C to A i s e u l to th t rom C to B b ec us e it is l ial f q a a f , a a fal t f rom a com m on point to poi n s of equal potential. Le t p represe n t

t s P . D. A n the rom A to D e u s t t rom B to D hi gai , fall f q al ha f , ec use the a l is rom o nts of e u otent to comm n b a f l f p i q al p ial a o poi nt . ’ Let p represen t this P . D . ’ ’ " zX : B O m s law also R R . ence y h p ; p p H ,

' " R : X R : R .

S nce the res st nce of w re is ro ort on to its en t we ca n i i a a i p p i al l g h , ’ " sub stitute f or the resi stances R a nd R the lengths of the wire A C an d B C or a a nd 100 a hence , ( ) , — a zX z (100 a) : R

X = R

Procedure Connect the apparatus as sho wn in

ﬁ ur u s in s r th ck w r s n R a n d the g e , g ho t, i i e to joi X to the

B e s u r ha v r bind n i b ridge . e t t e e y i g pos t s scre wed do wn

D ra w a d a ram the a a ra us in r tight . i g of pp t yo u n ote

e te r in the ar s a 1 00 a R a n d X book . l t g p t , , , .

M a the res s ta nc R som e n w n va u as 1 0 m s ke i e k o l e , Oh ,

1 62 M AGNETISM AND E LECTRICITY

an d m asu r r r s s anc a nd s w a is ua e e thei e i t e, ho th t it eq l to the reciproca l of the s um of thei r reciprocals Als o m easure the sa me W i re you m easured in E xe rc is e 73 an d m ar o r u co p e the tw es lts . Record the results as follows

K m n o r (Lu mp D IA M ET ER D m n sr s u m r u a 100 — a W uu: No IN M u s SQ U A R E D o e s

T ab 20 A nd x f or d am r a nd s ua r d i See le , ppe i , i ete q e of

m eter of th r h r s s anc one t a e wi e . C al culate t e e i t e of foo of wi re one mil i n dia mete r f or K

EXE R C I SE 7 5

R ESISTANC E OF CE LL S

ea e the intern ta ce o a o Purpose . To m sur a l resis n f n n polar iz ing cell or

Apparatu

- azo -Li i- l- — as toi a g g b e e r whose res is tan ce is k n own . A re

i t x T D a n a u e —-re w - -s s s ance bo . wo iell cells tw g a tr eeH ;

— ‘ ead m c elL- b eia g nﬁ mbm dr Shor t thick wires ha vi ng

r n P acticall n o re sis tan ce f or con necti the a PPa atus . y 3 l " 1 r n Procedure . n on e l a d ( ) Joi cel , the , the

' i box n resis ta nce box in s e r ies the r . st ce of the bei g a n ) 4. M . — m r . R e rd th th. tho mﬁ zr me ta ze o co e w eal . s ome -resis ta nce by means o f t he m i stanee b axgm siderhrg

hi - o t s resis ta nce as a pa rt f R in the table . )

2 If res s ta nc of m am m r is z r in ( ) the i e the il ete e o , c rease the res is ta n ce of the ci rcuit by m eans of the resis t a nce b ox u n til the curre n t is j us t hal f as grea t as at

rs . Or w ther r s s anc is r or not add a ﬁ t , he the e i t e ze o , R ESIST ANCE OF CE LLS 163

ﬁn e r s s anc r u as 2 3 or 5 m s an de it e i t e to the ci c it, , , oh , d

r u rr reco d the c en t . (3) Substitute the other cell f or the ﬁ rst one used and r repeat the wo k .

4 J n two s in r d r a r ( ) oi the cell se ies an epe t the wo k . T n n m ara n r he joi the p llel a d epeat . Reco rd the res ults as follows :

R es stance of the m l m mete r R i i a ,

" C U RR E NT I It R

— ’ i h Discussion . R R s t e exte rnal resistan ce of the ci rc uit an d r the resistan ce of the cell or batte ry to be fo und . If urr n is m ad a as r a as at ﬁ rs re the c e t e h lf g e t t, the ’ s istance c rc u m us t b O m s la w be d ub d of the i it y h o le , the

F n u n an d n d if h r E M . . a t e s s an c . bei g ch ge ; e i t e of the m amm r is r n r s s an c in r u il ete ze o , the o ly e i t e the ci c it

a rs is a s . H nc w n r s s t ﬁ t th t of the cell it elf e e , he the e i t an i ub d add d r s s an c m us ua ce s do le , the e e i t e t eq l the resistan ce of the cell .

If w v r ou do n ot tr m a u rr n us a , ho e e , y y to ke the c e t j t h lf as r a as at rs but s m add a d ﬁn r s s an e g e t ﬁ t, i ply e ite e i t c , the resistance r may be calculated as follows E By Ohm s law I By substituting the

’ va u s b a n d f or R a nd R in s ua n f or l e o t i e L , thi eq tio , the two cases you will ha ve two in depe ndent eq uatio ns with

two un n w n uan s E an d r . Fr m se tw o ua k o q titie , o the eq

ns b m na n va u s b E and r can be tio , y eli i tio , the l e of oth obtained . 1 64 M AGNETISM AND ELECTR ICITY

r n a a s a a e r Calculate the esista ce of e ch cell , l o of e ch b tt y, and compare the resistance of two cells in se ries with the D o am s n resis tan ce of one cell . the s e with the cell joi ed parallel . h D a t A a n a sum E . M . F . t e n o g i , s e the of iell cell be v s or a rav be v and r m h s olt , of g ity cell to olt, f o t i ’ and the curren t obtai ned calcula te by Ohm s la w the whole If x rna r s an i n resistance of the circuit . the e te l esi t ce s the sub rac r m w r s an r ma nd r w t ted f o the hole esi t ce, the e i e ill In ba r be the resi stance of the cell or batte ry . the tte y of

M . F b n w i r . i e a as a two cells n se ies the E . s to t ke t ice th t of on e cell . EXE R C ISE 7 6

R ESISTANCE AND OF A CELL

m i a c a c ll or b tt Purpose. To easure the res st n e of e a ery b s an v n y m ean of a t gent ga l a ometer .

— n m Apparatus . A tangent galva o eter whose constan t

d r n r n A mm u a r . A r an esi sta ce a e k own . co t to esistance

x . r bo A Daniell or a g avity cell .

Procedure . 1 C nn c the ns rum n s in s r s ( ) o e t i t e t e ie , . an d dra w d ram m i n n a iag of the the otebook . ’ (2) Make the resista nce (R ) of the resistance b ox s uch that the deﬂection shall be nearly and determi ne

r the ave age defle ction . (3) Change the resista nce of the box so that the deflec tion shall b e about designating the resistan ce in this b " D . case y R . etermine the a verage deflection

— ’ Discussion . O m s law I nd a s a I is h , g, i ic te th t

r r in ve sely p oportional to R when E is constan t . In this e xperi men t the R of the ci rcuit is the s um of the resistan ces = of the a van m r box and c . et g l o ete , the , the ell L g the ’ r s s an alvan m r and r a e i t ce of the g o ete , th t of the cell , R

1 66 M AGNETISM AND E LECTRICITY i nto the w ater and also the bare end of the other gal va nom eter w r s c r w r wa r and n c i e ; thi oppe i e, the te , the zi

If i no s r n n u make a ve ry weak cell . it s t t o g e o gh to gi ve

d r a n ab d c n a d a a n c m m n sa . otice le eﬂe tio , g i of o o lt to it Record in tabular fo rm whether the c urren t enters the r r rm n m r ight o the left te i al of the gal va n o ete . Als o r c rd d r n d n w t r is e o the i ectio of the eﬂectio , he he it to the r h T w nab ou n i ur ig t or left . his ill e le y to k ow n the fut e

r n n curr n r u n m r the di e ctio of a y e t th o gh this gal va o ete . (2) Remove the cell an d join the spool of wi re to the m t n n m u galvano ete r . Wi h the eye o the gal va o eter th r st

N ba r m a n t n t s w r the pole of the g e i o the pool of i e,

If a c urr n t i r d av n t r . s uc d how n d s le i g it he e e p o e , lo g oe

? h ur r n is sa d b u d n it last S uc a c e t i to e ca se by i d uction .

If ou r er ou m a m v c and m a n y p ef , y y o e the oil keep the g et

r s tationa y .

3 R a No. 2 bs r v n d ﬂ c n an d r ( ) epe t , o e i g the e e tio dete mini ng the di rect i on of the c ur ren t th rough the galva

m r T n b w n r d r n o ete . he (a) y follo i g the wi e s to an a ou nd the spool trace ou t the di rectio n of the curre nt arou nd the spool ; the n (6) thrust a S pole i nto the spool ; then ( c) withd ra w the N pole ; an d l ast (d) withdra w the S t d r c n rr r n pole . Trace ou the i e tio of the cu en t a ou d the

FI G. 67 . CURRENT INDUCTION 167

. Spool in each cas e an d record the results by drawing diagrams like those of Figure 68 and placing arrowheads

n d ca d r c n r on the wires to i i te the i e tio s of the cu re nts . (4) Grasp the coil so that the ﬁ ngers exten d through it in the sam e di rection as the lines of force did in each of th a v as s us n the an d w n n r e bo e c e , i g left h he the li es of fo ce thro ugh it we re i ncreased an d the right ha nd f or thos e cases in which they were decreased by the m ovem en t m ar d r of the m agn et . Co p e the i ection of the c urren ts u d d r c n m i ind ce w ith the i e tio the th u b poi nts n each case . Form ulate a r ule by which you can tell the di rection of an ndu d urr n in a i b use and ou i ce c e t co l y the of the h , if y

n r n n s r k o w the di ectio of the li e of fo ce . (5) In each cas e con side r the coil a temporary elect ro In nd b i m agn et . (a ) a ( ) s the en d of the coil tow ard which the m agnet mo ves like or unli ke the pole of the m agn et used ? Wo uld it op pose or help the motion ? In ( c) a nd (d) is the en d of the spool where the m agnet leaves it like or unlike the pole of the m agnet with drawn ? Would it oppose or help the m otion ? (6) Support tw o m agnets on s on ab as book the t le, wn in F ur 69 an d ac sho ig e , pl e the coil between them with

the rod of soft iron within it . Place it ﬁ rst in position (a) and turn it quickly abo ut a ax s t n b vertical is to po i io ( ) , n oting the directio n of the de

r the alvanom ﬂection . Afte g 168 M AGNETISM A ND ELECTRICITY

h m r s urn c s n c ete r coil as co e to e t, t the oil to po itio ( ) an d note the deﬂection ; then t urn it to position (d ) ; an d

as s n a us m a n a m r v u n . l tly to po itio ( ) , th ki g co plete e ol tio r T ry it again without the i ro n co e . If w r r a d n nu us in h s wa w a the coil e e ot te co ti o ly t i y, h t parts of the re volution would produce c urren ts i n one wa and w a a r s in r d r c n ? At w at y , h t p t the othe i e tio h poi n ts in the re volution would the curre nt change direc tion ? H ow m any times in each revolution w ould the c urrent change di rection What ki nd of a curren t w ould it be called ? This ex periment illustrates the principle of the dyna mo . Record the results as follows

Cu rrent entering the galvanom eter on the D eﬂection of galvanometer is toward the (a ) Poles are m otion is (b) Poles are motion is (c) Poles are m otion is (d) Poles are m otion is

— “ " Nor m Insert a like or u nlik e after are and helped or opp osed f ter is a .

EX E R C I SE 7 8

CUR RE NT INDUCTION

t d i c i coi b Purpose . To s u y cu rren ts n du ed n one l y m ea n s

o cu rr en ts in a nother coil 524 f , — Apparatus . T wo s pools or coils of wire each h avi n g ’ b u 00 turn r A d r l n a 8 s w . A on a a a m t r o t of i e s v g l v o e e .

r n r r r r . A b atte y of o e o two d y cells . A od of soft i on A

r comm utato .

Procedure . (1 ) Join one of the spools of w ire to the

ba r t r u h com m u a r av n r u n tte y h o g the t to , le i g the ci c it ope at the comm utator un til all is ready ; this spool is the

1 70 M AGNETISM AND ELECTR ICITY

f n a m h graph 5 . Note the ef ect of havi g co plete pat of iron f or the lines of force . This a rrangement with the horseshoe s illustrates the pri nciple of the transformer The procedure of parag raph 4 illustrates the in duction If ss b s u n xam n an in coil po i le , let the t de t e i e n n d ud i n r ductio coil a st y ts pri ciple of Ope ation . It u s rv a two s r mar and n sho ld be ob e ed th t the coil , p i y seco d ar m a u an s n r a v a r ro y, y occ py y po itio el ti e to e ch othe , p vided that the li nes of force of one coil extend through the othe r . Re co rd the results as follows

Paocs ouas Rs suurs m Ss oonnxar

Coils brought together Coils stationary Coils separated Current m ade in primary Current broken in primary Current alternated i n prim ary Eff ect of iron core APPENDIX

NOTES AND SUGGE STIONS

SINCE it is possible to buy apparatus f or the high school laboratory at reasonable prices a nd m uch bette r apparatus

an a r rd nar can m a ns ru ns f r th the te che o i ily ke , i t ctio o making apparatus have in the m ain been omitted from

n It ha b n u b s n th is appe dix . s ee tho ght e t to i troduce a f ew useful hints about some of the exe rcises an d about the a ara us w c are n nd d f or a r n n pp t , hi h i te e the te che o ly a d u n us u mb d in h which wo ld co f e the p pil if e o ied t e tex t .

THE NOTEB OOK

The n otebook is one of the m ost difﬁ cult problems of the c The au r b v s a an s s m physi s teache r . tho elie e th t y y te of takin g notes that permits a p upil to copy an d discard the r na n s nc ura s car ss and s v n not di o igi l ote e o ge ele lo e ly , if s

nes w r . For a r as n m rar n t b ho t, o k th t e o te po y o e ooks,

s a r and n s - a n s are un sheet of p pe , eve loo e le f otebook s atisfactory . The followi ng method with notebooks has been found

r L r n n n in en ve ry satisfacto y . et the o igi al otes be take p

in rm an n n b n h m be d in cil the pe e t ote ook , the let t e copie ll ink on the followi ng pages of the same book . A the calcula tions should be m ade in the n otebook and not on r N n s craps of pape ; they are useful f or referen ce . eat ess and ac urac in s m rar n s s u d au c y the e te po y ote ho l be t ght, and co rrections of m istakes by disﬁguri ng the book in any

e r n I n ta n way should b f ow ed upo n . f the otebook is ke

r m a ra r at the s ur w r s u d f o the l bo to y clo e of the ho , the o k ho l 171 1 72 APPENDIX be examined and approved or signed by the instructo r before it is taken aw ay . A dthough s uch a book does not look quite so well as one

n o m rar n in is r a a b tt r b an d w ith te po y otes it, it e lly e e ook , the instructo r can conscie n tio usly certi fy that it contains the original notes of the pupil f or those colleges that dem and it . M uch mo re atten tion than is usual should be gi ve n to

r u r s n he doubtful ﬁgures . It requi es co age ometimes o t pa rt of older people to reject ﬁg ures o f unk n own val ue . The p upil will ha ve m uch mo re respect f or his work if he is ta ught co rrectly in this rega rd .

EXERCISE 13

This exercise often pro ves u nsatisfactory largely be

aus of rr rs ba anc s b ut b a us e c e the e o of the l e , chieﬂy ec the fractions of u n its of fo rce ca nn ot be estim ated at all

T r ub m a r m accurately . his last t o le y be o ve co e by ad j usting the apparatus so that all the readi ngs shall be e xact

r whole n umbe rs . Let the ba be m ade of a m ete r stic k

i D r ba r d out n two le ngthwise . ess this ow n un til with

its w r s w s xac 60 . or un bar w i e hook it eigh e tly g , til the ith no weight upon it registe rs an exact whole numbe r of

r m in a n g a s e ch bala ce .

E XE R CISE 14

The ndu um m s wn in F ur 1 2 a 5 . 4 i m ad pe l cl p ho ig e , p , s e

4 in 3 t o es brass ac . w d a d n c i . w n c . of pie of , e h } i e T6 thi k i d b 2 n . n Th 1 n . n in 0 n a is i a lo g . e p a d the screw e pas s

r u 6 a nd are s d r d in ac ut h th o gh , ol e e pl e ; b the ole s th ro ugh a a re la rge en ough to allow it to move f reely

T r upon c and e . he th ead of the pe ndul um can be passed

v r in 0 w c m a be us d as a u n c o e the p , hi h y e p lley whe ha ng n nd u ing the le gth of the pe l um .

1 74 APPE NDIX

E XERCISE 46

The focal length of the mi rror in this exe rcise shou ld m i m n ot ex ceed about 1 2 c . It s difﬁ c ult to locate i ages by the m icroscope if the focal length is large .

E XERCISE 53

The bore of the tube f or this ex ercise should not be

m m n d m r Th d i e . e u u more th an 2 . ia te t be shoul be abo t n The m r ur is n r duc n b the 40 cm . lo g . e c y i t o ed i to it y i r n r x n d f or Ex rc 23 L n a d of an i o wi e as e plai e e ise . o g r d m ur r m r a r n th ea s of erc y a e o e pt to b eak tha sho rt ones .

T o n r du s u ur ac d ma a unn r i t o ce the lph ic i , ke f el by d a w ing out a piece of glass tubing i nto a thread about a m illi m eter in diam ete r and lon g enough to reach nea rly to the b m x n n ub Ins r ca a r otto of the e pa sio t e . e t this pill y tube n ar ub and ac in n a r d u r ar i to the l ge t e, pl e the e l ge ppe p t a f e w dr d b a m d n dr r I of it ops of the aci y e ici e oppe . t r will slowly wo k its w ay down into the tube .

E XER CISE 54

in d m r Alum i num rods 1 in . ia ete can be obtained

r For m thro ugh the hardwa e dealer . the ass to be used w um n um ca r m r cut r m suc a rod ith al i lo i ete , f o h with a n f . I h ack saw a cylinder about 3 in lo g . a coppe r calo

rim eter is us d cut r m a r rod 1 in . in d am e , f o coppe i ete r a

r n . n cylinde about 2 i lo g .

u u r r 00 . m Al umi n m liq o shake s of about 5 c . c ake ex cel len t calorim ete rs and can be obtained at ve ry reas onable prices .

EXERCISE 69

If rad us a a c in n m rs n um r n the i of oil ce ti ete , the be of

u rns w r in and r n a n ns H t of i e the coil, the ho izo t l i te ity of APPENDIX 1 75

’ ar s ma n sm are n w n n r uc n a r the e th g eti k o , the the ed tio f cto 0 in amperes can be found by the followi ng fo rm ula :

1 0 H a

° This formula applies to 45 only . H in the northern part of the U nited States is about

d n d nam a r s can b a n d r m y e . Iso y ic ch t be o t i e f o the

. C nd G d ur w v va u U . S oast a eo etic S vey hich gi e the l e of

H f or all parts of the United States .

EXERCISE 70

A high resistance of 5000 to ohms m ay be m ade by covering the roughened surface of a piece of h ard rubber with a ve ry thin laye r of a mixtu re of ins ulati ng r d r A r ﬁ rs c a is d r add va nish an g aphite . fte the t o t y an othe r coat until the resistance is reduced to that desired .

The piece of r ubbe r should be about 6 x 3 cm . and should be mounted on a block and held in place by a binding

ra post at each end . A strip of b ss should be placed under

A x n u n ar each bi ndi ng post . ( j a i s lati g v nish m ade by i x rw n ams Co. C v an O s n . the She i Willi , le el d , hio , e celle t )

— M u r The Daniell Cell . ake p a 5 pe cent solution of n su a and w n is us zi c lph te, , he the cell to be ed, ﬁll the r us cu w a n on a r u a f e w po o p ith it, pl ci g the cell ci c it of m s r f r r m u r u n Th oh esistance o se ve al in tes befo e s i g it . e n u r zi c sho ld be tho o ughly am algam ated . When the cell is n ot in use n u a s u urn d out th , the zi c s lph te ho ld be t e of e B h r us cu w c s u be i a r . e sur a po o p, hi h ho ld kept n w te e t t the copper sulphate sol ution is kept satu rated by always av n s m c r sta i 1 h i g o e y ls n the pocket 0 1 the copper plate .

A Tuning Fork s uitable f or laboratory e xe rcises can be m d a b m A a ac s ut in . h n i e by l k ith o of s teel 5 t ick a d } n . 1 76 APPE NDIX

u i . wide . The prongs should be abo t 6 n long an d shou ld be s at nds so a can be fi d aw a f or left oft the e , th t they le y adj ustmen t . fl To bend Glass Tubing . H old the t ube in the at lu m i n ous fla me of an ordi na ry g as b urne r s o that it will be

d f r a u 3 i n c n an ur n n a o b n . its s he te o t of le gth , o t tly t i g

ub ab u in ﬁ n rs . As s n as has s n d the t e o t the ge oo it ofte e , n n rem ove it from the ﬂam e a d be d it q uite q uickly .

n is d r m v s b a da m . Whe it col , e o e the oot y p cloth — Boring Glass . Use an awl or tool h a vi ng a roun ded w d - s a d n — a n m u a a e n e ge h pe poi t, poi t ch like th t of p ggi g P a wl b ut muc m r b un . a a c c s , h o e l t l ce pie e of thi k heet lead under the glass at the poin t whe re the hole is to be

r d an d m s n w a so u n m ad 8 ar s bo e , oi te the tool ith l tio e of p t w am r 1 6 ar s u r n n an d 3 ar s by eight of c pho , p t of t pe ti e, p t of ether .

B v n a w s n m n a wl or a is y gi i g t i ti g otio to the tool , hole

r quickly a nd e asily m ade th ough the glass .

— d r n d r Soldering . S uccess in sol e i g epends upon th ee

h n s : fi rst sur ac s be s d r d m us be a n t i g , the f e to ol e e t cle ; s c n d m us b e d fi rm in s n an d rd e o , they t hel ly po itio ; thi , they m ust be heated s uffi cie ntly hot to allow the solde r to ow If a s d r n r n is us d m us c an and fl . ol e i g i o e , it t be le n well ti ned . The o rdinary solde ring fl uid is m ade by dissol vin g zinc in h d r c r c ac d b ut s is ab ab s rb m s tur y o hlo i i , thi li le to o oi e I u d a a s be w d off and corrode the pa rts . t sho l lw y ashe as

Non - c rr s v s d r n as r tho ro ughly as possible . o o i e ol e i g p tes o

ﬂ uxes m ay be had of the electrician .

A Usef ul Cement is m ade by m ix i ng 1 part of gutta ° - rcha a n d one ar n c a t 100 C . s r r n pe p t of pi e pit h , ti i g it

r u r tho o ghly togethe .

1 78 APPENDIX

TABLE 3

D E NSITIE S or SUBSTANC E S I N GR AM S P E R CUBIC CE NTIM E TE R

A r n te gate . G a i

A co o so ute . r te . l h l , ab l G aphi A co ol comm on Gun met l h , al

A u m num roc or c c a . 80 1. l i Hyd hl i a id , q A n t m on c st Ice i y, a A sh dr Iron b ar , y , As t Iron c s t phal , a Beesw x Iron wrou t a , gh B ell m etal Iron pyrites Benz ine to Ivory “ B smut c st Le c st i h , a ad , a Box woo Le s eet d ad , h Brass c st L num vitae , a ig B r s s s eet L mestone a , h i B rick to Mahogany to Ced r Am er c n M e a , i a apl Chalk to M arble Cherry M ercury Co l nt r c te to N tr c c to a , a h a i i i a id Co l tu minou s to Oak Amer c n red a , bi , i a Cor Oak Am er c n wh te k , i a i Co er cast Oil t ur en t ne pp , , p i Co e r s eet Paraﬂi ne to pp , h Diam ond 3 530 Petroleum Eb ony Phosphorus Em er ne w te dr y Pi , hi , y Ether Platin um wi re Fir s ruce orcel n c n , p P ai , hi a Fl uor-Spar Q uartz en S ver c st to Gal a il , a erm n -s ver Stee l un h m mere G a il , a d G ss nt to Sul ur n t ve la , ﬂi ph , a i ss crown Su hur c c Gla , lp i a id ss ate Ti n c st Gla , pl , a Glycer ine Waln ut Go ter sea ld Wa ,

G sum cr s . Z nc c st yp , y i , a APPEND IX 179

TABL E 4

TH E D E NSITY AND V OL UM E OF W ATE R A T V AR IO US TE M PE R AT UR E S

1 u in f c . . o w ter at 16 we hs oz . vo r. a C . ig a i

TAB LE 5

AC CE L E RATION g D U E To GR AVIT Y AND L E NGTH l OF TH E SE CONDS PE ND UL UM S F O R D IF F E R E NT LA TI TU DE S 1 80 APPE NDIX

TABLE 6

° R E UCTION OF B AR OM E TE R R E A IN o D D G T 0 C . Subtract the correc ion t .

TABL E 7

AVE R AGE H E IGR T b o r B A R O M E T E R AT E LE V AT ION H A BO V E ° V E L 10 SE A L E ( C . )

1 82 APPENDIX

TABLE 9

FOR R E UC ING O SE R AT IONS O F T H E B AR OM E TE R To SE A L E E L D B V V , CO R R ECTION IN INCH E S ADDIT IVE APPENDIX 183

TABLE 9 Continued

FOR R E UC ING O SE R ATIONS or T R E B AR O M E TE R To SE A L E E L D B V V , CO R R E CT IO N IN INCH E S A DDITI V E 184 APPENDIX

TABLE 9 Continued

FOR R E UC ING O SE R ATIONS or TE E BAR OM E TE R TO SE A L E E L D B V V , CO R R E C TIO N IN INC R E S A DD ITI VE

Temperature of External Air Degrees Fahrenheit

° ° ° - 10° 0° 10° 20° 30° 40° 50 60 70 80° 90°

1 86 APPENDIX

TABLE 10

V E L OC ITY o r SO UND I N M E TE R S P E R SECOND

° 0 C . Brass 3500 ° ° 11 0 C . 1286 Co er pp 20 C . 3560 O ° xygen 0 C . 317 Glass 5000 to 6000 ° ° C r on ox e 0 C . 261 Iron a b di id 20 C . 5130 ° Water 8 C . 1435 Steel 5200

TABLE 1 1

SIZ E S AND NUM BE R S or STE E L M USIC OR PIANO W IR E (E NGL ISH )

TABLE 12

INDICE S R E F R A C TION (FOR TH E D L INE )

Air Diamond A co o et Fl nt l ss l h l, hyl i g a Benz ine Glycerine Can ada balsam Ice Carbon disulphide Wate r Crown glass APPENDIX 187

TABLE 13

NATU R AL SINE S AND TANGE NTS 188 APPENDIX

TABL E 14

COEF F IC IE NT OP L INE AR EXPANSION

Lead Sil ver Stee tem ere l , p d Stee untem ere l , p d Z inc

TABL E 15

SPE C IF IC H E ATS

Lead M ercury 33 Nickel Silver Z inc

TABLE 16

TE NSION OF W ATE R V A PO R I N M I L L IM E TE R S O F M E R CUR Y T D I PE R E N E M E R T U E S A P T T P A R C .

190 APPENDIX

TABL E 19 TABL E OF PR OPOR TIONAL PAR TS FOR USE W ITH TE E WB E ATSTONE SLIDE - W IR E BR I DGE The table gives the value of a (100 a ) f or all values of a from r nd rm l e m . F e 66 a e 159 a o u a cm . to c See u ( ig , p g , f a , p g APPENDIX 191

TABLE 19 Continued 1 92 APPENDIX

TABLE 20

O E WIR E . B St U E $12 17 E TC . OF C R . S. GA G , , PP